116839195
Some results on empirical processes and stochastic complexity
This thesis contains two parts. In Part I, an intuitive and simple approach is used to obtain uniform convergence and Central Limit Theorems for empirical processes indexed by families of functions, for stationary mixing sequences with not too slow a $\beta$-mixing (or $\phi$-mixing) rate. The conditions imposed are in terms of random metric entropies, and the $\beta$-mixing (or $\phi$-mixing) rate. In the case of a Vapnik-Cervonenkis class, the uniform convergence result holds for any strictly stationary sequence with $\beta$-mixing (or $\phi$-mixing) rate $\beta\sb{n}$ (or $\phi\sb{n}$) = $o$($n\sp{-d}$) for some d $>$ 0, while the Central Limit Theorem requires the rate $\beta\sb{n}$ (or $\phi\sb{n}$ = $o$($n\sp{-d}$) for some d $>$ 3. 
In Part II, we use a shortest code length criterion to select the bin width of a histo-gram from a string of i.i.d. observations. Under smoothness conditions on the underlying density on (0, 1), this criterion is shown to be optimal as a code selection criterion in reaching the smallest redundancy within the class of codes under consideration. Furthermore, the criterion consistently selects the underlying density when it is uniform on (0, 1). 
Minimax lower bounds for the redundancy over many smooth families of underlying densities are also derived. In a special case, the lower bound is shown to be achieved almost surely, and in expectation, by a predictive code based on a sequence of histograms. In the case of Sobolev balls, the minimax optimal code is described and a heuristic proof is provided.
12165073
On the Convergence of Boosting Procedures
A boosting algorithm seeks to minimize empirically a loss function in a greedy fashion. The resulted estimator takes an additive function form and is built iteratively by applying a base estimator (or learner) to updated samples depending on the previous iterations. This paper studies convergence of boosting when it is carried out over the linear span of a family of basis functions. For general loss functions, we prove the convergence of boosting's greedy optimization to the infinimum of the loss function over the linear span. As a side product, these results reveal the importance of restricting the greedy search step sizes, as known in practice through the works of Friedman and others.
11765401
Looking at Markov samplers through cusum path plots: a simple diagnostic idea
In this paper, we propose to monitor a Markov chain sampler using the cusum path plot of a chosen one-dimensional summary statistic. We argue that the cusum path plot can bring out, more effectively than the sequential plot, those aspects of a Markov sampler which tell the user how quickly or slowly the sampler is moving around in its sample space, in the direction of the summary statistic. The proposal is then illustrated in four examples which represent situations where the cusum path plot works well and not well. Moreover, a rigorous analysis is given for one of the examples. We conclude that the cusum path plot is an effective tool for convergence diagnostics of a Markov sampler and for comparing different Markov samplers.
2105049
Model Selection in Gaussian Graphical Models: High-Dimensional Consistency of l1-regularized MLE
We consider the problem of estimating the graph structure associated with a Gaussian Markov random field (GMRF) from i.i.d. samples. We study the performance of study the performance of thel1-regularized maximum likelihood estimator in the high-dimensional setting, where the number of nodes in the graph p, the number of edges in the graph s and the maximum node degree d, are allowed to grow as a function of the number of samples n. Our main result provides sufficient conditions on (n, p, d) for thel1-regularized MLE estimator to recover all the edges of the graph with high probability. Under some conditions on the model covariance, we show that model selection can be achieved for sample sizes n = Ω(d log(p)), with the error decaying as O(exp(−c log(p))) for some constant c. We illustrate our theoretical results via simulations and show good correspondences between the theoretical predictions and behavior in simulations.
6762008
Perceptual audio coding using adaptive pre- and post-filters and lossless compression
This paper proposes a versatile perceptual audio coding method that achieves high compression ratios and is capable of low encoding/decoding delay. It accommodates a variety of source signals (including both music and speech) with different sampling rates. It is based on separating irrelevance and redundancy reductions into independent functional units. This contrasts traditional audio coding where both are integrated within the same subband decomposition. The separation allows for the independent optimization of the irrelevance and redundancy reduction units. For both reductions, we rely on adaptive filtering and predictive coding as much as possible to minimize the delay. A psycho-acoustically controlled adaptive linear filter is used for the irrelevance reduction, and the redundancy reduction is carried out by a predictive lossless coding scheme, which is termed weighted cascaded least mean squared (WCLMS) method. Experiments are carried out on a database of moderate size which contains mono-signals of different sampling rates and varying nature (music, speech, or mixed). They show that the proposed WCLMS lossless coder outperforms other competing lossless coders in terms of compression ratios and delay, as applied to the pre-filtered signal. Moreover, a subjective listening test of the combined pre-filter/lossless coder and a state-of-the-art perceptual audio coder (PAC) shows that the new method achieves a comparable compression ratio and audio quality with a lower delay.
