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We consider the problem of learning a policy for a Markov decision process consistent with data captured on the state-actions pairs followed by the policy. We assume that the policy belongs to a class of parameterized policies which are…

Optimization and Control · Mathematics 2017-01-24 Manjesh K. Hanawal , Hao Liu , Henghui Zhu , Ioannis Ch. Paschalidis

We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product…

Machine Learning · Statistics 2016-10-31 Aaron J. Molstad , Adam J. Rothman

The Markov assumption in Markov Decision Processes (MDPs) is fundamental in reinforcement learning, influencing both theoretical research and practical applications. Existing methods that rely on the Bellman equation benefit tremendously…

Methodology · Statistics 2024-09-24 Chuyun Ye , Lixing Zhu , Ruoqing Zhu

A penalized maximum likelihood estimation approach is proposed for discrete-time hidden Markov models where covariates affect the observed responses and serial dependence is considered. The proposed penalized maximum likelihood method…

Methodology · Statistics 2025-07-04 Luca Brusa , Fulvia Pennoni , Francesco Bartolucci , Romina Peruilh Bagolini

In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed. Exponential…

Probability · Mathematics 2021-12-30 Li-Xin Zhang

Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is…

Statistics Theory · Mathematics 2011-03-10 Randal Douc , Eric Moulines , Jimmy Olsson , Ramon van Handel

In simulation-based inferences for partially observed Markov process models (POMP), the by-product of the Monte Carlo filtering is an approximation of the log likelihood function. Recently, iterated filtering [14, 13] has originally been…

Methodology · Statistics 2018-02-26 Dao Nguyen

It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough…

Populations and Evolution · Quantitative Biology 2018-01-09 Vu Dinh , Lam Si Tung Ho , Marc A. Suchard , Frederick A. Matsen

Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the…

Machine Learning · Statistics 2025-06-26 Johan Pensar , Henrik Nyman , Juha Niiranen , Jukka Corander

We compare different selection criteria to choose the number of latent states of a multivariate latent Markov model for longitudinal data. This model is based on an underlying Markov chain to represent the evolution of a latent…

Methodology · Statistics 2012-12-04 Silvia Bacci , Silvia Pandolfi , Fulvia Pennoni

Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…

Artificial Intelligence · Computer Science 2012-06-26 Vibhav Gogate , Bozhena Bidyuk , Rina Dechter

Maximum Likelihood Estimation (MLE) and Likelihood Ratio Test (LRT) are widely used methods for estimating the transition probability matrix in Markov chains and identifying significant relationships between transitions, such as equality.…

Methodology · Statistics 2024-06-04 Yining Zhou , Ming Gao , Yiting Chen , Xiaoping Shi

In this work, we study a natural nonparametric estimator of the transition probability matrices of a finite controlled Markov chain. We consider an offline setting with a fixed dataset, collected using a so-called logging policy. We develop…

Machine Learning · Statistics 2026-03-17 Imon Banerjee , Harsha Honnappa , Vinayak Rao

In this paper, a class of piecewise deterministic Markov processes with underlying fast dynamic is studied. Using a "penalty method" , an averaging result is obtained when the underlying dynamic is infinitely accelerated. The features of…

Probability · Mathematics 2016-08-31 Alexandre Genadot

In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed. Exponential…

Probability · Mathematics 2021-06-16 Li-Xin Zhang

Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned…

Machine Learning · Statistics 2025-07-28 Erik Jahn , Frederick Eberhardt , Leonard J. Schulman

In this study, we consider unsupervised clustering of categorical vectors that can be of different size using mixture. We use likelihood maximization to estimate the parameters of the underlying mixture model and a penalization technique to…

Statistics Theory · Mathematics 2017-09-08 Esther Derman , Erwan Le Pennec

Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum…

Methodology · Statistics 2016-01-06 Jiahe Lin , Sumanta Basu , Moulinath Banerjee , George Michailidis

Estimation in exploratory factor analysis often yields estimates on the boundary of the parameter space. Such occurrences, known as Heywood cases, are characterised by non-positive variance estimates and can cause issues in numerical…

Methodology · Statistics 2026-02-25 Philipp Sterzinger , Ioannis Kosmids , Irini Moustaki

We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the…

Statistics Theory · Mathematics 2007-06-13 A. B. Tsybakov , S. A. van de Geer