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Fengpei Li

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6 papers

2 author rows

AAAI Conference 2026 Conference Paper

Positive Definite Sparse Covariance Estimation via Dual Space Optimization

Fengpei Li
Wenfu Xia
Ziping Zhao

Covariance matrix estimation in high dimensions is a fundamental problem in machine learning and signal processing. A common structural assumption used to mitigate the challenges posed by high dimensionality is sparsity, which posits that most variable pairs exhibit negligible correlations. In this paper, we revisit the classical problem of positive definite sparse covariance estimation (PDSCE) introduced by Rothman (2012). Unlike many earlier approaches, this formulation incorporates a logarithmic barrier, which guarantees that the resulting covariance estimator is positive definite and thereby ensures the well-posedness of the estimation problem. However, the inclusion of the logarithmic barrier also leads to nontrivial optimization difficulties. To overcome these difficulties, we propose a dual proximal gradient method (DPGM) for solving the PDSCE problem. In contrast to existing primal-space approaches, DPGM operates directly in the dual space. This dual perspective provides several key advantages. First, DPGM significantly reduces computational costs, because positive definiteness is preserved automatically and no iterative subproblem solvers are required. Second, compared with primal optimization algorithms, DPGM offers stronger theoretical guarantees, including principled step size selection and improved iteration complexity. Extensive numerical experiments demonstrate that DPGM consistently outperforms existing methods, which confirms its effectiveness and scalability for high-dimensional sparse covariance estimation.

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TMLR Journal 2025 Journal Article

Reweighting Improves Conditional Risk Bounds

Yikai Zhang
Jiahe Lin
Fengpei Li
Songzhu Zheng
Anant Raj
Anderson Schneider
Yuriy Nevmyvaka

In this work, we study the weighted empirical risk minimization (weighted ERM) schema, in which an additional data-dependent weight function is incorporated when the empirical risk function is being minimized. We show that under a general ``balanceable" Bernstein condition, one can design a weighted ERM estimator to achieve superior performance in certain sub-regions over the one obtained from standard ERM, and the superiority manifests itself through a data-dependent constant term in the error bound. These sub-regions correspond to large-margin ones in classification settings and low-variance ones in heteroscedastic regression settings, respectively. Our findings are supported by evidence from synthetic data experiments.

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UAI Conference 2023 Conference Paper

Detection of Short-Term Temporal Dependencies in Hawkes Processes with Heterogeneous Background Dynamics

Yu Chen
Fengpei Li
Anderson Schneider
Yuriy Nevmyvaka
Asohan Amarasingham
Henry Lam

Many kinds of simultaneously-observed event sequences exhibit mutually exciting or inhibiting patterns. Reliable detection of such temporal dependencies is crucial for scientific investigation. A common model is the Multivariate Hawkes Process (MHP), whose impact function naturally encodes a causal structure in Granger causality. However, the vast majority of existing methods use a transformed standard MHP intensity with a constant baseline, which may be inconsistent with real-world data. On the other hand, modeling irregular and unknown background dynamics directly is a challenge, as one struggles to distinguish the effect of mutual interaction from that of fluctuations in background dynamics. In this paper, we address the short-term temporal dependency detection issue. We show that maximum likelihood estimation (MLE) for cross-impact from MHP has an error that can not be eliminated, but may be reduced by an order of magnitude using a heterogeneous intensity not for the target HP but for the interacting HP. Then we propose a robust and computationally-efficient modification of MLE that does not rely on the prior estimation of the heterogeneous intensity and is thus applicable in a data-limited regime (e. g. , few-shot, unrepeated observations). Extensive experiments on various datasets show that our method outperforms existing ones by notable margins, with highlighted novel applications in neuroscience.

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UAI Conference 2023 Conference Paper

Information theoretic clustering via divergence maximization among clusters

Sahil Garg
Mina Dalirrooyfard
Anderson Schneider
Yeshaya Adler
Yuriy Nevmyvaka
Yu Chen
Fengpei Li
Guillermo A. Cecchi

Information-theoretic clustering is one of the most promising and principled approaches to finding clusters with minimal apriori assumptions. The key criterion therein is to maximize the mutual information between the data points and their cluster labels. Such an approach, however, does not explicitly promote any type of inter-cluster behavior. We instead propose to maximize the Kullback-Leibler divergence between the underlying data distributions associated to clusters (referred to as cluster distributions). We show it to entail the mutual information criterion along with maximizing cross entropy between the cluster distributions. For practical efficiency, we propose to empirically estimate the objective of KL-D between clusters in its dual form leveraging deep neural nets as a dual function approximator. Remarkably, our theoretical analysis establishes that estimating the divergence measure in its dual form simplifies the problem of clustering to one of optimally finding k-1 cut points for k clusters in the 1-D dual functional space. Overall, our approach enables linear-time clustering algorithms with theoretical guarantees of near-optimality, owing to the submodularity of the objective. We show the empirical superiority of our approach w. r. t. current state-of-the-art methods on the challenging task of clustering noisy timeseries as observed in domains such as neuroscience, healthcare, financial markets, spatio-temporal environmental dynamics, etc.

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ICML Conference 2023 Conference Paper

Provably Convergent Schrödinger Bridge with Applications to Probabilistic Time Series Imputation

Yu Chen
Wei Deng 0002
Shikai Fang
Fengpei Li
Nicole Tianjiao Yang
Yikai Zhang 0003
Kashif Rasul
Shandian Zhe

The Schrödinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized optimal transport problem, which conducts projections onto every other marginal alternatingly. However, in practice, only approximated projections are accessible and their convergence is not well understood. To fill this gap, we present a first convergence analysis of the Schrödinger bridge algorithm based on approximated projections. As for its practical applications, we apply SBP to probabilistic time series imputation by generating missing values conditioned on observed data. We show that optimizing the transport cost improves the performance and the proposed algorithm achieves the state-of-the-art result in healthcare and environmental data while exhibiting the advantage of exploring both temporal and feature patterns in probabilistic time series imputation.

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IROS Conference 2022 Conference Paper

Scalable Safety-Critical Policy Evaluation with Accelerated Rare Event Sampling

Mengdi Xu
Peide Huang
Fengpei Li
Jiacheng Zhu
Xuewei Tony Qi
Kentaro Oguchi 0001
Zhiyuan Huang
Henry Lam

Evaluating rare but high-stakes events is one of the main challenges in obtaining reliable reinforcement learning policies, especially in large or infinite state/action spaces where limited scalability dictates a prohibitively large number of testing iterations. On the other hand, a biased or inaccurate policy evaluation in a safety-critical system could potentially cause unexpected catastrophic failures during deployment. This paper proposes the Accelerated Policy Evaluation (APE) method, which simultaneously uncovers rare events and estimates the rare event probability in Markov decision processes. The APE method treats the environment nature as an adversarial agent and learns towards, through adaptive importance sampling, the zero-variance sampling distribution for the policy evaluation. Moreover, APE is scalable to large discrete or continuous spaces by incorporating function approximators. We investigate the convergence property of APE in the tabular setting. Our empirical studies show that APE can estimate the rare event probability with a smaller bias while only using orders of magnitude fewer samples than baselines in multi-agent and single-agent environments.

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