We present a framework for efficient perceptual inference that explicitly reasons about the segmentation of its inputs and features. Rather than being trained for any specific segmentation, our framework learns the grouping process in an unsupervised manner or alongside any supervised task. By enriching the representations of a neural network, we enable it to group the representations of different objects in an iterative manner. By allowing the system to amortize the iterative inference of the groupings, we achieve very fast convergence. In contrast to many other recently proposed methods for addressing multi-object scenes, our system does not assume the inputs to be images and can therefore directly handle other modalities. For multi-digit classification of very cluttered images that require texture segmentation, our method offers improved classification performance over convolutional networks despite being fully connected. Furthermore, we observe that our system greatly improves on the semi-supervised result of a baseline Ladder network on our dataset, indicating that segmentation can also improve sample efficiency.
Another closely related line of research @cite_12 @cite_22 has focused on multi-causal modeling of the inputs. Many of the works in that area @cite_5 @cite_4 @cite_14 @cite_30 build upon Restricted Boltzmann Machines. Each input is modeled as a mixture model with a separate latent variable for each object. Because exact inference is intractable, these models approximate the posterior with some form of expectation maximization @cite_32 or sampling procedure. Our assumptions are very similar to these approaches, but we allow the model to learn the amortized inference directly (more in line with ).
@cite_30 @cite_14 @cite_4 @cite_22 @cite_32 @cite_5 @cite_12
2787211894 2165225968 2271522117 1503100111
This paper presents new statistical methods of multichannel audio source separation based on unified source and spatial models that, respectively, represent the generative process of latent source spectrograms and that of observed mixture spectrograms. One possibility of the source model is a factor model based on nonnegative matrix factorization that represents each time-frequency (TF) bin as the weighted sum of basis spectra. Another possibility is a mixture model inspired by latent Dirichlet allocation that exclusively classifies each TF bin into one of basis spectra. Similarly, the spatial model can either be a factor model that represents each TF bin as the weighted sum of source spectra or a mixture model that classifies each bin into one of those spectra. To unify these models in a principled manner and incorporate prior knowledge of a microphone array, we propose hierarchical Bayesian models of all the source–spatial combinations (factor–factor, mixture–factor, factor–mixture, and mixture–mixture models) and derive efficient Gibbs sampling algorithms for posterior inference. Experimental results showed that the proposed unified models outperformed the state-of-the-art method using only the spatial mixture model. Among the four unified models, the spatial factor model tended to work better than the spatial mixture model in exchange for larger computational cost, and the choice of source models had a little impact on the performance and computational cost. We present a distribution model for binary vectors, called the influence combination model and show how this model can be used as the basis for unsupervised learning algorithms for feature selection. The model can be represented by a particular type of Boltzmann machine with a bipartite graph structure that we call the combination machine. This machine is closely related to the Harmonium model defined by Smolensky. In the first part of the paper we analyze properties of this distribution representation scheme. We show that arbitrary distributions of binary vectors can be approximated by the combination model. We show how the weight vectors in the model can be interpreted as high order correlation patterns among the input bits, and how the combination machine can be used as a mechanism for detecting these patterns. We compare the combination model with the mixture model and with principle component analysis. In the second part of the paper we present two algorithms for learning the combination model from examples. The first learning algorithm is the standard gradient ascent heuristic for computing maximum likelihood estimates for the parameters of the model. Here we give a closed form for this gradient that is significantly easier to compute than the corresponding gradient for the general Boltzmann machine. The second learning algorithm is a greedy method that creates the hidden units and computes their weights one at a time. This method is a variant of projection pursuit density estimation. In the third part of the paper we give experimental results for these learning methods on synthetic data and on natural data of handwritten digit images. Latent variable time-series models are among the most heavily used tools from machine learning and applied statistics. These models have the advantage of learning latent structure both from noisy observations and from the temporal ordering in the data, where it is assumed that meaningful correlation structure exists across time. A few highly-structured models, such as the linear dynamical system with linear-Gaussian observations, have closed-form inference procedures (e.g. the Kalman Filter), but this case is an exception to the general rule that exact posterior inference in more complex generative models is intractable. Consequently, much work in time-series modeling focuses on approximate inference procedures for one particular class of models. Here, we extend recent developments in stochastic variational inference to develop a black-box' approximate inference technique for latent variable models with latent dynamical structure. We propose a structured Gaussian variational approximate posterior that carries the same intuition as the standard Kalman filter-smoother but, importantly, permits us to use the same inference approach to approximate the posterior of much more general, nonlinear latent variable generative models. We show that our approach recovers accurate estimates in the case of basic models with closed-form posteriors, and more interestingly performs well in comparison to variational approaches that were designed in a bespoke fashion for specific non-conjugate models. Consider data (x1,y1),…,(xn,yn), where each xi may be vector valued, and the distribution of yi given xi is a mixture of linear regressions. This provides a generalization of mixture models which do not include covariates in the mixture formulation. This mixture of linear regressions formulation has appeared in the computer science literature under the name “Hierarchical Mixtures of Experts” model. This model has been considered from both frequentist and Bayesian viewpoints. We focus on the Bayesian formulation. Previously, estimation of the mixture of linear regression model has been done through straightforward Gibbs sampling with latent variables. This paper contributes to this field in three major areas. First, we provide a theoretical underpinning to the Bayesian implementation by demonstrating consistency of the posterior distribution. This demonstration is done by extending results in Barron, Schervish and Wasserman (Annals of Statistics 27: 536–561, 1999) on bracketing entropy to the regression setting. Second, we demonstrate through examples that straightforward Gibbs sampling may fail to effectively explore the posterior distribution and provide alternative algorithms that are more accurate. Third, we demonstrate the usefulness of the mixture of linear regressions framework in Bayesian robust regression. The methods described in the paper are applied to two examples.