Conversely, if female students are given ratings that are off by 2 points in either direction while male students are rated within 1 point of their true preferences, absolute unfairness is high, while value unfairness may be low.

and reducing any unfairness metric does not lead to a significant increase in reconstruction error.


Socher and Fei-Fei [13] and Hodosh et al.

we found it critical to keep track of the validation error and freeze the model before it overfits.


The accuracy of an algorithm is judged by the area under its ROC curve.

all of these principles do little to address the cause of saliency mechanisms in the brain.


Finally, we assume that the Causal Markov Assumption and the Causal Faithfulness Assumption [23] both hold.

although still super-exponential, the number of ancestral structures grows asymptotically much slower than the number of DAGs and even more so, ADMGs.


For a fixed w, g(x; w) partitions the input space into two sets of regions, depending on whether g(x; w) is positive or negative at those points.

the margin in the input space is computationally intractable for deep models.


We also maintain the primal variables W = XA and stop when the relative duality gap is below .

we also prove an auxiliary Lemma 2, which is then used in Theorem 1.


The resulting estimator is shown to be effective for difficult estimation problems arising in Markov random field inference.

the latter two objectives are summaries of the quantities needed to estimate gradients in standard Boltzmann machine learning algorithms [1].


Intuitively speaking, such q init already encodes certain preferences towards a few preconditioned shift truncations of the ground truth.

6 In light of the above observations, a natural computational approach to sparse blind deconvolution is to attempt to find x 0 by searching for a sparse vector in the linear subspace row(X 0 ), e.g., by solving an optimization problem where • is chosen to encourage sparsity of the target signal [20,21,22,23].


For instance, the parents of a multiset label ABCDE are {ABCD, ABCE, ABDE, ACDE}.

pTC [26] is a dataset of 344 chemical compounds has 19 discrete labels.


regret) to scenarios where learner is constrained to a unit ball of an arbitrary Banach space (not necessarily and p space) and the objective functions have sub-gradients that lie in the dual ball of the space-for reasons that will become clear shortly, we refer to this as the data domain.

on the other hand given a matrix W , its max-norm is given by .


As we can see from the left panel of Figure 1, both Mixed LBP and SAA match the performance of our proposed XOR_MMAP on easy instances.

then for a binary image that only contains the upper part of a digit, we ask the solver to complete the lower part, based on the learned model.


Our computing network consists of m machines, where machine i stores X i , y i = (S i X, S i y) and S = S 1 S 2 . . . S m . The optimization process is oblivious to the encoding, i.e., once the data is stored at the nodes, the optimization algorithm proceeds exactly as if the nodes contained uncoded, raw data (X, y).

using the existing results on the eigenvalue scaling of large i.i.d.


When W N is greater than 200, the ENT has lost its capability to increase class separation and the DOM curve gradually goes towards the best separation without normalization.

as a side benefit, the ENT can also make the design less sensitive to the mean input scale.


Note that in the term tr(WΣ −1 W ⊤ ), the inverse covariance matrix Σ −1 plays the role of coupling pairs of weight vectors, and therefore controls the amount of sharing between any pair of tasks.

among other works, Graph-guided Fused Lasso [11] (GFlasso) incorporates task structure to some degree by assuming that the regression coefficients of all the outputs have similar sparsity patterns.


Compared to that, the number of modes can be dramatically reduced in the conditional distribution since the conditioning variables may restrict the support of random variable effectively.

we apply our method to restricted Boltzmann machines and introduce learning methods based on contrastive divergence and multi-prediction training.


The lengthscales are set to 14.5 m and the prior standard deviation of heights is 10 m. We assume a noise standard deviation of 0.075 m. Since the safety feature of each state transition is a linear combination of heights, the GP model of the heights induces a GP model over the differences of heights, which we use to classify whether state transitions fulfill the safety constraint.

we introduce SAFEMDP, a novel algorithm for safe exploration in MDPs.


We illustrate the concept on simulated data: We will use a similarity measure based on the metric D interval [ 1 9] to estimate the receptive field of a neuron which does not use its firing rate, but rather the occurrence of specific interspike intervals to convey information about the stimulus.

right from the first synapse, the information of an individual photoreceptor is signaled to many different cells with different temporal filtering properties, each of which is only a small unit within a complex neural network [ 20] .


For each game, subjects first practiced the game for several one-hour sessions on different days until reaching a success criterion (definition follows), and then returned for a one-hour eye tracking session with that game.

these windows then propagate through our model-based analysis, where we compare the eye position traces (row c) with the maps predicted by the BU salience (row f) and TD relevance (row g) to generate a continuous sequence of NSS values for each model (row d).


Proof: Refer Appendix-5.6  A factorization that satisfies this condition will be called admissible.


If the direction of movement is blocked, the taxi remains in the same location.

we use betweenness, a measure of centrality on graphs [1,2], to define a set of skills that allows efficient navigation on the interaction graph.


In the linear case, MSPBE was chosen as a projection of the Bellman error on a natural hyperplane-the subspace to which V θ is restricted.

to illustrate the convergence properties of the algorithms, we applied them to the "spiral" counterexample of Tsitsikilis & Van Roy (1997), originally used to show the divergence of TD(0) with nonlinear function approximation.


Prior to decomposition, if a node Z is dseparated from a node V then we trivially obtain the constraint that Σ ZV = 0.

we then incorporate recursive c-component decomposition and show that the resulting identification method is able to identify more models and constraints than the existing linear and non-parameteric algorithms.


A policy π is some decision tree that represents a strategy for adaptively selecting items.

there have been several studies on adaptive submodular maximization in other settings, for example, selecting multiple instances at the same time before observing their states [7], guessing an unknown prior distribution in the bandit setting [18], and maximizing non-monotone adaptive submodular functions [22].


We then extend the basic model to incorporate dependencies between labels across time and between subjects.

we incorporate a bias in favor of jointly selecting nearby voxels.


The above decomposition may be possible for any density p since g can be any function.

perform PCA on the set of remaining v (k) .


This term provides subtractive normalization that counteracts the use-dependent LTD [4, p. 290].

decrease) of v in the dark shown in Fig.


From the above, for n sufficiently large, the maximizer of the KDE in [y 0 − 2τ, y 0 + 2τ ] ∩ Y is contained in [y 0 − τ, y 0 + τ ].

if x 1 and x 2 are (r s , δ)-separated, then there cannot exist a directed path from x 1 to x 2 in G. Proof.


Efficient trades are unique up to zero-sum cash transfers: Given efficient trades dr * , dr ∈ R N on S, we have dr = dr * + (z 1 r $ , .

we say F is L i -Π i -smooth if for all i there are constants L i > 0 such that for all y ∈ im(Π i ), Finally, let F min := min y∈span{im(Πi)}i F (x 0 + y) be the global minimizer of F subject to the constraints from the Π i .


As with the Bethe approximation and its generalizations [12], the optimizing arguments of this problem can be taken as approximations to the exact marginals.

(for a graph G = (V, E), we simply set θ st = 0 for all pairs (s, t) / ∈ E.) We first focus on the marginal polytope MARG(K n ) ≡ MARG(K n ; φ) of valid dual variables {µ s , µ st }, as defined in Eqn.


Partially shifting cells where also found for auditory targets in LIP [5] and in the superior colliculus [3].

cells outside of primary sensory cortex are either gain modulated by postural input or partially shifting.


By doing so, MetaModelNet encodes a trajectory over the space of model parameters that captures their evolution with increasing sample sizes, as shown in Fig.

the model regression network from [21] empirically shows a generic nonlinear transformation from small-sample to large-sample models for different types of feature spaces and classifier models.


Regretfully, this goal turns out to be impossible without making additional assumptions.

. . , (x T , y T ) be a sequence of examples such that K(x t , x t ) ≤ 1 for all t. Let g be an arbitrary function in H K and define lt = ℓ g; (x t , y t ) .


During optimization, dimensions sharing the same block matrix can conveniently be merged, i.e.

later, automatic parameter selection was proposed with a non-convex objective [5].


It would be useful, in future work, to explore bounds on the error of this approximation.

we will define a partition, or a many-to-one mapping, from T E observations (the bridging tests T B ) to abstract observations A.


Furthermore, we choose the bandwidth σ for the Gaussian RBF kernel needed for the covariance operators using median distance between pairs of training points.

. . , φ(x n t )), and estimate C ts = 1 n ΦΥ .


We use kernel descriptors (KDES) to capture low-level image statistics: color, shape and texture [3].

the commonality usually is a part of the global shape, and can be observed in bird images across different species and in different poses.


Figure 5 shows the top scoring constituents by several orderings.

in some ways this makes the problem easier, such as by reducing sparsity, but in other ways it complicates the task (even supervised parsers perform relatively poorly with the actual words replaced by parts-of-speech).


For Ω ⊆ [m] × [n], let P Ω : R m×n → R m×n denote the projection onto the index set Ω.

figure 1 (b) shows that our method incurs significantly smaller reconstruction error than SVT for the same number of measurements.


We propose a novel method with provable guarantees for unsupervised estimation of discrete graphical model mixtures.

note that for a general graph G ∪ with treewidth tw(G ∪ ) and maximum degree ∆(G ∪ ), we have that η ≤ min(∆(G ∪ ), tw(G ∪ )).


Note that Lévy flights (i.e., randomly selecting a flight direction and then execute a flight distance that has power-law scaling as in Equation 1) are random walks and so produce 1/f 2 noise instead of 1/f noise (see Supplementary Material for details).

additionally, it may be that a cognitive load manipulation would reduce the number of available chains and thus reduce exploration, which is an interesting prediction to test in future work.


Finally, Section 5 presents a discussion of our findings.

( 1) is not possible, since it requires computation of the convolution between infinite dimensional processes h(t) and x(t).


Since we have a penalized empirical risk minimization at hand, we can study it within the classical PAC-learning framework.

in Section 5 we introduce the ADD- 1 2 -SMOOTHED LOW-RANK algorithm, which essentially consists of EM-style alternating minimizations, with the addition of smoothing at each stage.


Clearly, image descriptors or low-layer network activations can be used.

if the two domains are highly related, it was demonstrated that just by sharing weights between the networks working on the two domains, and without any further supervision, one can map samples between the two domains [21,13].


