Sparse Covariance Estimation in Logit Mixture Models

• URL: http://arxiv.org/abs/2001.05034v1
• Date: Tue, 14 Jan 2020 20:19:15 GMT
• Title: Sparse Covariance Estimation in Logit Mixture Models
• Authors: Youssef M Aboutaleb, Mazen Danaf, Yifei Xie, and Moshe Ben-Akiva
• Abstract summary: This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Our objective is to find optimal subsets of correlated coefficients for which we estimate covariances.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Researchers typically specify covariance matrices in logit mixture models under one of two extreme assumptions: either an unrestricted full covariance matrix (allowing correlations between all random coefficients), or a restricted diagonal matrix (allowing no correlations at all). Our objective is to find optimal subsets of correlated coefficients for which we estimate covariances. We propose a new estimator, called MISC, that uses a mixed-integer optimization (MIO) program to find an optimal block diagonal structure specification for the covariance matrix, corresponding to subsets of correlated coefficients, for any desired sparsity level using Markov Chain Monte Carlo (MCMC) posterior draws from the unrestricted full covariance matrix. The optimal sparsity level of the covariance matrix is determined using out-of-sample validation. We demonstrate the ability of MISC to correctly recover the true covariance structure from synthetic data. In an empirical illustration using a stated preference survey on modes of transportation, we use MISC to obtain a sparse covariance matrix indicating how preferences for attributes are related to one another.

Related papers

• Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Information [3.9748528039819977]
  This paper investigates statistical inference for noisy matrix completion in a semi-supervised model. We apply an iterative least squares (LS) estimation approach in our considered context. We show that our method only needs a few iterations, and the resulting entry-wise estimators of the low-rank matrix and the coefficient matrix are guaranteed to have normal distributions.
  arXiv  Detail & Related papers  (2024-03-22T01:06:36Z)
• Entropic covariance models [0.7614628596146602]
  We present a general framework for linear restrictions on different transformations of the covariance matrix. Our proposed estimation method solves a convex problem and yields an $M$-estimator.
  arXiv  Detail & Related papers  (2023-06-06T11:25:05Z)
• Learning Graphical Factor Models with Riemannian Optimization [70.13748170371889]
  This paper proposes a flexible algorithmic framework for graph learning under low-rank structural constraints. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution. We leverage geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models.
  arXiv  Detail & Related papers  (2022-10-21T13:19:45Z)
• Equivariance Discovery by Learned Parameter-Sharing [153.41877129746223]
  We study how to discover interpretable equivariances from data. Specifically, we formulate this discovery process as an optimization problem over a model's parameter-sharing schemes. Also, we theoretically analyze the method for Gaussian data and provide a bound on the mean squared gap between the studied discovery scheme and the oracle scheme.
  arXiv  Detail & Related papers  (2022-04-07T17:59:19Z)
• Test Set Sizing Via Random Matrix Theory [91.3755431537592]
  This paper uses techniques from Random Matrix Theory to find the ideal training-testing data split for a simple linear regression. It defines "ideal" as satisfying the integrity metric, i.e. the empirical model error is the actual measurement noise. This paper is the first to solve for the training and test size for any model in a way that is truly optimal.
  arXiv  Detail & Related papers  (2021-12-11T13:18:33Z)
• Optimal Clustering in Anisotropic Gaussian Mixture Models [3.5590836605011047]
  We study the clustering task under anisotropic Gaussian Mixture Models. We characterize the dependence of signal-to-noise ratios on the cluster centers.
  arXiv  Detail & Related papers  (2021-01-14T00:31:52Z)
• Coupled regularized sample covariance matrix estimator for multiple classes [14.41703014203756]
  We consider regularized SCM (RSCM) estimators for multiclass problems that couple together two different target matrices for regularization. We derive the MSE optimal tuning parameters for the estimators as well as propose a method for their estimation. The MSE performance of the proposed coupled RSCMs are evaluated with simulations and in a regularized discriminant analysis (RDA) classification set-up on real data.
  arXiv  Detail & Related papers  (2020-11-09T10:39:53Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)
• Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants [94.46276668068327]
  In [1], an ensemble of randomly projected linear discriminants is used to classify datasets. We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator. We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
  arXiv  Detail & Related papers  (2020-04-17T12:47:04Z)
• Covariance Estimation for Matrix-valued Data [9.739753590548796]
  We propose a class of distribution-free regularized covariance estimation methods for high-dimensional matrix data. We formulate a unified framework for estimating bandable covariance, and introduce an efficient algorithm based on rank one unconstrained Kronecker product approximation. We demonstrate the superior finite-sample performance of our methods using simulations and real applications from a gridded temperature anomalies dataset and a S&P 500 stock data analysis.
  arXiv  Detail & Related papers  (2020-04-11T02:15:26Z)
• Clustering Binary Data by Application of Combinatorial Optimization Heuristics [52.77024349608834]
  We study clustering methods for binary data, first defining aggregation criteria that measure the compactness of clusters. Five new and original methods are introduced, using neighborhoods and population behavior optimization metaheuristics. From a set of 16 data tables generated by a quasi-Monte Carlo experiment, a comparison is performed for one of the aggregations using L1 dissimilarity, with hierarchical clustering, and a version of k-means: partitioning around medoids or PAM.
  arXiv  Detail & Related papers  (2020-01-06T23:33:31Z)

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.