arXiv subjects

Yves Atchadé

Publications and source records attributed to Yves Atchadé.

10 recordsLinked to original sources

arXiv2026

Predicting Dry Spells of the West African Monsoon Season Using Machine Learning Methods

Characteristics of the West African Monsoon (WAM) season, such as its onset and dry spell occurrences, are notoriously difficult to predict. However, these characteristics are key indicators farmers use to decide when to plant crops, having a major influence on their overall yield. While many studies have shown correlations between global sea surface temperatures and characteristics of the WAM season, there are few that effectively implement this information into machine learning (ML) prediction models. This study is focused on predicting dry spells, that is, if there will be a period of consecutive days without rain after the onset of the WAM. We first investigated the best ways to define onset and dry spells and gathered sea surface temperature training data from both real-world observations and a climate simulation model. Then we constructed an adaptive-threshold logistic regression model for dry spell prediction, to which we applied a custom feature selection method and spatial regularization. Using Leave-One-Out cross validation testing, we found significant results in multiple binary classification metrics. These models overcome some limitations that current approaches have, such as being computationally intensive and needing bias correction. We also aim for this study to serve as a framework for ML use in the context of targeted prediction of certain weather phenomena using climatologically relevant variables.

stat.AP↗

arXiv2024

Laplace approximation for Bayesian variable selection via Le Cam's one-step procedure

Variable selection in high-dimensional spaces is a pervasive challenge in contemporary scientific exploration and decision-making. However, existing approaches that are known to enjoy strong statistical guarantees often struggle to cope with the computational demands arising from the high dimensionality. To address this issue, we propose a novel Laplace approximation method based on Le Cam's one-step procedure (\textsf{OLAP}), designed to effectively tackles the computational burden. Under some classical high-dimensional assumptions we show that \textsf{OLAP} is a statistically consistent variable selection procedure. Furthermore, we show that the approach produces a posterior distribution that can be explored in polynomial time using a simple Gibbs sampling algorithm. Toward that polynomial complexity result, we also made some general, noteworthy contributions to the mixing time analysis of Markov chains. We illustrate the method using logistic and Poisson regression models applied to simulated and real data examples.

stat.ME↗

arXiv2023

Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood Estimation for Latent Gaussian Models

Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models is the expectation-maximization (EM) algorithm. For problems with high-dimensional latent variables and large datasets, EM scales poorly because it needs to invert as many large covariance matrices as the number of data points. We introduce probabilistic unrolling, a method that combines Monte Carlo sampling with iterative linear solvers to circumvent matrix inversion. Our theoretical analyses reveal that unrolling and backpropagation through the iterations of the solver can accelerate gradient estimation for maximum likelihood estimation. In experiments on simulated and real data, we demonstrate that probabilistic unrolling learns latent Gaussian models up to an order of magnitude faster than gradient EM, with minimal losses in model performance.

cs.LG↗

arXiv2021

A fast asynchronous MCMC sampler for sparse Bayesian inference

We propose a very fast approximate Markov Chain Monte Carlo (MCMC) sampling framework that is applicable to a large class of sparse Bayesian inference problems, where the computational cost per iteration in several models is of order $O(ns)$, where $n$ is the sample size, and $s$ the underlying sparsity of the model. This cost can be further reduced by data sub-sampling when stochastic gradient Langevin dynamics are employed. The algorithm is an extension of the asynchronous Gibbs sampler of Johnson et al. (2013), but can be viewed from a statistical perspective as a form of Bayesian iterated sure independent screening (Fan et al. (2009)). We show that in high-dimensional linear regression problems, the Markov chain generated by the proposed algorithm admits an invariant distribution that recovers correctly the main signal with high probability under some statistical assumptions. Furthermore we show that its mixing time is at most linear in the number of regressors. We illustrate the algorithm with several models.

stat.CO↗

arXiv2019

Bayesian variable selection in linear regression models with instrumental variables

Many papers on high-dimensional statistics have proposed methods for variable selection and inference in linear regression models by relying explicitly or implicitly on the assumption that all regressors are exogenous. However, applications abound where endogeneity arises from selection biases, omitted variables, measurement errors, unmeasured confounding and many other challenges common to data collection Fan et al. (2014). The most common cure to endogeneity issues consists in resorting to instrumental variable (IV) inference. The objective of this paper is to present a Bayesian approach to tackling endogeneity in high-dimensional linear IV models. Using a working quasi-likelihood combined with an appropriate sparsity inducing spike-and-slab prior distribution, we develop a semi-parametric method for variable selection in high-dimensional linear models with endogeneous regressors within a quasi-Bayesian framework. We derive some conditions under which the quasi-posterior distribution is well defined and puts most of its probability mass around the true value of the parameter as $p \rightarrow \infty$. We demonstrate through empirical work the fine performance of the proposed approach relative to some other alternatives. We also include include an empirical application that assesses the return on education by revisiting the work of Angrist and Keueger (1991).

