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Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is…

Robust and efficient optimization methods for variance component estimation using Restricted Maximum Likelihood (REML) models for genetic mapping of quantitative traits are considered. We show that the standard Newton-AI scheme may fail…

We present an efficient algorithm for maximum likelihood estimation (MLE) of exponential family models, with a general parametrization of the energy function that includes neural networks. We exploit the primal-dual view of the MLE with a…

Community detection is one of the most important problems in network analysis. Among many algorithms proposed for this task, methods based on statistical inference are of particular interest: they are mathematically sound and were shown to…

Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood…

We study the problem of efficiently recovering the matching between an unlabelled collection of $n$ points in $\mathbb{R}^d$ and a small random perturbation of those points. We consider a model where the initial points are i.i.d. standard…

We present an efficient and flexible method for computing likelihoods of phenotypic traits on a phylogeny. The method does not resort to Monte-Carlo computation but instead blends Felsenstein's discrete character pruning algorithm with…

In this paper, we consider distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic…

We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume…

Randomized neural networks (NNs) are an interesting alternative to conventional NNs that are more used for data modeling. The random vector functional-link (RVFL) network is an established and theoretically well-grounded randomized learning…

We study the problem of learning multi-index models in high-dimensions using a two-layer neural network trained with the mean-field Langevin algorithm. Under mild distributional assumptions on the data, we characterize the effective…

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…

Tree-based priors for probability distributions are usually specified using a predetermined, data-independent collection of candidate recursive partitions of the sample space. To characterize an unknown target density in detail over the…

The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of…

Likelihood-free inference provides a rigorous approach to preform Bayesian analysis using forward simulations only. The main advantage of likelihood-free methods is its ability to account for complex physical processes and observational…

In-context learning (ICL) and supervised fine-tuning (SFT) are two common strategies for improving the performance of modern large language models (LLMs) on specific tasks. Despite their different natures, these strategies often lead to…

The inference of astrophysical and cosmological properties from the Lyman-$\alpha$ forest conventionally relies on summary statistics of the transmission field that carry useful but limited information. We present a deep learning framework…

Complex networked systems driven by latent inputs are common in fields like neuroscience, finance, and engineering. A key inference problem here is to learn edge connectivity from node outputs (potentials). We focus on systems governed by…

We introduce a simple modification to the standard maximum likelihood estimation (MLE) framework. Rather than maximizing a single unconditional likelihood of the data under the model, we maximize a family of \textit{noise conditional}…

The seminal work of Chow and Liu (1968) shows that approximation of a finite probabilistic system by Markov trees can achieve the minimum information loss with the topology of a maximum spanning tree. Our current paper generalizes the…