Efficient Approximations for the MarginalLikelihood of Bayesian Networks with Hidden Variables
Machine Learning - Special issue on learning with probabilistic representations
Asymptotic Model Selection for Naive Bayesian Networks
The Journal of Machine Learning Research
Algebraic Statistics for Computational Biology
Algebraic Statistics for Computational Biology
Solving the Likelihood Equations
Foundations of Computational Mathematics
Algebraic Analysis for Nonidentifiable Learning Machines
Neural Computation
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Inference in Bayesian statistics involves the evaluation of marginal likelihood integrals. We present algebraic algorithms for computing such integrals exactly for discrete data of small sample size. Our methods apply to both uniform priors and Dirichlet priors. The underlying statistical models are mixtures of independent distributions, or, in geometric language, secant varieties of Segre-Veronese varieties.