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Chenyang Zhong

Publications and source records attributed to Chenyang Zhong.

At least 19 recordsLinked to original sources
arXiv2026

Graph-Enabled Efficient Federated Bayesian Modeling

Federated Bayesian modeling requires combining evidence across distributed data holders while preserving posterior uncertainty and keeping local data decentralized. We propose Federated Latent Graph MCMC (FLaG-MCMC), a framework for sequential posterior transfer in which accumulated posterior information is represented by a reservoir of Monte Carlo samples. FLaG-MCMC constructs a graph that captures the geometry of the posterior reservoir and uses graph-enabled proposals whose per-iteration cost is independent of the reservoir size. Each data holder updates the inherited posterior using its local likelihood and returns an updated reservoir for subsequent inference. We apply FLaG-MCMC in two health science settings. Using mobile and wearable device data from GLOBEM, we investigate associations between depression status and behavioral patterns while sequentially accumulating posterior information across participants. FLaG-MCMC accurately reconstructs the corresponding pooled Bayesian posterior while closely tracking evolving posterior location and uncertainty in these associations. We also conduct a simulation study motivated by Bayesian evidence synthesis for opioid use disorder prevalence across studies, transferring posterior information from an Ohio study to a subsequent New York analysis under covariate shift. In this setting, FLaG-MCMC demonstrates reliable posterior transfer and favorable computational scaling. Theoretical results establish the validity and consistency of the framework.

stat.CO↗
arXiv2026

Entropic regularization of Monge's problem

We study the vanishing-regularization limit of entropically regularized optimal transport (EOT) for the Euclidean distance cost $c(x,y)=\|x-y\|$ in dimension $d>1$. We develop a comprehensive variational convergence framework that entails two main results. First, we resolve the longstanding entropic selection problem: the EOT minimizer converges to a distinguished optimal transport plan that is characterized explicitly as the solution of a constrained EOT problem on each transport ray. Denoting by $\varepsilon>0$ the regularization parameter, this selection holds for all $o(\varepsilon)$-approximate minimizers, with sharp failure at the $O(\varepsilon)$ scale. Second, we establish an explicit second-order expansion of the entropic transport cost. The second-order term encodes the geometry of the regularization and reveals the optimal asymptotic tradeoff between entropy and transport cost.

math.OC↗
arXiv2026

Efficient Sampling for Ising and Potts Models using Auxiliary Gaussian Variables

Ising and Potts models are an important class of discrete probability distributions which originated from statistical physics and since then have found applications in several disciplines. Simulation from these models is a well known challenging problem. In this paper, we study a class of Markov chain Monte Carlo algorithms, in which we introduce an auxiliary Gaussian variable such that, conditional on this variable, the discrete states are independent. This approach is broadly applicable to Ising and Potts models, including ones in which the coupling matrix admits negative entries, as in spin glass and Hopfield models. We focus on a block Gibbs sampler version of this algorithm, which alternates between sampling the auxiliary Gaussian and the discrete states, and derive mixing time bounds for a wide class of Ising/Potts models at both high and low temperatures, yielding results analogous to those derived for the Heat Bath and Swendsen-Wang algorithms. We present novel choices of auxiliary Gaussian variables which scale well with the number of states in the Potts model, and which can take advantage of the low rank structure of the coupling matrix, if any. Finally, we numerically evaluate the performance of the auxiliary Gaussian Gibbs sampler with several competing algorithms, across a range of examples.

stat.CO↗
arXiv2026

Heights of butterfly trees

Binary search trees (BSTs) are fundamental data structures whose performance is largely governed by tree height. We introduce a block model for constructing BSTs by embedding internal BSTs into the nodes of an external BST -- a structure motivated by parallel data architectures -- corresponding to composite permutations formed via Kronecker or wreath products. Extending Devroye's result that the height $h_n$ of a random BST satisfies $h_n / \log n \to c^* \approx 4.311$, we show that block BSTs with $nm$ nodes and fixed external size $m$ satisfy $h_{n,m} / \log n \to c^* + h_m$ in distribution. We then study butterfly trees: BSTs with $N = 2^n$ nodes generated from permutations built using iterated Kronecker or wreath products. For simple butterfly trees (from iterated Kronecker products of $S_2$), we give a full distributional description showing polynomial height growth: $\mathbb{E} h_n^{\operatorname{B}} = Θ(N^α)$ with $α= \log_2(3/2) \approx 0.58496$. For nonsimple butterfly trees (from wreath products), we prove power-law bounds: $cN^α\cdot (1 + o(1)) \le \mathbb{E} h_n^{\operatorname{B}} \le dN^β\cdot (1 + o(1))$, with $β\approx 0.913189$.

