Symmetry Regularization

The properties of a representation, such as smoothness, adaptability, generality, equivari- ance/invariance, depend on restrictions imposed during learning. In this paper, we propose using data symmetries, in the sense of equivalences under transformations, as a means for learning symmetry- adapted representations, i.e., representations that are equivariant to transformations in the original space. We provide a sufficient condition to enforce the representation, for example the weights of a neural network layer or the atoms of a dictionary, to have a group structure and specifically the group structure in an unlabeled training set. By reducing the analysis of generic group symmetries to per- mutation symmetries, we devise an analytic expression for a regularization scheme and a permutation invariant metric on the representation space. Our work provides a proof of concept on why and how to learn equivariant representations, without explicit knowledge of the underlying symmetries in the data.This material is based upon work supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF-1231216

Efficient Data Representation by Selecting Prototypes with Importance Weights

Prototypical examples that best summarizes and compactly represents an underlying complex data distribution communicate meaningful insights to humans in domains where simple explanations are hard to extract. In this paper we present algorithms with strong theoretical guarantees to mine these data sets and select prototypes a.k.a. representatives that optimally describes them. Our work notably generalizes the recent work by Kim et al. (2016) where in addition to selecting prototypes, we also associate non-negative weights which are indicative of their importance. This extension provides a single coherent framework under which both prototypes and criticisms (i.e. outliers) can be found. Furthermore, our framework works for any symmetric positive definite kernel thus addressing one of the key open questions laid out in Kim et al. (2016). By establishing that our objective function enjoys a key property of that of weak submodularity, we present a fast ProtoDash algorithm and also derive approximation guarantees for the same. We demonstrate the efficacy of our method on diverse domains such as retail, digit recognition (MNIST) and on publicly available 40 health questionnaires obtained from the Center for Disease Control (CDC) website maintained by the US Dept. of Health. We validate the results quantitatively as well as qualitatively based on expert feedback and recently published scientific studies on public health, thus showcasing the power of our technique in providing actionability (for retail), utility (for MNIST) and insight (on CDC datasets) which arguably are the hallmarks of an effective data mining method.Comment: Accepted for publication in International Conference on Data Mining (ICDM) 201

Improving Sequential Determinantal Point Processes for Supervised Video Summarization

It is now much easier than ever before to produce videos. While the ubiquitous video data is a great source for information discovery and extraction, the computational challenges are unparalleled. Automatically summarizing the videos has become a substantial need for browsing, searching, and indexing visual content. This paper is in the vein of supervised video summarization using sequential determinantal point process (SeqDPP), which models diversity by a probabilistic distribution. We improve this model in two folds. In terms of learning, we propose a large-margin algorithm to address the exposure bias problem in SeqDPP. In terms of modeling, we design a new probabilistic distribution such that, when it is integrated into SeqDPP, the resulting model accepts user input about the expected length of the summary. Moreover, we also significantly extend a popular video summarization dataset by 1) more egocentric videos, 2) dense user annotations, and 3) a refined evaluation scheme. We conduct extensive experiments on this dataset (about 60 hours of videos in total) and compare our approach to several competitive baselines