A Stochastic Path-Integrated Differential EstimatoR Expectation Maximization Algorithm

• URL: http://arxiv.org/abs/2012.01929v1
• Date: Mon, 30 Nov 2020 15:49:31 GMT
• Title: A Stochastic Path-Integrated Differential EstimatoR Expectation Maximization Algorithm
• Authors: Gersende Fort (IMT), Eric Moulines (X-DEP-MATHAPP), Hoi-To Wai
• Abstract summary: The Expectation Maximization (EM) algorithm is of key importance for inference in latent variable models including mixture of regressors and experts, missing observations. This paper introduces a novel EM, called textttSP, for inference from a conditional expectation estimator.
• Score: 19.216497414060658
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Expectation Maximization (EM) algorithm is of key importance for inference in latent variable models including mixture of regressors and experts, missing observations. This paper introduces a novel EM algorithm, called \texttt{SPIDER-EM}, for inference from a training set of size $n$, $n \gg 1$. At the core of our algorithm is an estimator of the full conditional expectation in the {\sf E}-step, adapted from the stochastic path-integrated differential estimator ({\tt SPIDER}) technique. We derive finite-time complexity bounds for smooth non-convex likelihood: we show that for convergence to an $\epsilon$-approximate stationary point, the complexity scales as $K_{\operatorname{Opt}} (n,\epsilon )={\cal O}(\epsilon^{-1})$ and $K_{\operatorname{CE}}( n,\epsilon ) = n+ \sqrt{n} {\cal O}(\epsilon^{-1} )$, where $K_{\operatorname{Opt}}( n,\epsilon )$ and $K_{\operatorname{CE}}(n, \epsilon )$ are respectively the number of {\sf M}-steps and the number of per-sample conditional expectations evaluations. This improves over the state-of-the-art algorithms. Numerical results support our findings.

Related papers

• Inverting the Leverage Score Gradient: An Efficient Approximate Newton Method [10.742859956268655]
  This paper aims to recover the intrinsic model parameters given the leverage scores gradient. We specifically scrutinize the inversion of the leverage score gradient, denoted as $g(x)$.
  arXiv  Detail & Related papers  (2024-08-21T01:39:42Z)
• Efficiently Learning One-Hidden-Layer ReLU Networks via Schur Polynomials [50.90125395570797]
  We study the problem of PAC learning a linear combination of $k$ ReLU activations under the standard Gaussian distribution on $mathbbRd$ with respect to the square loss. Our main result is an efficient algorithm for this learning task with sample and computational complexity $(dk/epsilon)O(k)$, whereepsilon>0$ is the target accuracy.
  arXiv  Detail & Related papers  (2023-07-24T14:37:22Z)
• Near-Optimal Bounds for Learning Gaussian Halfspaces with Random Classification Noise [50.64137465792738]
  We show that any efficient SQ algorithm for the problem requires sample complexity at least $Omega(d1/2/(maxp, epsilon)2)$. Our lower bound suggests that this quadratic dependence on $1/epsilon$ is inherent for efficient algorithms.
  arXiv  Detail & Related papers  (2023-07-13T18:59:28Z)
• Private estimation algorithms for stochastic block models and mixture models [63.07482515700984]
  General tools for designing efficient private estimation algorithms. First efficient $(epsilon, delta)$-differentially private algorithm for both weak recovery and exact recovery.
  arXiv  Detail & Related papers  (2023-01-11T09:12:28Z)
• ReSQueing Parallel and Private Stochastic Convex Optimization [59.53297063174519]
  We introduce a new tool for BFG convex optimization (SCO): a Reweighted Query (ReSQue) estimator for the gradient of a function convolved with a (Gaussian) probability density. We develop algorithms achieving state-of-the-art complexities for SCO in parallel and private settings.
  arXiv  Detail & Related papers  (2023-01-01T18:51:29Z)
• An Optimal Stochastic Algorithm for Decentralized Nonconvex Finite-sum Optimization [25.21457349137344]
  We show a proof to show DEAREST requires at most $mathcal O(+sqrtmnLvarepsilon-2)$ first-order oracle (IFO) calls and $mathcal O(Lvarepsilon-2/sqrt1-lambda_W)$ communication rounds.
  arXiv  Detail & Related papers  (2022-10-25T11:37:11Z)
• Multi-block-Single-probe Variance Reduced Estimator for Coupled Compositional Optimization [49.58290066287418]
  We propose a novel method named Multi-block-probe Variance Reduced (MSVR) to alleviate the complexity of compositional problems. Our results improve upon prior ones in several aspects, including the order of sample complexities and dependence on strongity.
  arXiv  Detail & Related papers  (2022-07-18T12:03:26Z)
• Robust Sparse Mean Estimation via Sum of Squares [42.526664955704746]
  We study the problem of high-dimensional sparse mean estimation in the presence of an $epsilon$-fraction of adversarial outliers. Our algorithms follow the Sum-of-Squares based, to algorithms approach.
  arXiv  Detail & Related papers  (2022-06-07T16:49:54Z)
• On the complexity of All $\varepsilon$-Best Arms Identification [2.1485350418225244]
  We consider the problem of identifying all the $varepsilon$-optimal arms in a finite multi-armed bandit with Gaussian rewards. We propose a Track-and-Stop algorithm that identifies the set of $varepsilon$-good arms w.h.p and enjoys optimality (when $delta$ goes to zero) in terms of the expected sample complexity.
  arXiv  Detail & Related papers  (2022-02-13T10:54:52Z)
• Hybrid Stochastic-Deterministic Minibatch Proximal Gradient: Less-Than-Single-Pass Optimization with Nearly Optimal Generalization [83.80460802169999]
  We show that HSDMPG can attain an $mathcalObig (1/sttnbig)$ which is at the order of excess error on a learning model. For loss factors, we prove that HSDMPG can attain an $mathcalObig (1/sttnbig)$ which is at the order of excess error on a learning model.
  arXiv  Detail & Related papers  (2020-09-18T02:18:44Z)

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.