Results 1  10
of
188
Independent Factor Analysis
 Neural Computation
, 1999
"... We introduce the independent factor analysis (IFA) method for recovering independent hidden sources from their observed mixtures. IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square no ..."
Abstract

Cited by 219 (9 self)
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We introduce the independent factor analysis (IFA) method for recovering independent hidden sources from their observed mixtures. IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square noiseless mixing, but also the general case where the number of mixtures differs from the number of sources and the data are noisy. IFA is a twostep procedure. In the first step, the source densities, mixing matrix and noise covariance are estimated from the observed data by maximum likelihood. For this purpose we present an expectationmaximization (EM) algorithm, which performs unsupervised learning of an associated probabilistic model of the mixing situation. Each source in our model is described by a mixture of Gaussians, thus all the probabilistic calculations can be performed analytically. In the second step, the sources are reconstructed from the observed data by an optimal nonlinear ...
The Helmholtz Machine
, 1995
"... Discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning. One fruitful approach is to build a parameterized stochastic generative model, independent draws from which are likely to produce the patterns. For all but the simplest generative model ..."
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Cited by 194 (22 self)
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Discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning. One fruitful approach is to build a parameterized stochastic generative model, independent draws from which are likely to produce the patterns. For all but the simplest generative models, each pattern can be generated in exponentially many ways. It is thus intractable to adjust the parameters to maximize the probability of the observed patterns. We describe a way of finessing this combinatorial explosion by maximizing an easily computed lower bound on the probability of the observations. Our method can be viewed as a form of hierarchical selfsupervised learning that may relate to the function of bottomup and topdown cortical processing pathways.
Greedy layerwise training of deep networks
 In NIPS
, 2007
"... Complexity theory of circuits strongly suggests that deep architectures can be much more efficient (sometimes exponentially) than shallow architectures, in terms of computational elements required to represent some functions. Deep multilayer neural networks have many levels of nonlinearities allow ..."
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Cited by 184 (32 self)
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Complexity theory of circuits strongly suggests that deep architectures can be much more efficient (sometimes exponentially) than shallow architectures, in terms of computational elements required to represent some functions. Deep multilayer neural networks have many levels of nonlinearities allowing them to compactly represent highly nonlinear and highlyvarying functions. However, until recently it was not clear how to train such deep networks, since gradientbased optimization starting from random initialization appears to often get stuck in poor solutions. Hinton et al. recently introduced a greedy layerwise unsupervised learning algorithm for Deep Belief Networks (DBN), a generative model with many layers of hidden causal variables. In the context of the above optimization problem, we study this algorithm empirically and explore variants to better understand its success and extend it to cases where the inputs are continuous or where the structure of the input distribution is not revealing enough about the variable to be predicted in a supervised task. Our experiments also confirm the hypothesis that the greedy layerwise unsupervised training strategy mostly helps the optimization, by initializing weights in a region near a good local minimum, giving rise to internal distributed representations that are highlevel abstractions of the input, bringing better generalization.
Separating style and content with bilinear models
 NEURAL COMPUTATION
, 2000
"... PERCEPTUAL systems routinely separate content from style, classifying familiar words spoken in an unfamiliar accent, identifying a font or handwriting style across letters, or recognizing a familiar face or object seen under unfamiliar viewing conditions. Yet a general and tractable computational mo ..."
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Cited by 173 (3 self)
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PERCEPTUAL systems routinely separate content from style, classifying familiar words spoken in an unfamiliar accent, identifying a font or handwriting style across letters, or recognizing a familiar face or object seen under unfamiliar viewing conditions. Yet a general and tractable computational model of this ability to untangle the underlying factors of perceptual observations remains elusive. Existing factor models are either insufficiently rich to capture the complex interactions of perceptually meaningful factors such as phoneme and speaker accent or letter and font, or do not allow efficient learning algorithms. Here we show how perceptual systems may learn to solve these crucial tasks using surprisingly simple bilinear models. We report promising results in three realistic perceptual domains: spoken vowel classification with a benchmark multispeaker database, extrapolation of fonts to unseen letters, and translation of faces to novel illuminants.
Hierarchical Bayesian Inference in the Visual Cortex
, 2002
"... this paper, we propose a Bayesian theory of hierarchical cortical computation based both on (a) the mathematical and computational ideas of computer vision and pattern the ory and on (b) recent neurophysiological experimental evidence. We ,2 have proposed that Grenander's pattern theory 3 could pot ..."
