机器学习

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…

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…

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…

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…

Dimension reduction techniques usually lose information in the sense that reconstructed data are not identical to the original data. However, we argue that it is possible to have reconstructed data identically distributed as the original…

PAC-Bayes generalisation bounds are derived via change-of-measure inequalities that transfer concentration properties from a reference measure to all posterior measures. The specific choice of change of measure determines the assumptions…

The generalized linear model (GLM) plays a key role in regression analyses. In high-dimensional data, the sparse GLM has been used but it is not robust against outliers. Recently, the robust methods have been proposed for the specific…

Valiant's 1984 paper is widely credited with introducing the PAC learning model, but it, in fact, introduced a different model: unlike PAC learning, the learner receives only positives, may issue membership queries, and must output a…

Most anomaly detection systems output scores rather than calibrated decisions, leaving practitioners to choose thresholds heuristically and without clear statistical interpretation. Conformal anomaly detection addresses this limitation by…

Causal discovery, the problem of inferring the direction of causality, is generally ill-posed. We use the language of structural causal models (SCM) to show that assuming that the causal relations are acyclic and invariant across multiple…

Diffusion models are often trained in low-dimensional latent spaces, which are then reused for related but shifted datasets. In this work, we study when such latent reuse remains reliable under distribution shift. We consider a…

Recent advancements in large language models demonstrate that injecting perturbations can substantially enhance extrapolation performance. However, current approaches often rely on discrete perturbations with fixed designs, which limits…

We study multiple change point localization under bandit feedback. An unknown piecewise-constant function on a compact interval can be queried sequentially at adaptively chosen inputs, and each query returns a noisy evaluation of the…

Large language models (LLMs) are increasingly deployed in settings where the available context is incomplete or degraded. We argue that an LLM generating answers under incomplete context can be viewed as an implicit imputer, and evaluated…

A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables. By exploiting a block-triangular structure in the transport map, the analysis step of filtering is reformulated as the…