arXiv subjects

Ismaïla Ba

Publications and source records attributed to Ismaïla Ba.

4 recordsLinked to original sources

arXiv2024

A Bayesian factor analysis model for high-dimensional microbiome count data

Dimension reduction techniques are among the most essential analytical tools in the analysis of high-dimensional data. Generalized principal component analysis (PCA) is an extension to standard PCA that has been widely used to identify low-dimensional features in high-dimensional discrete data, such as binary, multi-category and count data. For microbiome count data in particular, the multinomial PCA is a natural counterpart of the standard PCA. However, this technique fails to account for the excessive number of zero values, which is frequently observed in microbiome count data. To allow for sparsity, zero-inflated multivariate distributions can be used. We propose a zero-inflated probabilistic PCA model for latent factor analysis. The proposed model is a fully Bayesian factor analysis technique that is appropriate for microbiome count data analysis. In addition, we use the mean-field-type variational family to approximate the marginal likelihood and develop a classification variational approximation algorithm to fit the model. We demonstrate the efficiency of our procedure for predictions based on the latent factors and the model parameters through simulation experiments, showcasing its superiority over competing methods. This efficiency is further illustrated with two real microbiome count datasets. The method is implemented in R.

stat.ME↗

arXiv2023

Regularization techniques for inhomogeneous (spatial) point processes intensity and conditional intensity estimation

Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on inhomogeneous parametric forms of these functions assumed to depend on a certain number of spatial covariates. When this number of covariates is large, we are faced with a high-dimensional problem. This paper provides an overview of these questions and existing solutions based on regularizations.

math.ST↗

arXiv2023

Pairwise interaction function estimation of Gibbs point processes using basis expansion

The class of Gibbs point processes (GPP) is a large class of spatial point processes able to model both clustered and repulsive point patterns. They are specified by their conditional intensity, which for a point pattern $\mathbf{x}$ and a location $u$, is roughly speaking the probability that an event occurs in an infinitesimal ball around $u$ given the rest of the configuration is $\mathbf{x}$. The most simple and natural class of models is the class of pairwise interaction point processes where the conditional intensity depends on the number of points and pairwise distances between them. This paper is concerned with the problem of estimating the pairwise interaction function non parametrically. We propose to estimate it using an orthogonal series expansion of its logarithm. Such an approach has numerous advantages compared to existing ones. The estimation procedure is simple, fast and completely data-driven. We provide asymptotic properties such as consistency and asymptotic normality and show the efficiency of the procedure through simulation experiments and illustrate it with several datasets.

math.ST↗

arXiv2021

Inference for possibly high-dimensional inhomogeneous Gibbs point processes

Gibbs point processes (GPPs) constitute a large and flexible class of spatial point processes with explicit dependence between the points. They can model attractive as well as repulsive point patterns. Feature selection procedures are an important topic in high-dimensional statistical modeling. In this paper, composite likelihood approach regularized with convex and non-convex penalty functions is proposed to handle statistical inference for possibly high-dimensional inhomogeneous GPPs. The composite likelihood incorporates both the pseudo-likelihood and the logistic composite likelihood. We particularly investigate the setting where the number of covariates diverges as the domain of observation increases. Under some conditions provided on the spatial GPP and on the penalty functions, we show that the oracle property, the consistency and the asymptotic normality hold. Our results also cover the low-dimensional case which fills a large gap in the literature. Through simulation experiments, we validate our theoretical results and finally, an application to a tropical forestry dataset illustrates the use of the proposed approach.

math.ST↗