arXiv subjects

Chihao Zhang

Publications and source records attributed to Chihao Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Discrete Optimal Transport: Rapid Convergence of Simulated Annealing Algorithms

We develop a discrete optimal transport framework for analyzing simulated annealing algorithms on finite state spaces. Building on the discrete Wasserstein metric introduced by Maas (J. Funct. Anal., 2011), we define a generalized discrete Wasserstein-2 distance and the associated notion of \emph{discrete action} for paths of probability measures on graphs. Using these tools, we establish non-asymptotic convergence guarantees for simulated annealing: the KL divergence between the algorithm's output and the target distribution is controlled by the discrete action of the annealing path. This can be viewed as the discrete counterpart of the action-based analysis of annealed Langevin dynamics in continuous spaces by Guo, Tao, and Chen (ICLR 2025). As applications, we analyze simulated annealing for two fundamental models in statistical physics. For the \emph{mean-field Ising model}, we show that annealed single-site Glauber dynamics achieves $\varepsilon$ error in KL divergence in $O(n^5\beta^2/\varepsilon)$ steps at \emph{any} inverse temperature $\beta \ge 0$. For the \emph{mean-field $q$-state Potts model}, we show that annealed $(q-1)$-block Glauber dynamics achieves $\varepsilon$ error in $\mathrm{poly}(n, \beta, 1/\varepsilon)$ steps for all $\beta \ge \beta_{\mathsf{s}}=q/2$, the regime where the disordered phase has completely lost stability. In both cases, the key technical contribution is a polynomial upper bound on the discrete action, obtained by exploiting the symmetry of the model to reduce the analysis to a low-dimensional projected chain.

cs.DS↗

arXiv2025

Multi-Agent Intelligence for Multidisciplinary Decision-Making in Gastrointestinal Oncology

Multimodal clinical reasoning in the field of gastrointestinal (GI) oncology necessitates the integrated interpretation of endoscopic imagery, radiological data, and biochemical markers. Despite the evident potential exhibited by Multimodal Large Language Models (MLLMs), they frequently encounter challenges such as context dilution and hallucination when confronted with intricate, heterogeneous medical histories. In order to address these limitations, a hierarchical Multi-Agent Framework is proposed, which emulates the collaborative workflow of a human Multidisciplinary Team (MDT). The system attained a composite expert evaluation score of 4.60/5.00, thereby demonstrating a substantial improvement over the monolithic baseline. It is noteworthy that the agent-based architecture yielded the most substantial enhancements in reasoning logic and medical accuracy. The findings indicate that mimetic, agent-based collaboration provides a scalable, interpretable, and clinically robust paradigm for automated decision support in oncology.

cs.AI↗

arXiv2025

Graph Generation with Spectral Geodesic Flow Matching

Graph generation is a fundamental task with wide applications in modeling complex systems. Although existing methods align the spectrum or degree profile of the target graph, they often ignore the geometry induced by eigenvectors and the global structure of the graph. In this work, we propose Spectral Geodesic Flow Matching (SFMG), a novel framework that uses spectral eigenmaps to embed both input and target graphs into continuous Riemannian manifolds. We then define geodesic flows between embeddings and match distributions along these flows to generate output graphs. Our method yields several advantages: (i) captures geometric structure beyond eigenvalues, (ii) supports flexible generation of diverse graphs, and (iii) scales efficiently. Empirically, SFMG matches the performance of state-of-the-art approaches on graphlet, degree, and spectral metrics across diverse benchmarks. In particular, it achieves up to 30$\times$ speedup over diffusion-based models, offering a substantial advantage in scalability and training efficiency. We also demonstrate its ability to generalize to unseen graph scales. Overall, SFMG provides a new approach to graph synthesis by integrating spectral geometry with flow matching.

