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We develop a stochastic algorithm for independent component analysis that incorporates multi-trial supervision, which is available in many scientific contexts. The method blends a proximal gradient-type algorithm in the space of invertible…
Neural processes are a family of probabilistic models that inherit the flexibility of neural networks to parameterize stochastic processes. Despite providing well-calibrated predictions, especially in regression problems, and quick…
Consider $K$ processes, each generating a sequence of identical and independent random variables. The probability measures of these processes have random parameters that must be estimated. Specifically, they share a parameter $\theta$…
We consider (stochastic) convex-concave saddle point (SP) problems with high-dimensional decision variables, arising in various applications including machine learning problems. To contend with the challenges in computing full gradients, we…
A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…
This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process (PP's) models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon…
The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general…
At the scale of the individual cell, protein production is a stochastic process with multiple time scales, combining quick and slow random steps with discontinuous and smooth variation. Hybrid stochastic processes, in particular…
This work deals with systems of interacting reinforced stochastic processes, where each process $X^j=(X_{n,j})_n$ is located at a vertex $j$ of a finite weighted direct graph, and it can be interpreted as the sequence of "actions" adopted…
In risk management it is desirable to grasp the essential statistical features of a time series representing a risk factor. This tutorial aims to introduce a number of different stochastic processes that can help in grasping the essential…
This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
A multivariate fractional Poisson process was recently defined in Beghin and Macci (2016) by considering a common independent random time change for a finite dimensional vector of independent (non-fractional) Poisson processes; moreover it…
We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
A random walk with counterbalanced steps is a process of partial sums $\check S(n)=\check X_1+ \cdots + \check X_n$ whose steps $\check X_n$ are given recursively as follows. For each $n\geq 2$, with a fixed probability $p$, $\check X_n$ is…
This article presents a short and concise description of stochastic approximation algorithms in reinforcement learning of Markov decision processes. The algorithms can also be used as a suboptimal method for partially observed Markov…
Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with…
Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson…