Statistics
Researchers have adopted deep learning for classical discrete choice analysis as it can capture complex feature relationships and achieve higher predictive performance. However, the existing deep learning approaches cannot explicitly…
Sparse Principal Component Analysis (SPCA) is a fundamental technique for dimensionality reduction, and is NP-hard. In this paper, we introduce a randomized approximation algorithm for SPCA, which is based on the basic SDP relaxation. Our…
Clustering methods are often used in physics education research (PER) to identify subgroups of individuals within a population who share similar response patterns or characteristics. K-means (or k-modes, for categorical data) is one of the…
Machine learning (ML) models often exhibit bias that can exacerbate inequities in biomedical applications. Fairness auditing, the process of evaluating a model's performance across subpopulations, is critical for identifying and mitigating…
Sparse linear regression is a fundamental tool in data analysis. However, traditional approaches often fall short when covariates exhibit structure or arise from heterogeneous sources. In biomedical applications, covariates may stem from…
In this work, we propose new matrix- and tensor-based methodologies for estimating multivariate intensity functions of inhomogeneous point processes. By viewing multivariate intensity functions as infinite-dimensional matrices or tensors…
As demand for Large Language Models (LLMs) and AI agents grows rapidly, optimizing systems for efficient LLM inference becomes critical. While significant efforts have targeted system-level engineering, little has been explored from a…
Random feature ridge regression is often analyzed in the high-dimensional regime under the homogeneous sampling model $x_i=\Sigma^{1/2}x_i'$, where the vectors $x_i'$ have iid entries and the same covariance matrix $\Sigma$ is shared by all…
While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…
This paper investigates the theoretical foundation and develops analytical formulas for sample size and power calculations for causal inference with observational data. By analyzing the variance of an inverse probability weighting estimator…
The closure principle is a standard tool for achieving strong family-wise error rate (FWER) control in multiple testing problems. We develop an e-value-based closed testing framework that inherits nice properties of e-values, which are…
Spherical regression, in which both covariates and responses lie on the sphere, arises in many scientific applications and has attracted considerable methodological attention in recent years. Despite this progress, constructing flexible and…
This paper deals with tactics for fast computation in least squares regression in high dimensions. These tactics include: (a) the majorization-minimization (MM) principle, (b) smoothing by Moreau envelopes, and (c) the proximal distance…
Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…
Effect modification means the size of a treatment effect varies with an observed covariate. Generally speaking, a larger treatment effect with more stable error terms is less sensitive to bias. Thus, we might be able to conclude that a…
Understanding the links between diet, metabolic changes, and health outcomes is a key focus in nutritional science and broader biological research. Analyzing relationships, such as those between ultra-processed food (UPF) intake and…
As a rigorous statistical approach, statistical Taylor expansion extends the conventional Taylor expansion by replacing precise input variables with random variables of known distributions and sample counts to compute the mean, the…
Query-driven machine learning models have emerged as a promising estimation technique for query selectivities. Yet, surprisingly little is known about the efficacy of these techniques from a theoretical perspective, as there exist…
Replication of scientific studies is important for assessing the credibility of their results. However, there is no consensus on how to quantify the extent to which a replication study replicates an original result. We propose a novel…
Chatterjee (2021) introduced a novel independence test that is rank-based, asymptotically normal and consistent against all alternatives. One limitation of Chatterjee's test is its low statistical power for detecting monotonic…