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In this paper, we study inference for chains of variable order under two distinct contamination regimes. Consider we have a chain of variable memory on a finite alphabet containing zero. At each instant of time an independent coin is…
Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…
We prove a complete class theorem that characterizes \emph{all} stationary time reversible Markov processes whose finite dimensional marginal distributions (of all orders) are infinitely divisible. Aside from two degenerate cases (iid and…
We study the problem of evaluating the excess risk of large-scale empirical risk minimization under the square loss. Leveraging the idea of wild refitting and resampling, we assume only black-box access to the training algorithm and develop…
Large Language Models (LLMs) have achieved significant performance gains through test-time scaling methods. However, existing approaches often incur redundant computations due to the accumulation of historical dependency information during…
In this paper, we build a model for biological neural nets where the activity of the network is described by Hawkes processes having a variable length memory. The particularity of this paper is to deal with an infinite number of components.…
In this paper we prove that the asymptotic rate of exponential loss of memory of a finite state hidden Markov model is bounded above by the difference of the first two Lyapunov exponents of a certain product of matrices. We also show that…
Continual learning, the setting where a learning agent is faced with a never ending stream of data, continues to be a great challenge for modern machine learning systems. In particular the online or "single-pass through the data" setting…
We present a new perfect simulation algorithm for stationary chains having unbounded variable length memory. This is the class of infnite memory chains for which the family of transition probabilities is represented by a probabilistic…
We discuss the properties of the dynamics of purely memristive circuits using a recently derived consistent equation for the internal memory variables of the involved memristors. In particular, we show that the number of independent memory…
Recent sequential pattern mining methods have used the minimum description length (MDL) principle to define an encoding scheme which describes an algorithm for mining the most compressing patterns in a database. We present a novel…
We consider the task of estimating a structural model of dynamic decisions by a human agent based upon the observable history of implemented actions and visited states. This problem has an inherent nested structure: in the inner problem, an…
We investigate the parameter recovery of Markov-switching ordinary differential processes from discrete observations, where the differential equations are nonlinear additive models. This framework has been widely applied in biological…
The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…
In this paper, we study a mean-variance optimization problem in an infinite horizon discrete time discounted Markov decision process (MDP). The objective is to minimize the variance of system rewards with the constraint of mean performance.…
Recently, several works have shown that natural modifications of the classical conditional gradient method (aka Frank-Wolfe algorithm) for constrained convex optimization, provably converge with a linear rate when: i) the feasible set is a…
This paper delves into a comprehensive analysis of fault-tolerant memory systems, focusing on recovery techniques modeled using Markov chains to address transient errors. The study revolves around the application of scrubbing methods in…
We propose a class of interleavers for a novel deep neural network (DNN) architecture that uses algorithmically pre-determined, structured sparsity to significantly lower memory and computational requirements, and speed up training. The…
The formal verification of large probabilistic models is important and challenging. Exploiting the concurrency that is often present is one way to address this problem. Here we study a restricted class of asynchronous distributed…
We propose polynomial-time algorithms to minimise labelled Markov chains whose transition probabilities are not known exactly, have been perturbed, or can only be obtained by sampling. Our algorithms are based on a new notion of an…