On the adequacy of current empirical evaluations of formal models of categorization

Categorization is one of the fundamental building blocks of cognition, and the study of categorization is notable for the extent to which formal modeling has been a central and influential component of research. However, the field has seen a proliferation of noncomplementary models with little consensus on the relative adequacy of these accounts. Progress in assessing the relative adequacy of formal categorization models has, to date, been limited because (a) formal model comparisons are narrow in the number of models and phenomena considered and (b) models do not often clearly define their explanatory scope. Progress is further hampered by the practice of fitting models with arbitrarily variable parameters to each data set independently. Reviewing examples of good practice in the literature, we conclude that model comparisons are most fruitful when relative adequacy is assessed by comparing well-defined models on the basis of the number and proportion of irreversible, ordinal, penetrable successes (principles of minimal flexibility, breadth, good-enough precision, maximal simplicity, and psychological focus)

Complexity Bounds for Ordinal-Based Termination

`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times. Our main tool for this are length function theorems, which provide complexity bounds on the use of well quasi orders. We illustrate how to prove such theorems in the simple yet until now untreated case of ordinals. We show how to apply this new theorem to derive complexity bounds on programs when they are proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability Problems (RP 2014, 22-24 September 2014, Oxford

Discriminatively Trained Latent Ordinal Model for Video Classification

We study the problem of video classification for facial analysis and human action recognition. We propose a novel weakly supervised learning method that models the video as a sequence of automatically mined, discriminative sub-events (eg. onset and offset phase for "smile", running and jumping for "highjump"). The proposed model is inspired by the recent works on Multiple Instance Learning and latent SVM/HCRF -- it extends such frameworks to model the ordinal aspect in the videos, approximately. We obtain consistent improvements over relevant competitive baselines on four challenging and publicly available video based facial analysis datasets for prediction of expression, clinical pain and intent in dyadic conversations and on three challenging human action datasets. We also validate the method with qualitative results and show that they largely support the intuitions behind the method.Comment: Paper accepted in IEEE TPAMI. arXiv admin note: substantial text overlap with arXiv:1604.0150