Related papers: On the minimal penalty for Markov order estimation

The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…

In this work, we study the problem of learning partially observed linear dynamical systems from a single sample trajectory. A major practical challenge in the existing system identification methods is the undesirable dependency of their…

In many applications, data come with a natural ordering. This ordering can often induce local dependence among nearby variables. However, in complex data, the width of this dependence may vary, making simple assumptions such as a constant…

Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…

We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on $\ell_1$-regularized logistic regression, in which the neighborhood of any given node is estimated by…

Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…

We observe a length-$n$ sample generated by an unknown,stationary ergodic Markov process (\emph{model}) over a finite alphabet $\mathcal{A}$. Given any string $\bf{w}$ of symbols from $\mathcal{A}$ we want estimates of the conditional…

This paper discusses algorithms for solving Markov decision processes (MDPs) that have monotone optimal policies. We propose a two-stage alternating convex optimization scheme that can accelerate the search for an optimal policy by…

We establish adaptive results for trend filtering: least squares estimation with a penalty on the total variation of $(k-1)^{\rm th}$ order differences. Our approach is based on combining a general oracle inequality for the…

Let $\{(X_t)_{t\geq 0}, \mathbb{P}_{\delta_x}, x\in E\}$ be a supercritical branching Markov process (which is not necessary symmetric) on a locally compact metric measure space $(E,\mu)$ with spatially dependent local branching mechanism.…

Let $\{X(t):t\in\mathbb R_+\}$ be a stationary Gaussian process with almost surely (a.s.) continuous sample paths, $\mathbb E X(t) = 0$, $\mathbb E X^2(t) = 1$ and correlation function satisfying (i) $r(t) = 1 - C|t|^{\alpha} +…

We study the problem of learning Markov decision processes with finite state and action spaces when the transition probability distributions and loss functions are chosen adversarially and are allowed to change with time. We introduce an…

We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…

Parameter estimation in logistic regression is a well-studied problem with the Newton-Raphson method being one of the most prominent optimization techniques used in practice. A number of monotone optimization methods including…

The problem of finding the maximum likelihood estimates for the regression coefficients in generalised linear models with an L1 sparsity penalty is shown to be equivalent to minimising the unpenalised maximum log-likelihood function over a…

We propose a novel constrained reinforcement learning method for finding optimal policies in Markov Decision Processes while satisfying temporal logic constraints with a desired probability throughout the learning process. An…

The penalized profile sampler for semiparametric inference is an extension of the profile sampler method (Lee, Kosorok and Fine, 2005) obtained by profiling a penalized log-likelihood. The idea is to base inference on the posterior…

This paper extends some prominent statistical results including \emph{Fisher Theorem and Wilks phenomenon} to the penalized maximum likelihood estimation with a quadratic penalization. It appears that sharp expansions for the penalized MLE…

Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions. Optimizing the penalized likelihood function…

We consider the segmentation problem of univariate distributions from the exponential family with multiple parameters. In segmentation, the choice of the number of segments remains a difficult issue due to the discrete nature of the…