The BNN transition function scales significantly better to larger and more complex problems.

acknowledgements We thank Mike Hughes, Andrew Miller, Jessica Forde, and Andrew Ross for their helpful conversations.


The overall structure of these moves could be easily converted to an MCMC or simulated annealing algorithm.

nET-VISA computes a single most-likely explanation: a set of hypothesized events with their associated detections, marking all other detections as noise.


The experiments in this paper were designed to investigate how to improve the performance by using the richer syntactic and semantic structures within texts.

the HDAG kernel subsumes some of the discrete kernels, such as sequence, tree, and graph kernels.


Our method learns a recurrent encoder which extracts motion dynamics insensitive to viewpoint changes.

one particularly challenging aspect of action recognition is to recognize actions from varied unknown and unseen views, referred to as cross-view action recognition in the literature.


Figure 4 compares this average time of CTGP and GPTD up to five updates with standard deviations until when stable policy improvement becomes difficult without some heuristic techniques such as adding noises to policies.

note, on the other hand, a larger time interval poorly represents the system dynamics evolving in continuous time.


In summary, the memory requirement of this algorithm is 2m and the number of kernel calculations is not more than d•m.

in this paper we present a method based on the simple perceptron learning algorithm which allows to overcome this algorithmic drawback.


Of course, regression-based learning can produce an accurate model of the entire valuation function, which would also allow us to find the best valuation.

[Chu and Ghahramani, 2005a] adds active learning to the model, though the method presented there differs from ours in that realizations are selected from a finite pool to maximize informativeness.


The analysis of this paper is restricted to graphs with singleton ('l/Js) and pairwise ('l/Jst} cliques.

our results also have natural extensions to more structured approximations [e.g.


For ResNets, we used the standard data augmentation advocated for in [23].

altogether, these experiments show that, by providing more compact models, our regularizer lets us consistently reduce the computational cost over the baseline.


Next, the target set of points T = {x 1 , .

the main contribution of this paper is a message-passing scheme for max-product inference that can exploit combinatorial optimization algorithms for tractable subnetworks.


We learn hyperparameters α ψ and β ψ jointly with θ using an automatically derived Gibbs sampling algorithm [7].

it is significantly better than the n-gram multinomial model for h = 1.


Our techniques extend to the general setting of N experts, where the related problem of trading off regret to the best expert for regret to the 'special' expert has been studied by .

finally, we show another adaptive regret property of Algorithm 3.


We also use convolutional neural networks (CNN) as hidden layers [25] in our experiments.

this is impossible when X is continuous.


These terms are a consequence of the special case analysis for L 1 norm.

(10) The right hand side of the inequality has two issues: it depends on θ * , and it is a random variable, since it depends on Z n . In this section, we characterize E[R * (∇L(θ * ; Z n ))] in terms of the Gaussian width of the unit norm ball Ω R = {u : R(u) ≤ 1}, and also discuss large deviation bounds around the expectation.


In this paper, our objective is to modify the Poisson graphical model distribution so that it can capture a rich dependence structure between count-valued variables.

accordingly in this section, we investigate the possibility of modifying the Poisson distribution more fundamentally, by modifying its sufficient statistic and base measure.


4 We let F i,max := max S⊆V |f i (S)|, DSFM thus requires algorithms on two levels.

for certain potential types, we use tailored subroutines exploiting the specific form of the problem.


We define the following key geometric constant that capture the impact of manifold curvature: We note that most (if not all) practical manifold optimization problems can satisfy these assumptions.

with assumptions and parameters in Theorem 2, choosing ↵ 1 = 2/3, the IFO complexity for achieving an ✏-accurate solution is:  The same reasoning allows us to also capture the class of gradient dominated functions (2), for which Reddi et al.


Without trying hard to optimize the code, we observed that in time 0.3T we can detect if good clustering exists, and if so, in time around 3T we find the actual clustering.

this is a fast-enough preprocessing step to help experimentalists choose to use clustering-based methods or not.


A form of seeding is that each agent k can independently and randomly perturb observations in the buffer.

we now explain how the algorithms we propose satisfy the three properties of efficient coordinated exploration.


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.

a previously observed trend [4,23] of decreasing benefit of privileged information with increasing training set sizes is also apparent here.


Let p(y) be a two-component mixture of a (univariate) Bernoulli distribution.

whether the criterion can be satisfied in this and other cases depends both on the brain's generative model and on the true generative process by which the stimulus is encoded in neurons.


Dynamic Programming For T = 1000 msec and N = 10 there are about 2 100 spike trains among which one wants to find the optimally fitted one.


I.e., minimize where J(θ m ) is now the node potential, and the term R(θ i , θ j ) corresponds to the edge potentials.

[7] use an additional set of 26,000 images to training baseline detectors [13], and select 107 object categories to evaluate their contextual model.


Let us focus on non-degenerate saddle points for which the Hessian is not singular.

alternatively, one could take the square of the distance, but this would yield an optimization problem with a constraint that is quartic in ∆θ, and therefore also difficult to solve.


Multi-dimensional scaling can be used for this purpose.

if we denote T X = [log µ (x i )], the matrix of tangent vectors corresponding to all data-points, and if Π is the permutation matrix that orders the columns such that the first K columns of T X correspond to the most diverse selection, then Here, R 11 ∈ R K×K is the upper triangular matrix of R ∈ R n×n , R 12 ∈ R K×(n−K) and R 22 ∈ R (n−K)×(n−K) .


The use of GPUs [1,2,3,8] is a significant advance in recent years that makes the training of modestly sized deep networks practical.

deep learning and unsupervised feature learning have shown great promise in many practical applications.


In our interactions with industry, we also found stability to be a frequently raised concern for online learning.

it is possible to show a partial converse to Theorem 3.4 that certain large, "reasonable" classes of adaptive control methods will always have their proposed controllers accepted by our method.


Our approach achieves lower oracle error compared to existing methods on a wide range of tasks and deep architectures.

sMCL discovers specialization as a consequence of minimizing oracle loss.


To train the model we make use of the approach described in Section 2.6.

however, here we pre-train class-conditionally, and initialize the whole model at once, rather than layer-by-layer.


Split-sample growth rate is similar in spirit to the notion of local Rademacher complexity [3], which looks at the Rademacher complexity on a subset of hypotheses with small empirical error.

we define the notion of a split-sample hypothesis space: Definition 2 (Split-Sample Hypothesis Space).


Tuning is a major problem for these methods, since it requires rough knowledge of the optimal value.

we may employ Jensen's inequality to bound its error as follow, Combining this with T −1 t=0 α t ≥ Ω(T 2 ), implies that in order to substantiate the proof it is sufficient to show that, , is bounded by a constant.


This impose a well-behaved geometric structure on the feature space, which we take advantage of in order to perform statistical analysis according to the learned metrics.

practical experience, however, indicates that this is a good tradeoff; see [19] for a more in-depth discussion of when the approximation is suitable.


The solution ŵ can therefore be interpreted as the superposition of a vector which has small `2 norm, and a vector which has small k-support norm, with the parameter a regulating these two components.

a classical result by von Neumann [10] establishes that a norm is orthogonally invariant if and only if it is of the form kW k = g( (W )), where (W ) is the vector formed by the singular values of W in nonincreasing order, and g is a symmetric gauge function, that is a norm which is invariant under permutations and sign changes of the vector components.


As we have two different discount factors, we use a subscript to denote the discount factor used in calculating the value.

a bound of the loss due to using π β instead of the optimal policy for discount factor γ is the sum of the error on the optimal value function due to the change of discount and the error due to the approximation for discount β.


Metric-based fairness offers a way to balance these conflicting fairness desiderata.

in addition to its conceptual simplicity, the modularity of fairness through awareness makes it a very appealing framework.


We refer to [3,5] and [4] for more details.

for each dimension, we randomly select nr entries and replace them with either 5 or -5 with equal probability.


For "dynamic" actions, where the subjects can move globally e.g., walk, run, or dive, the subvolume constraint is no longer suitable.

max-Path algorithm [23] was proposed to detect dynamic video events.


So using much larger depths may lead to bad performance (On Movie, tree depth h = 18: K-L = 0.1162 vs h = 9: K-L = 0.0831).

x, i.e., the mapping function g, is defined by g(x; Θ, T ) = ∈L p( |x; Θ)q .


Each of the components is trivially parallelized using OpenMP (http://openmp.org/).

[11] showed that the Multinomial assumption was often violated in real world data.


Furthermore, we provide a procedure to perform this decomposition given general polynomials.

we employ L-BFGS, mainly due to its super-linear convergence and its storage efficiency [12].


The uniformity assumption leads to an estimate of maximum cluster radius, r x ∼ K −1/d [13].

for near-optimal bandwidths, our approach is either faster or comparable to the other approaches.


We perform the Gaussian kernel experiment similarly with model parameter C equals to 2 i , i = {0, 3, 6, 9, 12} and kernel parameter γ equals to 2 i , i = {−12, −9, −6, −3, 0} in the first stage.

we then show that adding other rows and columns in L xi,w to the game matrix does not change the game value.


At each iteration, the computational cost is dominated by the update of Z (−n) (n = n), which can be obtained by where (−n, −n) denotes every mode except n and n, which greatly reduces the computation.

note that when α > 0, each subproblem is strongly convex and the generated solution sequence is uniformly bounded, we can show that ACS can converge to a coordinate-wise minimum point of (8) with properly chosen initial value [Mishra et al., 2017].


[5] proposed a similar problem, namely robust principal component analysis (RPCA), which studies the problem of recovering the low-rank and sparse matrices by solving a convex program.

in order to address this problem, [15] [20] extended the trace norm of matrices [19] to tensors, and generalized convex matrix completion [8] [7] and matrix decomposition [6] to convex tensor completion/decomposition.


( 23) since placing a Dirac delta outside a convolution will result on a degenerate covariance.

we will calculate the statistics of the complex-valued F c (ξ) for notational simplicity, to then calculate the statistics of the real-valued processes F c (ξ) and F c (ξ) according to: The above expressions are due to the identity in eq.


By replacing batchnorm with Batch Renorm, we ensured that the inference model can effectively classify individual images.

minibatch-wise normalization may have significant drawbacks: For small minibatches, the estimates of the mean and variance become less accurate.


