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Latent Markov (LM) models represent an important class of models for the analysis of longitudinal data (Bartolucci et. al., 2013), especially when response variables are categorical. These models have a great potential of application for…

AI researchers and practitioners increasingly apply large language models (LLMs) to what we call reasoning-intensive regression (RiR), i.e., deducing subtle numerical scores from text. Unlike standard language regression tasks such as…

Successful management of wildlife populations requires accurate estimates of abundance. Abundance estimates can be confounded by imperfect detection during wildlife surveys. N-mixture models enable quantification of detection probability…

What role should assumptions play in inference? We present a small theoretical case study of a simple, clean case, namely the nonparametric comparison of two continuous distributions using (essentially) information about quartiles, that is,…

This is an overview of the R package iprior, which implements a unified methodology for fitting parametric and nonparametric regression models, including additive models, multilevel models, and models with one or more functional covariates.…

Inspired by recent findings on the fractal geometry of language, we introduce Recursive INference Scaling (RINS) as a complementary, plug-in recipe for scaling inference time in language and multimodal systems. RINS is a particular form of…

Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…

A data analyst might worry about generalization if dropping a very small fraction of data points from a study could change its substantive conclusions. Checking this non-robustness directly poses a combinatorial optimization problem and is…

The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big data analysis. We propose an orthogonal…

This paper investigates statistical inference for noisy matrix completion in a semi-supervised model when auxiliary covariates are available. The model consists of two parts. One part is a low-rank matrix induced by unobserved latent…

A novel IV estimation method, that we term Locally Trimmed LS (LTLS), is developed which yields estimators with (mixed) Gaussian limit distributions in situations where the data may be weakly or strongly persistent. In particular, we allow…

Model checking is essential to evaluate the adequacy of statistical models and the validity of inferences drawn from them. Particularly, hierarchical models such as latent Gaussian models (LGMs) pose unique challenges as it is difficult to…

This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of…

Informal mathematics has been central to modern large language model (LLM) reasoning, offering flexibility and enabling efficient construction of arguments. However, purely informal reasoning is prone to logical gaps and subtle errors that…

Motivated by questions about dense (non-sparse) signals in high-dimensional data analysis, we study the unconditional out-of-sample prediction error (predictive risk) associated with three popular linear estimators for high-dimensional…

In this paper, we ask: what truly determines the effectiveness of RL training data for enhancing language models' reasoning capabilities? While recent advances like o1, Deepseek R1, and Kimi1.5 demonstrate RL's potential, the lack of…

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…

This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…

Many modern time-series datasets contain large numbers of output response variables sampled for prolonged periods of time. For example, in neuroscience, the activities of 100s-1000's of neurons are recorded during behaviors and in response…

In analyzing high-dimensional models, sparsity of the model parameter is a common but often undesirable assumption. In this paper, we study the following two-sample testing problem: given two samples generated by two high-dimensional linear…