Everitt, B. S. (1984). An introduction to latent variable models. Chapman and Hall, London.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....In a generative unsupervised framework, the environment generates training examples which we will refer to as observations by sampling from one distribution; the other distribution is embodied in the model. Examples of generative frameworks are mixtures of Gaussians (MoG) 2] factor analysis [4], and Boltzmann machines [8] In the recoding unsupervised framework, the model transforms points from an obser vation space to an output space, and the output distribution is compared either to a reference distribution or to a distribution derived from the output distribution. An example is ....

B. S. Everitt. An introduction to latent variable models. Chapman and Hall, 1984.

....1 1 Introduction Automated learning of low dimensional linear or multi linear models from training data has become a standard paradigm in computer vision. A variety of linear learning models and techniques such as Principal Component Analysis (PCA) 20, 37, 38, 44, 67] Factor Analysis (FA) [22, 44], Autoregressive analysis (AR) 9] and Singular Value Decomposition (SVD) 28] have been widely used for the representation of high dimensional data such as appearance, shape, motion, temporal dynamics, etc. These approaches differ in their noise assumptions, the use of prior information, and ....

B. S. Everitt. An Introduction to Latent Variable Models. London: Chapman and Hall, 1984.

....usually assumed here that X was generated by a latent additive model, X =M e; 1) where M is a random vector concentrated to the manifold M , and e is an independent multivariate random noise with zero mean. The task is to recover M based on the noisy observation X. ffl Latent variable models [Eve84, Mac95, BSW96]. It is presumed that X, although sitting in a high dimensional space, has a low intrinsic dimension. This is a special case of (1) when the additive noise is zero or nearly zero. In practice, M is usually highly nonlinear otherwise the problem is trivial. When M is two dimensional, using M for ....

....This is a special case of (1) when the additive noise is zero or nearly zero. In practice, M is usually highly nonlinear otherwise the problem is trivial. When M is two dimensional, using M for representing X can serve as an effective visualization tool [Sam69, KW78, BT98] ffl Factor analysis [Eve84, Bar87] is another special case of (1) when M is assumed to be a Gaussian random variable concentrated on a linear subspace of R , and e is a Gaussian noise with diagonal covariance matrix. 1.1.3 The Simplest Case In simple unsupervised models the set of admissible functions F or the corresponding ....

B. S. Everitt. An Introduction to Latent Variable Models. Chapman and Hall, London, 1984.

....There are two important cases in which the hidden states are such that it is computationally tractable to calculate the sum in equation 1 exactly. First, if all the units are linear and are subject to Gaussian noise, the resulting Helmholtz machine performs a standard form of factor analysis (Everitt, 1984; Neal et al., in preparation) The second case is mixtures of Gaussians, in which the hidden units are non linear, but interact in a simple way. The generative model for mixtures of Gaussians has that p(ffj ) ff where X ff ff = 1 (2) and p(djff; N [ ff ; Sigma ff ] Tractability ....

Everitt, BS (1984). An Introduction to Latent Variable Models. London: Chapman and Hall.

....are imposed that force neighboring hidden units to have similar generative weight vectors. These constraints typically lead to a model of the data that is worse when measured by the likelihood of the data. On the other side are dimensionality reduction models, typified by factor analysis (Everitt, 1984). In factor analysis, the D dimensional sensory data is assumed to have been generated by linearly combining K independent Gaussian variables, the factors, and then adding Gaussian noise. The goal of learning is to find the linear transformation from the K factors that maximizes the likelihood of ....

Everitt, B. S. (1984). An Introduction to Latent Variable Models. Chapman and Hall, London.

....using real values. A great deal of work has been done on Gaussian random variables that are linked linearly such that the joint distribution over all variables is also Gaussian (Pearl 1988; Shachter and Kenley 1989; Spiegelhalter 1990; Heckerman and Geiger 1995) see also factor analysis (Everitt 1984). Lauritzen and Wermuth (1989) and Lauritzen, Dawid, Larsen, and Leimer (1990) have included discrete random variables within the linear Gaussian framework. Recently, inference in networks of Gaussian random variables that are linked nonlinearly have been explored by Driver and Morrell (1995) All ....

.... is approximately linear over the span of the added noise, the postsigmoid distribution will be approximately Gaussian with the mean and standard deviation linearly transformed (figure 1b) This mode is useful for representing latent Gaussian random variables, such as those used in factor analysis (Everitt 1984). Stochastic nonlinear mode: If the variance of a unit in the stochastic linear mode is increased so that the squashing function is used in its nonlinear region, a variety of distributions are producible that range from skewed Gaussian to uniform to bimodal (figure 1c) Stochastic binary mode: ....

