A Morphism Double Category and Monoidal Structure

A double category is constructed from a `fattened' version of a given category, motivated in part by a context of parallel transport. We also study monoidal structures on the underlying category and on the fattened category

Methodologies in Predictive Visual Analytics

abstract: Predictive analytics embraces an extensive area of techniques from statistical modeling to machine learning to data mining and is applied in business intelligence, public health, disaster management and response, and many other fields. To date, visualization has been broadly used to support tasks in the predictive analytics pipeline under the underlying assumption that a human-in-the-loop can aid the analysis by integrating domain knowledge that might not be broadly captured by the system. Primary uses of visualization in the predictive analytics pipeline have focused on data cleaning, exploratory analysis, and diagnostics. More recently, numerous visual analytics systems for feature selection, incremental learning, and various prediction tasks have been proposed to support the growing use of complex models, agent-specific optimization, and comprehensive model comparison and result exploration. Such work is being driven by advances in interactive machine learning and the desire of end-users to understand and engage with the modeling process. However, despite the numerous and promising applications of visual analytics to predictive analytics tasks, work to assess the effectiveness of predictive visual analytics is lacking. This thesis studies the current methodologies in predictive visual analytics. It first defines the scope of predictive analytics and presents a predictive visual analytics (PVA) pipeline. Following the proposed pipeline, a predictive visual analytics framework is developed to be used to explore under what circumstances a human-in-the-loop prediction process is most effective. This framework combines sentiment analysis, feature selection mechanisms, similarity comparisons and model cross-validation through a variety of interactive visualizations to support analysts in model building and prediction. To test the proposed framework, an instantiation for movie box-office prediction is developed and evaluated. Results from small-scale user studies are presented and discussed, and a generalized user study is carried out to assess the role of predictive visual analytics under a movie box-office prediction scenario.Dissertation/ThesisDoctoral Dissertation Engineering 201

TWISTED ACTIONS OF CATEGORICAL GROUPS

Abstract. We develop a theory of twisted actions of categorical groups using a notion of semidirect product of categories. We work through numerous examples to demonstrate the power of these notions. Turning to representations, which are actions that respect vector space structures, we establish an analog of Schur’s lemma in this context. Keeping new terminology to a minimum, we concentrate on examples exploring the essential new notions introduced. 1

Negative forms and path space forms

We present an account of negative differential forms within a natural algebraic framework of differential graded algebras, and explain their relationship with forms on path spaces.Comment: 12 pp.; the Introduction has been rewritten and mention of cohomology dropped in Proposition 3.2; material slightly reorganize

Parallel Transport over Path Spaces

We develop a differential geometric framework for parallel transport over path spaces and a corresponding discrete theory, an integrated version of the continuum theory, using a category-theoretic framework.Comment: 27pp 3fig pdflatex only; v2: rewritten with several clarifications; v3: minor changes, added references. Version to be published, 30p