Mixing-Free and Signal-Optimal Learning of Gaussian Graphical Models from Glauber Dynamics

• URL: http://arxiv.org/abs/2607.18559v1
• Date: Mon, 20 Jul 2026 22:44:45 GMT
• Title: Mixing-Free and Signal-Optimal Learning of Gaussian Graphical Models from Glauber Dynamics
• Abstract summary: We study exact recovery of the graph from one trajectory of random-scan Gaussian Glauber dynamics.<n>We propose two algorithms that are mixing-free and attain the $-2$ dependence of the information-theoretic lower bounds.
• Score: 5.844015313757267
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process. We study exact recovery of the graph from one trajectory of random-scan Gaussian Glauber dynamics. Existing techniques for this problem either inherit the mixing time of the chain, which can be super-polynomial in the dimension $p$ without strong assumptions, or are suboptimal in the minimum normalized edge strength $κ$. We propose two algorithms that are mixing-free and attain the $κ^{-2}$ dependence of the information-theoretic lower bounds. Both instantiate a shared dueling-neighborhood search meta-algorithm with a local statistic built directly from the update sequence. The first fits a least-squares regression at the updates of each node and recovers the graph from $\widetilde O(pd^{2}/κ^{2})$ updates, where $d$ is the maximum degree. This algorithm's data requirement depends on a local conditioning quantity, but only logarithmically and is provably optimal even when the underlying chain mixes slowly. The second algorithm is based on counting occurences of a specific update pattern and requires $\widetilde O(pd^{4}/κ^{2})$ updates, with no dependence on any condition number. The central technical challenge is that both statistics are built from dependent, non-stationary observations. Our analysis tackles this by demonstrating how to extract fresh Gaussian innovations from the update sequence, which yields mixing-free control of appropriate quantities. Neither the algorithms nor their analyses invoke stationarity, a spectral gap, or mixing conditions, and all guarantees hold from an arbitrary initialization.

Related papers

• Learning Gaussian Graphical Models from a Glauber Trajectory Without Mixing [13.453178572042125]
  We study the task of learning the structure of a $d$-sparse Gaussian graphical model on $n$ variables from a single trajectory of Glauber dynamics.<n>Motivated in part by this gap, we give a conditional-time algorithm that recovers the trajectory-length guarantee from a single Glauber trajectory.
  arXiv  Detail & Related papers  (2026-06-30T07:07:57Z)
• Can Neural Networks Achieve Optimal Computational-statistical Tradeoff? An Analysis on Single-Index Model [53.6316818897326]
  We propose a gradient-based algorithm for training a two-layer neural network in time.<n>We show that our algorithm learns a sparse representation that strongly aligns with the unknown signal $star$.<n>We extend our approach to the setting where $star$ is $k$-sparse for $k = o(sqrtd)$ by introducing a novel weight technique.
  arXiv  Detail & Related papers  (2026-06-13T09:34:39Z)
• Finite-Time Error Bounds for Greedy-GQ [20.51105692499517]
  We show that Greedy-GQ algorithm converges fast as finite-time error. Our analysis provides for faster convergence step-sizes for choosing step-sizes.
  arXiv  Detail & Related papers  (2022-09-06T15:04:57Z)
• Statistical Inference of Constrained Stochastic Optimization via Sketched Sequential Quadratic Programming [53.63469275932989]
  We consider online statistical inference of constrained nonlinear optimization problems.<n>We apply the Sequential Quadratic Programming (StoSQP) method to solve these problems.
  arXiv  Detail & Related papers  (2022-05-27T00:34:03Z)
• Convergence of First-Order Methods for Constrained Nonconvex Optimization with Dependent Data [7.513100214864646]
  We show the worst-case complexity of convergence $tildeO(t-1/4)$ and MoreautildeO(vareps-4)$ for smooth non- optimization. We obtain first online nonnegative matrix factorization algorithms for dependent data based on projected gradient methods with adaptive step sizes and optimal convergence.
  arXiv  Detail & Related papers  (2022-03-29T17:59:10Z)
• An Improved Analysis of Gradient Tracking for Decentralized Machine Learning [34.144764431505486]
  We consider decentralized machine learning over a network where the training data is distributed across $n$ agents. The agent's common goal is to find a model that minimizes the average of all local loss functions. We improve the dependency on $p$ from $mathcalO(p-1)$ to $mathcalO(p-1)$ in the noiseless case.
  arXiv  Detail & Related papers  (2022-02-08T12:58:14Z)
• Single-Timescale Stochastic Nonconvex-Concave Optimization for Smooth Nonlinear TD Learning [145.54544979467872]
  We propose two single-timescale single-loop algorithms that require only one data point each step. Our results are expressed in a form of simultaneous primal and dual side convergence.
  arXiv  Detail & Related papers  (2020-08-23T20:36:49Z)
• Optimal Robust Linear Regression in Nearly Linear Time [97.11565882347772]
  We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = langle X,w* rangle + epsilon$ We propose estimators for this problem under two settings: (i) $X$ is L4-L2 hypercontractive, $mathbbE [XXtop]$ has bounded condition number and $epsilon$ has bounded variance and (ii) $X$ is sub-Gaussian with identity second moment and $epsilon$ is
  arXiv  Detail & Related papers  (2020-07-16T06:44:44Z)
• Least Squares Regression with Markovian Data: Fundamental Limits and Algorithms [69.45237691598774]
  We study the problem of least squares linear regression where the data-points are dependent and are sampled from a Markov chain. We establish sharp information theoretic minimax lower bounds for this problem in terms of $tau_mathsfmix$. We propose an algorithm based on experience replay--a popular reinforcement learning technique--that achieves a significantly better error rate.
  arXiv  Detail & Related papers  (2020-06-16T04:26:50Z)
• Learning nonlinear dynamical systems from a single trajectory [102.60042167341956]
  We introduce algorithms for learning nonlinear dynamical systems of the form $x_t+1=sigma(Thetastarx_t)+varepsilon_t$. We give an algorithm that recovers the weight matrix $Thetastar$ from a single trajectory with optimal sample complexity and linear running time.
  arXiv  Detail & Related papers  (2020-04-30T10:42:48Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.