Submodularity of Energy Related Controllability Metrics

The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of actuators and sensors that optimize real-valued controllability and observability metrics of the network. We show that several classes of energy related metrics associated with the controllability Gramian in linear dynamical systems have a strong structural property, called submodularity. This property allows for an approximation guarantee by using a simple greedy heuristic for their maximization. The results are illustrated for randomly generated systems and for placement of power electronic actuators in a model of the European power grid.Comment: 7 pages, 2 figures; submitted to the 2014 IEEE Conference on Decision and Contro

Budget-Constrained Item Cold-Start Handling in Collaborative Filtering Recommenders via Optimal Design

It is well known that collaborative filtering (CF) based recommender systems provide better modeling of users and items associated with considerable rating history. The lack of historical ratings results in the user and the item cold-start problems. The latter is the main focus of this work. Most of the current literature addresses this problem by integrating content-based recommendation techniques to model the new item. However, in many cases such content is not available, and the question arises is whether this problem can be mitigated using CF techniques only. We formalize this problem as an optimization problem: given a new item, a pool of available users, and a budget constraint, select which users to assign with the task of rating the new item in order to minimize the prediction error of our model. We show that the objective function is monotone-supermodular, and propose efficient optimal design based algorithms that attain an approximation to its optimum. Our findings are verified by an empirical study using the Netflix dataset, where the proposed algorithms outperform several baselines for the problem at hand.Comment: 11 pages, 2 figure

Adaptive Information Gathering via Imitation Learning

In the adaptive information gathering problem, a policy is required to select an informative sensing location using the history of measurements acquired thus far. While there is an extensive amount of prior work investigating effective practical approximations using variants of Shannon's entropy, the efficacy of such policies heavily depends on the geometric distribution of objects in the world. On the other hand, the principled approach of employing online POMDP solvers is rendered impractical by the need to explicitly sample online from a posterior distribution of world maps. We present a novel data-driven imitation learning framework to efficiently train information gathering policies. The policy imitates a clairvoyant oracle - an oracle that at train time has full knowledge about the world map and can compute maximally informative sensing locations. We analyze the learnt policy by showing that offline imitation of a clairvoyant oracle is implicitly equivalent to online oracle execution in conjunction with posterior sampling. This observation allows us to obtain powerful near-optimality guarantees for information gathering problems possessing an adaptive sub-modularity property. As demonstrated on a spectrum of 2D and 3D exploration problems, the trained policies enjoy the best of both worlds - they adapt to different world map distributions while being computationally inexpensive to evaluate.Comment: Robotics Science and Systems, 201

Click Carving: Segmenting Objects in Video with Point Clicks

We present a novel form of interactive video object segmentation where a few clicks by the user helps the system produce a full spatio-temporal segmentation of the object of interest. Whereas conventional interactive pipelines take the user's initialization as a starting point, we show the value in the system taking the lead even in initialization. In particular, for a given video frame, the system precomputes a ranked list of thousands of possible segmentation hypotheses (also referred to as object region proposals) using image and motion cues. Then, the user looks at the top ranked proposals, and clicks on the object boundary to carve away erroneous ones. This process iterates (typically 2-3 times), and each time the system revises the top ranked proposal set, until the user is satisfied with a resulting segmentation mask. Finally, the mask is propagated across the video to produce a spatio-temporal object tube. On three challenging datasets, we provide extensive comparisons with both existing work and simpler alternative methods. In all, the proposed Click Carving approach strikes an excellent balance of accuracy and human effort. It outperforms all similarly fast methods, and is competitive or better than those requiring 2 to 12 times the effort.Comment: A preliminary version of the material in this document was filed as University of Texas technical report no. UT AI16-0