A key example is when h : R d → R describes the least-squares Using that this h is twice differentiable with ∇ 2 h(Ax) = I n , it is easy to see that we can track the evolution of all gradient entries, when performing CD steps, as follows: for i k being the coordinate changed in step k (here we also used the separability of the regularizer).

all gradient changes can be tracked exactly if the inner products of all datapoints are available, or approximately if those inner products can be upper and lower bounded.


By applying the discussion following Theorem 1 when G ?

is rank d, we can state an upperbound of  This shows that D is uniquely determined as a function of C. since (D) = (C) and because C is orthogonal to the kernel of , the distance matrix D can be recovered from (D), even though the linear operator is non-invertible.


Thus, the gradients g θ, w and h θ, w are stochastic approximations to the true gradients.

we analyze convergence of GANs by two time-scale stochastic approximations algorithms.


Theorem 1 implies that the stronger column-wise independence constraint (10) does not degrade approximation accuracy, and the VB solution under matrix-wise independence (5) essentially agrees with the simpleVB solution.

we can obtain a global analytic solution for VB, by combining Theorem 1 above with Theorem 1 in [15]: Let γ h be the second largest real solution of the following quartic equation with respect to t: where the coefficients are defined by Let Then, the global VB solution under matrix-wise independence (5) can be expressed as Theorem 1 holds also in the empirical Bayesian scenario, where the hyperparameters (C A , C B ) are also estimated from observation.


The algorithms in [4,13,5] all fall into this category.

if we choose I to be the set {a, a + 1, . . . , b} for some integers 0 ≤ a < b < m, and A updates its hypothesis k times during rounds a + 1 through b, then h A I is defined by at most B + k support patterns.


In addition, suppose there exists c ∈ K such that A t F t ≤ K c for all t, then where κ is given by κ c,ψ,ψ S = inf{r | c, ∇ψ S (0) − ∇ψ S (u) ≤ rψ(u), u ∈ K} Proof: Since ψ S satisfies Assumption 1, we have ŷt+1 ≤ K * ŷt .

we can write: Now by combining the duality gap given by Lemma 1 with 11, we get The conclusion follows from the definition of α ψ,ψ S , κ c,ψ,ψ S and the fact that D seq ≥ D . Based on the result of the previous theorem we can modify the optimization problem set up in Section 3.2 for separable functions on R n + to maximize the lower bound on the competitive ratio of the sequential algorithm.


In the first phase of the algorithm we are making l > kη cluster-assignment queries.

using the pigeonhole principle, we know that there exists cluster index p such that |Z p | > η.


If predictions are accurate, the dynamic range of the error is much smaller than that of the natural stimuli.

minimizing dynamic range using predictive coding reduces to optimizing prediction.


That is, the amount of objective decrease -i.e., f (y k ) − f (x) if x moves out of the safe zone-must be proportional to the distance x − y k 2 we travel in space.

if x moves out of the safe zone, then we can decrease sufficiently the objective.


Since no prior knowledge of α is known, the prior of each α i , i ∈ {w, u, θ}, P (α i ) is chosen to be a constant on log-scale or flat.

the value of α maximizing the posterior of α P (α|Y, X) can be found by maximizing By Laplace's approximation [14], this integral is approximated around the MAP estimation of weights.


The lower bounds {LB m } m≥1 are monotone and submodular.

for any k ≤ n, a greedy algorithm that maximizes LB m at each step yields a 1 − 1 e -approximation to max A⊆V :|A|≤k LB m (A).


The number of calls k to a blackbox vector-valued function f needed to compute an approximate Jacobian via finite difference technique in the noiseless setting satisfies k ≤ χ(G int ), where G int is the corresponding intersection graph.

blackboxes whose unknown Jacobian happens to be associated with intersection graphs of low chromatic number admit accurate Jacobian estimation with few function calls.


We remark that the detailed problem instance and the greedy regret can be found in Theorem E.2 of the supplementary material.

furthermore, we may also restrict the maximum gap ∆ max to Θ(1), and the lower bound R G (T ) = Ω( mW ∆max ln T ∆ 2 ), for any sufficiently large T . For the upper bound, OG-UCB (Theorem 3.1) gives that R G (T ) = O( mW ∆max ∆ 2 log T ), our upper bound of OG-UCB matches the lower bound within a constant factor.


The test loss of ĝ0 is expected to be roughly 0.5 b, where b is the bias mentioned in the previous section.


Since neural firing does not show such a severe scaling in variability, such a model would fit poorly.

to maintain more even firing-rate fluctuations, we instead take The corresponding Gaussian integrals must then be approximated by quadrature methods.


Furthermore, time correlation, and consequently the dynamic of the signal, inside each HMM state is also usually disregarded (although the use of temporal delta and delta-delta features can capture some of this correlation).

only medium-term dependencies are captured via the topology of the HMM model, while short-term and long-term dependencies are usually very poorly modeled.


Typical multilabel problems have hundreds of possible labels or tags, but any single instance has only a few tags [17].

a function which takes in a vector in R K and outputs a sparse version of the vector is of great value.


Instead, approximate ML learning relies on either Monte-Carlo or deterministic approximations to the posterior.

such methods may be computationally intensive, suffer from varying degrees of approximation error, and are subject to the same concerns about multiple likelihood optima as is the linear-Gaussian case 2 a consistent spectral method is likely to be of particular value for such models.


Note that the problem setting of our study is to select a batch of data points to label without training a classifier.

we do not compare our method with typical active learning methods such as SVM active learning [19,18] and agnostic active learning [2].


Building an accurate observationprediction model is often very challenging when the observation space is large [23,5,13,4] (e.g., highdimensional pixel-level image frames), and even more difficult when the environment is stochastic.

a natural question is whether it is possible to plan without predicting future observations.


Scaling up/down this sum of currents is equivalent to scaling the capacitor and, thus, speeding up/down the network dynamics.

scaling the input current with the help of a current mirror, for instance, will have the effect of scaling the timeconstant.


From Proposition 1, any continuous PWL function can be expressed by the virtual unit, a difference of two convex PWL functions.

then, according to Proposition 2, any continuous function can be approximated arbitrarily well by this network to achieve the desired degree of with sufficiently large n 1 and d 2 on the compact domain C. a two-layer neural network satisfies Theorem 3 and then the Theorem holds.


As the variables φ n,t are expected to be large when xn,t cannot explain the observation x n,t -typically due to a corruption or a high noise -the weights will accordingly suppress the importance of the particular point x n,t .

the overall approach will be more robust to corrupted data than the Gaussian models where all weights would be deterministic and equal to 0.5.


The accuracy of the proposed system with the default configuration was 0.87.

this configuration displays a good balance between recognition performance and memory usage.


However, both approaches assume a common covariance matrix for all the classes, which is too strict in many practical applications, especially in high-dimensional problems where the covariance matrices of different classes tend to be different.

the linear transformation explored by LDA may not be effective.


Additionally, when the network cannot be accessed in full but can only be probed via crawling [28], we may only have access to similarity estimates rather than their exact values.

understanding what information can be learned from a partial, potentially noisy, set of node similarities is important when using these metrics in large scale graph mining.


Let the divergence-generating function φ be such that the mapping Proof.

define the indicator random variable where the first step is by the data processing inequality (10), the second is due to the fact that Z is binary, and the third is by the assumed monotonicity property of φ.


increasing the depth moderately above L opt may not harm significantly the performance.


Figure 3 shows the results obtained with binary descriptors of varying dimensionality.

while our approach can accommodate easily the case were the number of feature dimensions (C) is different from the number of feature-training categories (K), the classeme learning method can only produce descriptors of size K. the descriptor size is typically reduced through a subsequent feature selection stage [27,19].


While the classification-calibration of unh is encouraging, Proposition 6 implies that its (unrestricted) Bayes-risk is −∞.

the regret of every non-optimal scorer s is identically +∞, which hampers analysis of consistency.


Finally, in the n-th sweep, x n is used in the first step.

this process mixes in n(n − 1) + 1 steps, which is O(n 2 ).


The first term minimizes the distance between positive pairs and the second term pushes negative pairs to be at least margin m away from each other.

the second term is only active when the distance between the features F I (x i ) and F I (x i ) are smaller than the margin m. Such boundary defines the metric space, so it is crucial to find the negatives that violate the constraint and train the network to push the negatives away.


In this case, left association is also more computationally efficient than the right one.

for common cases where (dhw) 2 > nm, we suggest implementation in Eqn.


Σ = Σ + αϕ i ϕ T i , where α = 1 2 ( si − s i )σ 2 i .

to compute ∆E x we can take advantage of the Sherman-Morrison formula and of a similar formula for the log det term Using ( 1) and ( 2) ∆E x can be written as The transition probabilities can thus be computed efficiently, and if a new state is accepted we update Σ and Σ −1 using (1).


However, our setting is different since we only get to view the maximizing assignment of the MRF rather than samples from it.

a particular x will always be paired with the same y rather than samples y drawn from the conditional distribution p(y|x; θ).


By Proposition 4.2, for a fixed W ∈ IR d×T there is a unique minimizer of Penalty ε (under the constraints in (2.5)), given by the formula Moreover, there exists a minimizer of problem (2.4), which is unique if p ∈ (1, 2].

we can solve problem (2.4) using an alternating minimization algorithm, which is an extension of the one presented in [4] for the special case F (D) = D −1 .


The trainable transformations t however, are defined for fixed positions of the local receptive field, which is agnostic to those translations.

the composition of pose vectors and trainable transformations to compute the votes depends on the input transformation, which prevents equivariance and invariance.


Our second application is motivated by statistical models for time series prediction, and in particular by statistical models for multi-step ahead AR prediction.

let {X t } T t=1 be a time series (that is, a series of signal observations).


If then with probability at least 1 − c 2 exp (−c 3 m), the TWF estimates (Algorithm 1) satisfy for all x ∈ R n . Here, 0 < ρ < 1 and µ 0 , c 0 , c 1 , c 2 , c 3 > 0 are some universal constants.

alternatively, if one regards the SNR for the model (12) as follows then we immediately arrive at another form of performance guarantee stated in terms of SNR: the relative error of TWF reaches O(SNR −1/2 ) within a logarithmic number of iterations.


