7,591 research outputs found
Probabilistic Inference from Arbitrary Uncertainty using Mixtures of Factorized Generalized Gaussians
This paper presents a general and efficient framework for probabilistic
inference and learning from arbitrary uncertain information. It exploits the
calculation properties of finite mixture models, conjugate families and
factorization. Both the joint probability density of the variables and the
likelihood function of the (objective or subjective) observation are
approximated by a special mixture model, in such a way that any desired
conditional distribution can be directly obtained without numerical
integration. We have developed an extended version of the expectation
maximization (EM) algorithm to estimate the parameters of mixture models from
uncertain training examples (indirect observations). As a consequence, any
piece of exact or uncertain information about both input and output values is
consistently handled in the inference and learning stages. This ability,
extremely useful in certain situations, is not found in most alternative
methods. The proposed framework is formally justified from standard
probabilistic principles and illustrative examples are provided in the fields
of nonparametric pattern classification, nonlinear regression and pattern
completion. Finally, experiments on a real application and comparative results
over standard databases provide empirical evidence of the utility of the method
in a wide range of applications
Neural Expectation Maximization
Many real world tasks such as reasoning and physical interaction require
identification and manipulation of conceptual entities. A first step towards
solving these tasks is the automated discovery of distributed symbol-like
representations. In this paper, we explicitly formalize this problem as
inference in a spatial mixture model where each component is parametrized by a
neural network. Based on the Expectation Maximization framework we then derive
a differentiable clustering method that simultaneously learns how to group and
represent individual entities. We evaluate our method on the (sequential)
perceptual grouping task and find that it is able to accurately recover the
constituent objects. We demonstrate that the learned representations are useful
for next-step prediction.Comment: Accepted to NIPS 201
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