Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis

Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these models can be recovered through the Gaussian process latent variable model. This gives us a flexible formalism for multi-view learning where the latent variables can be used both for exploratory purposes and for learning representations that enable efficient inference for ambiguous estimation tasks. Learning is performed in a Bayesian manner through the formulation of a variational compression scheme which gives a rigorous lower bound on the log likelihood. Our Bayesian framework provides strong regularization during training, allowing the structure of the latent space to be determined efficiently and automatically. We demonstrate this by producing the first (to our knowledge) published results of learning from dozens of views, even when data is scarce. We further show experimental results on several different types of multi-view data sets and for different kinds of tasks, including exploratory data analysis, generation, ambiguity modelling through latent priors and classification.Comment: 49 pages including appendi

A Nonparametric Approach to Segmentation of Ladar Images

The advent of advanced laser radar (ladar) systems that record full-waveform signal data has inspired numerous inquisitions which aspire to extract additional, previously unavailable, information about the illuminated scene from the collected data. The quality of the information, however, is often related to the limitations of the ladar camera used to collect the data. This research project uses full-waveform analysis of ladar signals, and basic principles of optics, to propose a new formulation for an accepted signal model. A new waveform model taking into account backscatter reflectance is the key to overcoming specific deficiencies of the ladar camera at hand, namely the ability to discern pulse-spreading effects of elongated targets. A concert of non-parametric statistics and familiar image processing methods are used to calculate the orientation angle of the illuminated objects, and the deficiency of the hardware is circumvented. Segmentation of the various ladar images performed as part of the angle estimation, and this is shown to be a new and effective strategy for analyzing the output of the AFIT ladar camera

Syntactic Topic Models

The syntactic topic model (STM) is a Bayesian nonparametric model of language that discovers latent distributions of words (topics) that are both semantically and syntactically coherent. The STM models dependency parsed corpora where sentences are grouped into documents. It assumes that each word is drawn from a latent topic chosen by combining document-level features and the local syntactic context. Each document has a distribution over latent topics, as in topic models, which provides the semantic consistency. Each element in the dependency parse tree also has a distribution over the topics of its children, as in latent-state syntax models, which provides the syntactic consistency. These distributions are convolved so that the topic of each word is likely under both its document and syntactic context. We derive a fast posterior inference algorithm based on variational methods. We report qualitative and quantitative studies on both synthetic data and hand-parsed documents. We show that the STM is a more predictive model of language than current models based only on syntax or only on topics