Then, K Φ is bounded by: with probability exceeding 1 − ρ. Theorem 3.1 is a worst-case bound and serves as a sufficient condition for stable ID estimation using random projections.

if we choose a sufficiently small value for δ and ρ, we are guaranteed estimation accuracy levels as close as desired to those obtained with ID estimation in the original signal space.


The main idea behind our work is to generate the future frames with parameters adapted to the motion pattern within a particular video.

we propose a learnable parameter layer that provides custom parameters for different samples.


In text classification tasks have large sparse input spaces (bag of words), and presence/absence of features (words) is more important than their real values (frequencies).

(distributions over) binary weights and a threshold activation function may work well.


Chebyshev's inequality 1 states that for a random variable X, if the E[X] and V[X] are bounded, then for any ✏ 0: Pr Now we have characterized the variance of the weights, but what we really want is to characterize the variance of the value estimates.

notice that the variance of the value-estimate, for state-action x is the variance of the estimate is characterized by the variance of the weights.


See Proposition 2 for the formal statement.

our measures are inherently equality preferring.


Let also µ = μπ E − µ π E : S × A → R p be the feature expectation error.

we define the action-value function error as We finally define the mean delta-max action-value function error as Theorem 1.


ChannelNet-v1 outperforms ChannelNet-v1(-) by 0.8%, which is significant as ChannelNet-v1 has only 32 more parameters with group channel-wise convolutions.

group channel-wise convolutions are extremely efficient and effective information fusion layers for solving the problem incurred by group convolutions.


The fact that this edge was not bought implies that δ(v, u) α = Ω(d 3 ).

we have that In other words, for "small enough" values of α (quantified in the full proof), vertices quite distant from u in the grid have an incentive to buy an edge to u, by virtue of the dense population in S δ u .


in what follows, we focus on learning M k and b k . For the k-th component, the relevant terms in the expected log-likelihood, given the posteriors, from a single similarity assessment s on (u, v), is Learning the parameters Note that J k is not jointly convex in b k and M k . we optimize them alternatively.


The present work, being concerned with the way in which reinforcement guides sensory representational learning, focuses exclusively on the first of these two steps.

we take the value associated with the current sensory input to be given.


Ideally we want to force the policy gradient estimates to pay at least some attention to the high-reward trajectories.

we adopt a clipping mechanism over the memory weight ⇡ B , which ensures that the memory weight is greater or equal to ↵, i.e.


As it can be observed in Figure 5, the performance of the model including the centrality estimated from X 1 is better than the performance of the classical model, both when using just the data X 2 and the concatenated data X 1 |X 2 .

we can discard the old data X 1 and keep only the structure (centrality) and still be able to infer a more accurate version of G 2 .


Denote by y i kt the observed spike-count of neuron i ∈ {1 . . . q} at time bin t ∈ {1 . . . T } of trial k ∈ {1 . . . N }, and by y k = vec (y k,i=1:q,t=1:T ) the qT × 1 vector of all data observed on trial k. Neurons are assumed to be conditionally independent given the low-dimensional latent state x kt (of dimensionality p with p < q).

correlated neural variability arises from variations of this latent population state, and not from direct interaction between neurons.


Note that while the only scores that directly contribute to the loss are the ones coming from hard-assigned matches, all matching scores affect the loss because of the normalization in (6).

all matching scores will be updated at each training step.


We only require that the kernel spans the value function of an optimal policy.

the value function of an optimal policy is assumed to have a low approximation error, measured by the Bellman error, using that kernel.


So the MABs of the nodes in level H − 1 become stationary as well.

thompson sampling will also converge to the optimal actions for nodes in level H − 1.


We choose Dict+LA instead of BDL-STM+LA, because the BDLSTM embedding of each token does not correspond to the token itself only -it will contain the information passing from previous and subsequent tokens in the sequence.

the attention of BDLSTM+LA is not as easy to interpret as Dict+LA.


For example, if the generative model is described by a Bayesian network, the joint distribution can be written as } denotes the set of all variables (hidden or visible) and PA n are the parents of the n − th of these variables, i.e., v (t) n . The cross-entropy term in the equation above further decomposes into For each discrete hidden variable v (t) n , the appropriate terms above can be further broken down into individual terms in the summation over the D n possible configurations of the variable, e.g., In a similar fashion, the entropy term can also be decomposed further into a sum of terms as dictated by the factorization of the family Q.

the free energy for a single sample t can be expressed as the sum where all the free energy pieces f t i, θ derive from the finest decomposition ( 5) or ( 4).


Moreover, from standard concentration arguments, the `1/`1 matrix norm for a diagonal ("separable") subgaussian random matrix has at most logarithmic dimension dependence 1 , but for a dense ("non-separable") random matrix, the `1/`1 matrix norm could possibly scale linearly in the dimension.

the scaling of `1/`1 matrix norm gives us an indication how "separable" the matrix is.


There is no requirement that can be efficiently computed or stored -for example, in the case of the Gaussian kernel, F is an infinite dimensional space.

kernel methods typically work with the kernel matrix K 2 R n⇥n with K i,j = (a i , a j ).


as m → ∞ the upper bound on v 1 2 G (equation ( 8)) for the flower graph is matched by a lower bound with a gap of 1.


A Pareto-dominated convention is unpreferable because there is another convention that makes both agents better off.

we advocate that a MARL algorithm should at least cause agents to learn a PO convention.


However, the foreground of some images appears a dog or a cat, yielding noisy labels [35].

human cognition masks invalid class transitions (i.e., beach mountain), and highlights valid class transitions (i.e., beach ↔ dog).


The ratio becomes more and more favorable as both Q increases and K increases up to Q/2, but the number of different clusters P must also be large.

the method should be most efficient on datasets with a very large number of labels, assuming that P increases with L in practice.


[18,Lemma 12] showed that V (K g ) = 1 (also see [19]) and All these classes satisfy the conditions of Theorem 7 and Corollary 10 and therefore provide consistent estimates of γ(P, Q) for any P, Q ∈ P. Examples of kernels on R d that are covered by these classes include the Gaussian, Laplacian, inverse multiquadratics, Matérn class etc.

other choices for K that are popular in machine learning are the linear combination of kernels, Lemma 7] have shown that V (K con ) ≤ V (K lin ) ≤ l. instead of using a class based on a fixed, parameterized kernel, one can also use a finite linear combination of kernels to compute γ.


2 (t = 10.8s), since the former is much closer in frequency than the latter.

we a priori expect smaller values for s f than for s t . We encode this prior information by means of conjugate priors for s t and s f , i.e., scaled inverse chi-square distributions.


This approach often leads to simple formulations of these problems and to more efficient vision algorithms.

we must study issues related to the differential geometry and topology of a shape space.


When the number and times of transitions are known a priori (KNKT setting), we only need to identify the most likely initial network G 1 and sets of edge changes ∆g 1 . . . ∆g m−1 .


Hence, the distance/similarity measurements are overdetermined in these applications.

a new type of multi-metric learner which can describe the ambiguous linkages is desired.


We also studied circumstances when this assumption proves unreasonable.

our first contribution was to clarify the implicit assumptions and limitations in multi-view consensus learning in general, and co-regularization in particular.


The reasoning behind this approach is that each marginal is expressed through an average of all possible realizations of dynamics with a given initial condition; this is in contrast with the likelihood function which considers only particular instance realized in the given cascade.

equation ( 9) summarizes the effect of different propagation paths, and the maximization of this probability function will yield the most likely consensus between the ensemble of couplings in the network.


1 CF-2g closely resembles the serial Ser-2g, but the elements e ∈ V are no longer processed in a fixed order.

the sets A, B are replaced by potentially stale local estimates (bounds) A, B, where A is a subset of the true A and B is a superset of the actual B on each iteration.


On the other hand if you already knew that "blicket" meant the object in the window, you might be able to infer these elements of syntax and social cues.

the problem of early word-learning is a classic chicken-and-egg puzzle: in order to learn word meanings, learners must use their knowledge of the rest of language (including rules of syntax, parts of speech, and other word meanings) as well as their knowledge of social situations.


However, observing spike times may be misleading since there are many combinations that can produce the same output [15,16].

in this framework, variability in spiking is not a lack of precision but is the consequence of the redundancy in the representation.


Σ XY can be decomposed as Y Y for a bounded operator V (Theorem 1, [10]).

we see Σ−1 XX Σ XY is well-defined, because RangeΣ XY ⊂ RangeΣ XX = (KerΣ XX ) ⊥ .


Thus, if we construct the sequence (e n ) n∈N such that ∀n ∈ N, e n+1 ∈ argmin e∈E f en and e 0 ∈ E, then we obtain a decreasing sequence (f (e n )) n∈N .

the algorithm DCA solves a sequence of convex optimization problems in order to solve a DC optimization problem.


Since, N ≥ n Λ = Λ/λ (M ) , any multi-fidelity strategy which plays a suboptimal arm a polynomial number of times at any fidelity after n time steps, will have worse regret than MF-UCB (and UCB).

in our lower bound we will only consider strategies which satisfy the following condition.


This is a delicate step, because some of the bounds given above involve quantities that are defined in terms of Z.

all these parameters need to be controlled in order to ensure that the bounds do not grow too large.


This new model is parametric (the number of texton clusters has to be tuned by hand for different texture images) and model selection which might be unstable in practice, is needed to avoid overfitting.

the learning is sensitive to the parameter settings.


centered random variables with variance σ 2 and kurtosis κ.

a reasonable estimate of (2) Clearly this estimator is unbiased and has variance if we are to expect good estimation of σ 2 , then the kurtosis should be finite.


Finally, we verify the convergence of the summation of the serial { 1 t b t } ∞ t=1 .


It is immediate that any classifier which coincides with the Bayes classifier g * on the region tΩ c = {x ∈ R d + : x > t} is optimal w.r.t.

the distribution P t . In particular g * minimizes L t and the associated risk is for all classifier g, L t (g) ≥ L t (g * ), and taking the limit superior shows that g * minimizes L ∞ , that is Optimality.


Each ancestor node maintains a vector of pointers to all observations attributed to it.

these entries can be removed from the observation vectors in the global grid in constant time.


For the scalar case, the fundamental solution is given by the closed form formula φ T,0 = e T 0 At dt .

the positivity of R is seen to be necessary to obtain a meaningful solution.


