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      Learning Attribute Patterns in High-Dimensional Structured Latent Attribute Models

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          Abstract

          Structured latent attribute models (SLAMs) are a special family of discrete latent variable models widely used in social and biological sciences. This paper considers the problem of learning significant attribute patterns from a SLAM with potentially high-dimensional configurations of the latent attributes. We address the theoretical identifiability issue, propose a penalized likelihood method for the selection of the attribute patterns, and further establish the selection consistency in such an overfitted SLAM with diverging number of latent patterns. The good performance of the proposed methodology is illustrated by simulation studies and two real datasets in educational assessment.

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          A general framework for updating belief distributions

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            Likelihood-based selection and sharp parameter estimation.

            In high-dimensional data analysis, feature selection becomes one means for dimension reduction, which proceeds with parameter estimation. Concerning accuracy of selection and estimation, we study nonconvex constrained and regularized likelihoods in the presence of nuisance parameters. Theoretically, we show that constrained L(0)-likelihood and its computational surrogate are optimal in that they achieve feature selection consistency and sharp parameter estimation, under one necessary condition required for any method to be selection consistent and to achieve sharp parameter estimation. It permits up to exponentially many candidate features. Computationally, we develop difference convex methods to implement the computational surrogate through prime and dual subproblems. These results establish a central role of L(0)-constrained and regularized likelihoods in feature selection and parameter estimation involving selection. As applications of the general method and theory, we perform feature selection in linear regression and logistic regression, and estimate a precision matrix in Gaussian graphical models. In these situations, we gain a new theoretical insight and obtain favorable numerical results. Finally, we discuss an application to predict the metastasis status of breast cancer patients with their gene expression profiles.
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              A modified likelihood ratio test for homogeneity in finite mixture models

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                Author and article information

                Journal
                08 April 2019
                Article
                1904.04378
                f1d48536-fcb2-4136-9471-4018870cf65c

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                stat.ME stat.ML

                Machine learning,Methodology
                Machine learning, Methodology

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