Related papers: Saddlepoint approximation for moment generating fu…
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…
In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD)…
Generalized Method of Moments (GMM) estimators in their various forms, including the popular Maximum Likelihood (ML) estimator, are frequently applied for the evaluation of complex econometric models with not analytically computable moment…
Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…
We consider the problem of simulating a Gaussian vector X, conditional on the fact that each component of X belongs to a finite interval [a_i,b_i], or a semi-finite interval [a_i,+infty). In the one-dimensional case, we design a table-based…
Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…
Temporal difference learning with linear function approximation is a popular method to obtain a low-dimensional approximation of the value function of a policy in a Markov Decision Process. We give a new interpretation of this method in…
Two-time-scale stochastic approximation is a popular iterative method for finding the solution of a system of two equations. Such methods have found broad applications in many areas, especially in machine learning and reinforcement…
In this work, approximations for real two variables function $f$ which has continuous partial $(n-1)$-derivatives $(n \ge 1)$ and has the $n$--th partial derivative of bounded bivariation or absolutely continuous are established. Explicit…
In this paper, we compute doubly truncated moments for the selection elliptical (SE) class of distributions, which includes some multivariate asymmetric versions of well-known elliptical distributions, such as, the normal, Student's t,…
Spatio-Temporal Multivariate time series Forecast (STMF) uses the time series of $n$ spatially distributed variables in a period of recent past to forecast their values in a period of near future. It has important applications in…
In this paper we analyze the joint rate distortion function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual distortion criteria. First, we derive structural…
Large deviations for additive path functionals of stochastic dynamics and related numerical approaches have attracted significant recent research interest. We focus on the question of convergence properties for cloning algorithms in…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…
Time series forecasting is essential for our daily activities and precise modeling of the complex correlations and shared patterns among multiple time series is essential for improving forecasting performance. Spatial-Temporal Graph Neural…
Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
Motivated by broad applications in reinforcement learning and machine learning, this paper considers the popular stochastic gradient descent (SGD) when the gradients of the underlying objective function are sampled from Markov processes.…
High-dimensional generative modeling is fundamentally a manifold-learning problem: real data concentrate near a low-dimensional structure embedded in the ambient space. Effective generators must therefore balance support fidelity -- placing…
Purpose: To facilitate the implementation/validation of signal representations and models using parametric matrix-variate distributions to approximate the diffusion tensor distribution (DTD) $\mathcal{P}(\mathbf{D})$. Theory: We establish…