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Title: Fast M-Estimation of Generalized Linear Latent Variable Models in High Dimensions
Abstract: Dimension reduction for high dimensional data is an important and challenging task, relevant to both machine learning and statistical applications. Generalized Linear Latent Variable Models (GLLVMs) provide a probabilistic alternative to matrix factorization when the data are of mixed types, whether discrete, continuous, or a mixture of both. They achieve the reduction of dimensionality by mapping the correlated multivariate data to so-called latent variables, defined in a lower-dimensional space. The benefit of GLLVMs is twofold: the latent variables can be estimated and used as features to be embedded in another model, and the model parameters themselves are interpretable and provide meaningful indications on the very structure of the data. Moreover, GLLVM can naturally be extended to dynamic processes such as those used to model longitudinal data. However, with a likelihood based approach, GLLVM’s estimation represents a tremendous challenge for even moderately large dimensions, essentially due to the multiple integrals involved in the likelihood function. Numerous methods based on approximations of this latter have been proposed: Laplace approximation, adaptive quadrature, or, recently, extended variational approximation. For GLLVMs, however, these methods do not scale well to high dimensions, and they may also introduce a large bias in the estimates. In this paper, we consider an alternative route, which consists in proposing an alternative estimator, based on drastically simplified estimating equations, complemented with a numerically efficient bias reduction methods in order to recover a consistent estimator for the GLLVM parameters. The resulting estimator is an M-estimator, which has a negligible efficiency loss compared to the (exact) MLE. For larger data sets, the proposed M-estimator, whose computational burden is linear in npq, remains applicable when the state-of-the-art method fails to converge. To compute the M-estimator, we propose to use a stochastic approximation algorithm.
Biography: Graduated from the University of Geneva (Ph. D. in econometrics and statistics) in 1993, Maria-Pia Victoria-Feser has held several positions in different institutions or Departments. She was appointed as lecturer in statistics at the London School of Economics (1993-1996), as assistant and associate professor in statistics (part time) at the Faculty of psychology and educational sciences at the University of Geneva (1997-2005), financed by a Swiss National Science Found grant, full professor in statistics at the University of Geneva since 2001. She now holds, since 2023, a full professor position at the department of statistics of the University of Bologna. She has also acted for the foundation and as founding dean (2013-2017) of the Geneva School of Economics and Management (GSEM) of the University of Geneva, and as founding director of the Research Center for Statistics of the University of Geneva (created in 2011).
Maria-Pia Victoria-Feser’s research interests are in fundamental statistics (robust statistics, model selection and simulation based inference in high dimensions for complex models) with applications in economics (welfare economics, extremes), psychology and social sciences (generalized linear latent variable models, media analytics), and engineering (time series for geo-localization). She has published in leading journals of statistics as well as top journals in related fields. Throughout her career, she has supervised several PhD students, three of which currently hold professorial positions and one a senior researcher position, in leading academic institutions.