Probabilistic Latent Semantic Indexing is a novel approach to automated document indexing which is based on a statistical latent class model for factor analysis of count data. Fitted from a training corpus of text documents by a generalization of the Expectation Maximization algorithm, the utilized model is able to deal with domain-specific synonymy as well as with polysemous words. In contrast to standard Latent Semantic Indexing (LSI) by Singular Value Decomposition, the probabilistic variant has a solid statistical foundation and defines a proper generative data model. Retrieval experiments on a number of test collections indicate substantial performance gains over direct term matching methodsaswell as over LSI. In particular, the combination of models with different dimensionalities has proven to be advantageous.

Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities, we show how independent component analysis is also a variation of the same basic generative model. We show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models.

Grouping people into clusters based on the items they have purchased allows accurate recommendations of new items for purchase: if you and I have liked many of the same movies, then I will probably enjoy other movies that you like. Recommending items based on similarity of interest (a.k.a. collaborative filtering) is attractive for many domains: books, CDs, movies, etc., but does not always work well. Because data are always sparse -- any given person has seen only a small fraction of all movies -- much more accurate predictions can be made by grouping people into clusters with similar movies and grouping movies into clusters which tend to be liked by the same people. Finding optimal clusters is tricky because the movie groups should be used to help determine the people groups and visa versa. We present a formal statistical model of collaborative filtering, and compare different algorithms for estimating the model parameters including variations of K-means clustering and Gibbs Sampling. This...

We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics.

Introduction When we say we are making a model of a system, we are setting up a tool which can be used to make inferences, predictions and decisions. Each model can be seen as a hypothesis, or explanation, which makes assertions about the quantities which are directly observable and which can only be inferred from their eect on observable quantities. In the Bayesian framework, knowledge is contained in the conditional probability distributions of the models. We can use Bayes' theorem to evaluate the conditional probability distributions for the unknown parameters, y, given the set of observed quantities, x, using p (y jx ) = p (x jy ) p (y) p (x) (1) The prior distribution p (y) contains our knowledge of the unknown variables before we make any observ

We introduce a statistical model for times series data with nonlinear dynamics which iteratively segments the data into regimes with approximately linear dynamics and learns the parameters of each of those regimes. This model combines and generalizes two of the most widely used stochastic time series models---the hidden Markov model and the linear dynamical system---and is related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network model (Jacobs et al., 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact Expectation Maximization (EM) alogithm cannot be applied. However, we present a variational approximation which maximizes a lower bound on the log likelihood and makes use of both the forward--backward recursio...

The EM algorithm is a popular method for parameter estimation in a variety of problems involving missing data. However, the EM algorithm often requires signi cant computational resources and has been dismissed as impractical for large databases. We presenttwo approaches that signi cantly reduce the computational cost of applying the EM algorithm to databases with a large number of cases, including databases with large dimensionality. Both approaches are based on partial E-steps for which we can use the results of Neal and Hinton (1998) to obtain the standard convergence guarantees of EM. The rst approach is a version of the incremental EM, described in Neal and Hinton (1998), which cycles through data cases in blocks. The number of cases in each block dramatically e ects the e ciency of the algorithm. We provide a method for selecting a near optimal block size. The second approach, which we call lazy EM, will, at scheduled iterations, evaluate the signi cance of each data case and then proceed for several iterations actively using only the signi cant cases. We demonstrate that both methods can signi cantly reduce computational costs through their application to high-dimensional real-world and synthetic mixture modeling problems for large databases. Keywords: Expectation Maximization Algorithm, incremental EM, lazy EM, online EM, data blocking, mixture models, clustering.

Recent advances in various display and virtual technologies coupled with an explosion in available computing power have given rise to a numberofnovel human-computer interaction (HCI) modalities -- speech, vision-based gesture recognition, eye tracking, EEG, etc. However, despite the abundance of novel interaction devices, the naturalness and efficiency of HCI has remained low. This is due in particular to the lack of robust sensory data interpretation techniques. To deal with the task of interpreting single and multiple interaction modalities this dissertation establishes a novel probabilistic approach based on dynamic Bayesian networks (DBNs). As a generalization of the successful hidden Markov models, DBNs are a natural basis for the general temporal action interpretation task. The problem of interpretation of single or multiple interacting modalities can then be viewed as a Bayesian inference task. In this work three complex DBN models are introduced: mixtures of DBNs, mixed-state DBNs, and coupled HMMs. In-depth study of these models yields efficient approximate inference and parameter learning techniques applicable to a wide variety of problems. Experimental validation of the proposed approaches in the domains of gesture and speech recognition con rms the model's applicability to both unimodal and multimodal interpretation tasks.

Grouping people into clusters based on the items they have purchased allows accurate recommendations of new items for purchase: If you and I have liked many of the same movies, then I will probably enjoy other movies that you like. Recommending items based on similarityofinterest #a.k.a. collaborative #ltering# is attractive for many domains: books, CDs, movies, etc., but does not always work well. Because data are always sparse # any given person has seen only a small fraction of all movies #much more accurate predictions can be made by grouping people into clusters with similar taste in movies and grouping movies into clusters which tend to be liked by the same people. Finding optimal clusters is tricky because the movie groups should be used to help determine the people groups and visa versa. We present a formal statistical model of collaborative #ltering, and compare di#erent algorithms for estimating the model parameters including variations of K-means clustering and Gibb...

In this article, we review unsupervised neural network learning procedures which can be applied to the task of preprocessing raw data to extract useful features for subsequent classification. The learning algorithms reviewed here are grouped into three sections: information-preserving methods, density estimation methods, and feature extraction methods. Each of these major sections concludes with a discussion of successful applications of the methods to real-world problems.