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Despite recent improvements in training methodology, discrete latent variable models have failed to achieve the performance and popularity of their continuous counterparts. Here, we evaluate several approaches to training large-scale image models on CIFAR-10 using a probabilistic variant of the recently proposed Vector Quantized VAE architecture. We find that biased estimators such as continuou...

Latent variable models, such as the popular Knowledge Tracing method, are often used to enable adaptive tutoring systems to personalize education. However, finding optimal model parameters is usually a difficult non-convex optimization problem when considering latent variable models. Prior work has reported that latent variable models obtained from educational data vary in their predictive perf...

Zipf’s law, which states that the probability of an observation is inversely proportional to its rank, has been observed in many different domains. Although there are models that explain Zipf’s law in each of them, there is not yet a general mechanism that covers all, or even most, domains. Here we propose such a mechanism. It relies on the observation that real world data is often generated fr...

This paper gives an overview of methods for utilizing large process data matrices. These data matrices are almost always of less than full statistical rank, and therefore latent variable methods are shown to be well suited to obtaining useful subspace models from them for treating a variety of important industrial problems. An overview of the important concepts behind latent variable models is ...

To find he precursor of contemporary latent variable modelling one must go back to the beginning of the 20th century and Charles Spearman’s invention of factor analysis. This was followed, half a century later, by latent class and latent trait analysis and, from the 1960’s onwards, by covariance structure analysis. The most recent additions to the family have been in the area of time series. We...

In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the algorithm of Titterington (1984), this approach is more directly connected to the usual EM algorithm and does not rely on integration with respect to the complete d...

Parameter constraints in generalized linear latent variable models are discussed. Both linear equality and inequality constraints are considered. Maximum likelihood estimators for the parameters of the constrained model and corrected standard errors are derived. A significant reduction in the dimension of the optimization problem is achieved with the proposed methodology for fitting models subj...

This paper takes a discourse-oriented perspective for disambiguating common and proper noun mentions with respect to Wikipedia. Our novel approach models the relationship between disambiguation and aspects of cohesion using Markov Logic Networks with latent variables. Considering cohesive aspects consistently improves the disambiguation results on various commonly used data sets.