For any network N (G, π, p), consider N (G, π, p) where for any i, pi = p 2 i .

define the function g : R |Vin| → R to be the sum of outputs of this network: Then κ (1) and κ (2) can be calculated as follows where 1 is the all-ones input vector: In the process of calculating the gradient ∇ pg(1), we need to calculate h u (p) and ∂g(1)/∂h v (p) for any u, v. the only remaining term to calculate (besides Recall that T is the length (maximum number of propagations through time) and d is the number of layers in an RNN.


Then, I(q | Q 0 = v 0 ) on G is equal to I(q) on G . Thus, after each query, we can incorporate the new evidence by updating the probabilities of all the nodes along the path from the query node to the root.

finding the next best node to query can still be computed in linear time.


Current approaches mostly rely on simplifying assumptions to map both domains into a shared-latent space.

they are only able to model the domain-invariant information between the two modalities.


The probabilities of observation errors are designed as 10%, 20%, 30% and 40%.

there are in total 16 simulated tests, each test repeats 100 times.


It is well-known [5] that if (Σ −1 ) ij = 0 then the random scalar variables in the i-th and j-th entries in x are conditionally independent.

in this work we adopt the notion of estimating the inverse of the covariance, Σ −1 , assuming that it is sparse.


In this case, the data analyst is interested in inferring whether the data was generated from P n 0 or P n 1 , where P n ν is one of two possible joint priors on X 1 , ..., X n . This is a challenging problem because knowing X i reveals information about X j , j = i.

the utility maximization problems for different individuals are coupled in this setting.


For 2-player Leduc, we use r, cr, ccr, and cccrexperts for both players.

the base strategy plays until the first raise occurs, at which point an expert takes over for the remainder of the hand.


In this section, we provide an empirical evaluation of the performance of the regularized Laplacian estimator, compared with the unregularized estimator.

to do this, we need a ground truth population Laplacian L and a noisily-observed sample Laplacian L. in Section 5.1, we construct a family of distributions for L; importantly, this family will be able to represent both low-dimensional graphs and expander-like graphs.


Letting g i (t) ∈ ∂f i (x i (t)) be a subgradient of f i at x i (t), By definition of z(t) and y(t), we have y(t) = argmin x∈X { 1 n t−1 s=1 n i=1 g i (s), x + 1 α(t) ψ(x)}.

we see that the first term in the decomposition (8) can be written in the same way as the bound in Lemma 2, and as a consequence, we have the bound It remains to control the final two terms in the bounds ( 7) and ( 8).


It is also notable that the loss term on the LHS of ( 7) is invariant to the scale of W , but the upper bound on the right side of ( 7) is not.

as with binary SVM and margin-rescaling formulations of structural SVM [24], we introduce a regularizer on the norm of W when optimizing the bound.


The mechanism which accepts examples from the oracle with some probability is called the filter.

on each round, a boosting-by-filtering algorithm draws a set of examples from D t via the filter, trains the weak learner on this set, and receives a weak hypothesis h t . Though a batch booster would estimate t using the fixed set S, filtering boosters may use new examples from the filter.


(4) However, this is not necessary if we require only the percept represented by the network to be fixed.

instead, ṡ = D ȧ = D(−a + La) = 0 (5) setting the derivative of s to zero is tantamount to If we require persistent percepts for any a, then: Equation ( 7) has a trivial solution L = I, which corresponds to a network with no actual lateral connections and only autapses.


It is also easy to show that, under the assumptions above, both l(x) and r(x) are locally Lipschitz continuous.

the Clarke subdifferential [7] is well-defined.


Compiler Data: For this particular application, in a real-life scenario it is critical to achieve good performance with a low number of training data-points per task given that a training data-point requires the compilation and execution of a (potentially) different version of a program.

although there are a total of 88214 training points per program we have followed a similar set up to [3] by considering N = 16, 32, 64 and 128 transformation sequences per program for training.


Since we are usually interested in selecting a variable assignment with maximum posterior probability (10), we do not need to derive these distributions.

in this example, it is sufficient for us to determine that the assignment of Y 1 to label 2 maximizes Going back to our application in contour grouping, the RV ⊕T 2 is an append of three RVs representing segments 2, 7, 8 in Fig.


The classification might be based on color, symbol, or numerosity; instructions require participants to identify the current dimension through trial and error, and perform the appropriate classification until the dimension switches after some unspecified number of trials.

it requires participants to maintain a task set-the classification dimension-in working memory (WM).


Now, the full connectivity of the graph implies that the total number of arcs in the graph is exactly |D|(|D| 1)/2.

|D|(|D| 1)/2  |D|d and the claim follows.


Neural networks that implement the softmax function, usually via some form of lateral inhibition, have been extensively investigated [2,[8][9][10][11]21].

inference in our model reduces to well-understood neural circuit dynamics.


This model has only one transition probability matrix for the entire data.

it cannot represent more complicated time variations such as split & merge of clusters that only occur temporarily.


Even the best known upper bounds have constants that blow up in the case of non-unique minimizers.

whereas stochastic mixability implies fast rates, a sort of converse is also true, where learning is hard in a "neighborhood" of statistical learning problems for which stochastic mixability does not hold.


However, as n/k → 1, the quantizer begins to "see" isolated samples instead of the manifold structure.

the training slope begins to fall to zero, and the test slope rises, reflecting the failure of the quantizer to generalize to the test set.


6 can be obtained from a subsample of the node's non-links.

the gradient of L with respect to the membership parameter γ a , computed using all of the nodes' links and a subsample of its non-links, is a noisy but unbiased estimate of the natural gradient in Eq.


For each question, the entity encoding g C w (e) is computed for every entity e in the entity set E. Note that an entity e is generally composed of multiple words.

similar to the question encoding, the hidden representation of an LSTM net is used.


Note that using the results of section 2, we would have obtained exactly the same bound for estimating the D-th eigenvector only -or even a worse bound since δ D = δ D ∧ δ D−1 appears in this case.

at least from the point of view of this technique (which could still yield suboptimal bounds), there is no increase of complexity between estimating the D-th eigenvector alone and estimating the span of the first D eigenvectors.


For any pair of domains D (i) and , or , then all parameters of the system are unchanged across D (i) and D (j) , i.e., , and a (i) = a (j) , and Assumption 1 is mild in the sense that it only rules out a 2-dimensional subspace of a 3-dimensional space.

considering Lebesgue measure on the 3-dimensional space, we are only ruling out a measure-zero subset.


Of course, using the true test labels in method 3 would be the ideal measure of the degree of confusion between models, but these are of course not available (see Figure 2, however, showing the results of a cheating experiment).

we use the hypothesized labels from a first stage to compute  is used if either one of 9 5 @ 3 Using 4 state per phone, 12 Gaussian mixtures per state HMMs, totaling 200k free model parameters for the system.


However [25] empirically showed that the per-window methodology fails to predict the performance per-image and therefore is not adequate for real applications.

we evaluate the per-image accuracy using the source code available from [25], which matches bounding boxes with the 50% PASCAL matching measure ( intersection union > 0.5).


For each observed timestamp ⌧ v , the estimator creates a ball of radius ⌧ v 1, centered at v. For example, in our figure, the green node (node 1) has ⌧ 1 = 2.

the adversary would make a ball of radius 1 centered at node 1; this ball is depicted by the green bubble in our figure.


The similarity measure d (T ) (r, s) could, for example, be squared Euclidean distance: T . However, this similarity measure only looks at the first T time steps of training time series r. Since time series in our training data are known, we need not restrict our attention to their first T time steps.

we use the following similarity measure: where we minimize over integer time shifts with a pre-specified maximum allowed shift max 0.


In particular, the verifiability property allows us to design new recovery routines with explicit confidence bounds for the recovery error and optimize these bounds with respect to the method parameters.

the major novelty in what follows is the emphasis on verifiable conditions on A and the representation structure which guarantee good recovery of Bx from noisy observations of Ax, provided that Bx is nearly s-block-sparse, and the observation noise is low.


To incorporate MC-SURE into a stochastic gradient-based optimization algorithm for training, such as the SGD or the Adam optimization algorithms, we modify the risk (7) in accordance with where ( 11) is equivalent to (7) owing to conditioning.

from Theorem 1, an unbiased estimator for E n∼N 0,σ 2 x − h(y; θ) 2 |x can be derived as such that for a fixed x, using the empirical risk expression in (10), an unbiased estimator for ( 7) is noting that no noiseless ground truth data x (j) were used in (13).


Because of the high dimension of the third-order features, the estimation of the whitening transformation itself is already computationally very expensive.

we only performed a mean and variance normalization of the third-order features, but initialized the models incrementally from first to second to third-order features.


We split the data into training and testing sets by picking alternate yaw angles.

there is no overlap of θ between the two sets.


Computing the Type I cost for each with h(z) = z gives g (I) (X (1) ) = 2 √ 2 and g (I) (X (2) ) = 2(1 + ǫ).

if we allow ǫ to be small, g (I) (X (2) ) < g (I) (X (1) ), so X (1) = X 0 cannot be the minimizing solution.


Since we obtain that for any λ > 0, E 2n πe h ≤ 1.

for any β > 0, we have On the event log πe h+log β ≤ 0 , by the Legendre's transform, for any probability distribution ρ ∈ M 1 + (F), we have which proves the lemma.


It mainly consists in computing the Vapnik-Chervonenkis dimension of the residual.

if we were able to compute a function such as Q N , we would have, thanks to Eq .


To this end, let (X, d X ) be an arbitrary metric space, H be a separable Hilbert space and ρ : X → H be an injective map.

we write V := ρ(X) and equip this space with the metric defined by H. ρ : X → V is bijective by definition.


Consequently, we endow the model with the ability to select only some bigrams and leave other letter pairings unspecified.

we allow the extraction component to consider symbolic partial orderings-i.e., a subset of the letter pairings in a complete ordering.


. . , x n }, the goal of random fields is to find a label assignment f that maximizes the posterior probability p(f |X) (of that assignment): (1) we want to select the label assignment with the largest possible probability given the observed data.


On the other hand, the computation of our analytic-form solution took only 0.055 [sec] on average, including the single-parameter search for σ 2 .

our method provides the reduction of computation time in 4 orders of magnitude, with better accuracy as a minimizer of the VB free energy.


We can immediately notice that F β is fractional-linear, hence pseudo-convex, with respect to FN 1 and FP 1 .

with a slight (yet convenient) abuse of notation, we write the F β -measure for binary classification as a function of vectors in R 4 = R 2L which represent error profiles of classifiers: Multilabel Classification In multilabel classification, there are several definitions of F -measures.