stat.ME↗

arXiv2018

Likelihood Inference for Large Scale Stochastic Blockmodels with Covariates based on a Divide-and-Conquer Parallelizable Algorithm with Communication

We consider a stochastic blockmodel equipped with node covariate information, that is helpful in analyzing social network data. The key objective is to obtain maximum likelihood estimates of the model parameters. For this task, we devise a fast, scalable Monte Carlo EM type algorithm based on case-control approximation of the log-likelihood coupled with a subsampling approach. A key feature of the proposed algorithm is its parallelizability, by processing portions of the data on several cores, while leveraging communication of key statistics across the cores during each iteration of the algorithm. The performance of the algorithm is evaluated on synthetic data sets and compared with competing methods for blockmodel parameter estimation. We also illustrate the model on data from a Facebook derived social network enhanced with node covariate information.

stat.CO↗

arXiv2015

On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods

A large number of statistical models are "doubly-intractable": the likelihood normalising term, which is a function of the model parameters, is intractable, as well as the marginal likelihood (model evidence). This means that standard inference techniques to sample from the posterior, such as Markov chain Monte Carlo (MCMC), cannot be used. Examples include, but are not confined to, massive Gaussian Markov random fields, autologistic models and Exponential random graph models. A number of approximate schemes based on MCMC techniques, Approximate Bayesian computation (ABC) or analytic approximations to the posterior have been suggested, and these are reviewed here. Exact MCMC schemes, which can be applied to a subset of doubly-intractable distributions, have also been developed and are described in this paper. As yet, no general method exists which can be applied to all classes of models with doubly-intractable posteriors. In addition, taking inspiration from the Physics literature, we study an alternative method based on representing the intractable likelihood as an infinite series. Unbiased estimates of the likelihood can then be obtained by finite time stochastic truncation of the series via Russian Roulette sampling, although the estimates are not necessarily positive. Results from the Quantum Chromodynamics literature are exploited to allow the use of possibly negative estimates in a pseudo-marginal MCMC scheme such that expectations with respect to the posterior distribution are preserved. The methodology is reviewed on well-known examples such as the parameters in Ising models, the posterior for Fisher-Bingham distributions on the $d$-Sphere and a large-scale Gaussian Markov Random Field model describing the Ozone Column data. This leads to a critical assessment of the strengths and weaknesses of the methodology with pointers to ongoing research.

stat.ME↗

arXiv2014

On the Convergence Rates of Some Adaptive Markov Chain Monte Carlo Algorithms

This paper studies the mixing time of certain adaptive Markov Chain Monte Carlo algorithms. Under some regularity conditions, we show that the convergence rate of Importance Resampling MCMC (IRMCMC) algorithm, measured in terms of the total variation distance is $O(n^{-1})$, and by means of an example, we establish that in general, this algorithm does not converge at a faster rate. We also study the Equi-Energy sampler and establish that its mixing time is of order $O(n^{-1/2})$.

math.PR↗

arXiv2012

Iterated filtering

Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed Markov process models by solving a recursive sequence of filtering problems. We present new theoretical results pertaining to the convergence of iterated filtering algorithms implemented via sequential Monte Carlo filters. This theory complements the growing body of empirical evidence that iterated filtering algorithms provide an effective inference strategy for scientific models of nonlinear dynamic systems. The first step in our theory involves studying a new recursive approach for maximizing the likelihood function of a latent variable model, when this likelihood is evaluated via importance sampling. This leads to the consideration of an iterated importance sampling algorithm which serves as a simple special case of iterated filtering, and may have applicability in its own right.

math.ST↗

arXiv2009

Limit theorems for some adaptive MCMC algorithms with subgeometric kernels

This paper deals with the ergodicity and the existence of a strong law of large numbers for adaptive Markov Chain Monte Carlo. We show that a diminishing adaptation assumption together with a drift condition for positive recurrence is enough to imply ergodicity. Strengthening the drift condition to a polynomial drift condition yields a strong law of large numbers for possibly unbounded functions. These results broaden considerably the class of adaptive MCMC algorithms for which rigorous analysis is now possible. As an example, we give a detailed analysis of the Adaptive Metropolis Algorithm of Haario et al. (2001) when the target distribution is sub-exponential in the tails.

math.PR↗