相关论文: On the minimal penalty for Markov order estimation

The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…

Generalized linear models play an essential role in a wide variety of statistical applications. This paper discusses an approximation of the likelihood in these models that can greatly facilitate computation. The basic idea is to replace a…

We consider discrete graphical models Markov with respect to a graph $G$ and propose two distributed marginal methods to estimate the maximum likelihood estimate of the canonical parameter of the model. Both methods are based on a…

This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…

We consider a problem of model selection in high-dimensional binary Markov random fields. The usefulness of the Ising model in studying systems of complex interactions has been confirmed in many papers. The main drawback of this model is…

In this article, model selection via penalized empirical loss minimization in nonparametric classification problems is studied. Data-dependent penalties are constructed, which are based on estimates of the complexity of a small subclass of…

We consider whether ergodic Markov chains with bounded step size remain bounded in probability when their transitions are modified by an adversary on a bounded subset. We provide counterexamples to show that the answer is no in general, and…

This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of…

We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

The paper addresses two variants of the stochastic shortest path problem ('optimize the accumulated weight until reaching a goal state') in Markov decision processes (MDPs) with integer weights. The first variant optimizes partial expected…

If the edges of the complete graph $K_n$ are totally ordered, a simple path whose edges are in ascending order is called increasing. The worst-case length of the longest increasing path has remained an open problem for several decades, with…

In this note, we establish a compact law of the iterated logarithm under the upper capacity for independent and identically distributed random variables in a sub-linear expectation space. For showing the result, a self-normalized law of the…

We consider reinforcement learning in parameterized Markov Decision Processes (MDPs), where the parameterization may induce correlation across transition probabilities or rewards. Consequently, observing a particular state transition might…

Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses…

Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…

Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…

Variable selection is an old and pervasive problem in regression analysis. One solution is to impose a lasso penalty to shrink parameter estimates toward zero and perform continuous model selection. The lasso-penalized mixture of linear…

Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…

We consider the problem of identifying parameters of a particular class of Markov chains, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph. Incoming edges to a node in the graph…