The winner features in a group are set to large values, while the loser features are set to zeros.

it leads to sparsity at the intra-group level.


The proof can be directly derived from the PC set definition of a causal network.

using the topology-based MB discovery methods, if we can discover the exact causal identities of the PC nodes within the MB, causal discovery of direct causes and effects of the target can therefore be successfully accomplished.


(2) The training data can be considered noise free.

are there better ML models for the noise free case while regularizing away the intrinsic problem complexity to keep the ML model small?


The goal is to find the best bounding box given the learned weight vector w and the visual feature x. Privileged information is not available at testing time, and inference is performed on visual features only.

the same maximization problem as in standard SSVMs needs to be solved during prediction, which is given by This maximization problem is over the space of bounding box coordinates.


Recall from Remark 2.6 that the optimal estimator corresponding to a KL or τ -divergence ambiguity set of the type studied in [12,27] coincides with the Bayesian MMSE estimator irrespective of ρ.

we may restrict attention to Wasserstein ambiguity sets.


Similarly, the linear constraint in (3) that relates y and X, or equivalently x, can also be written as the linear constraint y = Cx for a suitable recovery matrix C. Details on constructing matrix B and C can be found in the appendix.


As the temperature is lowered, the entropy drops, and the probabilities become more extreme.

larger values of a lead to faster responses, because the greater expected signal-to-noise ratio makes evidence more reliable.


Moreover, we show that for a certain distance function S f on the graph, one can uniquely recover all the graph intrinsic properties while also being able to capture both local & global information about the graph.

we define R as the multiset of node pairwise distances based on some distance function S f , which will be the main focus of this paper.


The function P consists of two classifiers per phrase type: the start classifier (h k S ) and the end classifier (h k E ).

the P function is formed by a prediction vector for each classifier, noted as w k S or w k E , and a unique shared representation function φ w which maps a word in context into a feature vector.


To circumvent the limits of local differential privacy, we consider a slightly relaxed estimation guarantee.

specifically, we batch the rounds into T epochs, each consisting of rounds, and aim in each epoch t to estimate p t , the population-wide mean across the subgroups and rounds of epoch t. any sufficiently large changes in this mean will be identified after the current epoch completes, which we think of as introducing a small "delay".


This is not a straightforward task; the reason is that when we are aiming to induce a function that maps object descriptions into ratings, we must consider that consumers' ratings are just a way to express their preferences about the products presented in the same testing session.

we had to use a special purpose SVM polynomial kernel.


However, using variational methods are themselves computational intractable in high dimensional scenarios due to the requirement of a matrix inversion which is computationally intensive.

we explore much faster approximation schemes such as partial MAP inference which are highly scalable.


This observation makes us conjecture that Tetris is a game whose policy space is easier to represent, and as a result to search in, than its value function space.

in order to obtain a good performance with ADP algorithms in this game, we should use those ADP methods that search in a policy space, instead of the more traditional ones that search in a value function space.


Consider when the program grows longer and this statement may repetitively occur multiple times, it may be hard for a sequence-to-sequence model to capture the correspondence based on only token sequences without structural information.

such a correspondence makes it a natural solution to locate the referenced sub-tree in the source tree when expanding a non-terminal in the target tree into a sub-tree.


Moreover, each network is trained on exactly the same set of examples.

a natural question is to which extent the randomization, in terms of both connection weights and training examples, affects the network learning capabilities.


If the sensors were permitted to communicate on the basis of their pooled observations, then they would be able to smooth out their independent observation noises entirely as L goes to infinity.

the data center can achieve an arbitrary fidelity D(R), where D(•) denotes the distortion rate function of {X(t)}.


Then, as shown by [19] (see their Theorem 4), the performance of any binary classifier f 2 B cannot exceed ) for all f 2 B.

estimating posteriors first and adjusting a threshold afterward appears to be a reasonable strategy.


On the other hand, a wrapper method uses a classification algorithm's performance as a scoring function for testing.

the choice of the underlying (surrogate) loss function plays a critical role.


First, separate PFC stripes are used to encode each step in the sequence.

binding of phoneme identity and sequential order occurs in this model by using distinct neural substrates to represent the sequential information.


One of the motivations for using the Perceptron is its simplicity which can underscore differences in the kernels.

we ran the kernel learning algorithm with LogLoss and ExpLoss, using bith the training set and the test test as S. we obtained four different sets of kernels where each set consists of 45 kernels.


The denominator in the above equation is difficult to handle as it involves summation over all possible parameter values.

we need to resort to approximate inference.


in the energy ( 9)-( 10), submodular terms act within x 1 and x 2 sets of variables and supermodular terms act only across the two sets.


The GLC differs from previous loss corrections for label noise in that it reasonably assumes access to a high-quality annotation source.

to compare to other loss correction methods, we ask how each method performs when starting from the same dataset with the same label noise.


This approach is straightforward to extend to handle samples of continuous states and actions , in which case, a policy is represented by a vector Θ t ∈ R N of continuous parameters (for instance, the center and the width of a gaussian).

equation 2 defines a distribution P (Θ 0:H ).


. . = v x (K) , then we may never recover θ along the direction of v. In fact, Proposition 1 can be viewed as an instance of this result where v = 1 |S| (recall that 1 |S| η π µ,P ≡ 1), and that is why we have to remove such redundancy in Example 1 in order to discuss identification in MDPs.

to guarantee identification in a fixed environment, the feature vectors must have significant variation in all directions, and we capture this intuition by defining a diversity score spread(X) (Definition 2) and showing that the identification accuracy depends inversely on the score (Theorem 4).


Then We now provide a few remarks to explain and simplify the result.

under the more stringent condition that for the remainder of this section we take M 2 = d j=1 p j M 2 j , which upper bounds the Lipschitz continuity constant of the objective function f . We then obtain the following corollary.


Since the poisoning data is optimized based on the attacker's malicious objectives, the correlations among features within a feature vector may change to appear different from normal instances.

tracking and detecting deviations in the feature correlations and other accuracy metrics can be one potential defense.


Such structure is indexed by how distinctively different contents are represented in that region [21,4].

one way to directly quantify the structure of the representational space in the neural population activity is to estimate the neural activity pattern elicited by each sensory stimulus, and calculate the similarity between the patterns corresponding to each pair of stimuli.


10(a) demonstrates the tradeoff in choosing a block size: when block size is too small the statistical power of the M -statistic is weak and hence EDD is large; on the other hand, when block size is too large, although statistical power is good, EDD is also large because the way we update the test block.

there is an optimal block size for each case.


The prior over parameters w is assumed to be uniform.

given M independent training images, where If τ is given, the penalized log pseudo-likelihood in ( 5) is convex with respect to the model parameters and can be easily maximized using gradient descent.


We will show essentially that if the machines first collectively choose randomly a coordinate i, and run protocol ⇧ i for the one-dimensional problem, then the information cost and mean-squared loss of this protocol will be only 1/d factor of those of the d-dimensional problem.

the information cost of the d-dimensional problem is at least d times the information cost of one-dimensional problem.


The joint probability over input pixels and latent variables is proportional to exp(−E PoT (x, h c )).

the conditional distribution over the input pixels is a zero-mean Gaussian with covariance equal to: In order to make the mean of the conditional distribution non-zero, we define mPoT as the normalized product of the above zero-mean Gaussian that models the covariance and a spherical covariance Gaussian that models the mean.


It considers the model where π i is the overall skill of the ith individual.

given k individuals and r ij as the number of times that i beats j, an approximate skill p i can be found by minimizing the negative log likelihood of the model (1): from paired comparisons, we can obtain individual performance.


Both algorithms SVRG and SCSG are only capable of finding approximate stationary points, which may not necessarily be approximate local minima and are arguably bad solutions for deep neural nets [10,11,15].

can we turn stationary-point finding algorithms into local-minimum finding ones?


For example, it seems psychologically implausible that the ten amendments or Ten Commandments are mentally represented as coordinates on an interval scale.

we also applied probabilistic models where the group answer is based on a pure rank ordering.


Note that g is non-negative and submodular.

by Lemma 5 and the fact that A contains every element with probability at most q (because Algorithm 2 accepts an element into its solution with at most this probability), we get Combining the two above inequalities, we get the approximation ratio of the algorithm we got is at most 2p + 2 p p(p + 1) + 1.


To prove convergence of GANs learned by TTUR, we make the following assumptions (The actual assumption is ended by , the following text are just comments and explanations): (A1) The gradients h and g are Lipschitz.

networks with Lipschitz smooth activation functions like ELUs (α = 1) [11] fulfill the assumption but not ReLU networks.


After using l * labeled examples P error = P Bayes + O ( 2 ).

from the above theorem it can be thought that as labeled examples are added, initially the excess error reduces at a very fast rate (exponentially in the number of labeled examples) until P error − P Bayes = O ( 2 ).


Moving to a table changes the x and y coordinates of the robot without changing the joint angles of the robot's arms, while picking up a glass does the opposite.

the x and y coordinates and the arm joint angles of the robot belong to different factors.


It turns out that, for each potential query, all of the desired quantities can be obtained via two inference passes using a standard join tree algorithm [6] .

the run time complexity of the algorithm is: 0(1 QI .


Furthermore, the state persistence potentials capture duration information that is not available in the DBN representation of the HHMMs in [6].

the segmental nature of the HSCRF thus incorporates the recent semi-Markov CRF [8] as a special case [11].


Further, for any user, the number of items with positive engagement (e ij =1) can be quite different from those with negative engagement (e ij =0).

in our experiments, we choose to independently sample histories for the two classes up to a maximum size k for each class.


[30] ) on the robustness of eigenvector to perturbation, M(By) has top eigenvector 2 that is O(")-close to x itself.

definition 3.2 is a sufficient condition for the spectral decoding algorithm v max (By) to return x approximately, though it might be not necessary.


Empirically, such an SDP produces vacuous certificates (> 90% error).

these constraints at intermediate layers play a significant role in improving the empirical performance of the SDP relaxation.


A necessary and sufficient condition to achieve this is conjugate symmetry in the frequency domain.

namely, for any transform y = F (x) of some input x, it must hold that intuitively, given the left half of our frequency map, the diminished number of degrees of freedom allows us to reconstruct the right.


This is time consuming or even infeasible.

robots need to be able to learn and adapt to unknown environments autonomously [10,2].