B. S. Everitt 1984. An Introduction to Latent Variable Models. Chapman and Hall, London, England.

....justi cation apart from empirical utility. We have chosen a latent variable model in which the latent variables describe features that underlie the data. Within this model space our methods seek the most ecient description of the data. Our model is simple it is closely related to factor analysis (Everitt, 1984) and independent component analysis (Bell and Sejnowski, 1995; MacKay, 1996) and we do not claim it is the best model; but because it is a Bayesian model, the assumptions on which the model rests are clear, the model is readily extensible should those assumptions be modi ed, and the model is ....

Everitt, B. S. (1984) An Introduction to Latent Variable Models. London: Chapman and Hall.

....a component vector. L is an N K matrix with elements nk . Principal component analysis (Jolliffe 1986; Linsker 1988; Oja 1989) independent component analysis (Comon, Jutten and Herault 1991; Bell and Sejnowski 1995; Amari, Cichocki and Yang 1996) and factor analysis (Rubin and Thayer 1982; Everitt 1984) can be viewed as maximum likelihood estimation in models of this type, where we assume that the appropriate modulation levels are independent and the overall distortion is given by the sum of the individual sensor distortions. The two layer belief network that describes this process is shown in ....

Everitt, B. S. 1984. An Introduction to Latent Variable Models. Chapman and Hall, New York NY.

....independent components models where the components themselves are modelled as generalised autoregressive processes. The model is demonstrated on synthetic problems and EEG data. 1 Introduction Much recent research in unsupervised learning [17] 20] builds on the idea of using generative models [6] for modelling the probability distribution over a set of observations. These approaches suggest that powerful new data analysis tools may be derived by combining existing models using a probabilistic generative framework. In this paper, we follow this approach and combine hidden Markov models ....

B. S. Everitt. An Introduction to Latent Variable Models. Chapman and Hill, London and New York, 1984.

....in the rows of the matrix X, the corresponding (translated) outputs are the elements of the vector y, and the corresponding weights are in the diagonal matrix W. In some cases, we need the joint input and output data, denoted as Z= X y] 1) 3 2. 1 FACTOR ANALYSIS (LWFA) Factor analysis (Everitt, 1984) is a technique of dimensionality reduction which is the most appropriate given the generating process of our regression data. It assumes the observed data z was produced by a mean zero independently distributed k dimensional vector of factors v, transformed by the matrix U, and contaminated by ....

Everitt, B. S, (1984). An introduction to latent variable models. London: Chapman and Hall.

....latent variable 17 . q s s s (1) 2) 3) x x x (1) 2) 3) s s s (1) 2) 3) x (1) 2) 3) q q q a) b) Figure 9: a) Bayesian regression problem. b) The dual problem. density model over binary vectors is akin to the standard factor analysis model (see e.g. Everitt 1984). This model has already been used to facilitate visualization of high dimensional binary vectors (Tipping 1999) We now turn to a more technical treatment of this latent variable model. The joint distribution is given by P (S 1 ; S n jX) Z Y i P (S i jX i ; # P ( d (34) ....

B. Everitt (1984). An Introduction to Latent Variable Models. Cambridge University Press.

....identity matrix, then we recover exactly a standard statistical model known as maximum likelihood factor analysis. The unknown states x are called the factors in this context; the matrix C is called the factor loading matrix, and the diagonal elements of R are often known as the uniquenesses. See Everitt, 1984, for a brief and clear introduction. The inference calculation is done exactly as in equation 5.3b. The learning algorithm for the loading matrix and the uniquenesses is exactly an EM algorithm except that we must take care to constrain R properly (which is as easy as taking the diagonal of the ....

....is unimportant. If we were to change the units in which we measured some of the components of y, factor analysis could merely rescale the corresponding entry in R and 8 The correction k(k 1) 2 comes in because of degeneracy in unitary transformations of the factors. See, for example, Everitt (1984). A Unifying Review of Linear Gaussian Models 317 row in C and achieve a new model that assigns the rescaled data identical likelihood. On the other hand, if we rotate the axes in which we measure the data, we could not easily fix things since the noise v is constrained to have axis aligned ....

Everitt, B. S. (1984). An introduction to latent variable models. London: Chapman and Hill.

....well as in the original Shumway and Stoffer (1982) paper. It is worth pointing out that the linear Gaussian state space model is a generalization of a statistical method known as factor analysis. Factor analysis models high dimensional data through a smaller number of latent variables or factors (Everitt, 1984). The model relating the factors to the observations is exactly as specified by equation (3) X t is a Gaussian distributed vector of factor values; Y t is the observation vector; C is known as the factor loading matrix, and v t is zero mean Gaussian distributed noise with the further constraint ....