Alignment constraints on CTC paths have been previously explored in [28,32].

cTC [5] is a popular method for sequence learning.


The norm is defined, for every W 2 R d⇥m , as where S m = {S 2 R m⇥m , S ⌫ 0 : aI S bI, tr S = c}, and 0 < a  b.

as a tends to zero, in order to prevent the objective from blowing up, û must also tend to zero and we recover k-support norm regularization.


Based on the proximal average, a new tool from convex analysis, we proved that the new approximation leads to a novel algorithm that strictly improves the state-of-the-art.

we have managed to remove the secondary term in the complexity bound of S-APG.


For example, a strong predictor of an advisor-advisee link between a professor and a student is the fact that they jointly participate in several projects.

we introduce cliques over sets of three candidate links that form a triangle in the link graph.


This research was sponsored in part by the National Science Foundation IIS-1652539, IIS-1717205 and IIS-1717206.

we define the following solution set for Z: Note that 1 ( e Z) = p max and r ( e Z) = p min for any e Z 2 U.


In this paper, we presented fast stochastic methods for nonsmooth nonconvex optimization.

non-asymptotic convergence of PROXSGD was also shown recently, as noted below.


Our approach is learn one density model for the benign feature vectors and a second density model for the malignant feature vectors and then use Bayes rule to classify an input vector.

the hidden variables are independent and normally distributed with zero mean and unit variance: ( The input is modeled as a linear combination of the hidden variables, plus independent Gaussian noise: (2) The model parameters are the factor loading matrix A and the diagonal matrix of sensor noise variances, \]f. Factor analysis (d. (Rubin and Thayer 1982)) is the procedure for estimating A and lJI using a training set.


We believe that the project-and-test procedure that PG-means uses is a useful method for determining fitness of a given mixture of Gaussians.

high dimensional data of any finite-variance distribution looks more Gaussian when linearly projected to a randomly chosen lower-dimensional space.


This likelihood can be obtained analytically since after linearization of (4) with respect to µ l n (t) at µ l(i) n (t − 1), an extended Kalman filter (EKF) can be obtained, where the prediction likelihood of the EKF gives the weight, and the updated continuous state of EKF gives µ l(i) n (t).

it is well-known that noise statistics may vary during recognition.


(5) h () terms are estimated using parametric approximation to the total and conditional distribution It is assumed that the total distribution of features is a Gaussian distribution with covariance ~.

in the overall results for each domain, spectral domain has higher variability due to different phones than temporal domain.


We consider each parse as a set of constituent brackets, discarding all trivial brackets.

4 we expect the distribution of the λ σ to be skewed towards low values.


The BCM can yield high-quality predictions that avoid the pitfalls of local GPs (Figure 1c), while maintaining scalability to very large datasets [12].

if the noise is iid Gaussian, i.e., ε ∼ N (0, σ 2 n I), then the observations are themselves Gaussian, y ∼ N (0, K y ), where K y = k θ (X, X) + σ 2 n I.


All the LSTD approaches have the problem that the matrix to be inverted may be singular.

this allows to analyse if a certain reinforcement learning algorithm and a certain function approximator are compatible.


Within the machine learning community, Gaussian processes (GPs) [8] have proved particularly popular, due to their appealing properties which allow to reduce the infinite dimensional smoothing problem into a finite dimensional regression problem.

the only differences between prior and posterior process are the jump rates for the telegraph process µ and the drift of the diffusion process x.


In a PoE, linear combinations of an input vector are penalized according to their negative logprobability and act as constraints.

by adding white noise to this signal we obtain a non-singular covariance matrix.


Conceptually, the log-likelihood objective implicitly trades off between model error in different regions of the input/output space, but does so in a manner largely opaque to the modeler, and may ultimately not employ the correct tradeoffs for a given task.

(x; ✓), yet we adapt this model based on the task loss instead of any model prediction accuracy.


We provide an algorithmic framework for computing higher order derivatives of matrix and tensor expressions efficiently, which fully operates on tensors, i.e., all variables are allowed to be tensors of any order, including the output variables.

the GPU can deal with this even worse which leads to even larger speed-ups on the GPU.


The data was taken from the CSLU 'Speaker Recognition' corpus.

this is somewhat counterbalanced by the quadratic growth in the size of the hidden layer as M increases.


We plan to derive such lower bound in our future work.

in this section, we present some definitions that will be used throughout our analysis.


Furthermore, the explicit uncertainty information obtained from the posterior distribution enables us to identify ranges of statistical significance and therefore facilitates the interpretation of the solution.

we obtain a sequence of changepoints In the GLM neuron model setting the instantanious firing rate of neuron i is obtained by a linear filter of the feature map: where λ is the nonlinear transfer function.


expression quantitative trait loci (eQTL) mapping in computational biology [28], land surface temperature prediction in climate informatics [17], neural semantic basis discovery in cognitive science [30], etc.

in fact, this seemingly restrictive setting is general enough to encompass the model with response-specific parameters, which can be realized by block-diagonalizing rows of X i and stacking all coefficient vectors into a "long" vector.


For any ✏ 2 (0, 1], it holds that Our assumptions on the loss functions, as the Lipschitz assumption or the smoothness assumption, are stated in terms of the standard Euclidean norm (which we denote by k • k 2 ).

. . , ĝT that can plug into the dual averaging algorithm.


Note that this Bayesian nonparametric prior assigns a positive probability to all possible paths, including those not observed in the training data.

we show that the algorithm scales efficiently to millions of features.


We thus have and where in the last line, we use the Taylor expansion again to expand f around Q k c + 1 − Q 2 k e and the bracket • denotes the average over two independent random variables c ∼ P c and e ∼ N (0, 1).

to simplify the PDE in (6), we can assume that the two functions Q t and R t in ( 7) and ( 8) are given to us in an oracle way.


( 7), we arrive at the following optimization problem which solely depends on α.

all of them are informative to our MKL models.


This is the only experiment in which the calibrated framework incurs little additional cost, and therefore could be considered a viable option.

our goal is to further investigate the relationship between calibration and error rates.


Both of them are outperformed by PBM-TS and PBM-PIE.

to get the expression given in Theorem 6 from Corollary 5, we proceed as in [6] showing that the optimal coefficients (c a ) a∈A can be non-zero only for the K − L actions that put the suboptimal arm k in the position l that reaches the minimum of ∆ v k,l (θ)/d(κ l θ k , κ l θ L ).


Finding each binary classifier is computationally efficient, reducing to a convex problem with O(n) variables.

[14] proposed random forests to efficiently learn budgeted systems using greedy approximation over large data sets.


For convolution kernel K i with n i output channels, we determine which output channels are calculated and which to prune.

we use the decision network to approximate the expected Q-value Q * (s t , a i ), with all the decoders sharing parameters and outputting a k-length vector, each representing the Q * of corresponding action.


The second says that reflecting twice gives back the original string, and the third says that left-shifting then reflecting is the same as reflecting and then right-shifting.

we recall that the kernel of a group homomorphism π : G → G is a normal subgroup of G, and that normal subgroups N of G are invariant under the operation of conjugation by elements g of G. gN g −1 = N for all g ∈ G. With this picture in mind, the following Lemma establishes that T M , and further shows that M is isomorphic to T R with R = O 2 , and T a normal subgroup of M . Lemma 1.


Similarly, cost-sensitive metrics may useful for addressing asymmetry in real-world costs associated with specific classes.

it would be interesting to characterize the convergence rates of L( ✓) p !


Though the overall system is not short-order Markov, each local model is.

we show that the prediction for any test in a history of interest can be expressed as a prediction of a union test in T E. For the following, note that every history of interest h ∈ H I can be written as a corresponding sequence of bridging tests, which we will call s h . Also, we will use the subscript T E to distinguish predictions p T E (t|h) in T E from predictions p(t|h) in the original system.


The results are compared in terms of primal objective (achieved by w) and test accuracy.

the The contribution of this work is twofold.


Patients with prosopagnosia cannot recognize faces, but their ability for recognizing other objects are often spared.

this is because normalization processes tend to be less reliable at low SNR.


To avoid this effect, we convert the presence of additive factors into multiplicative factors by augmenting the model with a latent "selector" variable, which is similar to that used for the "complete likelihood" in mixture models (Liu and Ihler, 2012).

in the worst case, the size of the diagram still increases exponentially with the number of variables.


For instance, it requires a one-time O(2 k ) effort to generate the vocabulary of size ≤ k graphlets for graphlet kernel.

in order to smooth Weisfeiler-Lehman kernel, we first run the original algorithm and obtain the multiset representation of each graph in the dataset.


The first constraint of (P M ) for MFI i is violated.

it consists of eight MFIs operating in 10 regions.


The goal of the first clustering phase is to use IBSI to identify clusters of terms that extract the relevant structures of the data.

such auxiliary variables often contain more information than is actually required due to structures that are irrelevant for the task.


The increase may be arbitrary large if (Σ (i) ii ) −1 ≈ −W ii , but in practice it can be limited.

the drawback is that the predictive accuracy of the model can be significantly compromised if the observations are contaminated by outliers.


The only aspect that our model does not reproduce is the (more subtle) sensitivity difference between 0 and +/-5 degree flankers.

figure 4C;D shows repulsion in the data and model.


One crucial assumption made by both principal component analysis (PCA) and probabilistic PCA (PPCA) is that the instances are independent and identically distributed (i.i.d.).

if the task is to classify instances in the low-dimensional embedding, the classifiers based on the embedding results of PCA and PPCA are expected to achieve comparable results.


Instances of such bounds can be extracted, e.g., from [11] (Theorem 1), and from bounds discussed in [10].

as was discussed in [6], in many cases our objective is to explore the entire risk-coverage trade-off, in other words, to get a pointwise bound on |f * (x)−f (x)|, i.e., individually for any test point x.


Since 1 bit is needed to reliably distinguish between a pair of cells, Fig.

diversity also can improve the robustness of retinal signalling: as the retina is constantly setting its adaptive state in response to statistics of the environment that it cannot estimate without some noise, maintaining functional diversity can guard against adaptation that overshoots its optimum.


