Statistics

Online Multiple Testing (OMT), a fundamental pillar of sequential statistical inference, traditionally evaluates the False Discovery Rate (FDR) and statistical power in isolation, obscuring the highly asymmetric costs of false positives and…

Quantization is essential for efficient large language model (LLM) inference, yet the dequantization step-converting low-bit weights back to high-precision for matrix multiplication has become a critical bottleneck on modern AI…

Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…

We present a covariance-aware sampler that improves the quality of pixel-space Diffusion Model (DM) sampling in the few-step regime. We hypothesize that in the few-step regime samplers fail because they rely solely on the predicted mean of…

Reinforcement learning (RL) for large language models (LLMs) is dominated by the cost of rollout generation, which has motivated the use of low-precision rollouts (e.g., FP8) paired with a BF16 trainer to improve throughput and reduce…

Score-based generative models (SGMs) have achieved remarkable empirical success, motivating their application to a broad range of data distributions. However, extending them to heavy-tailed targets remains a largely open problem. Although…

We study a large-scale one-sided multiple testing problem in which test statistics follow normal distributions with unit variance, and the goal is to identify signals with positive mean effects. A conventional approach is to compute…

Flow matching (FM) constructs continuous-time ODE samplers by prescribing probability paths between a base distribution and a target distribution. In this note, we study FM through the lens of finite-sample plug-in estimation. In addition…

Estimating individualized treatment rules (ITRs) is fundamental to precision medicine, where the goal is to tailor treatment decisions to individual patient characteristics. While numerous methods have been developed for ITR estimation,…

Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges…

We present a general strategy for turning generative models into candidate solution samplers for batch Bayesian optimization (BO). The use of generative models for BO enables large batch scaling as generative sampling, optimization of…

Most existing manifold dimension estimators rely on the assumption that the underlying manifold is locally flat within the neighborhoods under consideration. More recently, curvature-adjusted principal component analysis (CA-PCA) has…

Causal discovery from i.i.d. observational data is known to be generally ill-posed. We demonstrate that if we have access to the distribution {induced} by a structural causal model, and additional data from (in the best case) \textit{only…

Climate policy modelling is a key tool for assessing mitigation strategies in complex systems, where uncertainty is inherent and unavoidable. We present a general methodology for extensive uncertainty analysis in this field. While other…

This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP) in both deterministic and stochastic settings. We investigate state-space…

Linear mixed models (LMMs), which incorporate fixed and random effects, are key tools for analyzing heterogeneous data, such as in personalized medicine. Nowadays, this type of data is increasingly wide, sometimes containing thousands of…

Estimating conditional average treatment effects (CATE) from randomized controlled trials (RCTs) and generalizing them to broader populations is essential for personalizing treatment rules but is complicated by selection bias due to trial…

Mixed-effects models are widely used to model data with hierarchical grouping structures and high-cardinality categorical predictor variables. However, for high-dimensional crossed random effects, current standard computations relying on…

Bayesian optimization is a widely used method for optimizing expensive black-box functions, with Expected Improvement being one of the most commonly used acquisition functions. In contrast, information-theoretic acquisition functions aim to…

Under a set of assumptions on a family of submanifolds $\subset {\mathbb R}^D$, we derive a series of geometric properties that remain valid after finite-dimensional and almost isometric Diffusion Maps (DM), including almost uniform…