Everitt, B. S. (1984). An Introduction to Latent Variable Models. Chapman and Hall, London.

....known a priori. The MFA is a complex model involving many parameters and a number of missing variables that is proportional to the sample under study. One also has to address the inherent diculty of non identi ability of both the Factor Analysis and the mixture models. See references like [1] [3], 11] and [10] for more details on identi ability in Factor Analysis, and [16] 13] and [15] for identi ability of mixture models. We address the uncertainty about both k and q (model selection) in our subsequent research [5] 3 Estimation and Inference via Bayesian Sampling 3.1 Basic ....

Everitt, B. S. (1984). An Introduction to Latent Variable Models. Monographs on Statistics and Applied Probability. Chapman and Hall.

....and identically distributed, such that each observation, y i , has m Bernoulli attributes, y i1 ; y im ) Given the class, c i , that observation i belongs to, the item s attributes are independent of each other. This type of model is common in latent class analysis (see, for example, Everitt 1984), in which the mixture components are considered latent classes that represent heterogeneous mechanisms which underly or produce the observed data. Neal (1992) considered a similar model when examining the performance of the Gibbs sampling procedure discussed in Section 2. For simplicity of ....

Everitt, B. S. (1984) An Introduction to Latent Variable Models, London: Chapman and Hall.

....probability under the generative model. p#d# = Z p#y#p#djy#dy #8# = Z Y j 1 p 2# e ,y 2 j =2 Y i 1 p 2## i e ,#d i , P j y j g ji # 2 =2# 2 i dy #9# Because the network is linear and the noise is Gaussian, this integral is tractable. Maximum likelihood factor analysis #Everitt, 1984# consists of #nding generativeweights and local noise levels for the visible units so as to maximize the likelihood of generating the observed data. Without loss of generality, the generative noise model for the hidden units can be set to be a zero mean Gaussian with a covariance equal to the ....

Everitt, B. S. #1984#. An Introduction to Latent Variable Models. Chapman and Hall, London.

....Introduction There have been many proposals for unsupervised, multilayer neural networks that contain a stochastic generative model and learn by adjusting their parameters to maximize the likelihood of generating the observed data. Two of the most tractable models of this kind are factor analysis (Everitt 1984) and independent component analysis (Comon, Jutten and Herault 1991; Bell and Sejnowski 1995; Amari, Cichocki and Yang 1996; MacKay 1997) 1.1 Linear generative models In factor analysis there is one hidden layer that contains less units than the visible layer. In the generative model, the ....

Everitt, B. S. 1984. An Introduction to Latent Variable Models. Chapman and Hall, New York NY.

....covariance becomes zero. 3 An EM algorithm for PCA The key observation of this note is that even though the principal components can be computed explicitly, there is still an EM algorithm for learning in the zero noise limit. It can be easily derived from the standard algorithms (see for example [3, 2]) by replacing the usual e step with the projection above. The algorithm is: e step: X = C T C) 1 C T Y m step: C new = YX T (XX T ) 1 where Y is a p n matrix of all the observed data and X is a k n matrix of the unknown states. The columns of C will span the space of the ....

B. S. Everitt. An Introduction to Latent Variable Models. Chapman and Hill, London, 1984.

....similar to the training data. The model speci es a distribution over some hidden variables and a conditional distribution over the input image given the values of the hidden variables. The representation for an input is the posterior distribution over the hidden variables. Factor analysis (FA) [3] is a generative model that is similar in spirit to PCA. The distribution over a small set of real valued hidden variables is a zero mean unitcovariance Gaussian and the distribution over the inputs given the hidden variables is also Gaussian, with a diagonal covariance matrix and a mean given by ....

B. S. Everitt, An Introduction to Latent Variable Models, Chapman and Hall, New York NY., 1984.

....are imposed that force neighboring hidden units to have similar generative weight vectors. These constraints typically lead to a model of the data that is worse when measured by the likelihood of the data. On the other side are dimensionality reduction models, typified by factor analysis (Everitt, 1984). In factor analysis, the D dimensional sensory data is assumed to have been generated by linearly combining K independent Gaussian variables, the factors, and then adding Gaussian noise. The goal of learning is to find the linear transformation from the K factors that maximizes the likelihood of ....

Everitt, B. S. (1984). An Introduction to Latent Variable Models.

....would have to use four categories to capture all four combinations of these binary attributes, whereas only two independent degrees of freedom are really present. These observations motivate the development of density models that have components rather than categories as their latent variables [10]. Let us denote the observables by t. If a density is de ned on the latent variables x, and a parameterized mapping is de ned from these latent variables to a probability distribution over the observables P (tjx; w) then a non trivial density over t is de ned. Simple linear models of this form in ....

