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Mengyang Gu

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AAAI Conference 2020 Conference Paper

GaSPing for Utility

  • Mengyang Gu
  • Debarun Bhattacharjya
  • Dharmashankar Subramanian

High-consequence decisions often require a detailed investigation of a decision maker’s preferences, as represented by a utility function. Inferring a decision maker’s utility function through assessments typically involves an elicitation phase where the decision maker responds to a series of elicitation queries, followed by an estimation phase where the state-ofthe-art for direct elicitation approaches in practice is to either fit responses to a parametric form or perform linear interpolation. We introduce a Bayesian nonparametric method involving Gaussian stochastic processes for estimating a utility function from direct elicitation responses. Advantages include the flexibility to fit a large class of functions, favorable theoretical properties, and a fully probabilistic view of the decision maker’s preference properties including risk attitude. Through extensive simulation experiments as well as two real datasets from management science, we demonstrate that the proposed approach results in better function fitting.

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JMLR Journal 2020 Journal Article

Generalized probabilistic principal component analysis of correlated data

  • Mengyang Gu
  • Weining Shen

Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a latent factor model for the observed data, assuming that the latent factors are independently distributed as standard normal distributions. However, the independence assumption may be unrealistic for many scenarios such as modeling multiple time series, spatial processes, and functional data, where the outcomes are correlated. In this paper, we introduce the generalized probabilistic principal component analysis (GPPCA) to study the latent factor model for multiple correlated outcomes, where each factor is modeled by a Gaussian process. Our method generalizes the previous probabilistic formulation of PCA (PPCA) by providing the closed-form maximum marginal likelihood estimator of the factor loadings and other parameters. Based on the explicit expression of the precision matrix in the marginal likelihood that we derived, the number of the computational operations is linear to the number of output variables. Furthermore, we also provide the closed-form expression of the marginal likelihood when other covariates are included in the mean structure. We highlight the advantage of GPPCA in terms of the practical relevance, estimation accuracy and computational convenience. Numerical studies of simulated and real data confirm the excellent finite-sample performance of the proposed approach. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2020. ( edit, beta )

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