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In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…

Nonparametric estimation for semilinear SPDEs, namely stochastic reaction-diffusion equations in one space dimension, is studied. We consider observations of the solution field on a discrete grid in time and space with infill asymptotics in…

Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length,…

Despite the abundance of methods for variable selection and accommodating spatial structure in regression models, there is little precedent for incorporating spatial dependence in covariate inclusion probabilities for regionally varying…

We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space…

Observed associations in a database may be due in whole or part to variations in unrecorded (latent) variables. Identifying such variables and their causal relationships with one another is a principal goal in many scientific and practical…

Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms. We consider the use of lattice-based convolutional neural network layers as a tool for the analysis of features arising from…

We introduce a restricted latent class exploratory model for longitudinal data with ordinal attributes and respondent-specific covariates. Responses follow a time inhomogeneous hidden Markov model where the probability of a respondent's…

This study presents a semi-nonparametric Latent Class Choice Model (LCCM) with a flexible class membership component. The proposed model formulates the latent classes using mixture models as an alternative approach to the traditional random…

We study time uncertainty-aware modeling of continuous-time dynamics of interacting objects. We introduce a new model that decomposes independent dynamics of single objects accurately from their interactions. By employing latent Gaussian…

Various processes can be modelled as quasi-reaction systems of stochastic differential equations, such as cell differentiation and disease spreading. Since the underlying data of particle interactions, such as reactions between proteins or…

The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…

A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…

We consider structural equation modeling (SEM) with latent variables for diffusion processes based on high-frequency data. We derive the quasi-likelihood estimators for parameters in the SEM. The goodness-of-fit test based on the…

Personality traits are latent variables, and as such, are impossible to measure without the use of an assessment. Responses on the assessments can be influenced by both transient (state-related) error and measurement error, obscuring the…

Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle…

Latent variable models are used to estimate variables of interest quantities which are observable only up to some measurement error. In many studies, such variables are known but not precisely quantifiable (such as "job satisfaction" in…

Discovering latent representations of the observed world has become increasingly more relevant in data analysis. Much of the effort concentrates on building latent variables which can be used in prediction problems, such as classification…

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…

Discrete latent space models have recently achieved performance on par with their continuous counterparts in deep variational inference. While they still face various implementation challenges, these models offer the opportunity for a…