Metric Properties of Structured Data Visualizations through Generative Probabilistic Modeling

Abstract

This paper proposes a systematic approach of representing abstract features in terms of low-level, subjective state representations. We demonstrate that a mapping between the agent's predictive state representation and an abstract feature representation can be derived automatically from high-level training data supplied by the designer. Our empirical evaluation demonstrates that an experience-oriented state representation built around a single-bit sensor can represent useful abstract features such as back against a wall, in a corner, or in a room. As a result, the agent gains virtual sensors that could be used by its control policy.Recently, generative probabilistic modeling principles were extended to visualization of structured data types, such as sequences. The models are formulated as constrained mixtures of sequence models - a generalization of density-based visualization methods previously developed for static data sets. In order to effectively explore visualization plots, one needs to understand local directional magnification factors, i.e. the extend to which small positional changes on visualization plot lead to changes in local noise models explaining the structured data. Magnification factors are useful for highlighting boundaries between data clusters. In this paper we present two techniques for estimating local metric induced on the sequence space by the model formulation. We first verify our approach in two controlled experiments involving artificially generated sequences. We then illustrate our methodology on sequences representing chorals by J.S. Bach.