Let q ∈ Q, the children of q in Q are not in Q 2r and therefore are all within 2r of Q; since these children an r-packing of B(q, 2r), there are at most 2 2d of them.

max |Q | ≤ 2 2d max |Q|. . At the end of each iteration we have Q ⊂ B(x, ρ (x, Q ) + 2r).


Traditional supervised learning is evidently a degenerated version of multi-instance learning as well as a degenerated version of multi-label learning, while traditional supervised learning, multi-instance learning and multi-label learning are all degenerated versions of MIML.

we can tackle MIML by identifying its equivalence in the traditional supervised learning framework, using multi-instance learning or multi-label learning as the bridge.


The case t 1 = 1 and t 2 = 1 cannot happen by the assumption that t ∈ Y.

since the concatenation, y, of the independent maximizers of ( 27) is feasible, i.e.


Notice that while Flat Q runs faster than MAXQ (because of the additional "bookkeeping" overhead due to the task hierarchy), Bayesian MAXQ runs much faster than Bayesian model-based Q.

taking advantage of the hierarchical task decomposition helps reduce the computational cost of Bayesian RL.


Actually, our key idea is to form a closed loop so that we can extract feedback signals by comparing the original input data with the final output data.

if more than two associated tasks can form a closed loop, we can apply our technology to improve the model in each task from unlabeled data.


Since the size of each descriptor is at most α, the number of constraints is O(α 2 ).

checking whether all the given constraints are satisfied can be done in O(α 2 ) time.


Importantly, when there is a stable generating structure, the algorithm's performance is indistinguishable from a standard batch-mode structure learning algorithm.

using this algorithm incurs no additional costs in "normal" structure learning situations.


Under mild assumptions, if we have sufficiently many mixtures, their means will span the affine space spanned by µ 1 , .

. . , µ K . the MSP algorithm estimates the E j 's and projects to the affine space they span.


At each of such round t, we have i ∈ Z (t) because of Lemma 1 and E, and therefore w i .


If F = φ, F is non-empty so there exists an S such that X i ⊥ X j | X S is faithful.

s separates i and j in G and (i, j) / ∈ E. If F = φ, then for any S ⊆ W, |S| ≤ K, we have either it is unfaithful.


In fact, each anchor plane can be considered as infinite number of anchor points, and for each data point only its closest point on each anchor plane is utilized for reconstruction.

intuitively the number of anchor planes in OCC should be much fewer than the number of anchor points in LCC.


These are all the synaptic weight parameters (β ij , i = j), as well as the values of the inhibitory neurons' firing rates in each attractor (v µ inh , µ = 1, . . . , m).

we may adjust a total of n(n − 1) + n I m parameters.


In the second mode we thresholded the prediction of the classifiers, ht(x) = sign(w •x+b) .

each binary classifier ht in this case is of the fonn ht : X -t {-I, +1}.


As figure 2 shows, variations in illumination significantly alter the individual brightness of different parts of the face, such as the eyes, cheeks, and forehead.

absolute image brightness distributions are unlikely to be adequate for classifying all of these images as depicting the same underlying object.


. . , z z z (i,α) }, so that the mini-samples have a distribution on their sizes (structure complexities) with the expected value n ′ = n/α.

we get with mα mini-samples with expected structure complexity n/α.


The goal is to ensure that the success of an attack (using a username-key pair) is low.

in other words, the attack succeeds with probability no larger than 1/δ i for a user which specified δ i ∈ N. the attack we seek to protect against is the use of the data to match usernames to keys (rather than attacks in which additional non-sensitive attributes about a user are discovered).


Smoothness is captured by a low pass filter with only lower frequencies passing through.

we define a zeromean Gaussian prior over the Fourier-transformed weights w using a diagonal covariance matrix C f with diagonal where χ i is the i th location of the regression weights w in frequency domain and δ 2 is the Gaussian covariance.


The case for examples with y n > k + 1 is similar and the change there is also non-positive.

by switching adjacent pairs of strictly decreasing thresholds, we can actually obtain a solution (g * , θ * ) with a smaller or equal objective value in (5), and g * = g. The optimality of (g, θ) shows that (g * , θ * ) is also optimal.


If the data space is isotropic then a stationary point of the error will correspond to a similarly isotropic map space 7 .

at a stationary point, we have for large ¡ : where & ¢ is the x identity matrix, and # " % and # " ) are the variances in the map space and the data space respectively.


Without loss of generality, we assume that all random variables are normalized to have expectation 0 and variance 1.

r 2 Z,S is simplified to be 1 − M SE Z,S .


A kNN regressor using only the labeled data outperformed DKL on two of three datasets for n = 100, beat SSDKL on all three for n = 100, beat DKL on two of three for n = 300, and beat SSDKL on one of three for n = 300.

the kNN regressor is often already outperforming SSDKL with only labeled data-it is unsurprising that SSDKL is unable to close the gap on a semi-supervised nearest neighbors method like COREG.


We propose to search a policy in P that minimizes the following Bellman residual: Notice that, as for the maximization of the mean value, we used a sampling distribution ν, possibly different from the distribution of interest µ.

from the basic properties of the Bellman operator, for any policy π we have that T * v π ≥ v π . Consequently, the ν-weighted 1 -norm of the residual is indeed the expected Bellman residual: there is naturally no bias problem for minimizing a residual here, contrary to other residual approaches [1].


As shown in Appendix H, the buffer size remains roughly constant throughout training.

we show the average ratio of memory requirements during training in Table 1.


The composite model we have described captures the interaction between short-and longrange dependencies between words.

the posterior distribution over the latent variables in this model picks out syntactic classes and semantic topics and identifies the role that words play in documents.


However, the exact factors ψ ik with i = 1, . . . , n and k = y i , corresponding to the likelihood, (2), only depend on f k (x i ), f yi (x i ) and z i .

the beta part of the corresponding approximate factors can be removed and the multivariate Gaussian distributions simplify to univariate Gaussians.


Assuming that the number of free parameters remains the same throughout the observations, and also assuming smooth variation of the parameters, one is in fact dealing with geometric restrictions which can be well modelled as a manifold.

the data must lie on, or near (accounting for noise) a manifold embedded in observation, or ambient space.


Bayesian model selection provides a consistent framework for setting such parameters.

it is essential to evaluate the accuracy of the marginal likelihood approximations as a function of the hyperparameters, in order to assess the practical usefulness of the approach Secondly, we need to assess the quality of the approximate probabilistic predictions.


We define the weight matrix as follows: Without loss of generality, we assume that the data points are ordered according to which class they are in, so that } are in the second class, etc.

s can be written as follows: where S i = 1 ni 11 T is an n i × n i matrix.


However, the original DMD has several numerical disadvantages related to the accuracy of the approximate expressions of the Koopman eigenfunctions from data.

several variants of DMD have been proposed to rectify this point, including exact DMD [33] and optimized DMD [8].


When strong community structure is present in A, however, these elements should instead be well separated for corresponding values of z.

it is of interest to examine a confidence set that relates Φ(z) ab to its expected value Φ(z) for a range of partitions z.


However, it is difficult to get a handle on L n (λ).

the main focus of this work is on deriving an asymptotic expansion for L n (λ).


The third term is 2E x∼f [ f (x)], and even though it cannot be computed exactly without knowledge of f , we can estimate it based on a held out validation dataset.

given a density estimator f and a validation dataset V = {z 1 , .


This is consistent with the information storage scheme in model-free RL, where cached action-values lose connection with the identity of the outcomes.

the habitual system doesn't know what specific action-values should be updated when a novel internal state is being experienced.


Once again according to the correspondence between graphs and ratings, we will get that 2 → 1 should be contained in graph G, which contradicts with G 2 .

g 2 will not exist in the setting of multi-level ratings.


However, it is known that the update rule (14) can diverge in some cases, for example, when Y ki are large.

a proof without extra conditions cannot be constructed.


If γ-feasibility holds, then we will denote by y * ∞ (y * ∞ is not necessarily unique) the minimizer of the following minimization problem: (1) and we define the γ-feasible optimal value as 1) is a convex minimization problem over Y().

the problem is equivalent to finding the saddle point of the Lagrangian function [15], namely, where the Lagrangian is We denote the optimal dual by λ * ∞ and assume that L can be maximize by a unique F ∞ -measurable function, λ * ∞ ().


Indeed, there may be a continuum between binary and Poisson modes.

even in conventional rate-modulated responses, the first spike is often privileged in that it carries most of the information in the spike train [5,14,18].


We note that for a hypergraph with no singleton hyperedge, given the c−cut function, it is easy to recover the hyper edges from (6).

we focus on learning the c−cut function to sketch the hypergraph.


In experiments, we found h << n, no more than 10 in simulations with hundreds of thousands of curves.

this search strategy takes O(n) time in practice to complete, mirroring the analysis of other output-sensitive algorithms such as the gift wrapping algorithm for computing convex hulls [8].


Definition 2 (Submodularity ratio) Let f be a non-negative set function.

the submodularity ratio of f with respect to a set U and a parameter k ≥ 1 is it captures how much f can increase by adding any subset S of size k to L, compared to the combined benefits of adding its individual elements to L. In particular, [5] defines the submodularity ratio for the R 2 function and relates it to the smallest eigenvalue of the covariance matrix of the data.


Since by definition of v t , subtracting ⌘t v t from x t can only decrease positive entries in x t (see proof of Observation 2), and both v t , v + t are vertices of P (and thus in {0, 1} n ), and ⌘t = 2 t , it follows that each entry i in x t+1 is given by: Thus, x t+1 can also be written in the form 2 t st+1 for some st+1 2 N n . By definition of t and the monotonicity of {⌘ t } t 1 , we have that 2 t 2 t+1 is a positive integer.

setting s t+1 = 2 t 2 t+1 st+1 , the induction holds also for t + 1.


As λf is increasing, L will additionally be convex.

the conditions below are only mildly stronger than what Lambert shows to be true of the desired properties.


The first is that the region X , Y, or Z that a sample (S j , f(S j )) belongs to is not known.

even before being able to train a classifier which learns the regions X , Ỹ, Z using the samples, we need to learn the region a sample S j belongs to using f (S j ).