When the size of the behaviour data is small, the clustering performances of both DPM-BIRL and EM-MLIRL were not good enough due to the sparsity of data, hence their EVD results were similar to that of the baseline algorithm that independently runs BIRL on each trajectory.

suppose that we would like to infer the reward function of a new trajectory after we finish IRL on the behaviour data consisting of M trajectories.


More formally, r * = min i∈A min j∈N (i,T ) r j , where the inner minimization can be carried out by querying r * (i).

this influence estimation problem is very challenging since both the time-sensitive nature of the task and the requirement of scalability need to be addressed simultaneously.


In our experiment, we use human face images from different domains to perform imageto-image translation.

we visualize domain-invariant representations with t-SNE and show the results in Figure 5.


Relating back to the experimental data, we plot the probability of not observing the current stimulus for each type of 5-stimulus sequences in Figure 1 for (b) FBM and (c) DBM, since RT is known to lengthen with reduced stimulus expectancy.

the new mean decision time is z+kb A tanh Az+Akb c 2 .


More specifically, we first use a coarse high probability upper bound on the queue-length (lemma 11) to get a first cut bound on the beginning of the regenerative cycle (lemma 12).

we show that this "early stage" of the queueing bandit eventually gives way to a "late stage", where the optimal queue-regret scaling is O(1/t).


Finally, if we focus on the sets of vertices near each corner, we see that the green and red sets have distinct degree (i.e.

the closer that θ i and θ j are, the higher the link probability.


We find that for individuals in executive or managerial occupations (12% of the sample), false negatives are more than twice as frequent for women (0.412) as for men (0.157).

instead, we study the degree to which such constraints are violated.


Our algorithm can therefore be applied (1) to analyze the interplay of data set and kernel in a geometric fashion, (2) to help in model selection, and to (3) de-noise in feature space in order to yield better classification results.

we define the relevant information vector as the vector  Proof The kernel PCA directions are given as (see [10]) and l k , u k being the eigenvalues and eigenvectors of the kernel matrix K. the kth PCA component for a point X j in the training set is The sum computes the jth component of Since the u k are orthogonal (K is a symmetric matrix), the projection of Y to the space spanned by the first d kernel PCA components is given by As we have just shown, the location of G is characterized by its scalar products with the eigenvectors of the kernel matrix.


Third, producing and storing item histories for every user can be expensive with respect to computational as well as storage cost.

figure 1: Proposed meta-learning architectures While bias b of the classifier is constant across users, its weight vector varies with user-specific item histories (i.e., based on the representative embeddings for classes).


We first briefly describe them as follows: Threshold Average Precision Curve (TAPC) Although the ground-truth target value (i.e., the overlap rate of segment and bounding box) is a real value in the range of [0, 1], we can transform original prediction problem to a series of binary problems, each of which is conducted by thresholding the original groundtruth overlap rate.

but this set of proposals may be very large, each proposal may be only partially correct (the correctness can be quantified by a continues value between 0 and 1 called "positiveness"), and several proposals may be required to obtain the correct label.


This approach was considered before in [8], who adapted the Shrinking Dartboard (SD) algorithm of [9] to cope with limited-delay coding.

from now on, we assume that Algorithm 1 1: Input: learning rate η > 0, σ-strongly convex and smooth regularization function R(x).


Using this we can write (16) as an unconstrained SOCP: (17 We can solve this problem in various ways, for example using interior-point methods for SOCP [8], which yield a worst-case complexity of O(n 3 ).

we do not wish to solve the COP in this form, because we want to avoid using f or cp explicitly.


In the case of graph Laplacians, empirically, the complexity is close to linear in n. By Proposition 7, the diffusion kernel and certain other graph kernels can also be approximated in about O(n log n) time.

the algorithm proceeds by taking K through a sequence of transformations  2.


Research in cognitive psychology has consistently shown that humans represent everyday objects with a large number of features (e.g., [7,8]).

the risk, defined as the expected 0-1 loss of the learner on a test instance, is R(t) ≡ E (x,y)∼p(x,y) E h∈V (t) 1 {h(x) =y} .


Moreover, the auxiliary variables are locally associated with each individual document, and this locality naturally allows us to develop a distributed sampler by splitting the documents into multiple subsets and allocating them to multiple machines.

as a result, we obtained T = 350 for gCTM and T = 8 for vCTM, as pointed out with corresponing verticle line segments in Fig.


The challenge for risk modelling is to produce fine-scale predictions from these coarse incidence data, leveraging the remote-sensing covariates and appropriate regularity conditions to ensure a well-behaved problem.

the data were provided by the Malaria Atlas Project supported by the Bill and Melinda Gates Foundation.


It is tempting to posit that conv(F) = C holds more generally in the Bethe case.

in the Bethe case with attractive potentials ✓, several recent results [22,19,18] establish that the Bethe approximation B(✓; ⇢) is an upper bound to the log partition function A(✓) when ⇢ lies in the spanning tree polytope, whereas B(✓; ⇢)  A(✓) when ⇢ = 1 F . By continuity, we must have B(✓; ⇢ ⇤ ) = A(✓) for some values of ⇢ ⇤ , and it would be interesting to characterize such values where the reweighted Bethe approximation is exact.


To define weighted extensions of the theta function, we need to first pass to the closely related Delsarte version of the Lovász number introduced by Schrijver [24].

in the first row are characterizations following the original definition.


The partition is determined by an answer to a phonetic question such as "is the preceding phoneme a vowel?"

in summary, the hyperparameter values do not greatly influence the quality of the SST-HMMs.


We randomly generate n = 50 warping functions {γ i } such that {γ −1 i } are i.i.d with mean γ id .

using Lemma 1, the Fisher-Rao distance between any two warping functions is found to be d F R (γ 1 , γ 2 ) = cos −1 ( 1 0 γ1 (t) γ2 (t)dt).


It follows that with a formulation like (3), the only way to utilize unlabeled data is to replace K by a kernel K in (3), or k by k in (2), where K (or k) depends on the unlabeled data.

the accuracy plot on the right is consistent with our theory.


This is because modeling missingness for each missing entry adds model complexity and is prone to overfitting.

as our goal to explore the effects of dynamic missingness to recommender systems, MF is also fair for comparison to baselines.


Indeed, the constraints coincides with the sequence-form constraints obtained when splitting Player 2's information set into two information sets, one for each action {A, B}.

this is not the case for games with more than two players, which remain one of the main open challenges in computational game theory.


At this stage, the generative models do not perform well, as the number of available examples is low compared to the number of parameters in the model.

in the classical supervised learning classification framework, a decision rule is to be learned from a learning set L n = {x i , y i } n i=1 , where each example is described by a pattern x i ∈ X and by the supervisor's response y i ∈ Ω = {ω 1 , .


The second set of experiments evaluates online VB in the setting where new documents are constantly being observed.

it still requires a full pass through the entire corpus each iteration.


It is straightforward to verify that the definition in Eq.

we are interested in learning to recognize rigid objects such as cars, motorbikes, and faces from one or more fixed view-points.


For comparison, all models have three-block layers (selected after a pilot test), using VGG-19 features and 1k answers, then, the number of learning blocks is explored to confirm the pilot test.

we carefully select alternative models (a)-(c) for the importance of embeddings in multimodal learning [18,24], (d) for the effectiveness of identity mapping as reported by [6], and (e) for the confirmation of using question-only shortcuts in the multiple blocks as in [29].


To solve (11) we need to set all of the binary bits in g corresponding to the path from the root to the leaf j to be consistent with the path direction toward the leaf j.

the work in [15] proposes a means for training decision forests in an online setting by incrementally extending the trees as new data points are added.


For single-round data collection, the mechanism 1BitMean in (1) preserves -LDP for each user.

[8] sends a 0-1 random response for each bucket: send 1 with probability e ε/2 /(e ε/2 + 1) if the value is in this bucket, and with probability 1/(e ε/2 + 1) if not.


[2014] to multiple resources turns out to be fairly non-trivial.

along the way we present some additional results for the related problem of minimising regret for stochastic linear bandits on the hypercube.


Stacked ConvLSTMs extract highly abstract features layer-by-layer and then make predictions by mapping them back to the pixel value space.

all experiments are implemented in TensorFlow [1] and conducted on NVIDIA TITAN-X GPUs.


As described below, we use these nonlinear classifier approximated via linear projections as the basis for learning our features.

state-of-the-art recognizers use kernel matching between these descriptors to define powerful classifiers, nonlinear in f I .


It is natural to expect that the distribution of the contribution weights for the same set of filters will change under different input noise levels, as shown in Figure 3.

performing blind deblurring by solving (5) in the last original scale directly (i.e., f p ≡ δ) cannot achieve successful kernel estimation (results not shown).


Within each layer, there is lateral inhibition.

there are also top-down connections in the visual system, and there is little consensus about their function.


Moreover, as it will be shortly explained (see Related Work), since the exogenous noise of the target variable has changed, the invariant prediction method [23], cannot discern the correct structure either.

by this definition, it can be seen that the entry (t, the entries of matrix A are multivariate polynomials of entries of B.


Let d A t,k denotes a size-n vector taking value in d * for j ∈ A t,k and taking value 0 for j / ∈ A t,k .

some dual or primal (stochastic) sub-gradient descent methods have cheap cost for each iteration, but require O(1/ 2 ) iterations to find a solution of precision, which in practice can even hardly find a feasible solution satisfying all constraints [14].


Our approach is related to the Multiple Kernel Learning framework (Lanckriet et al., 2004), although we do not aim here at learning linear combinations of the kernels k T , but rather start from an hierarchical belief on them to propose an algebraic combination.

in the kernel literature, structured objects are usually represented as histograms of components, e.g., images as histograms of colors and/or features, texts as bags of words and sequences as histograms of letters or n-grams.


We then marginalize over the weights A, i.e., Incorporating the Markov property (Eqn.

we set the latent position at each time-step to be the most-likely (mean) point given the previous step: xt = µ X (x t−1 ).


For example, in the semi-supervised classification problem, one usually strives to make sure that labels are equally distributed among the labeled dataset.

when the discriminator is optimal, the objective of ∆-GAN becomes the Jensen-Shannon divergence (JSD) among three distributions, which is symmetric; the objective of Triple GAN consists of a JSD term plus a Kullback-Leibler (KL) divergence term.


