Bayesian non-parametrics and the probabilistic approach to modelling.

Modelling is fundamental to many fields of science and engineering. A model can be thought of as a representation of possible data one could predict from a system. The probabilistic approach to modelling uses probability theory to express all aspects of uncertainty in the model. The probabilistic approach is synonymous with Bayesian modelling, which simply uses the rules of probability theory in order to make predictions, compare alternative models, and learn model parameters and structure from data. This simple and elegant framework is most powerful when coupled with flexible probabilistic models. Flexibility is achieved through the use of Bayesian non-parametrics. This article provides an overview of probabilistic modelling and an accessible survey of some of the main tools in Bayesian non-parametrics. The survey covers the use of Bayesian non-parametrics for modelling unknown functions, density estimation, clustering, time-series modelling, and representing sparsity, hierarchies, and covariance structure. More specifically, it gives brief non-technical overviews of Gaussian processes, Dirichlet processes, infinite hidden Markov models, Indian buffet processes, Kingman's coalescent, Dirichlet diffusion trees and Wishart processes.

Probabilistic computation in human perception under variability in encoding precision.

A key function of the brain is to interpret noisy sensory information. To do so optimally, observers must, in many tasks, take into account knowledge of the precision with which stimuli are encoded. In an orientation change detection task, we find that encoding precision does not only depend on an experimentally controlled reliability parameter (shape), but also exhibits additional variability. In spite of variability in precision, human subjects seem to take into account precision near-optimally on a trial-to-trial and item-to-item basis. Our results offer a new conceptualization of the encoding of sensory information and highlight the brain's remarkable ability to incorporate knowledge of uncertainty during complex perceptual decision-making.

Statistical inference for single- and multi-band probabilistic amplitude demodulation.

Amplitude demodulation is an ill-posed problem and so it is natural to treat it from a Bayesian viewpoint, inferring the most likely carrier and envelope under probabilistic constraints. One such treatment is Probabilistic Amplitude Demodulation (PAD), which, whilst computationally more intensive than traditional approaches, offers several advantages. Here we provide methods for estimating the uncertainty in the PAD-derived envelopes and carriers, and for learning free-parameters like the time-scale of the envelope. We show how the probabilistic approach can naturally handle noisy and missing data. Finally, we indicate how to extend the model to signals which contain multiple modulators and carriers.

Probabilistic Amplitude Demodulation

Auditory scene analysis is extremely challenging. One approach, perhaps that adopted by the brain, is to shape useful representations of sounds on prior knowledge about their statistical structure. For example, sounds with harmonic sections are common and so time-frequency representations are efficient. Most current representations concentrate on the shorter components. Here, we propose representations for structures on longer time-scales, like the phonemes and sentences of speech. We decompose a sound into a product of processes, each with its own characteristic time-scale. This demodulation cascade relates to classical amplitude demodulation, but traditional algorithms fail to realise the representation fully. A new approach, probabilistic amplitude demodulation, is shown to out-perform the established methods, and to easily extend to representation of a full demodulation cascade.

Probabilistic soil identification based on cone penetration tests

In geotechnical engineering, soil classification is an essential component in the design process. Field methods such as the cone penetration test (CPT) can be used as less expensive and faster alternatives to sample retrieval and testing. Unfortunately, current soil classification charts based on CPT data and laboratory measurements are too generic, and may not provide an accurate prediction of the soil type. A probabilistic approach is proposed here to update and modify soil identification charts based on site-specific CPT data. The probability that a soil is correctly classified is also estimated. The updated identification chart can be used for a more accurate prediction of the classification of the soil, and can account for prior information available before conducting the tests, site-specific data, and measurement errors. As an illustration, the proposed approach is implemented using CPT data from the Treporti Test Site (TTS) near Venice (Italy) and the National Geotechnical Experimentation Sites (NGES) at Texas A&M University. The applicability of the site-specific chart for other sites in Venice Lagoon is assessed using data from the Malamocco test site, approximately 20 km from TTS.

Detecting bipedal motion from correlated probabilistic trajectories

This paper is about detecting bipedal motion in video sequences by using point trajectories in a framework of classification. Given a number of point trajectories, we find a subset of points which are arising from feet in bipedal motion by analysing their spatio-temporal correlation in a pairwise fashion. To this end, we introduce probabilistic trajectories as our new features which associate each point over a sufficiently long time period in the presence of noise. They are extracted from directed acyclic graphs whose edges represent temporal point correspondences and are weighted with their matching probability in terms of appearance and location. The benefit of the new representation is that it practically tolerates inherent ambiguity for example due to occlusions. We then learn the correlation between the motion of two feet using the probabilistic trajectories in a decision forest classifier. The effectiveness of the algorithm is demonstrated in experiments on image sequences captured with a static camera, and extensions to deal with a moving camera are discussed. © 2013 Elsevier B.V. All rights reserved.

MoT - Mixture of trees probabilistic graphical model for video segmentation

We present a novel mixture of trees (MoT) graphical model for video segmentation. Each component in this mixture represents a tree structured temporal linkage between super-pixels from the first to the last frame of a video sequence. Our time-series model explicitly captures the uncertainty in temporal linkage between adjacent frames which improves segmentation accuracy. We provide a variational inference scheme for this model to estimate super-pixel labels and their confidences in nearly realtime. The efficacy of our approach is demonstrated via quantitative comparisons on the challenging SegTrack joint segmentation and tracking dataset [23].