Statistics

Algorithms in machine learning and AI do critically depend on at least three key components: (i) the risk function, which is the expectation of the loss function, (ii) the function space, which is often called the hypothesis space, and…

Double machine learning (DML) delivers valid inference on low-dimensional causal parameters while permitting flexible nuisance estimation, but its computational cost becomes prohibitive once cross-fitted learners must be trained on massive…

We investigate the ability of transformers to perform in-context reinforcement learning (ICRL), where a model must infer and execute learning algorithms from trajectory data without parameter updates. We show that a linear self-attention…

The role of AI-generated synthetic data has recently been expanded to support realistic Monte Carlo simulations. However, guidance is limited on generating data with multilevel structures and designing simulations based on such data. This…

The discrete Pareto (or Zeta, Zipf) distribution, arises naturally in modeling rank-frequency data across diverse fields such as linguistics, demography, biology, and computer science. Despite its widespread applicability, goodness-of-fit…

Differential item functioning (DIF) arises alongside latent population heterogeneity in many applications, and both must be accounted for when assessing measurement invariance. In many practical settings, however, the comparison groups are…

Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of…

Standard cardiovascular risk calculators, including the Framingham Risk Score and the ACC/AHA Pooled Cohort Equations, estimate the conditional probability P(CHD | SysBP = s) rather than the interventional quantity P(CHD | do(SysBP = s)).…

Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…

Express transportation network design is uncertain because origin--destination demand, travel time, operating cost, hub congestion, and realized sorting productivity vary over time. Existing multi-topology express network models usually…

Positive-unlabeled (PU) learning addresses binary classification when only a set of labeled positives is available alongside a pool of unlabeled samples drawn from a mixture of positives and negatives. Existing PU methods typically require…

Despite the growing availability of large datasets, causal structure learning remains computationally prohibitive at scale. We revisit sparsest-permutation learning for linear structural equation models and show that exact Cholesky…

Machine-learning systems used in survey-based social measurement require uncertainty estimates that are reliable across population subgroups, not merely valid in aggregate. We study ordinal conformal prediction for five-level AI-attitude…

This paper introduces the Statverse, a Metaverse framework designed to revolutionize statistical education in the digital age. Our key goal is to report our progress and encourage others to integrate similar strategies into their programs.…

Sparse regression based on global-local shrinkage priors are increasingly used for Bayesian modeling of modern high-dimensional data, but scaling up the Gibbs sampler for posterior inference remains a challenge. While much effort has gone…

We introduce a novel framework for constructing scalable and flexible covariance kernels for Gaussian processes (GPs) by directly learning the covariance structure under a regression-type parameterization induced by Vecchia approximations,…

We formally introduce a class of models inspired by renormalization group (RG) theory, built on additive hierarchical expansions analogous to those appearing in functional ANOVA and mixed-effects models. Like ReLU convolutional neural…

High-dimensional functional data are becoming increasingly common in fields such as environmental monitoring and neuroimaging. This paper studies high-dimensional functional linear regression models that relate a scalar response to…

Nonconvex methods have emerged as a dominant approach for low-rank matrix estimation, a problem that arises widely in machine learning and AI for learning and representing high-dimensional data. Existing analyses for these methods often…

Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…