Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Approximating probabilistic inference in Bayesian belief networks is NP-hard
Artificial Intelligence
Factorial Hidden Markov Models
Machine Learning - Special issue on learning with probabilistic representations
An introduction to variational methods for graphical models
Learning in graphical models
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
Combining phylogenetic and hidden Markov models in biosequence analysis
RECOMB '03 Proceedings of the seventh annual international conference on Research in computational molecular biology
Variational Approximations between Mean Field Theory and the Junction Tree Algorithm
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Graph partition strategies for generalized mean field inference
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Journal of Artificial Intelligence Research
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
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Probabilistic phylogenetic models which relax the site independence evolution assumption often face the problem of infeasible likelihood computations, for example for the task of selecting suitable parameters for the model. We present a new approximation method, applicable for a wide range of probabilistic models, which guarantees to upper bound the true likelihood of data, and apply it to the problem of probabilistic phylogenetic models. The new method is complementary to known variational methods that lower bound the likelihood, and it uses similar methods to optimize the bounds from above and below. We applied our method to aligned DNA sequences of various lengths from human in the region of the CFTR gene and homologous from eight mammals, and found the upper bounds to be appreciably close to the true likelihood whenever it could be computed. When computing the exact likelihood was not feasible, we demonstrated the proximity of the upper and lower variational bounds, implying a tight approximation of the likelihood.