math.PR↗
arXiv2025

A Particle Algorithm for Mean-Field Variational Inference

Variational inference is a fast and scalable alternative to Markov chain Monte Carlo and has been widely applied to posterior inference tasks in statistics and machine learning. A traditional approach for implementing mean-field variational inference (MFVI) is coordinate ascent variational inference (CAVI), which relies crucially on parametric assumptions on complete conditionals. We introduce a novel particle-based algorithm for MFVI, named PArticle VI (PAVI), for nonparametric mean-field approximation. We obtain non-asymptotic error bounds for our algorithm. To our knowledge, this is the first end-to-end guarantee for particle-based MFVI.

math.ST↗
arXiv2025

Variational Inference for Latent Variable Models in High Dimensions

Variational inference (VI) is a popular method for approximating intractable posterior distributions in Bayesian inference and probabilistic machine learning. In this paper, we introduce a general framework for quantifying the statistical accuracy of mean-field variational inference (MFVI) for posterior approximation in Bayesian latent variable models with categorical local latent variables (and arbitrary global latent variables). Utilizing our general framework, we capture the exact regime where MFVI 'works' for the celebrated latent Dirichlet allocation model. Focusing on the mixed membership stochastic blockmodel, we show that the vanilla fully factorized MFVI, often used in the literature, is suboptimal. We propose a partially grouped VI algorithm for this model and show that it works, and derive its exact finite-sample performance. We further illustrate that our bounds are tight for both the above models. Our proof techniques, which extend the framework of nonlinear large deviations, open the door for the analysis of MFVI in other latent variable models.

math.ST↗
arXiv2025

Efficient Generative Modeling via Penalized Optimal Transport Network

The generation of synthetic data with distributions that faithfully emulate the underlying data-generating mechanism holds paramount significance. Wasserstein Generative Adversarial Networks (WGANs) have emerged as a prominent tool for this task; however, due to the delicate equilibrium of the minimax formulation and the instability of Wasserstein distance in high dimensions, WGAN often manifests the pathological phenomenon of mode collapse. This results in generated samples that converge to a restricted set of outputs and fail to adequately capture the tail behaviors of the true distribution. Such limitations can lead to serious downstream consequences. To this end, we propose the Penalized Optimal Transport Network (POTNet), a versatile deep generative model based on the marginally-penalized Wasserstein (MPW) distance. Through the MPW distance, POTNet effectively leverages low-dimensional marginal information to guide the overall alignment of joint distributions. Furthermore, our primal-based framework enables direct evaluation of the MPW distance, thus eliminating the need for a critic network. This formulation circumvents training instabilities inherent in adversarial approaches and avoids the need for extensive parameter tuning. We derive a non-asymptotic bound on the generalization error of the MPW loss and establish convergence rates of the generative distribution learned by POTNet. Our theoretical analysis together with extensive empirical evaluations demonstrate the superior performance of POTNet in accurately capturing underlying data structures, including their tail behaviors and minor modalities. Moreover, our model achieves orders of magnitude speedup during the sampling stage compared to state-of-the-art alternatives, which enables computationally efficient large-scale synthetic data generation.

stat.ML↗
arXiv2024

On the longest increasing subsequence and number of cycles of butterfly permutations