Gaussian kernel To obtain the approximation of the Gaussian kernel, we use the following property [30].

given a smooth, shift-invariant kernel k(x − x ) = k(z) with Fourier transform p(w), then: Using the Gaussian distribution p(w) = N (0, σ −1 ), we obtain the Gaussian kernel the kernel value k(x, x ) can be approximated by the inner product between φ(x) and φ(x ), where φ is defined as and W B ∈ R d×D/2 as a random matrix with its entries drawn from N (0, σ −1 ).


Note that Z is query dependant, i.e., the values of Z depend on the query vector w, and n inner product values can be obtained by taking the column-wise summation of Z > .

in particular, for each j we have h > j w = P k t=1 z jt , j = 1, . . . , n. the ranking induced by the n inner product values can be characterized by the marginal ranking ⇡(j|w) defined on the implicit matrix Z as follows: ) As mentioned earlier, it is hard to design an ideal candidate screening procedure generating C(w) based on the marginal ranking.


By the triangle inequality, « -balls centered at ½ ¾ are disjoint.

the probability that an random element of À Ò is in a ball of radius « centered at one of ½ AE is at least AE´ ½ «µ Ò ½ .


However, the activity of principal neurons in the circuit is a dummy variable without its own dynamics.

such principal neurons do not integrate their input in time, contradicting existing experimental observations.


Points in S j may be dominated by the rightmost (non-dominated) point in S j−1 .

we compute the intersection of the rightmost point of S j−1 and the leftmost point of S j , iteratively dropping all dominated points of S j .


Due to the memory, computing and battery constraints, the prediction models on the edge devices are limited to low complexity.

to maintain high-accuracy, adaptive systems are desirable.


The goal is thus similar to the usual distributed averaging problem (4), with the  key difference that each local value h i is itself an average depending on the entire data sample.

our algorithms will combine two steps at each iteration: a data propagation step to allow each node i to estimate h i , and an averaging step to ensure convergence to the desired value Ûn (H).


But our method still produced acceptable results.

the experimental results show that our method is better than LDA+PCA in terms of both accuracy and efficiency.


The second baseline (denoted by |w|/cost) uses a cost-sensitive ranking scheme based on |w|/cost, the weight of a feature divided by its cost.

features having high scores are expected to be cost-efficient.


While images with high clutter have higher gain in PIFC coefficients.

the difference of FFC between different images increases nonlinearly with eccentricity, as observed in Fig.


In particular, with δ := max i δ i , we have the following result: Theorem 3 (Structural Coherence (SC) Condition) Let δ := max i δ i with δ i as defined in (14).

if δ < 1, then there exists a ρ > 0 such that for any ∆ i ∈ C i , i = 1, . . . , k, the SC condition in (9) holds, i.e., the SC condition is satisfied in the general case as long as the reflection −C i of any cone C i does not intersect, i.e., share a ray, with the Minkowski sum j =i C j of the other cones.


If we take the derivative, the numerator is a quartic in p q .


In other words, the vectors x associated with non-vanishing f.1i are those which lie on the hyperplanes or vectors tagged as margin errors.

all the thresholds aj, bj can be recovered from the support vectors -unlike the fixed-margin scheme which required another LP pass.


κ (2) (W rec ) can be written and calculated in the matrix form: where for any i, j, k we have The only terms that require extra computation are powers of W rec which can be done in O(dT H 3 ) and the rest of the matrix computations need O(dT 2 H 2 ).

the ratio of time complexity of calculating the first term and second term with respect to the gradient over mini-batch is O(1/B) and O((T + H)/B) respectively.


In this model, however, the α i are not uniform; the conductors with large α i will have the greatest influence on the potential function.

one can think of α i as the weight or importance of example i.


At a high level, our proof of Theorem 1 (as well as our new bounds on non-private estimation) follow from the fact that for all B and π, the expected score E[Score(B, π; G)] is equal to the score Score(B, π; Q), combined with a concentration argument.

the maximizer B of Score(B; G) will approximately minimize the L 2 -distance δ2 (B, Q), which in turn will approximately minimize 1 ρ W [B] − W 2 , thus relating the L 2 -error of our estimator B to the "oracle error" (O) k (W ) defined in (4).


The last equality in (23) follows from the definition of Θ * ∈ T , since it gives T ∆ .

thus, by the second inequalities of ( 8) and ( 9), Since Θ * = ∆ * − Θ ∈ T and the singular values of Θ is no smaller than (π ) by the second inequality in (7), Proposition 1 and (22) imply It follows from ( 23), ( 24) and (25) that the error bound (10) follows from (21), ( 22) and (26).


Intracellular recordings give clean signals on a spike train from a specific neuron, giving accurate spike times for that neuron.

if we detect a spike in a nearby extracellular recording within a close time period (<.5ms) to an intracellular spike, we assume that the spike detected in the extracellular recording corresponds to the known neuron's spikes.


In order to simplify these problems and exploit existing theorems, we will consider in this section that p ij = p is fixed for each edge {i, j} ∈ E. Infection dynamics thus only depend on p, the set of influencers A, and the structure of the underlying network.

for a star shaped network centered around a given node v 1 , and A = {v 1 }, the exact influence is computable and writes σ({v Proposition 1 states that σ({v 1 }) ≤ 1 + (n − 1)γ 1 where γ 1 is the solution of equation It is worth mentionning that, when p = 1 (17) and therefore the bound is σ({v 1 }) ≤ 1 + √ n − 1 which is tight.


v for m < M 2 are the same, this diversity measure can give only up to 3 different diverse labelings.

this diversity measure is not useful for M > 3, and can be seen as a limit of useful concave diversity measures.


If a presynaptic spike is active after the falling edge of a postsynaptic spike an activelow up pulse is applied to the gate of transistor P5.

the current flowing through N3 is mirrored to transistor P4 causing an increase in the voltage across Cw that corresponds to a decrease in the weight.


's that are "close" to the £ 1 's and which belong to a lower dimensional subspace of parameter space.

our approach is to find a basis ¤ 7¦ ©¦ in and to represent each !


BNSE can be interpreted as fitting a continuous-input interpolation to the observations, computing the Fourier transform of the interpolation and finally average over all the possibly infinitely-many interpolations.

as our interpolation is a GP, both the Fourier transform and the infinite average can be performed analytically.


Similarly, we can show that g cASO (W ) = tr (ηI + Λ * 2 ) −1 Σ 2 , where .


Let L + and Q − be the Laplacian and the signless Laplacian matrices of the graphs G + and G − , respectively.

we note that the matrix L SR blends the informations from G + and G − into (twice) the arithmetic mean of L + and Q − , namely the following identity holds ) as an alternative to the normalization defining L SN from L SR , it is natural to consider the arithmetic mean of the normalized Laplacians In the next section we introduce the geometric mean of L + sym and Q − sym and propose a new clustering algorithm for signed graphs based on that matrix.


[2]) consume O(n 2 i n 2 i ) time complexity for solving Problem 2, but the SOCP-specialized solvers that directly solve Problem 2 take only O(n 2 i n i ) computation [7].

sOCPs can be solved more efficiently than SDPs.


If γ < 1 and the agent makes a correct prediction at the end, the agent asking fewer questions receives more cumulative discounted reward G t than that asking more questions.

the agent shall learn to shorten the diagnosis process.


Both models are particularly suited for search contexts, where the user is assumed to be looking for something relative to a query.

the learner expects explicit feedback: in the Cascade Model each valid observation sequence must be either all zeros or terminated by a one, such that no ambiguity is left on the evaluation of the presented items, while multiple clicks are allowed in the DCM thus leaving some ambiguity on the last zeros of a sequence.


In order to make the learning problem tractable, we sample a smaller set T of K features from a suitably chosen distribution, implicitly setting the weights T of all other features to 0.

we will parametrize the learned influence function as The goal is then to learn weights T for the sampled features.


This, for example, is the case of fixed-length constraints [9,15,18] or unit norm constraints.

such constraints are hard to optimize and often yield solutions that are sub-optimal.


The log likelihood in this case reduces to a quadratic form: Substituting this into Eq.

(2) gives: T ∂f ∂ x for these models, the Fisher information matrix induces a locally adaptive Euclidean metric on the space of images, as specified by the Jacobian matrix, ∂f /∂ x. pixel 1 pixel 2 For unit vectors : (human) Figure 1: Measuring and comparing model-derived predictions of image discriminability.


See [1] for a proof of this fact in the case that G is the group of 2D affine transformations.

the empirical distribution of the inner products x, g t τ k is an estimate of an invariant.


Sequential Monte Carlo (SMC) is generally viewed as the leading candidate for massively parallel simulation, but because of particle resampling, existing implementations require the network transfer of a large number of particles and a central server with a global view on the weights carried by the particles.

the naive communication cost grows with the size of the inference problem.


The major obstruction is that the cubic complexity in M in the aforementioned upper-bound is also a lower-bound, which results from the inversion of an M -by-M covariance matrix defined on the inducing points.

these models can only afford to use a small set of M basis functions, limiting the expressiveness of GPs for prediction.


To determine the RG flow of the dimensionless coupling parameters the highfrequency components are integrated out from ω = λ − dλ to ω = λ to give a new effective action S over the low frequency modes ω < λ.

to accomplish this the function α and the new action is obtained by integrating over a > (ω), where the averaging is defined by In the weak-coupling limit, we may expand the exponential term in Eq.


Note that when K = 1, P 1 is simply the space of all linear classifiers.

importantly, when K ≥ 2, elements of P K are not guaranteed to have additive inverses in P K . the labels y = −1 and y = +1 are not interchangeable.


Here we obtain a slight generalization of the result in Kakade and Ng [2004] as a special case.

namely, the familiar linear model -with u(x) = θ • x, θ, x ∈ R d and Gaussian prior θ ∼ N (0, I) -can be seen as a GP model with the linear kernel: and so log |I + cK | = log I + cX T X our result gives an input-dependent version of the result of Kakade and Ng [2004].


Note that the only component that explicitly depends on the neural parameters θ i is the conditional probability P (F|X, θ).

the reward is conditionally independent of the neural parameters θ i given the coding feature F. if we want to optimize the expected reward by employing a gradient ascent method, we get a learning rule of the form If we choose a small learning rate η, the average over presynaptic patterns X and coding features F can be replaced by a time average.


Note that simply applying OVS in UM 2 L with impropriate regularizer Ω will lead to a trivial solution, i.e., M k = 0, which satisfies all similar pair restrictions yet has no generalization ability.

we need to set F or restrict the trace of M k to equal to 1.


