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Factorizing low-rank matrices is a problem with many applications in machine learning and statistics, ranging from sparse PCA to community detection and sub-matrix localization. For probabilistic models in the Bayes optimal setting, general…

Risk averse decision making under uncertainty in partially observable domains is a fundamental problem in AI and essential for reliable autonomous agents. In our case, the problem is modeled using partially observable Markov decision…

We propose a novel approach to select the best model of the data. Based on the exclusive properties of the nested models, we find the most parsimonious model containing the risk minimizer predictor. We prove the existence of probable…

We propose sequential Monte Carlo based algorithms for maximum likelihood estimation of the static parameters in hidden Markov models with an intractable likelihood using ideas from approximate Bayesian computation. The static parameter…

We consider parametric Markov decision processes (pMDPs) that are augmented with unknown probability distributions over parameter values. The problem is to compute the probability to satisfy a temporal logic specification with any concrete…

Sampling-based model predictive control (MPC) algorithms, such as model predictive path integral (MPPI), enable approximate, gradient-free solutions to optimal control problems by drawing samples from a proposal distribution, evaluating…

Safety in stochastic control systems, which are subject to random noise with a known probability distribution, aims to compute policies that satisfy predefined operational constraints with high confidence throughout the uncertain evolution…

In machine learning, the selection of a promising model from a potentially large number of competing models and the assessment of its generalization performance are critical tasks that need careful consideration. Typically, model selection…

Predictive posterior densities (PPDs) are of interest in approximate Bayesian inference. Typically, these are estimated by simple Monte Carlo (MC) averages using samples from the approximate posterior. We observe that the signal-to-noise…

When prospectively developing a new clinical prediction model (CPM), fixed sample size calculations are typically conducted before data collection based on sensible assumptions. But if the assumptions are inaccurate the actual sample size…

We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…

This paper proposes a novel sparse principal component analysis algorithm with self-learning ability for successive modes, where synaptic intelligence is employed to measure the importance of variables and a regularization term is added to…

The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…

Precision and Recall are fundamental metrics in machine learning tasks where both accurate predictions and comprehensive coverage are essential, such as in multi-label learning, language generation, medical studies, and recommender systems.…

We study Concave Constrained Markov Decision Processes (Concave CMDPs) where both the objective and constraints are defined as concave functions of the state-action occupancy measure. We propose the Variance-Reduced Primal-Dual Policy…

This paper deals with the estimation of the modes of an univariate mixture when the number of components is known and when the component density are well separated. We propose an algorithm based on the minimization of the "kp" criterion we…

Observing a stationary time series, we propose a two-step procedure for the prediction of the next value of the time series. The first step follows machine learning theory paradigm and consists in determining a set of possible predictors as…

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…

Many segmentation tasks, such as medical image segmentation or future state prediction, are inherently ambiguous, meaning that multiple predictions are equally correct. Current methods typically rely on generative models to capture this…

We consider a class of restless bandit problems that finds a broad application area in reinforcement learning and stochastic optimization. We consider $N$ independent discrete-time Markov processes, each of which had two possible states: 1…