arXiv subjects

Shouri Hu

Publications and source records attributed to Shouri Hu.

6 recordsLinked to original sources

arXiv2026

Structural Change Detection in High-Dimensional Transformed Factor Models via Canonical Correlation Analysis

This paper develops a canonical-correlation-based method for detecting structural changes in high-dimensional transformed factor models. The proposed approach exploits the low-rank canonical-correlation structure induced by dynamically dependent common factors, while serially uncorrelated idiosyncratic components correspond to a noise subspace with zero canonical correlations. We construct an eigenvalue-ratio criterion that measures residual dynamic dependence in the estimated noise subspace and identifies the true change point under sufficient separation of the regime-specific loading spaces or dynamic canonical correlation structures. Since the change-point location and the regime-specific factor numbers are both unknown, we further propose an alternating iterative estimation procedure that updates them sequentially until convergence. Under suitable mixing and moment conditions, we establish asymptotic properties of the proposed estimators, with convergence rates depending explicitly on factor strength, cross-sectional dimension, and sample size. Monte Carlo experiments and empirical applications to intraday stock returns and U.S. temperature series demonstrate the finite-sample

stat.ME↗

arXiv2024

An Adaptive Dimension Reduction Estimation Method for High-dimensional Bayesian Optimization

Bayesian optimization (BO) has shown impressive results in a variety of applications within low-to-moderate dimensional Euclidean spaces. However, extending BO to high-dimensional settings remains a significant challenge. We address this challenge by proposing a two-step optimization framework. Initially, we identify the effective dimension reduction (EDR) subspace for the objective function using the minimum average variance estimation (MAVE) method. Subsequently, we construct a Gaussian process model within this EDR subspace and optimize it using the expected improvement criterion. Our algorithm offers the flexibility to operate these steps either concurrently or in sequence. In the sequential approach, we meticulously balance the exploration-exploitation trade-off by distributing the sampling budget between subspace estimation and function optimization, and the convergence rate of our algorithm in high-dimensional contexts has been established. Numerical experiments validate the efficacy of our method in challenging scenarios.

stat.ML↗

arXiv2022

Adjusted Expected Improvement for Cumulative Regret Minimization in Noisy Bayesian Optimization

The expected improvement (EI) is one of the most popular acquisition functions for Bayesian optimization (BO) and has demonstrated good empirical performances in many applications for the minimization of simple regret. However, under the evaluation metric of cumulative regret, the performance of EI may not be competitive, and its existing theoretical regret upper bound still has room for improvement. To adapt the EI for better performance under cumulative regret, we introduce a novel quantity called the evaluation cost which is compared against the acquisition function, and with this, develop the expected improvement-cost (EIC) algorithm. In each iteration of EIC, a new point with the largest acquisition function value is sampled, only if that value exceeds its evaluation cost. If none meets this criteria, the current best point is resampled. This evaluation cost quantifies the potential downside of sampling a point, which is important under the cumulative regret metric as the objective function value in every iteration affects the performance measure. We establish in theory a high-probability regret upper bound of EIC based on the maximum information gain, which is tighter than the bound of existing EI-based algorithms. It is also comparable to the regret bound of other popular BO algorithms such as Thompson sampling (GP-TS) and upper confidence bound (GP-UCB). We further perform experiments to illustrate the improvement of EIC over several popular BO algorithms.

cs.LG↗

arXiv2021

Likelihood Scores for Sparse Signal and Change-Point Detection

We consider here the identification of change-points on large-scale data streams. The objective is to find the most efficient way of combining information across data stream so that detection is possible under the smallest detectable change magnitude. The challenge comes from the sparsity of change-points when only a small fraction of data streams undergo change at any point in time. The most successful approach to the sparsity issue so far has been the application of hard thresholding such that only local scores from data streams exhibiting significant changes are considered and added. However the identification of an optimal threshold is a difficult one. In particular it is unlikely that the same threshold is optimal for different levels of sparsity. We propose here a sparse likelihood score for identifying a sparse signal. The score is a likelihood ratio for testing between the null hypothesis of no change against an alternative hypothesis in which the change-points or signals are barely detectable. By the Neyman-Pearson Lemma this score has maximum detection power at the given alternative. The outcome is that we have a scoring of data streams that is successful in detecting at the boundary of the detectable region of signals and change-points. The likelihood score can be seen as a soft thresholding approach to sparse signal and change-point detection in which local scores that indicate small changes are down-weighted much more than local scores indicating large changes. We are able to show second-order optimality of the sparsity likelihood score in the sense of achieving successful detection at the minimum detectable order of change magnitude as well as at the minimum detection asymptotic constant with respect this order of change.

math.ST↗

arXiv2019

Optimal UCB Adjustments for Large Arm Sizes

The regret lower bound of Lai and Robbins (1985), the gold standard for checking optimality of bandit algorithms, considers arm size fixed as sample size goes to infinity. We show that when arm size increases polynomially with sample size, a surprisingly smaller lower bound is achievable. This is because the larger experimentation costs when there are more arms permit regret savings by exploiting the best performer more often. In particular we are able to construct a UCB-Large algorithm that adaptively exploits more when there are more arms. It achieves the smaller lower bound and is thus optimal. Numerical experiments show that UCB-Large performs better than classical UCB that does not correct for arm size, and better than Thompson sampling.

math.ST↗

arXiv2018

Infinite Arms Bandit: Optimality via Confidence Bounds

Berry et al. (1997) initiated the development of the infinite arms bandit problem. They derived a regret lower bound of all allocation strategies for Bernoulli rewards with uniform priors, and proposed strategies based on success runs. Bonald and Prouti\`{e}re (2013) proposed a two-target algorithm that achieves the regret lower bound, and extended optimality to Bernoulli rewards with general priors. We present here a confidence bound target (CBT) algorithm that achieves optimality for rewards that are bounded above. For each arm we construct a confidence bound and compare it against each other and a target value to determine if the arm should be sampled further. The target value depends on the assumed priors of the arm means. In the absence of information on the prior, the target value is determined empirically. Numerical studies here show that CBT is versatile and outperforms its competitors.

stat.ML↗