The subject has to learn the physical properties of the machine to play well.

3), these false hits can not be neglected.


Throughout our experiments, the GLC surpasses previous label noise robustness methods across various natural language processing and vision domains which we showed by considering several corruptions and numerous strengths, including severe strengths.

we apply no correction on examples from the trusted set encountered during training.


The first column of Table 3(a) only has one AL layer and the accuracy comparison demonstrates the benefits of exploring contexts as early as possible.

this approach limits the amount of data when the windows are not overlapped as in [28].


In Part 2 of this figure a volume holographic grating (VHG) is employed to diffract the photons in a wavelength-dependent manner, and therefore photons are distributed spatially across a digital mirror microdevice (DMD); distinct wavelengths are associated with each micromirror.

the elements of the rate vector of λ 0 vary from .07 to 1.5 per bin, and the cumulative dark current Φλ 0 can provide in excess of 50% of the signal energy, depending on the measurement (very noisy measurements).


Our goal is to highlight how shape prior (in terms of thick, thin, or arbitrary shapes) can be incorporated in LMIT using the parameter γ to obtain better AUC performance in finite size graphs.

on the other hand GLRT is minimax optimal for special classes of distributions and graphs and motivates development of tractable algorithms.


Specifically, we set F 0 = ∅, N = 0, and λ = σ 2 log m−s η 1 in the multi-stage method, and set p = 2, l = s, η 1 = m−s m η, and η 2 = s m η for a convenient of comparison with Theorem 1.

an approximate equivalence between the LASSO estimator and the Dantzig selector was shown in [1].


In this regime, the marginal distribution at a node is asymptotically independent of the configuration of a growing boundary.

we propose an efficient method for graph estimation, and establish its structural consistency when the number of samples n scales as n = Ω(θ −δη(η+1)−2 min log p), where θ min is the minimum edge potential, δ is the depth (i.e., distance from a hidden node to the nearest observed nodes), and η is a parameter which depends on the minimum and maximum node and edge potentials in the Ising model.


A direct comparison with the reported results in the literature for C. diff risk prediction is difficult because of the differences in the studies mentioned above.

this split was maintained across all experiments.


As seen in figure 1(b)-(c), our intuition is that easy examples should be resolved by the network, that is, classified correctly with high confidence at lower layer probes themselves, while hard examples would either not be resolved at all or be resolved only at or close to the final layer probes.

suppose, training the simple model on training dataset D train results in classifier M . We view this training procedure of simple models through a different lens: It is equivalent to the optimal classification algorithm trained on the following class distribution mixtures: P M (x|y = 1) and P M (x|y = 0).


This means that if v > g max , the network is unable to track the stimulus.

since λ 1 = 1 and all other eigenvalues are less than 1, the stationary state is neutrally stable in one component, and stable in all other components.


These results may be attributed to the fact that the joint density for local pixel blocks tend to be close to be elliptically symmetric [17,11].

divisive normalization provides a rough approximation to RG, which suggests that RG might provide a more principled justification for normalization-like nonlinear behaviors seen in biological sensory systems.


The same section also gives a much more general class of hypothesis for unsupervised learning which we call polynomial spectral decoding, and show how they can be efficient learned in our framework using convex optimization.

spectral norm distance is a much more effective measure of closeness since it exploits the underlying structure of the lifted data points.


One obvious improvement to the feature hashing method described above would be to learn an optimal hash function where important tokens do not collide.


Orabona [2013, 2016] pioneered the theoretical analysis of HTL for linear regression and recently Wang and Schneider [2015] analyzed Kernel Ridge Regression.

a total of 120 trials were presented to each participant and fMRI data was collected throughout the trials, and went through a standard post-processing scheme.


The details of the subroutines Oracle and Teacher for Ada-R are provided in the extended version of this paper [8].

most existing work in algorithmic machine teaching focuses on the batch setting, where adaptivity plays no role.


Var ⇤ , with x i , y i drawn from the empirical distribution defined by the training set.

the approach presented here is closely related to several popular methods in the literature that regularize by adding random noise; these relationships are discussed in section 4.


Our basic idea is that in order to determine the best arm, any optimal algorithm will need to explore all arms at least ln T times.

we consider a setting in which a platform faces many types of users that can arrive.


Improve model parameters by running a conventional clustering algorithm for a fixed k value.

there is a dependence of the results on the selected viewer.


Next, let us compare the generality of the algorithm when applying it to different network architectures.

moreover, one might attempt to improve the run-time of KF-RTRL by using approximate matrix multiplication algorithms or inducing properties on the H t matrix that allow for fast matrix multiplications, like sparsity or low-rank.


The parameter λ > 0 controls the trade-off between the closeness of σ(Φ(X, Θ)) and σ(Φ(X, Θ given )), and the computational cost.

consider a classification problem, of learning a mapping from an input space X ⊆ R d (e.g., images) to an output space Y ⊆ R (e.g., labels), given training points x 1 , x 2 , ...x n , and corresponding labels y 1 , y 2 , ...y n . We consider a neural network as our prediction model, which takes the form ŷi is the last intermediate layer feature in the neural network for input x i .


All these mechanisms are very powerful in the sense that they can answer general and adversely chosen queries.


We follow the data partition of [14], where each training sequence has a length of 180.

for recurrent neural networks, using ReLU activations is challenging in a different way, as even a small change in the direction of the leading eigenvector of the recurrent weights could get amplified and potentially lead to the explosion in forward or backward propagation [1].


In order to evaluate our strategies, a simple problem is considered in which K = 5, L = 3, κ = (0.9, 0.6, 0.3) and θ = (0.45, 0.35, 0.25, 0.15, 0.05).

we propose to analyze multiple-play bandits in the Position-based model (PBM) [5].


5; with the exception of [8], where sparseness was measured on awake animals), but do not indicate an active optimization of sparse responses (cf.

direct experimental evidence for optimal sparse coding remains inconclusive, mostly due to the lack of reference values on which to judge the measured sparseness.


Due to the optimal matching's complexity, researchers have developed approximation algorithms to compute close solutions for a fraction of the computational cost [4,8,1,7].

we call our algorithm the vocabulary-guided (VG) pyramid match, since the histogram pyramids are defined by the "vocabulary" or structure of the feature space, and the pyramids are used to count implicit matches.


θ 0 is F 0 -measurable, and for each θ ∈ H, the random variable For an introduction to martingales, σ-fields, and conditional expectations, see, e.g., [17].


in order to achieve the first two criteria, we need to construct an undirected graph and maximize the entropy rate of a random walk on this graph.


Discriminative visual dialog models produce a distribution over the candidate answer list A t and maximize the log-likelihood of the correct option a gt t . The loss function for D needs to be conducive for knowledge transfer.

', besides the ground-truth answer 'No, I do not', D can also assign high scores to other options that are valid responses to the question, including the one generated by G: 'Not that I can see'.


This will produce a graph G ∈ G s . In such a situation, the value of Ĝ is recovered by a general unipartite b-matching algorithm rather than a bipartite b-matching program.

furthermore, we warm-started the symmetric algorithm with the star-pattern solution of the asymmetric algorithm to make it converge more quickly.


Overall, subjects are thus always kept in the dark about the true outcome distribution of any one slot machine.

we would also like to thank Nathaniel Daw and Hanneke EM Den Ouden and René Hen for invaluable discussions.


At the time of submission, a recent work [40] applied a related double averaging distributed algorithm to a stochastic version of (22).

define θ(t) := 1 N N i=1 θ t i as the average of parameters.


Compute the sample variances, v i = Var(R (i) s ), for i = 1, . . . , L. 3.

we must therefore accurately approximate Ω from small amounts of data.


§2 gives an overview of probabilistic grammars.

these assumptions also hold in many cases when P itself is a probabilistic grammar.


Most of posterior inference methods for NRM mixture models rely on MCMC methods since they are easy to implement and their convergence is well studied.

more details on the algorithm can be found in the supplementary material.


The excellent survey by Guyon, Janzing and Schölkopf [GJS10] on causality from a machine learning perspective underlines the issue as one of the "ten open problems" in the area.

proof of Theorem 4. to pa(S), then using Lemma 1 and the obtained samples, test (with error probability at most 1/(3K d 2 n)): d+1) n . Output "∆(X , Y) > " if the latter.


The proof of Theorem 1 follows by applying Lemma 1 to Theorem 2.

we say the sparse vectors h \ and m \ have comparable effective sparsity if there exist an ↵ 2 R such that with ↵ satisfying 1 C  ↵  C for some C 2 R + .


The results for the K-arm case are from Freund and Schapire [1997], Auer et al.

for the full information case, the exponential weights algorithm, Hedge, of Freund and Schapire [1997] provides the regret listed.


The next proposition demonstrates the use of S n as a two-sample test statistic.

we would like to test the null hypothesis that the distributions of angular momenta P (no Higgs boson observed) and Q (Higgs boson observed) might yet be rejected.


Taking traffic signs as an example, an adversary performing perturbation-based attacks can draw graffiti [4] or place stickers [18] on an existing stop sign in order to exploit a classifier.

this enables them to assume adversarial examples have the same ground-truth labels as unperturbed images, while we use human evaluation to ensure the labels for our evaluation.


It also contains K = 2 categories of visual stimuli, i.e.

further, performances of the standard HA [1], RHA [2], KHA [3], SVDHA [4], SRM [5], and SL [9] are reported as state-of-the-arts HA methods.


Each pixel y i is associated with its own state process x i , and a different dynamic texture is defined for each pixel.

as a generative model, the layered dynamic texture assumes that the state processes X and the layer assignments Z are independent, i.e.


Ackley's function is composed of exponents of high frequency cosine waves, thus creating an extremely bumpy surface, consequently a method that tries to match the derivatives can behave badly during testing if one does not have enough data to capture this complexity.

deep Neural Networks (DNNs) are one of the main tools of modern machine learning.


ADAPT-GBRT is able to identify the ambiguous region in the center and send those examples to f 0 via g. Both of our algorithms maintain the same level of prediction accuracy as f 0 yet are able to classify large fractions of examples via much simpler models.

to maintain high-accuracy, adaptive systems are desirable.


