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The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where…
The recognition network in deep latent variable models such as variational autoencoders (VAEs) relies on amortized inference for efficient posterior approximation that can scale up to large datasets. However, this technique has also been…
We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…
Variational inference (VI) is a widely used framework in Bayesian estimation. For most of the non-Gaussian statistical models, it is infeasible to find an analytically tractable solution to estimate the posterior distributions of the…
Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…
We present the Mixed Likelihood Gaussian process latent variable model (GP-LVM), capable of modeling data with attributes of different types. The standard formulation of GP-LVM assumes that each observation is drawn from a Gaussian…
The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural…
A novel information-theoretic approach is proposed to assess the global practical identifiability of Bayesian statistical models. Based on the concept of conditional mutual information, an estimate of information gained for each model…
Missing data is an universal problem in statistics. We develop a unified framework for estimating parameters defined by general estimating equations under a missing-at-random (MAR) mechanism, based on generalized entropy calibration…
There has been a growing excitement that implicit graph generative models could be used to design or discover new molecules for medicine or material design. Because these molecules have not been discovered, they naturally lie in unexplored…
While Variational Inference (VI) is central to modern generative models like Variational Autoencoders (VAEs) and Denoising Diffusion Models (DDMs), its pedagogical treatment is split across disciplines. In statistics, VI is typically framed…
We propose a framework for the statistical evaluation of variational auto-encoders (VAEs) and test two instances of this framework in the context of modelling images of handwritten digits and a corpus of English text. Our take on evaluation…
In recent times, a considerable number of research studies have been carried out to address the issue of Missing Value Imputation (MVI). MVI aims to provide a primary solution for datasets that have one or more missing attribute values. The…
Machine learning applications require fast and reliable per-sample uncertainty estimation. A common approach is to use predictive distributions from Bayesian or approximation methods and additively decompose uncertainty into aleatoric…
We consider the task of estimating variational autoencoders (VAEs) when the training data is incomplete. We show that missing data increases the complexity of the model's posterior distribution over the latent variables compared to the…
When a statistical model $\{P_{\theta} : \theta \in \Theta\}$ lacks analytically tractable likelihoods, parametric statistical inference based on data generated from an unknown underlying distribution $P$ can still be performed as long as…
Ensuring model calibration is critical for reliable prediction, yet popular distribution-free methods such as histogram binning and isotonic regression offer only asymptotic guarantees. We introduce a unified framework for Venn and…
Variational inference is a popular method for estimating model parameters and conditional distributions in hierarchical and mixed models, which arise frequently in many settings in the health, social, and biological sciences. Variational…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
Gaussian graphical models have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a semiparametric generalization for…