B. S. Everitt. An Introduction to Latent Variable Models. Chapman and Hall, London, 1984.

....popularity is independent component analysis (ICA) which tries to nd components such that when the training data is projected on these components, the component activities are independent (not just uncorrelated) 3] ICA has been used for blind separation and deconvolution. Factor analysis (FA) [4] is a generative model that is similar in spirit to PCA. A generative model is trained to generate patterns that look similar to the training data and the representation of an input is the posterior distribution over some hidden variables. In a FA model, the distribution over a small set of ....

B. S. Everitt, An Introduction to Latent Variable Models, Chapman and Hall, New York NY., 1984.

....a component vector. L is an N K matrix with elements nk . Principal component analysis (Jolliffe 1986; Linsker 1988; Oja 1989) independent component analysis (Comon, Jutten and Herault 1991; Bell and Sejnowski 1995; Amari, Cichocki and Yang 1996) and factor analysis (Rubin and Thayer 1982; Everitt 1984) can be viewed as maximum likelihood estimation in models of this type, where we assume that the appropriate modulation levels are independent and the overall distortion is given by the sum of the individual sensor distortions. The two layer belief network that describes this process is shown in ....

Everitt, B. S. 1984. An Introduction to Latent Variable Models. Chapman and Hall, New York NY.

....it considerably complicates the training and decoding procedures, and it requires some artistry to design the tied HMMs. Unconstrained and diagonal covariance matrices clearly represent two extreme choices for the hidden Markov modeling of speech. The statistical method of factor analysis[22, 6] represents a compromise between these two extremes. The idea behind factor analysis is to map systematic variations of the data into a lower dimensional subspace. This enables one to represent, in a very compact way, the covariance matrices for high dimensional data. These matrices are expressed ....

....error (MCE) factor analysis. In section 5, we give results on two tasks in automatic speech recognition: connected alpha digits and New Jersey town names. Finally, in section 6, we present our conclusions as well as ideas for future research. 2 Dimensionality reduction Factor analysis[22, 6] is a linear method for the dimensionality reduction of Gaussian random variables. It is closely related to principal components analysis (PCA) 5] in which one extracts the subspace defined by the largest eigenvectors of the covariance matrix. In PCA, the data vectors are projected into this ....

Everitt, B. (1984) An introduction to latent variable models. London: Chapman and Hall.

....mixture of factor analyzers in section 3. We close with a discussion in section 4. 2 Factor Analysis In maximum likelihood factor analysis (FA) a p dimensional real valued data vector x is modeled using a k dimensional vector of real valued factors, z, where k is generally much smaller than p (Everitt, 1984). The generative model is given by: x = z u; 1) where is known as the factor loading matrix (see Figure 1) The factors z are assumed to be N (0; I) distributed (zero mean independent normals, with unit variance) The p dimensional random variable u is distributed N (0; Psi) where Psi is ....

Everitt, B. S. (1984). An Introduction to Latent Variable Models. Chapman and Hall, London.

....under the generative model. p(d) Z p(y)p(djy)dy (8) Z Y j 1 p 2 e Gammay 2 j =2 Y i 1 p 2 oe i e Gamma(d i Gamma P j y j g ji ) 2 =2oe 2 i dy (9) Because the network is linear and the noise is Gaussian, this integral is tractable. Maximum likelihood factor analysis (Everitt, 1984) consists of finding generative weights and local noise levels for the visible units so as to maximize the likelihood of generating the observed data. Without loss of generality, the generative noise model for the hidden units can be set to be a zero mean Gaussian with a covariance equal to the ....

Everitt, B. S. (1984). An Introduction to Latent Variable Models. Chapman and Hall, London.

....illustrate the performance of GTM through time using flight recorder data from a helicopter. GTM Through Time 2 1 Introduction Latent variable models provide a representation for the distribution of data in a multi dimensional space in terms of a reduced number of latent, or hidden, variables (Everitt 1984). A well known example of a latent variable algorithm is factor analysis which is based on a linear transformation between latent space and data space. The technique of principal component analysis can also be understood within the same framework and again involves a linear transformation from the ....

Everitt, B. S. (1984). An Introduction to Latent Variable Models. London: Chapman and Hall.

....correlations are explained by postulating the presence of one or more underlying factors . These factors play the role of latent or hidden variables, which are not directly observable, but which allow the dependencies between the visible variables to be expressed in a convenient way. Everitt (1984) gives a good introduction to latent variable models in general, and to factor analysis in particular. These models are widely used in psychology and the social sciences as a way of exploring whether observed patterns in data might be explainable in terms of a small number of unobserved factors. ....