cs.LG↗

arXiv2025

The Query Complexity of Uniform Pricing

Real-world pricing mechanisms are typically optimized using training data, a setting corresponding to the \textit{pricing query complexity} problem in Mechanism Design. The previous work [LSTW23] studies the \textit{single-distribution} case, with tight bounds of $\widetilde{\Theta}(\varepsilon^{-3})$ for a \textit{general} distribution and $\widetilde{\Theta}(\varepsilon^{-2})$ for either a \textit{regular} or \textit{monotone-hazard-rate (MHR)} distribution, where $\varepsilon \in (0, 1)$ denotes the (additive) revenue loss of a learned uniform price relative to the Bayesian-optimal uniform price. This can be directly interpreted as ``the query complexity of the {\em \textsf{Uniform Pricing}} mechanism, in the \textit{single-distribution} case''. Yet in the \textit{multi-distribution} case, can the regularity and MHR conditions still lead to improvements over the tight bound $\widetilde{\Theta}(\varepsilon^{-3})$ for general distributions? We answer this question in the negative, by establishing a (near-)matching lower bound $\Omega(\varepsilon^{-3})$ for either \textit{two regular distributions} or \textit{three MHR distributions}. We also address the \textit{regret minimization} problem and, in comparison with the folklore upper bound $\widetilde{O}(T^{2 / 3})$ for general distributions (see, e.g., [SW24]), establish a (near-)matching lower bound $\Omega(T^{2 / 3})$ for either \textit{two regular distributions} or \textit{three MHR distributions}, via a black-box reduction. Again, this is in stark contrast to the tight bound $\widetilde{\Theta}(T^{1 / 2})$ for a single regular or MHR distribution.

cs.GT↗

arXiv2025

Improved sampling algorithms and functional inequalities for non-log-concave distributions

We study the problem of sampling from a distribution $\mu$ with density $\propto e^{-V}$ for some potential function $V:\mathbb R^d\to \mathbb R$ with query access to $V$ and $\nabla V$. We start with the following standard assumptions: (1) $V$ is $L$-smooth. (2) The second moment $\mathbf{E}_{X\sim \mu}[\|X\|^2]\leq M$. Recently, He and Zhang (COLT'25) showed that the query complexity of this problem is at least $\left(\frac{LM}{d\epsilon}\right)^{\Omega(d)}$ where $\epsilon$ is the desired accuracy in total variation distance, and the Poincar\'e constant can be unbounded. Meanwhile, another common assumption in the study of diffusion based samplers (see e.g., the work of Chen, Chewi, Li, Li, Salim and Zhang (ICLR'23)) strengthens (1) to the following: (1*) The potential function of *every* distribution along the Ornstein-Uhlenbeck process starting from $\mu$ is $L$-smooth. We show that under the assumptions (1*) and (2), the query complexity of sampling from $\mu$ can be $\mathrm{poly}(L,d)\cdot \left(\frac{Ld+M}{\epsilon^2}\right)^{\mathcal{O}(L+1)}$, which is polynomial in $d$ and $\frac{1}{\epsilon}$ when $L=\mathcal{O}(1)$ and $M=\mathrm{poly}(d)$. This improves the algorithm with quasi-polynomial query complexity developed by Huang et al. (COLT'24). Our results imply that the seemingly moderate strengthening from (1) to (1*) yields an exponential gap in the query complexity. Furthermore, we show that together with the assumption (1*) and the stronger moment assumption that $\|X\|$ is $\lambda$-sub-Gaussian for $X\sim\mu$, the Poincar\'e constant of $\mu$ is at most $\mathcal{O}(\lambda)^{2(L+1)}$. We also establish a modified log-Sobolev inequality for $\mu$ under these conditions. As an application of our technique, we obtain a new estimate of the modified log-Sobolev constant for a specific class of mixtures of strongly log-concave distributions.

cs.DS↗

arXiv2025

On the Problem of Best Arm Retention

This paper presents a comprehensive study on the problem of Best Arm Retention (BAR), which has recently found applications in streaming algorithms for multi-armed bandits. In the BAR problem, the goal is to retain $m$ arms with the best arm included from $n$ after some trials, in stochastic multi-armed bandit settings. We first investigate pure exploration for the BAR problem under different criteria, and then minimize the regret with specific constraints, in the context of further exploration in streaming algorithms. - We begin by revisiting the lower bound for the $(\varepsilon,\delta)$-PAC algorithm for Best Arm Identification (BAI) and adapt the classical KL-divergence argument to derive optimal bounds for $(\varepsilon,\delta)$-PAC algorithms for BAR. - We further study another variant of the problem, called $r$-BAR, which requires the expected gap between the best arm and the optimal arm retained is less than $r$. We prove tight sample complexity for the problem. - We explore the regret minimization problem for $r$-BAR and develop algorithm beyond pure exploration. We conclude with a conjecture on the optimal regret in this setting.

