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Regularized regression models are well studied and, under appropriate conditions, offer fast and statistically interpretable results. However, large data in many applications are heterogeneous in the sense of harboring distributional…

The advancement of deep learning has led to the emergence of Mixture-of-Experts (MoEs) models, known for their dynamic allocation of computational resources based on input. Despite their promise, MoEs face challenges, particularly in terms…

The missing data issue often complicates the task of estimating generalized linear models (GLMs). We describe why the pseudo-marginal Metropolis-Hastings algorithm, used in this setting, is an effective strategy for parameter estimation.…

Count data play a critical role in medical research, such as heart disease. The Poisson regression model is a common technique for evaluating the impact of a set of covariates on the count responses. The mixture of Poisson regression models…

This paper presents a high-level description of the R software package mixdistreg to fit mixture of experts distributional regression models. The proposed framework is implemented in R using the deepregression software template, which is…

We consider the fitting of heavy tailed data and distribution with a special attention to distributions with a non--standard shape in the "body" of the distribution. To this end we consider a dense class of heavy tailed distributions…

Many relevant statistical and econometric models for the analysis of longitudinal data include a latent process to account for the unobserved heterogeneity between subjects in a dynamic fashion. Such a process may be continuous (typically…

For Mixture-of-Experts (MoE) models, an unbalanced expert load will lead to routing collapse or increased computational overhead. Existing methods commonly employ an auxiliary loss to encourage load balance, but a large auxiliary loss will…

Data sets obtained from linking multiple files are frequently affected by mismatch error, as a result of non-unique or noisy identifiers used during record linkage. Accounting for such mismatch error in downstream analysis performed on the…

While machine learning has emerged in recent years as a useful tool for rapid prediction of materials properties, generating sufficient data to reliably train models without overfitting is still impractical for many applications. Towards…

Mixture-of-experts (MoE) models are a powerful paradigm for modeling of data arising from complex data generating processes (DGPs). In this article, we demonstrate how different MoE models can be constructed to approximate the underlying…

Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…

Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust linear regression. Combining the likelihood of a multivariate robust linear regression model with a standard improper prior distribution yields an…

Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…

Data-driven weather models have recently achieved state-of-the-art performance, yet progress has plateaued in recent years. This paper introduces a Mixture of Experts (MoWE) approach as a novel paradigm to overcome these limitations, not by…

Discriminative latent-variable models are typically learned using EM or gradient-based optimization, which suffer from local optima. In this paper, we develop a new computationally efficient and provably consistent estimator for a mixture…

Insurance companies often operate across multiple interrelated lines of business (LOBs), and accounting for dependencies between them is essential for accurate reserve estimation and risk capital determination. In our previous work on the…

Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients,…

Mixture model-based clustering, usually applied to multidimensional data, has become a popular approach in many data analysis problems, both for its good statistical properties and for the simplicity of implementation of the…

Large datasets make it possible to build predictive models that can capture heterogenous relationships between the response variable and features. The mixture of high-dimensional linear experts model posits that observations come from a…