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Quantitatively assessing relationships between latent variables and observed variables is important for understanding and developing generative models and representation learning. In this paper, we propose latent-observed dissimilarity…
Differential dependencies (DDs) capture the relationships between data columns of relations. They are more general than functional dependencies (FDs) and and the difference is that DDs are defined on the distances between values of two…
Motivated by genome-wide association studies, we consider a standard linear model with one additional random effect in situations where many predictors have been collected on the same subjects and each predictor is analyzed separately.…
The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for splittable random…
The method of difference-in-differences (DID) is widely used to study the causal effect of policy interventions in observational studies. DID employs a before and after comparison of the treated and control units to remove bias due to…
Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this…
In prediction problems with more predictors than observations, it can sometimes be helpful to use a joint probability model, $\pi(Y,X)$, rather than a purely conditional model, $\pi(Y \mid X)$, where $Y$ is a scalar response variable and…
When the difference between treatments in a clinical trial is estimated by a difference in means, then it is well known that randomization ensures unbiassed estimation, even if no account is taken of important baseline covariates. However,…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
We develop inference procedures for longitudinal data where some of the measurements are censored by fixed constants. We consider a semi-parametric quantile regression model that makes no distributional assumptions. Our research is…
Linear mixed models (LMMs) are used as an important tool in the data analysis of repeated measures and longitudinal studies. The most common form of LMMs utilize a normal distribution to model the random effects. Such assumptions can often…
Aligning large language models (LLMs) with human preferences has been recognized as the key to improving LLMs' interaction quality. However, in this pluralistic world, human preferences can be diversified due to annotators' different…
In order to successfully model Long Distance Dependencies (LDDs) it is necessary to understand the full-range of the characteristics of the LDDs exhibited in a target dataset. In this paper, we use Strictly k-Piecewise languages to generate…
Composite likelihood estimation has an important role in the analysis of multivariate data for which the full likelihood function is intractable. An important issue in composite likelihood inference is the choice of the weights associated…
Probabilistic models such as logistic regression, Bayesian classification, neural networks, and models for natural language processing, are increasingly more present in both undergraduate and graduate statistics and data science curricula…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the…
The effects of different parametrizations on the convergence of Bayesian computational algorithms for hierarchical models are well explored. Techniques such as centering, noncentering and partial noncentering can be used to accelerate…
Recently, there has been significant interest in linear regression in the situation where predictors and responses are not observed in matching pairs corresponding to the same statistical unit as a consequence of separate data collection…
Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not…