One method to generate random permutations involves using Gaussian elimination with partial pivoting (GEPP) on a random matrix $A$ and storing the permutation matrix factor $P$ from the resulting GEPP factorization $PA=LU$. We are interested in exploring properties of random butterfly permutations, which are generated using GEPP on specific random butterfly matrices. Our paper highlights new connections among random matrix theory, numerical linear algebra, group actions of rooted trees, and random permutations. We address the questions of the longest increasing subsequence (LIS) and number of cycles for particular uniform butterfly permutations, with full distributional descriptions and limit theorems for simple butterfly permutations. We also establish scaling limit results and limit theorems for nonsimple butterfly permutations, which include certain $p$-Sylow subgroups of the symmetric group of $N=p^n$ elements for prime $p$. For the LIS, we establish power law bounds on the expected LIS of the form $N^{α_p}$ and $N^{β_p}$ where $\frac12 < α_p < β_p < 1$ for each $p$ with $α_p = 1 - o_p(1)$, showing distinction from the typical $O(N^{1/2})$ expected LIS frequently encountered in the study of random permutations (e.g., uniform permutations). For the number of cycles scaled by $(2-1/p)^n$, we establish a full CLT to a new limiting distribution depending on $p$ with positive support we introduce that is uniquely determined by its positive moments that satisfy explicit recursive formulas; this thus determines a CLT for the number of cycles for any uniform $p$-Sylow subgroup of $S_{p^n}$.

math.PR↗
arXiv2024

Large deviation bounds for the Airy point process

In this paper, we establish the first large deviation bounds for the Airy point process. The proof is based on a novel approach which relies upon the approximation of the Airy point process using the Gaussian unitary ensemble (GUE) up to an exponentially small probability, together with precise estimates for the stochastic Airy operator and edge rigidity for beta ensembles. As a by-product of our estimates for the Airy point process, we significantly improve upon previous results on the lower tail probability of the one-point distribution of the KPZ equation with narrow-wedge initial data and the half-space KPZ equation with Neumann boundary parameter $A=-\frac{1}{2}$ and narrow-wedge initial data in a unified and much shorter manner. Our bounds hold for all sufficiently large time $T$, and for the first time establish sharp super-exponential decay with exponent $3$ for tail depth less than $T^{\frac{2}{3}}$ (with sharp leading prefactors $\frac{1}{12}$ and $\frac{1}{24}$ for tail depth less than $T^{\frac{1}{6}}$).

math.PR↗
arXiv2024

Large deviation principle for the Airy point process

The Airy point process is a determinantal point process that arises from the spectral edge of the Gaussian Unitary Ensemble. In this paper, we establish a large deviation principle for the Airy point process. Our result also extends to point processes arising from the spectrum of the stochastic Airy operator.

math.PR↗
arXiv2024

Colored stochastic vertex models with U-turn boundary

In this paper, we introduce a class of colored stochastic vertex models with U-turn right boundary. The vertex weights in the models satisfy the Yang-Baxter equations and the reflection equation. Based on these equations, we derive recursive relations for partition functions of the models.

math.PR↗
arXiv2023

Cycle structure of Mallows permutation model with the $L^1$ distance

Introduced by Mallows as a ranking model in statistics, Mallows permutation model is a class of non-uniform probability distributions on the symmetric group $S_n$. The model depends on a distance metric on $S_n$ and a scale parameter $β$. In this paper, we take the distance metric to be the $L^1$ distance (also known as Spearman's footrule in the statistics literature), and investigate the cycle structure of random permutations drawn from Mallows permutation model with the $L^1$ distance. We focus on the parameter regime where $β>0$. We show that the expected length of the cycle containing a given point is of order $\min\{\max\{β^{-2},1\},n\}$, and the expected diameter of the cycle containing a given point is of order $\min\{e^{-2β}\max\{β^{-2},1\}, n-1\}$. Moreover, when $β\ll n^{-1\slash 2}$, the sorted cycle lengths (in descending order) normalized by $n$ converge in distribution to the Poisson-Dirichlet law with parameter $1$. The proofs of the results rely on the hit and run algorithm, a Markov chain for sampling from the model.

math.PR↗
arXiv2023

The length of the longest increasing subsequence of Mallows permutation models with $L^1$ and $L^2$ distances

