Publications

We consider the problem of estimating probability density functions based on sample data, using a finite mixture of densities from some …

Large classes of problems can be formulated as inverse problems, where the goal is to find parameter values that best explain some …

State-of-the-art medical multi-modal large language models (med-MLLM), like LLaVA-Med or BioMedGPT, leverage instruction-following data …

Increasing the throughput of the Transformer architecture, a foundational component used in numerous state-of-the-art models for vision …

We extend Bayesian Synthetic Likelihood (BSL) methods to non-Gaussian approximations of the likelihood function. In this setting, we …

A molecule’s 2D representation consists of its atoms, their attributes, and the molecule’s covalent bonds. A 3D (geometric) …

Empirical risk minimization (ERM) is a foundational framework for the estimation of statistical and machine learning models. …

Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in …

Originally introduced as a neural network for ensemble learning, mixture of experts (MoE) has recently become a fundamental building …

Sparse mixture of experts (SMoE) offers an appealing solution to scale up the model complexity beyond the mean of increasing the …

Understanding the parameter estimation of softmax gating Gaussian mixture of experts has remained a long-standing open problem in the …

By routing input tokens to only a few split experts, Sparse Mixture-of-Experts has enabled efficient training of large language models. …

We study the large sample behaviors of approximate Bayesian computation (ABC) posterior measures in situations when the data generating …

We are motivated by the problem of identifying potentially nonlinear regression relationships between high-dimensional outputs and …

A key ingredient in approximate Bayesian computation (ABC) procedures is the choice of a discrepancy that describes how different the …

Mixture of experts (MoE) are a popular class of statistical and machine learning models that have gained attention over the years due …

This study is devoted to the problem of model selection among a collection of Gaussian-gated localized mixtures of experts models …

A key ingredient in approximate Bayesian computation (ABC) procedures is the choice of a discrepancy that describes how different the …

The class of location-scale finite mixtures is of enduring interest both from applied and theoretical perspectives of probability and …

Mixtures of experts (MoE) models are a ubiquitous tool for the analysis of heterogeneous data across many fields including statistics, …

Mixture of experts (MoE) models are widely applied for conditional probability density estimation problems. We demonstrate the richness …

Model selection via penalized likelihood type criteria is a standard task in many statistical inference and machine learning problems. It has led to deriving criteria with asymptotic consistency results and an increasing emphasis on introducing non-asymptotic criteria. We focus on the problem of modeling non-linear relationships in regression data with potential hidden graph-structured interactions between the high-dimensional predictors, within the mixture of experts modeling framework. In order to deal with such a complex situation, we investigate a block-diagonal localized mixture of polynomial experts (BLoMPE) regression model, which is constructed upon an inverse regression and block-diagonal structures of the Gaussian expert covariance matrices. We introduce a penalized maximum likelihood selection criterion to estimate the unknown conditional density of the regression model. This model selection criterion allows us to handle the challenging problem of inferring the number of mixture components, the degree of polynomial mean functions, and the hidden block-diagonal structures of the covariance matrices, which reduces the number of parameters to be estimated and leads to a trade-off between complexity and sparsity in the model. In particular, we provide a strong theoretical guarantee$:$ a finite-sample oracle inequality satisfied by the penalized maximum likelihood estimator with a Jensen-Kullback-Leibler type loss, to support the introduced non-asymptotic model selection criterion. The penalty shape of this criterion depends on the complexity of the considered random subcollection of BLoMPE models, including the relevant graph structures, the degree of polynomial mean functions, and the number of mixture components.

Mixture-of-experts (MoE) models are a popular framework for modeling heterogeneity in data, for both regression and classification problems in statistics and machine learning, due to their flexibility and the abundance of statistical estimation and model choice tools. Such flexibility comes from allowing the mixture weights (or gating functions) in the MoE model to depend on the explanatory variables, along with the experts (or component densities). This permits the modeling of data arising from more complex data generating processes, compared to the classical finite mixtures and finite mixtures of regression models, whose mixing parameters are independent of the covariates. The use of MoE models in a high-dimensional setting, when the number of explanatory variables can be much larger than the sample size (i.e., $p \gg n)$, is challenging from a computational point of view, and in particular from a theoretical point of view, where the literature is still lacking results in dealing with the curse of dimensionality, in both the statistical estimation and feature selection. We consider the finite mixture-of-experts model with soft-max gating functions and Gaussian experts for high-dimensional regression on heterogeneous data, and its $l_1$-regularized estimation via the Lasso. We focus on the Lasso estimation properties rather than its feature selection properties. We provide a lower bound on the regularization parameter of the Lasso function that ensures an $l_1$-oracle inequality satisfied by the Lasso estimator according to the Kullback-Leibler loss.

Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (PDF) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is often left unclear. We prove that finite mixture models constructed from pdfs in $C_0$ can be used to conduct approximation of various classes of approximands in a number of different modes. That is, we prove approximands in C0 can be uniformly approximated, approximands in $C_b$ can be uniformly approximated on compact sets, and approximands in Lp can be approximated with respect to the $L_p$, for $p\in [1,\infty)$. Furthermore, we also prove that measurable functions can be approximated, almost everywhere.