cs.LG↗

arXiv2025

Tight Regret Bounds for Fixed-Price Bilateral Trade

We examine fixed-price mechanisms in bilateral trade through the lens of regret minimization. Our main results are twofold. (i) For independent values, a near-optimal $\widetilde{\Theta}(T^{2/3})$ tight bound for $\textsf{Global Budget Balance}$ fixed-price mechanisms with two-bit/one-bit feedback. (ii) For correlated/adversarial values, a near-optimal $\Omega(T^{3/4})$ lower bound for $\textsf{Global Budget Balance}$ fixed-price mechanisms with two-bit/one-bit feedback, which improves the best known $\Omega(T^{5/7})$ lower bound obtained in the work [BCCF24] and, up to polylogarithmic factors, matches the $\widetilde{\mathcal{O}}(T^{3 / 4})$ upper bound obtained in the same work. Our work in combination with the previous works [CCCFL24mor, CCCFL24jmlr, AFF24, BCCF24] (essentially) gives a thorough understanding of regret minimization for fixed-price bilateral trade. En route, we have developed two technical ingredients that might be of independent interest: (i) A novel algorithmic paradigm, called $\textit{{fractal elimination}}$, to address one-bit feedback and independent values. (ii) A new $\textit{lower-bound construction}$ with novel proof techniques, to address the $\textsf{Global Budget Balance}$ constraint and correlated values.

cs.GT↗

arXiv2025

Tight Gap-Dependent Memory-Regret Trade-Off for Single-Pass Streaming Stochastic Multi-Armed Bandits

We study the problem of minimizing gap-dependent regret for single-pass streaming stochastic multi-armed bandits (MAB). In this problem, the $n$ arms are present in a stream, and at most $m 0}\Delta_i^{1 - 2\alpha}\Big)$ and another applicable for $m<\frac{2}{3}n$ with regret at most $O_\alpha\Big(\frac{T^{\frac{1}{\alpha+1}}}{m^{\frac{1}{\alpha+1}}}\displaystyle\sum_{i:\Delta_i > 0}\Delta_i^{1 - 2\alpha}\Big)$. We also prove matching lower bounds for both cases by showing that for any constant $\alpha\ge 1$ and any $m\leq k < n$, there exists a set of hard instances on which the regret of any algorithm is $\Omega_\alpha\Big(\frac{(k-m+1) T^{\frac{1}{\alpha+1}}}{k^{1 + \frac{1}{\alpha+1}}} \sum_{i:\Delta_i > 0}\Delta_i^{1-2\alpha}\Big)$. This is the first tight gap-dependent regret bound for streaming MAB. Prior to our work, an $O\Big(\sum_{i\colon\Delta>0} \frac{\sqrt{T}\log T}{\Delta_i}\Big)$ upper bound for the special case of $\alpha=1$ and $m=O(1)$ was established by Agarwal, Khanna and Patil (COLT'22). In contrast, our results provide the correct order of regret as $\Theta\Big(\frac{1}{\sqrt{m}}\sum_{i\colon\Delta>0}\frac{\sqrt{T}}{\Delta_i}\Big)$.

cs.LG↗

arXiv2025

On the query complexity of sampling from non-log-concave distributions

We study the problem of sampling from a $d$-dimensional distribution with density $p(x)\propto e^{-f(x)}$, which does not necessarily satisfy good isoperimetric conditions. Specifically, we show that for any $L,M$ satisfying $LM\ge d\ge 5$, $\epsilon\in \left(0,\frac{1}{32}\right)$, and any algorithm with query accesses to the value of $f(x)$ and $\nabla f(x)$, there exists an $L$-log-smooth distribution with second moment at most $M$ such that the algorithm requires $\left(\frac{LM}{d\epsilon}\right)^{\Omega(d)}$ queries to compute a sample whose distribution is within $\epsilon$ in total variation distance to the target distribution. We complement the lower bound with an algorithm requiring $\left(\frac{LM}{d\epsilon}\right)^{\mathcal{O}(d)}$ queries, thereby characterizing the tight (up to the constant in the exponent) query complexity for sampling from the family of non-log-concave distributions. Our results are in sharp contrast with the recent work of Huang et al. (COLT'24), where an algorithm with quasi-polynomial query complexity was proposed for sampling from a non-log-concave distribution when $M=\mathtt{poly}(d)$. Their algorithm works under the stronger condition that all distributions along the trajectory of the Ornstein-Uhlenbeck process, starting from the target distribution, are $\mathcal{O}(1)$-log-smooth. We investigate this condition and prove that it is strictly stronger than requiring the target distribution to be $\mathcal O(1)$-log-smooth. Additionally, we study this condition in the context of mixtures of Gaussians. Finally, we place our results within the broader theme of ``sampling versus optimization'', as studied in Ma et al. (PNAS'19). We show that for a wide range of parameters, sampling is strictly easier than optimization by a super-exponential factor in the dimension $d$.

