Related papers: A Spectral Framework for Closed-Form Relative Dens…
The generalized Kullback-Leibler divergence (K-Ld) in Tsallis statistics [constrained by the additive duality of generalized statistics (dual generalized K-Ld)] is here reconciled with the theory of Bregman divergences for expectations…
In this paper, we propose a theoretical analysis of the algorithm ISDE, introduced in previous work. From a dataset, ISDE learns a density written as a product of marginal density estimators over a partition of the features. We show that…
Recent Reinforcement Learning (RL) algorithms making use of Kullback-Leibler (KL) regularization as a core component have shown outstanding performance. Yet, only little is understood theoretically about why KL regularization helps, so far.…
The Kullback-Leibler (KL) divergence is a foundational measure for comparing probability distributions. Yet in multivariate settings, its single value often obscures the underlying reasons for divergence, conflating mismatches in individual…
Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…
Robustness to noise and outliers is a desirable trait in phase retrieval algorithms for many applications in imaging and signal processing. In this paper, we develop novel robust phase retrieval algorithms based on the minimization of…
It is a well-known issue that in Item Response Theory models there is no closed-form for the maximum likelihood estimators of the item parameters. Parameter estimation is therefore typically achieved by means of numerical methods like…
In this paper, a nonparametric maximum likelihood (ML) estimator for band-limited (BL) probability density functions (pdfs) is proposed. The BLML estimator is consistent and computationally efficient. To compute the BLML estimator, three…
We study a worst-case approach to measure the sensitivity to model misspecification in the performance analysis of stochastic systems. The situation of interest is when only minimal parametric information is available on the form of the…
In this paper we introduce a method for nonparametric density estimation on geometric networks. We define fused density estimators as solutions to a total variation regularized maximum-likelihood density estimation problem. We provide…
Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…
We derive a new variational formula for the R\'enyi family of divergences, $R_\alpha(Q\|P)$, between probability measures $Q$ and $P$. Our result generalizes the classical Donsker-Varadhan variational formula for the Kullback-Leibler…
Expectation maximization (EM) is the default algorithm for fitting probabilistic models with missing or latent variables, yet we lack a full understanding of its non-asymptotic convergence properties. Previous works show results along the…
This paper extends the empirical minimum divergence approach for models which satisfy linear constraints with respect to the probability measure of the underlying variable (moment constraints) to the case where such constraints pertain to…
Reconstructing gamma-ray spectra from detector measurements is an ill-posed inverse problem. Standard methods, such as Folding Iteration with Compton Subtraction (FICS), provide point estimates but lack calibrated uncertainties and may bias…
We study the adaptation properties of the multivariate log-concave maximum likelihood estimator over three subclasses of log-concave densities. The first consists of densities with polyhedral support whose logarithms are piecewise affine.…
Deploying Large Language Models (LLMs) on edge devices faces severe computational and memory constraints, limiting real-time processing and on-device intelligence. Hybrid architectures combining Structured State Space Models (SSMs) with…
In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong…
While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and challenging. We introduce an efficient, geometric approach for…
In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a stochastic boundary value problem from a prior probability…