Related papers: Scalable expectation propagation for generalized l…

The power-expected-posterior (PEP) prior is an objective prior for Gaussian linear models, which leads to consistent model selection inference, under the M-closed scenario, and tends to favor parsimonious models. Recently, two new forms of…

Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…

Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of…

The expressive power of a Gaussian process (GP) model comes at a cost of poor scalability in the data size. To improve its scalability, this paper presents a low-rank-cum-Markov approximation (LMA) of the GP model that is novel in…

Statistical significance testing of neural coherence is essential for distinguishing genuine cross-signal coupling from spurious correlations. A widely accepted approach uses surrogate-based inference, where null distributions are generated…

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…

Ensembling is now recognized as an effective approach for increasing the predictive performance and calibration of deep networks. We introduce a new approach, Parameter Ensembling by Perturbation (PEP), that constructs an ensemble of…

Learning general latent-variable probabilistic graphical models is a key theoretical challenge in machine learning and artificial intelligence. All previous methods, including the EM algorithm and the spectral algorithms, face severe…

The generalized linear model (GLM) plays a key role in regression analyses. In high-dimensional data, the sparse GLM has been used but it is not robust against outliers. Recently, the robust methods have been proposed for the specific…

In this paper we introduce a novel Bayesian data augmentation approach for estimating the parameters of the generalised logistic regression model. We propose a P\'olya-Gamma sampler algorithm that allows us to sample from the exact…

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

Growth mixture models (GMMs) incorporate both conventional random effects growth modeling and latent trajectory classes as in finite mixture modeling; therefore, they offer a way to handle the unobserved heterogeneity between subjects in…

The analytic characterization of the high-dimensional behavior of optimization for Generalized Linear Models (GLMs) with Gaussian data has been a central focus in statistics and probability in recent years. While convex cases, such as the…

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models…

In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…

Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…

Probit models are useful for modeling correlated discrete responses in many disciplines, including consumer choice data in economics and marketing. However, the Gaussian latent variable feature of probit models coupled with identification…

Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly…

The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…

This is Part II of a two-part work on the estimation for a multi-layer generalized linear model (ML-GLM) in large system limits. In Part I, we had analyzed the asymptotic performance of an exact MMSE estimator, and obtained a set of coupled…