cs.DS↗

arXiv2025

Decay of correlation for edge colorings when $q>3\Delta$

We examine various perspectives on the decay of correlation for the uniform distribution over proper $q$-edge colorings of graphs with maximum degree $\Delta$. First, we establish the coupling independence property when $q\ge 3\Delta$ for general graphs. Together with the work of Chen et al. (2024), this result implies a fully polynomial-time approximation scheme (FPTAS) for counting the number of proper $q$-edge colorings. Next, we prove the strong spatial mixing property on trees, provided that $q> (3+o(1))\Delta$. The strong spatial mixing property is derived from the spectral independence property of a version of the weighted edge coloring distribution, which is established using the matrix trickle-down method developed in Abdolazimi, Liu and Oveis Gharan (FOCS, 2021) and Wang, Zhang and Zhang (STOC, 2024). Finally, we show that the weak spatial mixing property holds on trees with maximum degree $\Delta$ if and only if $q\ge 2\Delta-1$.

cs.DS↗

arXiv2024

Dynamical causality under invisible confounders

Causality inference is prone to spurious causal interactions, due to the substantial confounders in a complex system. While many existing methods based on the statistical methods or dynamical methods attempt to address misidentification challenges, there remains a notable lack of effective methods to infer causality, in particular in the presence of invisible/unobservable confounders. As a result, accurately inferring causation with invisible confounders remains a largely unexplored and outstanding issue in data science and AI fields. In this work, we propose a method to overcome such challenges to infer dynamical causality under invisible confounders (CIC method) and further reconstruct the invisible confounders from time-series data by developing an orthogonal decomposition theorem in a delay embedding space. The core of our CIC method lies in its ability to decompose the observed variables not in their original space but in their delay embedding space into the common and private subspaces respectively, thereby quantifying causality between those variables both theoretically and computationally. This theoretical foundation ensures the causal detection for any high-dimensional system even with only two observed variables under many invisible confounders, which is actually a long-standing problem in the field. In addition to the invisible confounder problem, such a decomposition actually makes the intertwined variables separable in the embedding space, thus also solving the non-separability problem of causal inference. Extensive validation of the CIC method is carried out using various real datasets, and the experimental results demonstrates its effectiveness to reconstruct real biological networks even with unobserved confounders.

cs.LG↗

arXiv2024

Understanding Memory-Regret Trade-Off for Streaming Stochastic Multi-Armed Bandits

We study the stochastic multi-armed bandit problem in the $P$-pass streaming model. In this problem, the $n$ arms are present in a stream and at most $m<n$ arms and their statistics can be stored in the memory. We give a complete characterization of the optimal regret in terms of $m, n$ and $P$. Specifically, we design an algorithm with $\tilde O\left((n-m)^{1+\frac{2^{P}-2}{2^{P+1}-1}} n^{\frac{2-2^{P+1}}{2^{P+1}-1}} T^{\frac{2^P}{2^{P+1}-1}}\right)$ regret and complement it with an $\tilde Ω\left((n-m)^{1+\frac{2^{P}-2}{2^{P+1}-1}} n^{\frac{2-2^{P+1}}{2^{P+1}-1}} T^{\frac{2^P}{2^{P+1}-1}}\right)$ lower bound when the number of rounds $T$ is sufficiently large. Our results are tight up to a logarithmic factor in $n$ and $P$.

cs.LG↗

arXiv2024

FPTAS for Holant Problems with Log-Concave Signatures

For an integer $b\ge 0$, a $b$-matching in a graph $G=(V,E)$ is a set $S\subseteq E$ such that each vertex $v\in V$ is incident to at most $b$ edges in $S$. We design a fully polynomial-time approximation scheme (FPTAS) for counting the number of $b$-matchings in graphs with bounded degrees. Our FPTAS also applies to a broader family of counting problems, namely Holant problems with log-concave signatures. Our algorithm is based on Moitra's linear programming approach (JACM'19). Using a novel construction called the extended coupling tree, we derandomize the coupling designed by Chen and Gu (SODA'24).

cs.DS↗

arXiv2024

Sampling Proper Colorings on Line Graphs Using $(1+o(1))Δ$ Colors

We prove that the single-site Glauber dynamics for sampling proper $q$-colorings mixes in $O_Δ(n\log n)$ time on line graphs with $n$ vertices and maximum degree $Δ$ when $q>(1+o(1))Δ$. The main tool in our proof is the matrix trickle-down theorem developed by Abdolazimi, Liu and Oveis Gharan (FOCS, 2021).

