arXiv subjects

Wu Su

Publications and source records attributed to Wu Su.

4 recordsLinked to original sources

arXiv2026

How Fast Do Signatures Learn? Statistical Theory and Applications for Path Regression

Many prediction and decision-making problems in operations research involve path-valued covariates -- data that evolve over time -- for which path signatures have become a canonical feature representation. Their use is justified by a universal approximation theorem, but this is an existence result: it guarantees that a finite-level signature can approximate any continuous path functional, without quantifying how fast the approximation error decreases as the truncation level grows. This paper develops approximation and statistical theory for signature-based path regression. We establish an \(L^2\) approximation rate for smooth functionals of It\^{o} diffusions and show that it is minimax optimal. We then propagate the truncation error through three statistical learning procedures -- Signature-OLS, Signature-LASSO, and Signature-Logistic -- and establish their consistency. Three real-data applications show that signatures provide informative finite-dimensional representations of path-valued covariates and can improve prediction relative to handcrafted features, in the context of finance -- foreign exchange realized volatility forecasting from intraday price paths; energy -- battery end-of-life prediction from early diagnostic current-voltage pulse paths; and medicine -- epileptic seizure detection from short electroencephalogram windows.

math.ST↗

arXiv2025

Likelihood Matching for Diffusion Models

We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To efficiently compute the reverse sample likelihood, a quasi-likelihood is considered to approximate each reverse transition density by a Gaussian distribution with matched conditional mean and covariance, respectively. The score and Hessian functions for the diffusion generation are estimated by maximizing the quasi-likelihood, ensuring a consistent matching of both the first two transitional moments between every two time points. A stochastic sampler is introduced to facilitate computation that leverages both the estimated score and Hessian information. We establish consistency of the quasi-maximum likelihood estimation, and provide non-asymptotic convergence guarantees for the proposed sampler, quantifying the rates of the approximation errors due to the score and Hessian estimation, dimensionality, and the number of diffusion steps. Empirical and simulation evaluations demonstrate the effectiveness of the proposed Likelihood Matching and validate the theoretical results.

stat.ML↗

arXiv2025

Glider Path Design and Control for Reconstructing Three-Dimensional Structures of Oceanic Mesoscale Eddies

Underwater gliders offer effective means in oceanic surveys with a major task in reconstructing the three-dimensional hydrographic field of a mesoscale eddy. This paper considers three key issues in the hydrographic reconstruction of mesoscale eddies with the sampled data from the underwater gliders. It first proposes using the Thin Plate Spline (TPS) as the interpolation method for the reconstruction with a blocking scheme to speed up the computation. It then formulates a procedure for selecting glider path design that minimizes the reconstruction errors among a set of pathway formations. Finally we provide a glider path control procedure to guide the glider to follow to designed pathways as much as possible in the presence of ocean current. A set of optimization algorithms are experimented and several with robust glider control performance on a simulated eddy are identified.

stat.AP↗

arXiv2025

High-dimensional Clustering and Signal Recovery under Block Signals

This paper studies computationally efficient methods and their minimax optimality for high-dimensional clustering and signal recovery under block signal structures. We propose two sets of methods, cross-block feature aggregation PCA (CFA-PCA) and moving average PCA (MA-PCA), designed for sparse and dense block signals, respectively. Both methods adaptively utilize block signal structures, applicable to non-Gaussian data with heterogeneous variances and non-diagonal covariance matrices. Specifically, the CFA method utilizes a block-wise U-statistic to aggregate and select block signals non-parametrically from data with unknown cluster labels. We show that the proposed methods are consistent for both clustering and signal recovery under mild conditions and weaker signal strengths than the existing methods without considering block structures of signals. Furthermore, we derive both statistical and computational minimax lower bounds (SMLB and CMLB) for high-dimensional clustering and signal recovery under block signals, where the CMLBs are restricted to algorithms with polynomial computation complexity. The minimax boundaries partition signals into regions of impossibility and possibility. No algorithm (or no polynomial time algorithm) can achieve consistent clustering or signal recovery if the signals fall into the statistical (or computational) region of impossibility. We show that the proposed CFA-PCA and MA-PCA methods can achieve the CMLBs for the sparse and dense block signal regimes, respectively, indicating the proposed methods are computationally minimax optimal. A tuning parameter selection method is proposed based on post-clustering signal recovery results. Simulation studies are conducted to evaluate the proposed methods. A case study on global temperature change demonstrates their utility in practice.

stat.ME↗