2020/01/14 by Burak Çakmak, Manfred Opper · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Approximate inference #Bayesian Methods and Mixture Models #Bayesian inference #Bayesian probability #Covariance #Gaussian Processes and Bayesian Inference #Gaussian process #Inference #Invariant (physics) #Latent variable #Markov Chains and Monte Carlo Methods #Statistical inference #cond-mat.dis-nn #cs.LG #stat.ML
paper · pdf · doi:10.1088/1751-8121/ab8ff4
published in Journal of Physics A Mathematical and Theoretical 53(27), 274001 (Institute of Physics) · 25 pages, 2 figures
arxiv created 2020/01/14 · openalex created_date 2020/01/23 · openalex publication_date 2020/05/04 · arxiv updated 2020/08/26 · openalex updated_date 2026/08/05
Abstract We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student–teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices drawn from rotation invariant ensembles. For the case of perfect data-model matching, the knowledge of static order parameters derived from the replica method allows us to obtain efficient algorithmic updates in terms of matrix–vector multiplications with a fixed matrix. Using the dynamical functional approach, we obtain an exact effective stochastic process in the thermodynamic limit for a single node. From this, we obtain closed-form expressions for the rate of the convergence. Analytical results are in excellent agreement with simulations of single instances of large models.