This function is data-dependent and thus unknown before seeing the data.

if one wants to make statements about its behaviour (e.g.


We model guessing by choosing an ordering uniformly from all possible orderings of N items.

in the extended model, we have To complete the model, we place a Bernoulli(1/2) prior over 𝑧 𝑗 .


This would likely require us to gather the initial samples through other methods, such as variational inference, since the chances for untrained proposals to "stumble upon" low energy regions is diminished by the curse of dimensionality.

it would be interesting to see whether we could bypass the bootstrap process and directly train on U (x) by leveraging the properties of flow models.


In test, the complexity is O(M JN test K) per step, with K being the number of samples taken to compute the variational lower bound.

shrinkage of nodes can linearly reduce the testing time.


However, ANNs generally require powerful GPUs and computing clusters to crunch their inputs into useful outputs.

in scenarios where power consumption is constrained, on-site use of ANNs may not be a viable option.


i where e i = y i − x T i βn , and holds, the excess risk of β for approximating βn is bounded in probability 1 − δ for δ > R log d 3nλmin(Σn) where Theorem 1 indicates that, β − βn can be bounded by Cr −1/2 .

from (6), the choice of sampling method has no effect on the decreasing rate of the bound, r −1/2 , but influences the constant C. a theoretical measure of efficiency for some sampling method is whether it can make the constant C attain its minimum.


It possesses a lower and upper envelope around its global optimum that are equivalent to x 2 and √ x; and therefore have different smoothness.

for a standard partitioning, there is no semi-metric of the form (x, y) = ||x − y|| α for which the near-optimality dimension is d = 0, as shown by Valko et al.


While deriving unbiased estimators is very useful for ensuring stable convergence of stochastic gradient methods, it is not sufficient: convergence rates of stochastic gradient descent methods depend on the variance of the stochastic gradients, and this can be rather large for naïve choices of degree distributions.

our main contribution is in establishing a provably optimal degree distribution minimizing the estimators' variances with respect to the Chebyshev series.


Therefore, we can set the values of K • u much larger than the theoretical values without compromising the quality of approximation.

before calculating the list of reachable tuples of u, we first estimate the upper bound and lower bound of the reachable values of νu , μu and ẑu using the list of tuples of its children.


Assume we conduct the update (7) T iterations, the mirror descent algorithm outputs z T x,ξ;θ for each pair of (x, ξ).

it naturally establishes another nonparametric function that maps from R d × Ξ to R r to approximate the sampler of the variational distribution point-wise, i.e., Since such an approximation function is generated by the mirror descent algorithm, we name the corresponding function class as optimization embedding.


As we will show in the next section, the natural choice for this purpose is the sample size, § 9 wA vC FH P @ % (' 0) ! .

to summarize, we define the G 8 ¢¡ 3 @ mapping by q C &r s!


Structure learning faces several challenges: the number of possible structures is super-exponential in the number of variables while the required sample size might be even exponential.

finding good regularization techniques is very important in order to avoid over-fitting and to achieve a better generalization performance.


One can check that the contribution based on these single-edge walks can be computed as: This weight provides a measure of the error-reduction capacity of edge {u, v} by itself at iteration n. These single-edge walks for edges in S n are a subset of all the walks in S n , and consequently provide a lower-bound on φ(|h (n−1) |; S n ).

the maximization  is equivalent to minimizing a looser upper-bound than ( 8).


More specifically, for expert i, her policy ⇡ Ei is at most ✏ i less than the optimal policy in M i .

each expert i provides a set of constraints that any consistent reward needs to satisfy, and P R is the set of rewards that satisfy all constraints imposed by the experts.


In batch mode, using the whole (infinite) dataset, one would not take a single optimization step in finite time.

one should really be concerned with making as much progress as possible per computational unit.


It can be easily checked that if the marginal distribution of z C for each clique C ∈ C is defined by (2) then these distributions are consistent as they yield the same distribution (2) over the separators.

the unique Markov distribution over G with Dirichlet multinomial distribution over the cliques is defined by [8] Pr(z where for each complete set B ⊆ G, we have Pr(z B ) given by (2).


Let M π j,k denote a normalised single-reward Markov chain (NSR-MC) of M π , which has exactly the same S, A, γ and P π as M π , but all rewards are trivially 0 except r j,k = 1.

for an NSR-MC M π j,k , the equation above becomes the next step of analysis is to examine the state values in NSR-MCs.


From the information-theoretical point of view, we want to reduce the uncertainty of the class variable Y by observing classifier responses.

a natural way to define the reward is to consider the negative residual entropy, that is the lower the entropy the higher the reward.


The q-OCSVM method estimates the level sets (MV-sets) directly without a density estimation step.

we expect to achieve more accurate results than approaches based on density estimation.


It is easy to verify that this is equivalent to replacing the optimal h ⋆ by an approximate ĥ ∈ H that satisfies g ĥ p ≥ ν g h ⋆ p . Sparse case.

when Ω(•) = • 1 , we need to solve It is well known that the optimal solution of max h∈H |h T Γ c h| is the dominant eigenvector of Γ c . we simply need to find the dominant eigenvector h c of each Γ c and select ĥ as the h c with largest singular value |h T c Γ c h c |.


We also use regularizers to constrain the embeddings,e.g., to be non-negative.

the objective is We maximize this objective with respect to the embeddings and context vectors.


We applied a Canny-based detector for the edges in each image, using the same parameterization each time.

the images contain some edge points considered noise or that are missing from obvious contours.


Correspondingly, the improvement over the forward model will also provide positive impact on the learning of the backward model.

the forward and backward models work in a synergistic manner to simultaneously make the encoder joint distribution p e pS, T q and decoder joint distribution p d pS, T q match the oracle joint distribution ppS, T q.


However, practical applications such as image matching require binary, short and compact representations for sake of efficiency.

the role of L DM R regularizer is to map the good embeddings from high-dimensional to the compact binary space.


Unfortunately, this objective is not convex and it is difficult to optimize.

we replace it with the following convex upper bound defined in terms of the hinge function ℓ: This objective can be globally optimized using an LP solver or software for SVM training.


Here the step d) of scaling the samples is important for obtaining an unbiased estimator (see details in the proof of Lemma 4 in supplementary material and [16]).

in the following PC updating based on standard PCA on the accepted data, authentic samples will contribute more than the outliers.


The table shows that the search times of the parti-game algorithm are substantial due to the large number of searches performed (even though each search is fast), and that the searches take up most of its run time.


With τ → ∞, the reliability of the momentary evidence becomes overwhelming, such that the latent variable z is again immediately known, resulting in V (g, τ ) → V d (1) (= V d (0)) for all g. For τ = 0, the infinitesimal moments are dg = dg 2 = dτ 2 = 0, and dτ = ηµdt, such that g remains unchanged and τ drifts deterministically towards positive values.

there is no leakage of V towards τ < 0, which makes this lower boundary well-defined.


As we discussed above, in most of the networks that are useful models for real applications, exact inference is intractable.

we must resort to approximate inference, which results in errors in the gradient.


The layers in the head are composed of concatenation, convolution with identity mapping, and max-pooling.

the gradient propagation problem from the previous backbone network in the tail are solved with the FishNet by 1) excluding I-conv at the head; and 2) using concatenation at the body and the head.


On the other hand, MTL-SVM(local/network) nicely captures the circular boundaries and the results are highly reliable.

given an appropriate task network, the proposed MTL-SVM(local/network) can effectively exploit information of the related tasks.


From the discussion preceding ICMC it follows that ICMC recovers M exactly if the cascading process starting at L 0 infects all vertices of G Ω and we get the following theorem.

we have reduced the matrix-completion problem to the graph-theoretic problem of finding a completely cascading set (if it exists) in a graph.


• Type Matching Rules: Type matching rules note that if the element is of type t1 and the text label is of type t2, then the element should be matched to the text label.

the rule can be written down as type(e, t1) ∧ type(t, tw) → Mto.


However, Wasserstein distance is not negative definite.

it is limited to build positive definite kernels upon the Wasserstein distance without approximation.


We conjecture that the same results holds in our case.

to achieve ε estimation error, any Algorithm would likely require Ω(ε −2 ) regret, showing that Algorithm 1 is optimal up to logarithmic factors in this sense.


Therefore, by Lemma 6, the assumption of non-emptiness of A cccp (x) for any x ∈ Ω ensures that A cccp is closed on Ω and so satisfies condition (3) in Theorem 2.

by Theorem 2, all the limit points of {x (l) } ∞ l=0 are the generalized fixed points of A cccp and lim l→∞ (u(x , where x * is some generalized fixed point of A cccp .


In section 3.1, we describe the effects on the document-specific conditional posterior distributions, or predictive distributions, of replacing u with a fixed asymmetric (i.e., nonuniform) base measure m. In section 3.2, we then treat m as unknown, and take a fully Bayesian approach, giving m a Dirichlet prior (with a uniform base measure and concentration parameter α ) and integrating it out.

if Θ is given an asymmetric Dirichlet prior with concentration parameter α and an known (nonuniform) base measure m, the predictive probability of topic t occurring in document d given Z is If topic t does not occur in z (d) , then N t|d will be zero, and the probability of generating z N d +1 = t will be m t . In other words, under an asymmetric prior, N t|d is smoothed with a topic-specific quantity αm t . different topics can be a priori more or less probable in all documents.


With similar reasoning, by lemma 2, reflection on a affine reflective boundary preserves volume.

since all component transformations of RHMC leapfrog simulation preserve volume, the proof is complete.


Summarizing the above, any point that satisfies the definition (and necessary conditions) of a local minimum is indeed a global minimum.

we conclude the proof sketch of Theorem 2.3 (ii).


Indeed, it is the finite sample error that governs the noise.

by analyzing the effect of this noise (and hence the finite samples), it is likely that we can obtain the error bound on the performance of the algorithm.


( 4) that the set (A, t)(T k ∩ P k ) coincide with the feasible set of problem (5).

if the system (5) has no solution, then (A, t)(T k ∩P k ) = ∅, and hence (A, t)(T k ∩ D) = ∅ (because D ⊂ P k ).


Our approach is a secure extension to Deluge.

our approach can be used for other code dissemination protocols as long as the assumptions in section 3.1 hold.


