Approximating a matrix by a small subset of its columns is a known problem in numerical linear algebra. Algorithms that address this problem have been used in areas which include, among others, sparse approximation, unsupervised feature selection, data mining, and knowledge representation. Such algorithms were investigated since the 1960's, with recent results that use randomization. The problem is believed to be NP-Hard, and to the best of our knowledge there are no previously published algorithms aimed at computing optimal solutions. We show how to model the problem as a graph search, and propose a heuristic based on eigenvalues of related matrices. Applying the A* search strategy with this heuristic is guaranteed to find the optimal solution. Experimental results on common datasets show that the proposed algorithm can effectively select columns from moderate size matrices, typically improving by orders of magnitude the run time of exhaustive search. We also show how to combine the proposed algorithm with other non-optimal (but much faster) algorithms in a ``two stage'' framework, which is guaranteed to improve the accuracy of the other algorithms.

We present an intuitive explanation for the limited effectiveness of front-to-end bidirectional heuristic search, supported with extensive evidence from many commonly-studied domains. While previous work has proved the limitations of specific algorithms, we show that any front-to-end bidirectional heuristic search algorithm will likely be dominated by unidirectional heuristic search or bidirectional brute-force search. We also demonstrate a pathological case where bidirectional heuristic search is the dominant algorithm, so a stronger claim cannot be made. Finally, we show that on the four-peg Towers Of Hanoi with arbitrary start and goal states, bidirectional brute-force search outperforms unidirectional heuristic search using pattern-database heuristics.

Commitment protocols provide an effective formalism for the regulation of agent interaction. Although existing work mainly focus on the design-time development of static commitment protocols, recent studies propose methods to create them dynamically at run-time with respect to the goals of the agents. These methods require agents to verify new commitment protocols taking their goals, and beliefs about the other agents’ behavior into account. Accordingly, in this paper, we first propose a probabilistic model to formally capture commitment protocols according to agents’ beliefs. Secondly, we identify a set of important properties for the verification of a new commitment protocol from an agent’s perspective and formalize these properties in our model. Thirdly, we develop probabilistic model checking algorithms with advanced reduction for efficient verification of these properties. Finally, we implement these algorithms as a tool and evaluate the proposed properties over different commitment protocols.

We show that without using any domain knowledge, we can predict the final performance of a team of voting agents, at any step towards solving a complex problem.

Living organisms adapt to challenges through evolution. This has proven to be a key difficulty in developing therapies, since the organisms evolve resistance.I propose the wild idea of steering evolution strategically — using computational game theory for (typically incomplete-information) multistage games and opponent exploitation techniques. A sequential contingency plan for steering evolution is constructed computationally for the setting at hand. In the biological context, the opponent (e.g., a disease) has a systematic handicap because it evolves myopically. This can be exploited by computing trapping strategies that cause the opponent to evolve into states where it can be handled effectively. Potential application classes include therapeutics at the population, individual, and molecular levels (drug design), as well as cell repurposing and synthetic biology.

As an important and challenging problem in computer vision and graphics, keypoint-based object tracking is typically formulated in a spatio-temporal statistical learning framework. However, most existing keypoint trackers are incapable of effectively modeling and balancing the following three aspects in a simultaneous manner: temporal model coherence across frames, spatial model consistency within frames, and discriminative feature construction. To address this issue, we propose a robust keypoint tracker based on spatio-temporal multi-task structured output optimization driven by discriminative metric learning. Consequently, temporal model coherence is characterized by multi-task structured keypoint model learning over several adjacent frames, while spatial model consistency is modeled by solving a geometric verification based structured learning problem. Discriminative feature construction is enabled by metric learning to ensure the intra-class compactness and inter-class separability. Finally, the above three modules are simultaneously optimized in a joint learning scheme. Experimental results have demonstrated the effectiveness of our tracker.

Face verification remains a challenging problem in very complex conditions with large variations such as pose, illumination, expression, and occlusions. This problemis exacerbated when we rely unrealistically on a singletraining data source, which is often insufficient to coverthe intrinsically complex face variations. This paperproposes a principled multi-task learning approachbased on Discriminative Gaussian Process Latent VariableModel (DGPLVM), named GaussianFace, for faceverification. In contrast to relying unrealistically on asingle training data source, our model exploits additional data from multiple source-domains to improve the generalization performance of face verification inan unknown target-domain. Importantly, our model can adapt automatically to complex data distributions, and therefore can well capture complex face variations inherent in multiple sources. To enhance discriminative power, we introduced a more efficient equivalent form of Kernel Fisher Discriminant Analysis to DGPLVM.To speed up the process of inference and prediction, we exploited the low rank approximation method. Extensive experiments demonstrated the effectiveness of the proposed model in learning from diverse data sources and generalizing to unseen domains. Specifically, the accuracy of our algorithm achieved an impressive accuracyrate of 98.52% on the well-known and challenging Labeled Faces in the Wild (LFW) benchmark. For the first time, the human-level performance in face verification (97.53%) on LFW is surpassed.

Automatically recognizing a large number of action categories from videos is of significant importance for video understanding. Most existing works focused on the design of more discriminative feature representation, and have achieved promising results when the positive samples are enough. However, very limited efforts were spent on recognizing a novel action without any positive exemplars, which is often the case in the real settings due to the large amount of action classes and the users' queries dramatic variations. To address this issue, we propose to perform action recognition when no positive exemplars of that class are provided, which is often known as the zero-shot learning. Different from other zero-shot learning approaches, which exploit attributes as the intermediate layer for the knowledge transfer, our main contribution is SIR, which directly leverages the semantic inter-class relationships between the known and unknown actions followed by label transfer learning. The inter-class semantic relationships are automatically measured by continuous word vectors, which learned by the skip-gram model using the large-scale text corpus. Extensive experiments on the UCF101 dataset validate the superiority of our method over fully-supervised approaches using few positive exemplars.

Interruptible pure exploration in multi-armed bandits (MABs) is a key component of Monte-Carlo tree search algorithms for sequential decision problems. We introduce Discriminative Bucketing (DB), a novel family of strategies for pure exploration in MABs, which allows for adapting recent advances in non-interruptible strategies to the interruptible setting, while guaranteeing exponential-rate performance improvement over time. Our experimental evaluation demonstrates that the corresponding instances of DB favorably compete both with the currently popular strategies UCB1 and Epsilon-Greedy, as well as with the conservative uniform sampling.

The classical planning problem can be enriched with quantitative and qualitative user-defined preferences on how the system behaves on achieving the goal. In this paper, we propose the probabilistic preference planning problem for Markov decision processes, where the preferences are based on an enriched probabilistic LTL-style logic. We develop P4Solver, an SMT-based planner computing the preferred plan by reducing the problem to quadratic programming problem, which can be solved using SMT solvers such as Z3. We illustrate the framework by applying our approach on two selected case studies.