....of small values for the learning rates. These experiments also provide data on how small the learning rates must be in practice, and reveal situations in which learning can be relatively slow. We also report in Section 4. 4 the results of applying the wake sleep algorithm to a real dataset used by Everitt (1984). 4.1 Experimental procedure All the systematic experiments described below were done with randomly generated synthetic data. Models for various numbers (p) of visible variables, using various numbers (k) of hidden factors were tested. For each such model, ten sets of model parameters were ....

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Everitt, B. S. (1984) An Introduction to Latent Variable Models, London: Chapman and Hall.

....more than a certain dimension, so data of higher dimension must be reduced before being fed into the system. Sometimes, a phenomenon which is in appearance high dimensional, and thus complex, can actually be governed by a few simple variables (sometimes called hidden causes or latent variables [29, 20, 21, 6, 74]) Dimension reduction can be a powerful tool for modelling such phenomena and improve our understanding of them (as often the new variables will have an interpretation) For example: ffl Genome sequences modelling. A protein is a sequence of aminoacids (of which there are 20 different ones) with ....

....modelling: density networks In generative modelling, all observables in the problem are assigned a probability distribution to which the Bayesian machinery is applied. Density networks (MacKay [74] are a form of Bayesian learning that attempts to model data in terms of latent variables [29]. First we will introduce Bayesian neural networks, then the density networks themselves and we will conclude with GTM, a particular model based in density networks. 5.2.1 Bayesian neural networks Assume we have data D which we want to model using parameters w and define the likelihood L(w) ....

B. S. Everitt, An Introduction to Latent Variable Models, Monographs on Statistics and Applied Probability, Chapman & Hall, London, New York, 1984.

....[8, 20] are an appropriate tool for modeling processes whose output is thought to be generated by several different underlying mechanisms, or to come from several different populations. One aim of a mixture model analysis may be to identify and characterize these underlying latent classes [2, 7], either for some scientific purpose, or as one realization of unsupervised learning in artificial intelligence. In other cases, prediction of future observations is the objective. In a classification application [6] for example, we are interested in predicting the category attribute of an ....

Everitt, B. S. (1984) An Introduction to Latent Variable Models, London: Chapman and Hall.

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Everitt, B. S. (1984). An introduction to latent variable models. Chapman and Hall, London.

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Everitt, B. S. (1984). An introduction to latent variable models. London: Chapman and Hall.

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Everitt, B. S. (1984). An introduction to latent variable models. Chapman and Hall, London. Fahlman, S. E., & Lebiere, C. (1990). The cascade-correlation learning architecture. In D. S. Touretzky (Ed.), Advances in Neural Information Processing Systems 2 (pp. 524--532). Morgan-Kaufmann, Los Altos CA.

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Everitt, B. S. (1984). An Introduction to Latent Variable Models. Chapman and Hall, London.

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Everitt, B. S. (1984). An Introduction to Latent Variable Models. Chapman and Hall, London.

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Everitt, B. S. (1984). An Introduction to Latent Variable Models. Chapman and Hall, London.

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Everitt, BS (1984) An Introduction to Latent Variable Models, London: Chapman and Hall.

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B. S. Everitt, An introduction to latent variable models, Chapman and Hall, 1984.

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Everitt, B. S.: An Introduction to Latent Variable Models, London: Chapman and Hall. (1984)

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B. S. Everitt. An Introduction to Latent Variable Models. Chapman and Hall, London, 1984.

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B. S. Everitt. An Introduction to Latent Variable Models. Chapman and Hall, London, 1984.

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B. S. Everitt, An Introduction to Latent Variable Models. London: Chapman and Hall, 1984.

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B. S. Everitt. An Introduction to Latent Variable Models. Chapman and Hall, London, 1984.

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B.S. Everitt, An Introduction to Latent Variable Models. London: Chapman and Hall, 1984.

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B.S. Everitt. An Introduction to Latent Variable Models. Monographs on Statistics and Applied Probability, Chapman & Hall, London, New York, 1984

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Everitt, B. S. (1984). An introduction to latent variable models. Chap- man and Hall, London.

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Everitt, BS (1984). An Introduction to Latent Variable Models. London: Chapman and Hall.

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Everitt, BS (1984). An Introduction to Latent Variable Models. London: Chapman and Hall.

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Everitt, BS (1984). An Introduction to Latent Variable Models. London: Chapman and Hall.

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Review. Everitt, B. S, (1984). An introduction to latent variable models. London: Chapman and Hall.

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