Since the seminal work of Angluin [2] and Littlestone [14], the paradigmatic application of (noisy) interactive learning has been online learning of a binary classifier when the algorithm is provided with feedback on samples it had previously classified incorrectly.

if feedback is not noisy (i.e., p = 1), all the non-zero node weights are equal.


The new data point x is then set as new center c k+1 .

during the control experiment we set the gains to very low values taking the aim of compliant control into account.


Our decoupled formulations generalize those in supervised binary code discovery [23] and semi-supervised learning [24], respectively; and more crucially, we propose a novel combined optimization to jointly estimate HDQC and learn LDS in large-scale unsupervised scenarios, from the labeled ImageNet 1.2M [25] to the unlabeled Flickr 100M dataset [26].

we want samples belonging to the same quasi-classes to be close to each other in the activation spaces, while samples from different quasi-classes should be far from each other in the activation spaces.


2) This approach is implemented by developing the Graphical Gaussian Vector feature, which is based on the GMRF and the information geometry.

several approaches inspired by a BoW have been proposed in recent years [9], [23], [28], [27], [29].


Figure 3 shows the optimization performance of the EM algorithm with 10 random starting points with ("DLC") and without ("rand-init") our initialization method.

for problems without pointwise positivity, [16,17] have considered low-rank representations of matrices T , of the form T = V V T where V has more than one column.


Two views of every non multi-view anomaly can be generated from a latent vector using view-dependent projection matrices.

robust PPCA and PCCA [4] use Student-t distributions instead of Gaussian distributions, which are stable to data containing single-view anomalies.


In general, the Kronecker Product representation is reducible, and so it can decomposed into a direct sum of irreducibles.

3(b)) we allow for consecutive conditioning steps and we see that that the projection step is fundamental, especially when mixing events are rare, reducing the error dramatically.


Let G j denote the 5 × 5 payoff matrix of game j and let the term strategy denote a distribution over all actions.

hence, the full likelihood for observed actions in game j in Steps 10 and 11 of Algorithm 1 is given by the product Multi(|I| • α j (t; j1); ᾱj (t; j1)).


REINFORCE gradually converges over ∼5000 trials whereas Bayesian optimization converges in 500 trials.

third, the site of reward learning would plausibly be the basal ganglia, and a similar 3-factor learning rule has already been used to model cortico-striatal plasticity [21].


This is an example of a Bayesian numerical integration method since the approach maintains knowledge of its own inaccuracy [16].

for the same reason, these components do not affect prediction of f (t).


For the purpose of illustration, consider a simple example h(x) = |x| without any constraint, and suppose that µ k = 0.08 for all k and that an initialization of x 0 = 0.1 is used.

its geometric analysis is based on quantities that are difficult to interpret and are not amenable to statistical analysis.


To avoid introducing auxiliary variables and still solve subproblems ( 4) and ( 5) efficiently, inspired by Yang et al.


Specifically, we assume that there are parameters ρ, µ (possibly dependent on p such that the class of graph-structured activation patterns x is given as follows.

then We are now sufficiently prepared to develop the test statistics that will be the focus of this paper.


Generalized least squares (GLS) is a method for selecting β when the y i are not necessarily independent and may have different variances.

the term r t+j + γ V (s t+j ) − V (s t+j−1 ) is the temporal difference error j steps in the future.


More descriptive models have been proposed to represent the typical choice phenomena in some representative cases [14,19].

the train can operate at the interval of 30, 60, or 120 minutes.


Stochastic gradient descent was used with a learning rate of 0.01.

this is because the purely discriminative RBM never learns meaningful features for the non-discriminative visual symbol at the center, which are essential for the controller to be able to predict the position of the white bar.


In order to obtain path consistency results of standard LBI in [Osh+16], they propose "Restricted Strong Convexity" and "Irrpresentable Condition" on X * X.

all of these are based on homotopy method of solving convex optimization (1.2).


For each frequency, q , and shift amount, d (where B ¦ @ rU Rd is an integer), we define the Gaussian-Fourier basis functions, 9 ¦ F s , by 9 ¦ F s 5 87 69 B ¦ d 5 87 ¨7 H d B e ut s v 3 Zweck and Williams [13] showed that the Gaussian-Fourier basis is shiftable-twistable.


number of parameters) to some small number would not usually fit in with our prior beliefs about the true data generating process, it makes sense to use large models (no matter how much data you have) and pursue the infinite limit if you can 2 • For example, we ought not to limit the number of basis functions in function approximation a priori since we don't really believe that the data was actually generated from a small number of fixed basis functions.

example: Should we use Occam's Razor to determine the optimal number of hidden units in a neural network or should we simply use as many hidden units as possible computationally?


In addition to applications in human behavior analysis, an automatic AU recognition system has great potential to advance emerging applications in human-computer interaction (HCI), such as online/remote education, interactive games, and intelligent transportation, as well as to push the frontier of research in psychology.

the proposed IB-CNN improves CNN learning significantly with limited training data.


While existing solutions to this problem require some prior knowledge of the parameters ✓ 0 , ✓ 1 , ↵, we propose an adaptive algorithm that requires no such knowledge yet still obtains near-optimal sample complexity guarantees.

the player can flip any coin she picks from the bag as many times as she wants, and the goal is to identify a heavy coin using as few total flips as possible.


The algorithm will converge to weights If we change the model to ∆P , then we get convergence to Observe that the equations ( 16) are largely decoupled.

our results assume genericity conditions on the distribution P ( C) of causes.


This procedure can be repeated for a fixed number of iterations, or until a convergence criteria is met.

our algorithm, SHAMO, performs the best with error of about 5% when allowing k = 2 models, and about 10% when allowing k = 14 models.


Following the spirit of a margin-based structured predictor such as M 3 N, we employ only the unnormalized energy function F (x, y, z; w) (which usually consists of linear combinations of feature functions or potentials) as the cost function for structured prediction, and we adopt a prediction rule directly extended from the MaxEnDNet-average over all the possible models defined by different w, and at the same time marginalized over all hidden variables z.

while likelihood-based methods have been extensively explored, to our knowledge, learning structured prediction models with latent variables based on the max-margin principle remains largely an open problem.


Both EP and our algorithm update posterior marginals, followed by a rank-one update of the covariance.

strict concavity of terms other than f b is well-known since both the least squares and covariance selection problems are concave.


The remainder of the paper is organized as follows.

formally related but motivated from a probabilistic perspective are deterministic annealing methods for maximum entropy clustering/vector quantization, see, e.g., [24,42].


All the competitors use the same settings and the features as ours.

the semantic descriptions of each category is an article collected from Wikipedia, and Term Frequency-Inverse Document Frequency (TF-IDF) [16] feature vector is then extracted to represent the class semantic features.


This family of non-smooth optimization problems has applications in numerous domains, e.g., machine learning and statistics [7], image processing [6], cone programming [11], and etc.

semialgebraic functions and (globally) subanalytic functions are for instance definable in their respective classes.


All experiments were conducted on workstations with Xeon(R) CPU (W5590@3.33GHz) and 48GB RAM, under Windows 7 System.

the efficiency of testing may be very important in practice, for example, when the classifier is deployed in a user-facing application (such as search), while the cost of training or preprocessing may be less critical and can be conducted off-line.


Theorem 6 The pure-Nash extension problem for n-player SC α-IDS games is NP-complete.

as you wonder about the cost and the effectiveness of the fire extinguishing mechanism, you notice that the fire extinguishing mechanism can only protect your apartment if a small fire originates in your apartment.


Hence, we sacrifice the probabilistic framework for a better performing heuristic (see Section 3.4 for more details).

if a latent dimension encodes a data generative factor that is irrelevant to the new dataset, then it will start behaving atypically and stray away from the prior.


Note that we have used y as the initial point (as opposed to y 0 ) to indicate that the semiflow representing the solution trajectory should be viewed as a function of the initial point y.

this would make the presentation significantly more cumbersome, so we stick with smooth objectives throughout.


Numerical simulations highlight the benefit of structured sparsity and the advantage offered by our approach over the Lasso and other related methods.

we have that Equation (3.1) now follows by a direct computation.


We combine the results of the two attention vectors and the equation ( 11) becomes: where W p , W q and b p are all trainable parameters.

for the formula form, the most popular objective is the maximum log likelihood estimation [Bahdanau et al., 2015;Xia et al., 2017]:  this results in the high frequency of some commonly used expressions such as "I don't know" in the output sentences because of the nature of the class imbalance in the corpus.


Note that while computations can be made efficient in several ways, we consider a simple algorithmic protocol and leave a more refined computational study for future work.

we prove that both the Laplacian kernel K(x, y) = e  In this section, we first discuss our framework and our main assumptions.


Qualitatively, however, generated samples from VEEGAN seem better than other methods.

across the methods, we see in Figure 3 that VEEGAN captures small details, such as the face of the poodle, that other methods miss.


Under multi-structure data, it is unknown what a suitable stopping criterion is (apart from solving the overall fitting and model selection problem itself).

let {θ m } M m=1 aggregate the set of hypotheses fitted on the minimal subsets proposed thus far in all birth and local update moves in Algorithm 1.


DCD-PSGD admits a slightly better convergence rate than ECD-PSGD when the data variation among nodes is very large.

comparison between DCD-PSGD and ECD-PSGD On one side, in term of the convergence rate, ECD-PSGD is slightly worse than DCD-PSGD due to additional terms that suggests that if σ is relatively large than σ, the additional terms dominate the convergence rate.


However it is clear that (0, 0) is not a local min-max.

assume f is twice differentiable and ∇f is Lipschitz with constant L. The set of initial vectors (x 0 , y 0 ) so that GDA converges to (linearly) GDA-unstable fixed points (critical points) is of measure zero.


A pseudo code of the LCV procedure is summarized in Figure 1-(b) One of the potential limitations of CV in general is that it is not reliable in small sample cases since data splitting by CV further reduces the sample size.

each data set consists of input/output samples {(x k , y k )} n k=1 .


noise draws to a sequence of `(k) that may be neither independent nor identically distributed.

the a single entry in X drawn from either P 0 or P 1 may be replaced without detection by another entry drawn from either P 0 or P 1 , even if the rest of the database is arbitrary.