828878
Image denoising via lossy compression and wavelet thresholding
Some past work has proposed to use lossy compression to remove noise, based on the rationale that a reasonable compression method retains the dominant signal features more than the randomness of the noise. Building on this theme, we explain why compression (via coefficient quantization) is appropriate for filtering noise from signal by making the connection that quantization of transform coefficients approximates the operation of wavelet thresholding for denoising. That is, denoising is mainly due to the zero-zone and that the full precision of the thresholded coefficients is of secondary importance. The method of quantization is facilitated by a criterion similar to Rissanen's minimum description length principle. An important issue is the threshold value of the zero-zone (and of wavelet thresholding). For a natural image, it has been observed that its subband coefficients can be well modeled by a Laplacian distribution. With this assumption, we derive a threshold which is easy to compute and is intuitive. Experiments show that the proposed threshold performs close to optimal thresholding.
27633879
A more efficient branch and bound algorithm for feature selection
Abstract An algorithm is presented to be able to select the globally optimal subset of d features from a larger D -feature set. This is a fundamental problem in statistical pattern recognition and combinatorial optimization. Exhaustive enumeration is computationally unfeasible in most applications. This algorithm dynamically searches for the globally optimal solution on a minimum solution tree which is a subtree of the solution tree used in the traditional branch and bound algorithm. The new algorithm is compared theoretically with the branch and bound algorithm. The analysis and the experimental results show that it is more efficient than the traditional algorithm.
8426940
A dynamic pricing mechanism for P2P referral systems
Most existing research on peer-to-peer systems focuses on protocol design. In this paper, we consider the issue of free riding in peer-to-peer referral systems. Free riders are agents that refuse either to answer a query or to give referrals. Free riding is detrimental to the system, since it may prevent requesters from finding high quality providers efficiently. To mitigate the issue of free riding, we propose a dynamic pricing mechanism to motivate the agents to behave rationally. Service providers learn appropriate prices of referrals and answers in order to maximize their payoffs through stochastic iterative learning algorithms.
15008871
Large Sample Properties of Weighted Monte Carlo Estimators
A general approach to improving simulation accuracy uses information about auxiliary control variables with known expected values to improve the estimation of unknown quantities. We analyze weighted Monte Carlo estimators that implement this idea by applying weights to independent replications. The weights are chosen to constrain the weighted averages of the control variables. We distinguish two cases (unbiased and biased), depending on whether the weighted averages of the controls are constrained to equal their expected values or some other values. In both cases, the number of constraints is usually smaller than the number of replications, so there may be many feasible weights. We select maximally uniform weights by minimizing a separable convex function of the weights subject to the control variable constraints. Estimators of this form arise (sometimes implicitly) in several settings, including at least two in finance: calibrating a model to market data (as in the work of Avellaneda et al. 2001) and calculating conditional expectations to price American options. We analyze properties of these estimators as the number of replications increases. We show that in the unbiased case, weighted Monte Carlo reduces asymptotic variance, and that all convex objective functions within a large class produce estimators that are very close to each other in a strong sense. In contrast, in the biased case the choice of objective function does matter. We show explicitly how the choice of objective determines the limit to which the estimator converges.
22909785
A dynamic holding strategy in public transit systems with real-time information
Abstract
Holding strategies are among the most commonly used operation control strategies in transit systems. In this paper, a dynamic holding strategy is developed, which consists of two major steps: (1) judging whether an early bus should be held, and (2) optimizing the holding times of the held bus. A model based on support vector machine (SVM), which contains four input variables (time-of-day, segment, the latest speed on the next segment, and the bus speed on the current segment) for forecasting the early bus departure times from the next stop is also developed. Then, in order to determine the optimal holding times, a model aiming to minimize the user costs is constructed and a genetic algorithm is used to optimize the holding times. Finally, the dynamic holding strategy proposed in this study is illustrated with the microscopic simulation model Paramics and some conclusions are drawn.

16993770
Service matchmaking with rough sets
With the wide adoption of open grid services architecture (OGSA) and Web services resource framework (WSRF), the grid is emerging as a service-oriented computing infrastructure for engineers and scientists to solve data and computationally intensive problems. It is envisioned that computing resources in a future grid environment will be exposed as services. Service discovery becomes an issue of vital importance for a wider uptake of the grid. This paper presents RSSM, a rough sets based service matchmaking algorithm for service discovery with an aim to tolerate uncertainty in identifying service properties. The evaluation results show that the RSSM algorithm is more effective in service discovery compared with other mechanisms such as UDDI and OWLS.