cs.DS↗

arXiv2023

Improved Algorithms for Bandit with Graph Feedback via Regret Decomposition

The problem of bandit with graph feedback generalizes both the multi-armed bandit (MAB) problem and the learning with expert advice problem by encoding in a directed graph how the loss vector can be observed in each round of the game. The mini-max regret is closely related to the structure of the feedback graph and their connection is far from being fully understood. We propose a new algorithmic framework for the problem based on a partition of the feedback graph. Our analysis reveals the interplay between various parts of the graph by decomposing the regret to the sum of the regret caused by small parts and the regret caused by their interaction. As a result, our algorithm can be viewed as an interpolation and generalization of the optimal algorithms for MAB and learning with expert advice. Our framework unifies previous algorithms for both strongly observable graphs and weakly observable graphs, resulting in improved and optimal regret bounds on a wide range of graph families including graphs of bounded degree and strongly observable graphs with a few corrupted arms.

cs.LG↗

arXiv2023

On Interpolating Experts and Multi-Armed Bandits

Learning with expert advice and multi-armed bandit are two classic online decision problems which differ on how the information is observed in each round of the game. We study a family of problems interpolating the two. For a vector $\mathbf{m}=(m_1,\dots,m_K)\in \mathbb{N}^K$, an instance of $\mathbf{m}$-MAB indicates that the arms are partitioned into $K$ groups and the $i$-th group contains $m_i$ arms. Once an arm is pulled, the losses of all arms in the same group are observed. We prove tight minimax regret bounds for $\mathbf{m}$-MAB and design an optimal PAC algorithm for its pure exploration version, $\mathbf{m}$-BAI, where the goal is to identify the arm with minimum loss with as few rounds as possible. We show that the minimax regret of $\mathbf{m}$-MAB is $Θ\left(\sqrt{T\sum_{k=1}^K\log (m_k+1)}\right)$ and the minimum number of pulls for an $(ε,0.05)$-PAC algorithm of $\mathbf{m}$-BAI is $Θ\left(\frac{1}{ε^2}\cdot \sum_{k=1}^K\log (m_k+1)\right)$. Both our upper bounds and lower bounds for $\mathbf{m}$-MAB can be extended to a more general setting, namely the bandit with graph feedback, in terms of the clique cover and related graph parameters. As consequences, we obtained tight minimax regret bounds for several families of feedback graphs.

cs.LG↗

arXiv2022

A Perfect Sampler for Hypergraph Independent Sets

The problem of uniformly sampling hypergraph independent sets is revisited. We design an efficient perfect sampler for the problem under a condition similar to that of the asymmetric Lovász Local Lemma. When applied to $d$-regular $k$-uniform hypergraphs on $n$ vertices, our sampler terminates in expected $O(n\log n)$ time provided $d\le c\cdot 2^{k/2}/k$ for some constant $c>0$. If in addition the hypergraph is linear, the condition can be weaken to $d\le c\cdot 2^{k}/k^2$ for some constant $c>0$, matching the rapid mixing condition for Glauber dynamics in Hermon, Sly and Zhang [HSZ19].

cs.DS↗

arXiv2022

Information-theoretic Classification Accuracy: A Criterion that Guides Data-driven Combination of Ambiguous Outcome Labels in Multi-class Classification

Outcome labeling ambiguity and subjectivity are ubiquitous in real-world datasets. While practitioners commonly combine ambiguous outcome labels for all data points (instances) in an ad hoc way to improve the accuracy of multi-class classification, there lacks a principled approach to guide the label combination for all data points by any optimality criterion. To address this problem, we propose the information-theoretic classification accuracy (ITCA), a criterion that balances the trade-off between prediction accuracy (how well do predicted labels agree with actual labels) and classification resolution (how many labels are predictable), to guide practitioners on how to combine ambiguous outcome labels. To find the optimal label combination indicated by ITCA, we propose two search strategies: greedy search and breadth-first search. Notably, ITCA and the two search strategies are adaptive to all machine-learning classification algorithms. Coupled with a classification algorithm and a search strategy, ITCA has two uses: improving prediction accuracy and identifying ambiguous labels. We first verify that ITCA achieves high accuracy with both search strategies in finding the correct label combinations on synthetic and real data. Then we demonstrate the effectiveness of ITCA in diverse applications including medical prognosis, cancer survival prediction, user demographics prediction, and cell type classification. We also provide theoretical insights into ITCA by studying the oracle and the linear discriminant analysis classification algorithms. Python package itca (available at https://github.com/JSB-UCLA/ITCA) implements ITCA and search strategies.

stat.ML↗