In some situations, emphasizing the short term trends is desirable, for example for the analysis of financial time series.

similarly, we are going to consider distribution over infinite sequences in the notation that follows, but if the goal is to model finite sequences, an additional special state θ end = θ beg can be introduced.


Standard approaches to object detection (e.g., [24,15]) usually look at local pieces of the image in isolation when deciding if the object is present or not at a particular location/ scale.

as mentioned in the introduction, the presence of many types of objects is correlated.


Assume we are given a large region R ⊂ Q and would like to estimate its evidence score LES(R|H ref ).

it can also be applied to compute similarity of a signal to a group of signals (i.e., compose a query signal from pieces extracted from multiple reference signals).


Instead of comparing absolute running times, we observe that all four solvers are based on the Z3 theorem prover [6] and rely on the counterexamples from Z3 to adjust their search strategy.

using predicate (x < 0 ∨ y > 0) as the loop invariant I suffices to prove the assertion, as shown in Figure 1(b).


Recent work has also been able to improve the complexity of RBM training on word observations.

an observation vector v is now a sequence of words indices v i taking values in {1, . . . , V }, while the size D of v can vary.


There also has been some recent work which examines the complexity of lifted inference independent of the specific algorithm used [13,2,8].

then, since constraints are in canonical form, for any other variable x ∈ x i involved in (in)equality constraint with x with V as the support, we have V = V every pair of values v i , v j ∈ V behave identically with respect to the constraint tuple T xi and hence, are symmetric to each other.


In contrast, a word embedding is trained to only represent individual words in isolation.

more complex supervised CNNs from [11] will be reviewed later.


Since the neighborhoods being compared are of fixed size, we assume that all points in a neighborhood have a corresponding point in the other.

the notion of similarity between pointsets is also different from those between sets of vectors, or graphs.


If in addition to r1 also q1 is known, the two local minimia of F ∞ (p 1 = 0 and p2 = 0) allow to recover t0 = t 0 only.

since global optimization is generally intractable, in practice it is implemented through an expectationmaximization (EM) procedure known as Baum-Welch algorithm [20,9].


Fig 4 shows examples where hierarchical constraints between layers improves segmentation quality relative to independent clustering at each threshold.

pairs (u, v) that do not correspond to an edge in the original graph can still be assigned a unique distance based on the coarsest level l at which they lie in different connected components of the cut specified by X l . To compute the quality of an ultrametric d with respect to an input set of edge weights θ, we measure the squared L 2 difference between the edge weights and the ultrametric distance θ − d 2 2 .


It turns out that Σ * can be well approximated by Σ r , r = 50, where Σ r is the best rank r approximation to Σ * obtained from computing its eigendecomposition and setting to zero all but the top r eigenvalues.

the approach of [7] treats (5) as an instance of (1) and uses nuclear norm regularization to enforce rank-one solutions.


For a M × N matrix X, the matrix-variate normal distribution is given by [10] N (X|M, Σ, Ω) = (2π) where M is the mean, and Σ, Ω are M × M row and N × N column covariances, respectively.

when σ 2 y = 0, q cannot directly be set and a trial-and-error procedure is required to find it.


By analyzing the complexity of these tasks in a more general framework than what is usually done, we shed light on some of the sources of complexity such as the stochasticity of the environment and the agent's policy.

any policy will have a 0.5 chance of committing a misprediction at each step of an episode.


There also are similarities to the work of Hoang Tuy who has shown that any arbitrary closed set is the projection of a difference of two convex sets in a space with one more dimension.

in the former, see [6], the introduction of auxiliary variables converts the problem to a min-max problem where the goal is to find a saddle point.


The weights β j are in turn generated by a Dirichlet distribution centered around π with a degree of variability determined by α.

due to the differences in the level of noise among subjects, we do not expect to find the same set of functional units in all subjects.


This paper tackles a significantly more general and more challenging problem than the specific instance just mentioned.

we study the specific case where p = 2 and (y, y ) = |y − y | for all (y, y ).


This distribution is conjugate to the multinomial, which greatly simplifies our Bayesian treatment.

( we approximate the posterior distribution of the hidden variables of the model by one in which the hidden states are decoupled from the parameters given the indicator variables and in which the indicators are decoupled from the parameters.


From the training set, we produce coresets and uniformly sampled subsets of sizes between 70 and 1000, using the parameters k = 33 (as in [11]), β = 66, and δ = 0.1, and fit GMMs.

one major advantage of coresets is that they can be constructed in parallel, as well as in a streaming setting where data points arrive one by one, and it is impossible to remember the entire data set due to memory constraints.


Then, encoder and decoder compute: where the function l is a point-wise logistic non-linearity of the form: with g fixed gain.

everything can be easily extended to any other choice of parameterized functions as long as these are differentiable and maintain symmetry between encoder and decoder.


losses and hinge/ramp loss realizability, the standard tools of classification calibration [8] can be used to deduce a proper policy regret bound from (3).

first, our bounds in Section 2 are likely suboptimal in the dependence on K, and improving this is a natural direction.


Several algorithms have been designed for learning HMM parameters for chromatin modeling, including stochastic variational inference [16] and contrastive learning of two HMMs [26].

next we compared the performance of Spectacle-Tree to a similar model which additionally constrained all transition and observation parameters to be the same on each branch [5].


note that the convexity of the expected reward of (9) only depends on the convexity of the functions I 1 (η) and I −1 (η).


Moreover, doing so would be difficult as the unconfounded sample is not expected to cover the confounded one.

the observational data are iid draws from the population given by conditioning on the event E Conf : Using potential outcome notation, assuming the standard Stable Unit Treatment Value Assumption (SUTVA), which posits no interference and consistency between observed and potential outcomes, we let Y (0), Y (1) be the potential outcomes of administering each of the two treatments and Y = Y (T ) = T Y (1) + (1 − T )Y (0).


The problem has been referred to as network 'tomography', a medical word to denote clinical techniques that produce detailed images of the interior of the body from external signals [9,10].

since full train information was recorded only on one of the 11 underground lines of the network (the Victoria Line), we have restricted the comparison to a small set of stations.


data arrive one at a time, and applies to this common situation.

first, the fact that (z, g) can be non-convex in g, yet solvable by convex optimization, is a major departure from previous work.


For example, only by seeing the entire face, the system can determine eyes and nose position, as shown in top-right of Figure 1.

in Figures 9, we show partial results of our method and CA [26] on CelebA and CelebA-HQ face datasets.


Feature sequences Simply matching the SIFT features by value [12] yields satisfactory results (see later in figure 2).

topological representations of routes spanning multiple kilometers are robuster than metric and cognitively more plausible for use by humans.


Note that these probabilities are much smaller than the Gabor responses in the body of the starfish, where the image is textured but there is no significant structure of orientation θ.

the ubiquity of orientation processing in visual cortex suggests that the estimation of local orientation is important for tasks such as object recognition.


Web images are a rich and free resource compared to traditional human-labeled object datasets.

most rely on a labeled seed set of inlier-sense images to initialize bootstrapping or to select the right cluster.


Unfortunately, the error bounds developed in [12] were also incorrect.

we first set τ = ǫ, halving τ until the error tolerance ǫ was met.


We set up a multi-state MRF on pixels for segmentation, where the states correspond to the K different image stack groups from section 3.

match each region in the input image to semantically similar regions in other images) than if we used a single best match.


Screening plays an important role in the diagnosis and treatment of a wide variety of diseases, including cancer, cardiovascular disease, HIV, diabetes and many others by leading to early detection of disease [1]- [3].

we show that if the estimation error and the approximation error are small, then the policy we construct is very close to the policy for the correctly estimated model.


Fifth, as already remarked [Nock et al., 2015], significantly subsampling rados (e.g.

this inequality ties an "accuracy" of θ (edges, left hand-side) and its sparsity (right-hand side).


To simplify the notation, we assume the latent variable h takes its value from a discrete set of labels.

1 enforces a large margin between clusters by constraining that the score of x i to the assigned cluster is sufficiently larger than the score of x i to any other clusters.


Result 4 (Distribution-free lower bound on simple regret [4]).

if T (N ) is sub-exponential we get an optimal δ of 0 representing a standard UCB during the experimentation phase.


Acknowledgments Kevin Jamieson is generously supported by ONR awards N00014-15-1-2620, and N00014-13-1-0129.

lower bounds on the sample complexity when the parameters are known and unknown follow by analyzing a simple binary and composite hypothesis test, respectively.


First, unlike other approximation schemes, KBRL always converges to a unique solution.

the first set was a 3 × 3 grid over [0.1, 0.3] × [0.3, 0.5] and the second one was composed of four states: {0.1, 0.3} × {0.9, 1.0}.


Then we show how this bound can be customized into a surrogate objective function in order to either search in the space of policies (Action-based POIS) or to search in the space of parameters (Parameter-bases POIS).

with little abuse of notation, we will replace D α (P Q) with D α (p q) whenever possible within the context.


Defining p = rp + 1 − r and q = rq + 1 − r, the number of constraints in (1.6) becomes statistically equivalent to those of a fully observed graph where p and q are replaced by p and q. Consequently, for a fixed r > 0, from (2.3), we require p ≥ p − q O( 1 √ n ) for success.

our analysis is helpful in understanding the phase transition from failure to success for the simple approach.


For s ≥ 0, define the moment generating function ϕ ].

in the specific context of differential privacy this result yields for every x X x : Table 1: Summary of privacy amplification bounds.


A natural choice in this context is to measure the log-likelihood difference between the positive and negative models, normalized by the length of the sequence.

input: HMM λ = {q j } j=n j=1 , M, π, A, B , heavy state q i , O 1: Draw random HMM, λ i = {q j } j=n+N j=n+1 , M, {π j } j=n+N j=n+1 , {a jk } j,k=n+N j,k=n+1 , {b jm } j=n+N,m=M j=n+1,m=1 2: For each 1 ≤ j ≤ n, j = i, replace transition q j q i with q j q n+1 .


