Generative modeling of high-dimensional data is a key problem in machine learning. Successful approaches include latent variable models and autoregressive models. The complementary strengths of these approaches, to model global and local image statistics respectively, suggest hybrid models combining the strengths of both models. Our contribution is to train such hybrid models using an auxiliary...

In many statistical problems, a more coarse-grained model may be suitable for population-level behaviour, whereas a more detailed model is appropriate for accurate modelling of individual behaviour. This raises the question of how to integrate both types of models. Methods such as posterior regularization follow the idea of generalized moment matching, in that they allow matching expectations b...

This rejoinder discusses the general comments on how to use BSEM wisely and how to get more people better trained in using Bayesian methods. Responses to specific comments cover how to handle sign switching, nonconvergence and non-identification, and prior choices in latent variable models. Two new applications are included. The first one revisits the Kaplan science model by considering priors ...

Numerical methods in higher dimensions using tensor factorizations I this talk I will collect recent advances in the solution of high-dimensional problems in different application areas: chemistry, biology, mathematics. The language of low-rank factorization gives a unified view on different algorithms for the solution of seemingly diverse and unconnected problems. Typical applications include ...

We consider the modelling of dependent defaults in large credit portfolios using latent variable models (the approach that underlies KMV and CreditMetrics) and mixture models (the approach underlying CreditRisk). We explore the role of copulas in the latent variable framework and show that for given default probabilities of individual obligors the distribution of the number of defaults in the p...

We develop a probabilistic latent-variable model to discover semantic frames—types of events or relations and their participants—from corpora. Our key contribution is a model in which (1) frames are latent categories that explain the linking of verb-subject-object triples in a given document context; and (2) cross-cutting semantic word classes are learned, shared across frames. We also introduc...

Restricted Boltzmann Machines (RBMs) are an important class of latent variable models for representing vector data. An under-explored area is multimode data, where each data point is a matrix or a tensor. Standard RBMs applying to such data would require vectorizing matrices and tensors, thus resulting in unnecessarily high dimensionality and at the same time, destroying the inherent higher-ord...

This teaching note starts with a demonstration of a straightforward procedure using Mplus Version 6 to produce a bias-corrected (BC) bootstrap confidence interval for testing a specific mediation effect in a complex latent variable model. The procedure is extended to constructing a BC bootstrap confidence interval for the difference between two specific mediation effects. The extended procedure...

In this paper we apply the latest techniques in sparse Gaussian process regression (GPR) to the Gaussian process latent variable model (GPLVM). We review three techniques and discuss how they may be implemented in the context of the GP-LVM. Each approach is then implemented on a well known benchmark data set and compared with earlier attempts to sparsify the model.

We wish to congratulate the authors for their innovative contribution, which is bound to inspire much further research. We find latent variable model selection to be a fantastic application of matrix decomposition methods, namely, the superposition of low-rank and sparse elements. Clearly, the methodology introduced in this paper is of potential interest across many disciplines. In the followin...