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Inference of the marginal probability distribution is defined as the calculation of the probability of a subset of the variables and is relevant for handling missing data and hidden variables. While inference of the marginal probability…

We provide a novel statistical perspective on a classical problem at the intersection of computer science and information theory: recovering the empirical frequency of a symbol in a large discrete dataset using only a compressed…

Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse…

Probabilistic survival analysis models seek to estimate the distribution of the future occurrence (time) of an event given a set of covariates. In recent years, these models have preferred nonparametric specifications that avoid directly…

We present a method for incorporating missing data in non-parametric statistical learning without the need for imputation. We focus on a tree-based method, Bayesian Additive Regression Trees (BART), enhanced with "Missingness Incorporated…

Multiple imputation (MI) has become popular for analyses with missing data in medical research. The standard implementation of MI is based on the assumption of data being missing at random (MAR). However, for missing data generated by…

Safety is a central requirement for automated vehicles. As such, the assessment of risk in automated driving is key in supporting both motion planning technologies and safety evaluation. In automated driving, risk is characterized by two…

This paper describes a method for a model-based analysis of clinical safety data called multivariate Bayesian logistic regression (MBLR). Parallel logistic regression models are fit to a set of medically related issues, or response…

Because anomalous samples cannot be used for training, many anomaly detection and localization methods use pre-trained networks and non-parametric modeling to estimate encoded feature distribution. However, these methods neglect the impact…

Objectives: Prior event rate ratio (PERR) is a method shown to perform well in mitigating confounding in real-world evidence research but it depends on several model assumptions. We propose an analytic strategy to correct biases arising…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

We present a sparse representation of model uncertainty for Deep Neural Networks (DNNs) where the parameter posterior is approximated with an inverse formulation of the Multivariate Normal Distribution (MND), also known as the information…

A probabilistic query may not be estimable from observed data corrupted by missing values if the data are not missing at random (MAR). It is therefore of theoretical interest and practical importance to determine in principle whether a…

This paper establishes a series of sensitivity analyses to investigate the impact of missing values in the electronic health records (EHR) that are possibly missing not at random (MNAR). EHRs have gained tremendous interest due to their…

Gradient descent is one of the most widely used iterative algorithms in modern statistical learning. However, its precise algorithmic dynamics in high-dimensional settings remain only partially understood, which has limited its broader…

We study the effects of missingness on the estimation of population parameters. Moving beyond restrictive missing completely at random (MCAR) assumptions, we first formulate a missing data analogue of Huber's arbitrary…

We present a new method of training energy-based models (EBMs) for anomaly detection that leverages low-dimensional structures within data. The proposed algorithm, Manifold Projection-Diffusion Recovery (MPDR), first perturbs a data point…

A significant limitation of one-class classification anomaly detection methods is their reliance on the assumption that unlabeled training data only contains normal instances. To overcome this impractical assumption, we propose two novel…

We propose a new method to define anomaly scores and apply this to particle physics collider events. Anomalies can be either rare, meaning that these events are a minority in the normal dataset, or different, meaning they have values that…

Safety is a critical aspect of the air transport system given even slight operational anomalies can result in serious consequences. To reduce the chances of aviation safety occurrences, accidents and incidents are reported to establish the…