Introduced by Mallows in statistical ranking theory, Mallows permutation model is a class of non-uniform probability measures on the symmetric group $S_n$ that depend on a distance metric $d(σ,τ)$ on $S_n$ and a scale parameter $β$. Taking the distance metric to be the $L^1$ and $L^2$ distances--which are respectively known as Spearman's footrule and Spearman's rank correlation in the statistics literature--leads to Mallows permutation models with $L^1$ and $L^2$ distances. In this paper, we study the length of the longest increasing subsequence of random permutations drawn from Mallows permutation models with $L^1$ and $L^2$ distances. For both models and various regimes of the scale parameter $β$, we determine the typical order of magnitude of the length of the longest increasing subsequence and establish a law of large numbers for this length. For Mallows permutation model with the $L^1$ distance, when $β\sim θn^{-1}$ for some fixed $θ>0$, the typical length of the longest increasing subsequence is of order $\sqrt{n}$; when $n^{-1}\ll β\ll 1$, this typical length is of order $n\sqrtβ$. For Mallows permutation model with the $L^2$ distance, when $β\sim θn^{-2}$ for some fixed $θ>0$, the typical length of the longest increasing subsequence is of order $\sqrt{n}$; when $n^{-2}\ll β\ll 1$, this typical length is of order $nβ^{\frac{1}{4}}$.

math.PR↗
arXiv2022

Computation of partition functions of free fermionic solvable lattice models via permutation graphs

In this paper, we introduce a novel and general method for computing partition functions of solvable lattice models with free fermionic Boltzmann weights. The method is based on the ``permutation graph'' and the ``$F$-matrix'': the permutation graph is a generalization of the $R$-matrix, and the $F$-matrix is constructed based on the permutation graph. The method allows generalizations to lattice models that are related to Cartan types B and C. Two applications are presented: they involve an ice model related to Tokuyama's formula and another ice model representing a Whittaker function on the metaplectic double cover of $\mathrm{Sp}(2r,F)$ with $F$ being a non-archimedean local field.

math-ph↗
arXiv2021

Mallows permutation models with $L^1$ and $L^2$ distances I: hit and run algorithms and mixing times

Mallows permutation model, introduced by Mallows in statistical ranking theory, is a class of non-uniform probability measures on the symmetric group $S_n$. The model depends on a distance metric $d(σ,τ)$ on $S_n$, which can be chosen from a host of metrics on permutations. In this paper, we focus on Mallows permutation models with $L^1$ and $L^2$ distances, respectively known in the statistics literature as Spearman's footrule and Spearman's rank correlation. Unlike most of the random permutation models that have been analyzed in the literature, Mallows permutation models with $L^1$ and $L^2$ distances do not have an explicit expression for their normalizing constants. This poses challenges to the task of sampling from these Mallows models. In this paper, we consider hit and run algorithms for sampling from both models. Hit and run algorithms are a unifying class of Markov chain Monte Carlo (MCMC) algorithms including the celebrated Swendsen-Wang and data augmentation algorithms. For both models, we show order $\log{n}$ mixing time upper bounds for the hit and run algorithms. This demonstrates much faster mixing of the hit and run algorithms compared to local MCMC algorithms such as the Metropolis algorithm. The proof of the results on mixing times is based on the path coupling technique, for which a novel coupling for permutations with one-sided restrictions is involved. Extensions of the hit and run algorithms to weighted versions of the above models, a two-parameter permutation model that involves the $L^1$ distance and Cayley distance, and lattice permutation models in dimensions greater than or equal to $2$ are also discussed. The order $\log{n}$ mixing time upper bound pertains to the two-parameter permutation model.

math.PR↗
arXiv2021

Convergence rate of a collapsed Gibbs sampler for crossed random effects models

In this paper, we analyze the convergence rate of a collapsed Gibbs sampler for crossed random effects models. Our results apply to a substantially larger range of models than previous works, including models that incorporate missingness mechanism and unbalanced level data. The theoretical tools involved in our analysis include a connection between relaxation time and autoregression matrix, concentration inequalities, and random matrix theory.

stat.CO↗
arXiv2021

Stochastic symplectic ice

In this paper, we construct solvable ice models (six-vertex models) with stochastic weights and U-turn right boundary, which we term ``stochastic symplectic ice''. The models consist of alternating rows of two types of vertices. The probabilistic interpretation of the models leads to novel interacting particle systems where particles alternately jump to the right and then to the left. Two colored versions of the models and related stochastic dynamics are also introduced. Using the Yang-Baxter equations, we establish functional equations and recursive relations for the partition functions of these models. In particular, the recursive relations satisfied by the partition function of one of the colored models are closely related to Demazure-Lusztig operators of type C.

math-ph↗