Learning the Structure of Deep Sparse Graphical Models

Deep belief networks are a powerful way to model complex probability distributions. However, learning the structure of a belief network, particularly one with hidden units, is difficult. The Indian buffet process has been used as a nonparametric Bayesian prior on the directed structure of a belief network with a single infinitely wide hidden layer. In this paper, we introduce the cascading Indian buffet process (CIBP), which provides a nonparametric prior on the structure of a layered, directed belief network that is unbounded in both depth and width, yet allows tractable inference. We use the CIBP prior with the nonlinear Gaussian belief network so each unit can additionally vary its behavior between discrete and continuous representations. We provide Markov chain Monte Carlo algorithms for inference in these belief networks and explore the structures learned on several image data sets.

Semi-supervised video segmentation using tree structured graphical models

We present a novel, implementation friendly and occlusion aware semi-supervised video segmentation algorithm using tree structured graphical models, which delivers pixel labels alongwith their uncertainty estimates. Our motivation to employ supervision is to tackle a task-specific segmentation problem where the semantic objects are pre-defined by the user. The video model we propose for this problem is based on a tree structured approximation of a patch based undirected mixture model, which includes a novel time-series and a soft label Random Forest classifier participating in a feedback mechanism. We demonstrate the efficacy of our model in cutting out foreground objects and multi-class segmentation problems in lengthy and complex road scene sequences. Our results have wide applicability, including harvesting labelled video data for training discriminative models, shape/pose/articulation learning and large scale statistical analysis to develop priors for video segmentation. © 2011 IEEE.

Phrase-based statistical language generation using graphical models and active learning

Most previous work on trainable language generation has focused on two paradigms: (a) using a statistical model to rank a set of generated utterances, or (b) using statistics to inform the generation decision process. Both approaches rely on the existence of a handcrafted generator, which limits their scalability to new domains. This paper presents BAGEL, a statistical language generator which uses dynamic Bayesian networks to learn from semantically-aligned data produced by 42 untrained annotators. A human evaluation shows that BAGEL can generate natural and informative utterances from unseen inputs in the information presentation domain. Additionally, generation performance on sparse datasets is improved significantly by using certainty-based active learning, yielding ratings close to the human gold standard with a fraction of the data. © 2010 Association for Computational Linguistics.

Layered Graphical Models for Tracking Partially-Occluded Objects

Partial occlusions are commonplace in a variety of real world computer vision applications: surveillance, intelligent environments, assistive robotics, autonomous navigation, etc. While occlusion handling methods have been proposed, most methods tend to break down when confronted with numerous occluders in a scene. In this paper, a layered image-plane representation for tracking people through substantial occlusions is proposed. An image-plane representation of motion around an object is associated with a pre-computed graphical model, which can be instantiated efficiently during online tracking. A global state and observation space is obtained by linking transitions between layers. A Reversible Jump Markov Chain Monte Carlo approach is used to infer the number of people and track them online. The method outperforms two state-of-the-art methods for tracking over extended occlusions, given videos of a parking lot with numerous vehicles and a laboratory with many desks and workstations.

The Conditional Phase-type distribution: Graphical Models for Continuous Non-Normal Data:The Conditional Phase-type (C-Ph) distribution:

Conditional Gaussian (CG) distributions allow the inclusion of both discrete and continuous variables in a model assuming that the continuous variable is normally distributed. However, the CG distributions have proved to be unsuitable for survival data which tends to be highly skewed. A new method of analysis is required to take into account continuous variables which are not normally distributed. The aim of this paper is to introduce the more appropriate conditional phase-type (C-Ph) distribution for representing a continuous non-normal variable while also incorporating the causal information in the form of a Bayesian network.

Global Sensitivity Analysis for MAP Inference in Graphical Models

We study the sensitivity of a MAP configuration of a discrete probabilistic graphical model with respect to perturbations of its parameters. These perturbations are global, in the sense that simultaneous perturbations of all the parameters (or any chosen subset of them) are allowed. Our main contribution is an exact algorithm that can check whether the MAP configuration is robust with respect to given perturbations. Its complexity is essentially the same as that of obtaining the MAP configuration itself, so it can be promptly used with minimal effort. We use our algorithm to identify the largest global perturbation that does not induce a change in the MAP configuration, and we successfully apply this robustness measure in two practical scenarios: the prediction of facial action units with posed images and the classification of multiple real public data sets. A strong correlation between the proposed robustness measure and accuracy is verified in both scenarios.

Differential associations of personal and general just-world beliefs with the Five-Factor and HEXACO models of personality.

Recent literature evidences differential associations of personal and general just-world beliefs with constructs in the interpersonal domain. In line with this research, we examine the respective relationships of each just-world belief with the Five-Factor and the HEXACO models of personality in one representative sample of the working population of Switzerland and one sample of the general US population, respectively. One suppressor effect was observed in both samples: Neuroticism and emotionality was positively associated with general just-world belief, but only after controlling for personal just-world belief. In addition, agreeableness was positively and honesty-humility negatively associated with general just-world belief but unrelated to personal just-world belief. Conscientiousness was consistently unrelated to any of the just-world belief and extraversion and openness to experience revealed unstable coefficients across studies. We discuss these points in light of just-world theory and their implications for future research taking both dimensions into account.

A Factor analysis of hidrochemical composition of Llobregat river basin

Hydrogeological research usually includes some statistical studies devised to elucidate mean background state, characterise relationships among different hydrochemical parameters, and show the influence of human activities. These goals are achieved either by means of a statistical approach or by mixing models between end-members. Compositional data analysis has proved to be effective with the first approach, but there is no commonly accepted solution to the end-member problem in a compositional framework. We present here a possible solution based on factor analysis of compositions illustrated with a case study. We find two factors on the compositional bi-plot fitting two non-centered orthogonal axes to the most representative variables. Each one of these axes defines a subcomposition, grouping those variables that lay nearest to it. With each subcomposition a log-contrast is computed and rewritten as an equilibrium equation. These two factors can be interpreted as the isometric log-ratio coordinates (ilr) of three hidden components, that can be plotted in a ternary diagram. These hidden components might be interpreted as end-members. We have analysed 14 molarities in 31 sampling stations all along the Llobregat River and its tributaries, with a monthly measure during two years. We have obtained a bi-plot with a 57% of explained total variance, from which we have extracted two factors: factor G, reflecting geological background enhanced by potash mining; and factor A, essentially controlled by urban and/or farming wastewater. Graphical representation of these two factors allows us to identify three extreme samples, corresponding to pristine waters, potash mining influence and urban sewage influence. To confirm this, we have available analysis of diffused and widespread point sources identified in the area: springs, potash mining lixiviates, sewage, and fertilisers. Each one of these sources shows a clear link with one of the extreme samples, except fertilisers due to the heterogeneity of their composition. This approach is a useful tool to distinguish end-members, and characterise them, an issue generally difficult to solve. It is worth note that the end-member composition cannot be fully estimated but only characterised through log-ratio relationships among components. Moreover, the influence of each endmember in a given sample must be evaluated in relative terms of the other samples. These limitations are intrinsic to the relative nature of compositional data