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Deep latent-variable models learn representations of high-dimensional data in an unsupervised manner. A number of recent efforts have focused on learning representations that disentangle statistically independent axes of variation by…

Discrete ordinal responses such as Likert scales are regularly proposed in questionnaires and used as dependent variable in modeling. The response distribution for such scales is always discrete, with bounded support and often skewed. In…

The critical infrastructures of the nation such as the power grid and the communication network are highly interdependent. Also, it has been observed that there exists complex interdependent relationships between individual entities of the…

Regression models describing the joint distribution of multivariate response variables conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models is that…

Joint modeling of spatially-oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes…

Large language models (LLMs) are increasingly deployed in decision-support systems for high-stakes domains such as hiring and university admissions, where choices often involve selecting among competing alternatives. While prior work has…

Higher-order information theory has become a rapidly growing toolkit in computational neuroscience, motivated by the idea that multivariate dependencies can reveal aspects of neural computation and communication that are invisible to…

Time-varying covariates in longitudinal studies frequently evolve through reciprocal feedback, undergo role reversal, and reflect unobserved individual heterogeneity. Standard statistical frameworks often assume fixed covariate roles and…

We study a class of conditional independence models for discrete data with the property that one or more log-linear interactions are defined within two different marginal distributions and then constrained to 0; all the conditional…

This work is motivated by the need to accurately model a vector of responses related to pediatric functional status using administrative health data from inpatient rehabilitation visits. The components of the responses have known and…

The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…

We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise…

Multivariate longitudinal data of mixed-type are increasingly collected in many science domains. However, algorithms to cluster this kind of data remain scarce, due to the challenge to simultaneously model the within- and between-time…

Data generated from a system of interest typically consists of measurements from an ensemble of subjects across multiple response and covariate features, and is naturally represented by one response-matrix against one covariate-matrix.…

We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…

Latent variable models provide a powerful framework for incorporating and inferring unobserved factors in observational data. In causal inference, they help account for hidden factors influencing treatment or outcome, thereby addressing…

This study investigates the identification of marginal treatment responses within multi-valued treatment models. Extending the hyper-rectangle model introduced by Lee and Salanie (2018), this paper relaxes restrictive assumptions, including…

Probabilistic modeling is one of the foundations of modern machine learning and artificial intelligence. In this paper, we propose a novel type of probabilistic models named latent dependency forest models (LDFMs). A LDFM models the…

We show that risk-aware behaviors in demand response originate from superquadratic state-dependent cost functions and price uncertainty with skewed distributions. We obtain such results through developing a novel theoretical demand response…

To construct models of large, multivariate complex systems, such as those in biology, one needs to constrain which variables are allowed to interact. This can be viewed as detecting "local" structures among the variables. In the context of…