1 Proposed Protocol 0.9 SCA with LEACH 0.8 Packet Loss Rate (PLR) 0.7 0.6 0.5 0.4 0.3 low values of SNR, the proposed protocol performance is similar to that observed for the SCA with LEACH, because the channel quality is severely degraded.

beyond 12dB, thePLR measuredin theproposedprotocoldecreases more than using SCA with LEACH, which also contributes to enhance the network lifetime.


By contrast, Nexus [17] is designed for high-performance communications and when layered with HPC++ [19] presents to the user a complete RMI system which can interoperate with Java [24].

nexus has robustness problems and the failure of a global pointer can lead to complete deadlock of the distributed computation.


For simplicity, the .gure shows that the route update timers are maintained in the source node.

in reality, it can be maintained in destinations as well (as in DSDV [16]).


IPv4 address lookup techniques have received a fair amount of attention in recent years [36, 1, 2, 11, 12], and we do not attempt to be exhaustive in our survey of this sub-.eld.

broadly speaking, there are two classes of lookup techniques: algorithmic approaches, exempli.ed by [12], attempt to cleverly compress forwarding tables compactly into memory, while hardware approaches rely on (ternary) content-addressable memories (CAMs) to perform fast lookup.


We used a con.guration similar to the one prescribed in [14] for an Ethernet switch.

when using RSTP switches, our con.guration has two differences from that in [14].


In DMAC implementation, if the receiving antenna beam direction is known then, the RTS packet can be sent directionally.

to overcome the hidden terminal problem due to asymmetry in gain, circular directional RTS is sent.


However, it is not feasible to simply forward messages generated by beaconing in large areas, due to the well-studied broadcast storm problem [27].

applications such as tra.c information systems often do not require exact information for their decisions.


CONCLUSIONS AND FUTURE WORK For SDN to support heterogeneous FEs, the common approach is to just provide higher level abstractions (WHAT) for the south-bound interface and ask a smart FE to handle all the detailed work (HOW).

every time a new feature is introduced, the FE needs to be amended to know how to handle it.


In this sense, CARD tries to achieve a similar goal as we discussed in Sections 5, 6, and 7.

cARD is an IP-level protocol, meaning that a lower layer (link-layer) decision will have to be depending on the operation of a higher layer (IP-layer) protocol.


When the .ows are suddenly stopped at t=l0seconds, XCP quickly reallocates the spare bandwidth and continues to have high utilization.

the sudden decrease in demand destabilizes TCP and causes a large sequence of oscillations.


We balanced the TPR and TNR to avoid biasing the model in one direction.

it is possible that network data samples taken in times and contexts that are di.erent than those encountered in our data collection phase could result in bias as well, thus reducing the accuracy of our models on real data.


Hence, in this case, the only subcase we should consider is that when the P as with side number less than six are pentagons.

given a pentagon with all edges equal, it will be a regular pentagon or has at least three different types of inner angles.


In his configuration the signal transmission and reception power is so low that the laptops are unable to communicate, although they may only be inches apart physically.

the presence of a third, unshielded node into the system adds a new dynamic.


We assume that later receptions of a message indicate a successful continuation of the forwarding process.

this assumption may not hold if only few retransmissions are received.


It allowed for scoped anycast addresses for groups con.ned to a topological region, which does not burden the global routing system.

a globally spread group still poses scalability problems.


Once LMA receives the DeRegister PBU, it waits given amount of time before removing BCE.

if there is no request from a new MAG, LMA gets rid of the BCE.


Actually, also retrieving an item in the cache does cause energy consumption, that may also be non negligible, depending, for example, on the cache size and the complexity of mana~ng the data structures needed for organizing items in the cache and to facilitate search.

our simplification should not affect the significance of the obtained results.


In practice, Duke University will deploy a wireless 802.11n network with 2500 access points [9] [10].

while 802.11n WLAN is replacing the current 802.11a/b/g, there will be time periods that the networks are coexisting.


The b~- sic principles of alignment, cohesion, and separation are the same.

the alignment rule is applicable regardless of whether a particle is too close or too far.


4.3 Routing Stability and Scalability Link-state routing protocols exhibit poor stability and scalability in IP due to the fast routing convergence requirement.

there is a simple method to address these issues in NDN.


the switch pre-establishes some connections with the servers so that the second three-way handshaking is avoided.

this optimization also has its downside.


In wireless ad-hoc networks, for the problem of poweref.cient routing, the type of a node includes the power levels to reach its neighbors.

a node alone cannot determine these power levels because it needs feedbacks from its neighbors [27].


receiver), the attacker cannot hear the wireless signals from the receiver, and thus it may not be able to generate speci.ed channel impulse responses at the receiver.

in this case, the attack impact still exists.


Figure 3(b) shows that IGI successfully estimates the available bandwidth when the link utilization is low.

iGI reacts little to the cross tra.c injected during the interval [5, 12].


ANALYTICAL ESTIMATION OF INTERFERENCE Experimentation of wireless networks is a valuable approach since it overcomes the problem of unrealistic/idealistic RF models.

experimentation might take too long and it is often di.cult to generalize/reproduce the results due to the large variety of settings.


With this extremely low drop ratio achieved by a maximum retry count of one, we conclude that setting the timeout to as short as three RTOs does not impact the performance due to spurious connection dropping.

this quick timeout (typically a fraction of a second) helps the server clean up the dormant connections state quickly and resist some DoS attacks.


Second, [7] proposes a replacement algorithm based on complex computation that would be impossible at line speed.

we propose a decision policy that is light-weight and easily implementable in an ICN-router.


Our application and specification tools lack the necessary user interface sophistication to make effective tools in a user study.

by measuring factors in the selections made we believe we can draw some general conclusions about the quality of the data loaded.


CONCLUSIONS With WiMAX deployment, we can extend the wireless access to the places without available network lines and the wireless coverage to 90% campus.

in the early stage of deployment, the WiMAX utilization is less than 5% in average, which is very low.


The total network rate maximization problem can be formulated as M L max um (p) p m m=1 L s.t.

pm,n = P¯m,m =1,...,M (22) m pm,n = 0 which unfortunately is a dif.cult problem, since the objective function in non-convex in p. a relaxation of this optimization problem (see in [12]) be considered a geometric programming problem [22], therefore, can be transformed into a convex optimization problem.


In summary, our experiments on Wilocity radios show that today s low-cost 60GHz radios already offer online array alignment to handle moderate user motions.

these radios are designed for quasi-static indoor environments, and the speed and amount  900 TCP Throughput (Mbps) 800 700 700 700 600 600 600 500 400 300 200 Link Rate (Mbps) TCP Throughput (Mbps) TCP Throughput (Mbps)   100 100 100 0 0 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 -150 -100 -50 0 50 100 150 -8 -6 -4 -2 0 2 4 6 8 Deviation from original position (m) Circular deviation (degree) at 0.5m radius Vertical deviation from original position (m) (a) Moving closer/further(b) Moving circularly(c) Moving perpendicularly Figure 8: Measured throughput using our Wilocity testbed (2x8) when the receiver moves in three different motion patterns.


The DT time caused by dependency between objects and retrieval, which would in turn affect whole page latency.

as most common web browsers use a limited the WT time caused by limited parallelism contribute even more parallelism width for the parallel retrieval of objects, so some EOs of a page may be held in waiting state due to the unavailability of parallelism when the number of objects contained in the page is larger than the parallelism width.


Moreover, with higher penetrations of femto base stations, interference is becoming more serious.

we could not verify these hypotheses as our two-dimensional interference model prevented us from adding more femto base stations without sacri.cing faithfulness, as explained in Section 2.3.


The number of used degrees of freedom is equal to the number of ongoing transmissions, which a node can learnfrompriorRTS-CTSmessages.As nodes contendfor the unused degrees of freedom, they again use a contention window and random backoff similar to802.11.

while carrier sensing, nodes need to ignore the signals from past contention winners.


We might reasonably expect to .nd in each trace a relatively steady baseline replication level that holds for a long time (minutes), pockmarked with brief depressions in the level caused by measurement loss.

across all of the traces we .nd that the median interval length was just 3.4 seconds, the 75th percentile 32 seconds, and the 95th percentile just over 10 minutes.


When the latency increases, the static setting of tcp rmem max fails to saturate the pipe, resulting in throughput degradation.

networks 0.4 0.2 0 Throughput (Mbps) Figure 16: DRWA improves the throughput by 23%  with small latencies do not show such degradation since the in AT&T HSPA+ network and 30% in Verizon LTE network when the BDP of the underlying network is large.


When applied to our scenario, the 1 becomes C = TW iF i · cW iF i (h) + TGP RS · cGP RS (h) (2) Thus, given the time that the user is accessing the networks (h) and the costs associated to the usage of each single network (cW iF i (h) and cGP RS (h)), by adopting a suitable handover decision s policy (in this case, by tuning the threshold Th) the willingness to pay expressed by the user can be reasonably satis.ed.

the adoption of a policy that allows the user to save money does not give guarantees that the performance of the running application sessions will be preserved.


The best one hop from ito jchooses among all paths i~k~ j.

since the modi.ed cost for i~k is that of the shortest path of length =2t-1 from i to k (and analogously for k ~ j), this now gives us the cost of the shortest path of length =2t .


As is expected, with the topology size increasing, pre-computation time increases, too.

it is rather faster compared with the regular simulation time.


The presence of large numbers of unreliable and energy-constrained sensors makes the task of energy-e.cient communication and security protocols essential to the operation of a .at sensor network.

the three-tier sensor network consists of three types of devices with di.erent degrees of computational capabilities.


As noted before, there are a myriad of DHT designs in the literature, all extensively analyzed and energetically promoted.

we envision that there will be only one or a few very large-scale DHT infrastructures.


Nemo has a non-negligible power consumption (about 150 uA) which is an inevitable overhead for its high .delity and low cost.

many applications do not always need to be monitored at the highest .delity.


VANETs, where cars communicate directly with Wi-Fi-like equipment [19], are well suited if local communication is needed.

when it comes to communication between many partners over longer distances, this kind of networks suffer from very bad connectivity until a signi.cant amount of vehicles is equipped with this technology.


Note that this 2-round strategy indeed maintains the waypoint at any time during the policy update.

the resulting solution may still be problematic, as it violates another desirable transient consistency property, namely loop-freedom: if the update for switch s3 arrives before the update at switch s2 , packets may be forwarded in a loop, from switch s2 to s3 and back.