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Cited by 173 (0 self)
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this paper, we propose a Bayesian theory of hierarchical cortical computation based both on (a) the mathematical and computational ideas of computer vision and pattern the ory and on (b) recent neurophysiological experimental evidence. We ,2 have proposed that Grenander's pattern theory 3 could potentially model the brain as a generafive model in such a way that feedback serves to disambiguate and 'explain away' the earlier representa tion. The Helmholtz machine 4, 5 was an excellent step towards approximating this proposal, with feedback implementing priors. Its development, however, was rather limited, dealing only with binary images. Moreover, its feedback mechanisms were engaged only during the learning of the feedforward connections but not during perceptual inference, though the Gibbs sampling process for inference can potentially be interpreted as topdown feedback disambiguating low level representations? Rao and Ballard's predictive coding/Kalman filter model 6 did integrate generafive feedback in the perceptual inference process, but it was primarily a linear model and thus severely limited in practical utility. The datadriven Markov Chain Monte Carlo approach of Zhu and colleagues 7, 8 might be the most successful recent application of this proposal in solving real and difficult computer vision problems using generafive models, though its connection to the visual cortex has not been explored. Here, we bring in a powerful and widely applicable paradigm from artificial intelligence and computer vision to propose some new ideas about the algorithms of visual cortical process ing and the nature of representations in the visual cortex. We will review some of our and others' neurophysiological experimental data to lend support to these ideas
Modeling the manifolds of images of handwritten digits
 IEEE Transactions on Neural Networks
, 1997
"... description length, density estimation. ..."
Probabilistic nonlinear principal component analysis with Gaussian process latent variable models
 Journal of Machine Learning Research
, 2005
"... Summarising a high dimensional data set with a low dimensional embedding is a standard approach for exploring its structure. In this paper we provide an overview of some existing techniques for discovering such embeddings. We then introduce a novel probabilistic interpretation of principal component ..."
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Cited by 134 (14 self)
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Summarising a high dimensional data set with a low dimensional embedding is a standard approach for exploring its structure. In this paper we provide an overview of some existing techniques for discovering such embeddings. We then introduce a novel probabilistic interpretation of principal component analysis (PCA) that we term dual probabilistic PCA (DPPCA). The DPPCA model has the additional advantage that the linear mappings from the embedded space can easily be nonlinearised through Gaussian processes. We refer to this model as a Gaussian process latent variable model (GPLVM). Through analysis of the GPLVM objective function, we relate the model to popular spectral techniques such as kernel PCA and multidimensional scaling. We then review a practical algorithm for GPLVMs in the context of large data sets and develop it to also handle discrete valued data and missing attributes. We demonstrate the model on a range of realworld and artificially generated data sets.
Generative models for discovering sparse distributed representations
 Philosophical Transactions of the Royal Society B
, 1997
"... We describe a hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network. The model uses bottomup, topdown and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has b ..."
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Cited by 120 (5 self)
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We describe a hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network. The model uses bottomup, topdown and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has been performed the connection strengths can be updated using a very simple learning rule that only requires locally available information. We demonstrate that the network learns to extract sparse, distributed, hierarchical representations.
Mean Field Theory for Sigmoid Belief Networks
 Journal of Artificial Intelligence Research
, 1996
"... We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. ..."
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Cited by 116 (12 self)
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We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics.
Learning with mixtures of trees
 Journal of Machine Learning Research
, 2000
"... This paper describes the mixturesoftrees model, a probabilistic model for discrete multidimensional domains. Mixturesoftrees generalize the probabilistic trees of Chow and Liu [6] in a different and complementary direction to that of Bayesian networks. We present efficient algorithms for learnin ..."
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Cited by 109 (2 self)
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This paper describes the mixturesoftrees model, a probabilistic model for discrete multidimensional domains. Mixturesoftrees generalize the probabilistic trees of Chow and Liu [6] in a different and complementary direction to that of Bayesian networks. We present efficient algorithms for learning mixturesoftrees models in maximum likelihood and Bayesian frameworks. We also discuss additional efficiencies that can be obtained when data are “sparse, ” and we present data structures and algorithms that exploit such sparseness. Experimental results demonstrate the performance of the model for both density estimation and classification. We also discuss the sense in which treebased classifiers perform an implicit form of feature selection, and demonstrate a resulting insensitivity to irrelevant attributes.