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Sparse approximation and recovery by greedy algorithms in Banach spaces
Sparse approximation recovery greedy algorithms Banach spaces
2013/4/28
We study sparse approximation by greedy algorithms. We prove the Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA), a generalization of the Weak Orthogonal Matching Pursuit to ...
Multi-dimensional sparse structured signal approximation using split Bregman iterations
Sparse approximation Regularization Fused-LASSO Split Bregman Multidimensional signals
2013/5/2
The paper focuses on the sparse approximation of signals using overcomplete representations, such that it preserves the (prior) structure of multi-dimensional signals. The underlying optimization prob...
Approximation for the Distribution of Three-dimensional Discrete Scan Statistic
Approximation for the Distribution Three-dimensional Discrete Scan Statistic
2013/4/27
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribut...
A Greedy Approximation of Bayesian Reinforcement Learning with Probably Optimistic Transition Model
Reinforcement Learning Uncertain Knowledge Probabilistic Reasoning Optimal Behavior in Polynomial Time
2013/5/2
Bayesian Reinforcement Learning (RL) is capable of not only incorporating domain knowledge, but also solving the exploration-exploitation dilemma in a natural way. As Bayesian RL is intractable except...
Local Gaussian process approximation for large computer experiments
sequential design sequential updating active learning surrogate model emulator compactly supported covariance local kriging neighborhoods
2013/4/27
We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential desi...
Smoothing effect of Compound Poisson approximation to distribution of weighted sums
characteristic function concentration function compound Poisson distribution Kolmogorov norm weighted random variables.
2013/4/27
The accuracy of compound Poisson approximation to the sum $S=w_1S_1+w_2S_2+...+w_NS_N$ is estimated.
Here $S_i$ are sums of independent or weakly dependent random variables, and $w_i$ denote weights...
Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution
Random Matrix Theory characteristic roots largest eigenvalue Tracy-Widom Distribution Wishart Matrices Gaussian Orthogonal Ensemble
2012/11/23
We derive the exact distribution of the largest eigenvalue for finite dimensions real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). We compare the exact distribution with the Tracy-...
Causal band-limited approximation and forecasting for discrete time processes
band-limited processes discrete time processes causal filters sampling low-pass filters forecasting.
2012/9/18
We study causal dynamic approximation of non-bandlimited discretetime processes by band-limited discrete time processes such that a part of the historical path of the underlying process is approximate...
Adaptive estimation in regression and complexity of approximation of random fields
regression and complexity approximation random fields
2012/9/17
In this thesis we study adaptive nonparametric regression with noise misspecifi-cation and the complexity of approximation of random fields in dependence of the dimension.
First, we consider the prob...
Scaling of Model Approximation Errors and Expected Entropy Distances
Scaling of Model Approximation Errors Expected Entropy Distances
2012/9/19
We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. This yields information about th...
Scaling of Model Approximation Errors and Expected Entropy Distances
Scaling of Model Approximation Errors Expected Entropy Distances
2012/9/19
We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. This yields information about th...
Asymptotic Normality of Maximum Likelihood and its Variational Approximation for Stochastic Blockmodels
network statistics stochastic blockmodeling, varia-tional methods maximum likelihood
2012/9/18
Variational methods for parameter estimation are an activere-search area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that ap...
Uniform Stability of a Particle Approximation of the Optimal Filter Derivative
Hidden Markov Models State-Space Models Sequential Monte Carlo
2011/7/5
Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models.
Approximation properties of certain operator-induced norms on Hilbert spaces
L2 approximation Empirical norm Quadratic functionals Hilbert spaces with reproducing kernels Analysis of M-estimators
2011/6/20
We consider a class of operator-induced norms, acting as finite-dimensional
surrogates to the L2 norm, and study their approximation properties over
Hilbert subspaces of L2. The class includes, as a...
Almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case
Kesten's stochastic approximation algorithm multidimensional
2011/6/20
It is shown the almost sure convergence and asymptotical normality of a generalization of
Kesten's stochastic approximation algorithm for multidimensional case.
In this generalization, the step incr...