It is easy to verify that adding εU i,j to J amounts to introducing a vortex of direction i → j → S → i, and any vortex of N states (N ≥ 3) N −1 n=1 U sn,sn+1 in the case of state S being in the vortex and assuming s N = S without loss of generality, or U s N ,s1 + N −1 n=1 U sn,sn+1 if S is not in the vortex, as demonstrated in Figure 1.

from Lemma 1, it follows immediately that in the discrete case, the comparison of MCMC estimators based on two Markov chains with the same stationary distribution can be cast as a different problem of matrix comparison, as stated in the following proposition.


Then the error rate of the form n −b , b ≥ 1, which is much faster than the rates of Monte Carlo methods, will be guaranteed with b being a constant representing the degree of smoothness of the RKHS (e.g., the order of differentiability).

one can incorporate one's knowledge or belief on f into the construction of weighted points {(w i , X i )} via the choice of α.


Only expanding the optimistic leaf would not be enough to make ASOP consistent; this is shown in the appendix.


Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems.

l-CCA has stable and close to best performance despite those variations in the datasets.


Here we drew 30 samples from the posterior and set H � = H, but investigation of a range of sample number and H � values yields the same results, suggesting that our approximation parameters do not have an effect on our results (see Supp.

the studies [28,30,12] suggest that globular fields are a consequence of occlusion nonlinearities.


Building on our previous findings, for each stage, the encoder is followed by and absolute value rectification, contrast normalization and average subsampling.

this contribution would be minor for dictionaries which have already been trained convolutionally in the unsupervised stage.


That is why the impact of the noisy set on training must be reduced by oversampling clean instances [14,3].

11 for each clean instance Do Gibbs sweeps to sample from the current p θ θ θ (y y y, ŷ y y, h h h|x x x (•) ) for each clean/noisy instance (m n , m c ) ← (# noisy instances in minibatch, # clean instances in minibatch) , y y y (c) , ŷ y y (c) ) by Eq.12 and 13 end end 4  In this section, we examine the proposed robust CNN-CRF model for the image labeling problem.


With a few exceptions, most human BCIs are based on extracranial electroencephalography (EEG).

we restrict the training set as well as the test set to these channels.


We further conduct the simulation studies to verify our theoretical results.

we begin by introducing some background on reproducing kernel Hilbert space (RKHS), and functional gradient descent algorithms in the RKHS, together with our nonparametric testing formulation.


We are grateful to Christian Sohler's research group for providing their code for the StreamKM++ algorithm.

the k-means objective is one of the most popular formalisms, and in particular Lloyd's algorithm [21] has significant usage [5,7,19,22,23,25,27,28].


The convergence analysis is given in supplementary material Section 1.3.

these relaxations are considerably tighter than naive concretizations shown in Figure 3(a), which introduces a larger error u up .


Retrieval is finally based on the Hamming distance between these hash codes.

since ( 7) and ( 10) are special cases of ( 2) and ( 3), respectively, the MC-SVM is a special case of the formulation of Section 2, with predictor f (x) = Φ(x) and codewords y l = w l . This leads to the duality of Figure 1.


In this paper, we introduce two strategies for conducting convolutions on the sphere, using either a spherical-polar grid or a grid based on the cubed-sphere representation.

we can apply the conventional 3D convolutions in equation ( 1) to features on the concentric cubedsphere and the concentric spherical-polar grids, and denote these as concentric cubed-sphere convolution (CCSconv) and concentric spherical-polar convolution (CSPconv).


Already, this restriction will prevent us from using a smaller sized study (fewer subjects), increasing the cost of pharmaceutical research.

(ii) What degree of computational speedup can we expect at various subsampling rates, and how does this affect the trade-off with approximation error?


We also compare the method to an "oracle least squares estimator" that knows the true support of the solutions.

we impose a Gaussian process [11] as a prior on the parameters γ i .


For inference, we assume Rayleigh-fading channels and, therefore, we place a circularly symmetric complex Gaussian prior distribution over the channel coefficients, h m |σ 2 ∼ CN (0, σ 2 I, 0), and over the noise term, n t ∼ CN (0, σ 2 y I, 0).

we artificially mix the data 10 times (corresponding to 10 microphones) with mixing weights sampled from Uniform(0, 1), such that each microphone receives a linear combination of all the considered signals, corrupted by Gaussian noise with standard deviation 0.3.


A complicated heuristic is developed in [5] to deal with the fact that the unconstrained linear problem they consider has a degenerate solution.

in the experiments that follow we were able to improve upon the initial VI solution using the simple fixed step size.


As in [LS05], noise tolerance is facilitated by the fact that the path through the network is not affected by altering the label of an example.

adaptiveness is an important property since it is often the case that the advantage of successive weak classifiers grows smaller and smaller as boosting proceeds.


We only consider the ℓ 2 norm throughout the paper.

in contrast to this study, most of these approaches do not have theoretical guarantees.


We found that our algorithm achieves the smallest error consistently in all trials, and that the error of our algorithm almost matches the error of the empirical conditional probabilities of the uncorrupted samples.

we study the following broad question: Question 1 (Robust Learning of Graphical Models).


in the decentralized setting of our interest, this is more challenging as consensus is not guaranteed.


We would like to consider a tight parameterization where no combination of subunits can take over another subunit's task. .

the two decompositions are identical up to scale and shift.


This has proven effective for image generation [48] and other tasks.

we aim at handling cases where there is only one target labeled sample, and there can even be some classes with no target samples at all.


The conditional intensity can thus be derived given by: where δ ap = t ap − t ap−1 with p being defined by arg max{p : t ai < t}.

given that datasets are sparse -as shown by the fraction of non-zeros in the ground truth, or %NZ, in Table 1 -the Kendall Correlations and Relative Errors are unreliable metrics for large networks.


Given the training data points {(x i , ŷi )} N i=1 , a natural candidate for the center of the Wasserstein ball is the empirical distribution PN = 1 N N i=1 δ (xi,ŷi) , where δ (xi,ŷi) denotes the Dirac point measure at (x i , ŷi ).

similarly, in each trial related to the MNIST dataset, we randomly select 10 shows that DRLR wins by a large margin (outperforming RLR by 4%-43%).


Algorithms of both type have been developed to provide PAC-MDP bounds polynomial in the number of states S and actions A [8,9,10].

but even these bounds grow with the cardinality of the state and action spaces, which may be extremely large or even infinite.


In order to get a partition of the input data into coherent groups, a simple approach is to iteratively finding a dominant set and then removing it from the graph, until all vertices have been grouped (see [9] for a hierarchical extension of this framework).

now, let n = | V | be the cardinality of V and let xS be the (n-dimensional) characteristic vector of S in Ĝ, which is obtained by padding x S with zeros.


Table 1 shows the results over the different networks for the different models.

poissonian degree distribution for readers and power-law degree distribution for books.


Recovering low-dimensional structure from a corrupted matrix is related to robust PCA [4,9,33].

most previous methods focus on shilling attacks, and the key idea for detecting such attacks is to find the common characteristics of attack profiles with the same attack strategy.


Boosting algorithms are an important recent development in classification.

if for some m we have Q(f m ) ≤ Q( f ), then theorem is trivially true for all m ≥ m. we are going to consider only the case when Let f m − f = αi hi , where αi and hi correspond to the best representation (with the smallest l * -norm).


To apply these methods, it suffices to be able to solve efficiently: which we refer to as the proximal problem.

it may be too slow for practical purposes, as the best generic algorithm has complexity O(p 6 ) [19] 3 .


We note that the traditional CRP is an instance of a ddCRP.

for each table t, sample region assignments k t ∼ CRP (γ).


The ground-truth labels are generated by NMS with IoU threshold 0.6, which produce decent results with NMS.

the detail is to calculate a set of attention weights S a for middle-grade feature f M as where f M and f H are both linearly transformed and tiled.


Clearly, with no constraints on B or W, we can trivially achieve zero reconstruction error in both cases by taking B = I p and W any p × p full-rank matrix.

so far, we have established CUR's connection to regression by showing that CUR can be thought of as an approximation algorithm for the sparse regression problem (7).


In this paper, we propose a new technique for imitation that explicitly handles uncertainty using a probabilistic model of actions and their sensory consequences.

we see experimentally that less than ten components have a weight which is within five orders of magnitude of the maximal weight.


As a result, we can reduce the problem of synthesizing programs in the Strategy language to the problem of synthesizing branches with predicates over a set of candidate strategies.

stratEVO has several limitations -it performs search using an evolutionary algorithm which does not incorporate any form of learning, the search does not depend on the actual formula, and local mutations tend to get stuck in local minima (as we show in our experiments in Section 5).


When γ is defined over the interval [0, 1], the Riemannian exponential map at p is defined as Exp p (v) = γ(1).

note the cost of the gradient ascent algorithm also linearly depends on the data size, dimensionality, and the number of samples drawn.


Consider a patch that contains the letter A and another one that contains the letter B.

in case of three centers, we use overlapping patches and dynamic programming to determine the best stitching.


Additionally, and although it achieves 0% error, it is learning very complicated and unintuitive coordinate transformations to represent the data in a linearly separable form.

they often overlook the fundamental process taking place, where successive layers successively warp the coordinate representation of the data manifold with nonlinear transformations into a form where the classes in the data manifold are linearly separable by hyperplanes.


The second one is a bit more technical and requires to use standard proof techniques such as symmetrization.

definition 1 (UniforIll stability) Let S = {Zl, ... ,zm} be a training set, Si = S\Zi be the training set where instance i has been removed and A a symmetric algorithm.


If Q and P factorize, then each of these two terms further breaks into a sum of individual terms, each quantifying the aspects of the fit of the data point with respect to different parts of the model.

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).


However, a caution should be exercised when using the measure of performance at the bag level as a surrogate for the measure of performance at the individual level: in order to perform well at the bag level, one can simply utilise spatial coordinates and ignore other covariates, as malaria intensity appears to smoothly vary between the bags (Left of Figure 2).

y a ∼ P oisson( i p a i λ a i ), where λ a i is the underlying pixel incidence rate of malaria per 1000 people that we are interested in predicting.


For this paper, we restrict our case to A, B ∈ R n×n being positive definite matrices so that the objective function is strongly convex.

one such point set in [0, 1] n is called the (t, m, n)-net in base η, which is defined as a set of N = η m points in [0, 1] n such that any axis parallel η-adic box with volume η t−m would contain exactly η t points.