In many applications of shortest-path algorithms, it is impractical to find a provably optimal solution; one can only hope to achieve an appropriate balance between search time and solution cost that respects the user's preferences. Preferences come in many forms; we consider utility functions that linearly trade-off search time and solution cost. Many natural utility functions can be expressed in this form. For example, when solution cost represents the makespan of a plan, equally weighting search time and plan makespan minimizes the time from the arrival of a goal until it is achieved. Current state-of-the-art approaches to optimizing utility functions rely on anytime algorithms, and the use of extensive training data to compute a termination policy. We propose a more direct approach, called Bugsy, that incorporates the utility function directly into the search, obviating the need for a separate termination policy. We describe a new method based on off-line parameter tuning and a novel benchmark domain for planning under time pressure based on platform-style video games. We then present what we believe to be the first empirical study of applying anytime monitoring to heuristic search, and we compare it with our proposals. Our results suggest that the parameter tuning technique can give the best performance if a representative set of training instances is available. If not, then Bugsy is the algorithm of choice, as it performs well and does not require any off-line training. This work extends the tradition of research on metareasoning for search by illustrating the benefits of embedding lightweight reasoning about time into the search algorithm itself.

Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here we introduce a new class of spectral algorithms based on a non-backtracking walk on the directed edges of the graph. The spectrum of this operator is much better-behaved than that of the adjacency matrix or other commonly used matrices, maintaining a strong separation between the bulk eigenvalues and the eigenvalues relevant to community structure even in the sparse case. We show that our algorithm is optimal for graphs generated by the stochastic block model, detecting communities all the way down to the theoretical limit. We also show the spectrum of the non-backtracking operator for some real-world networks, illustrating its advantages over traditional spectral clustering.

In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate feature maps for latent position graphs with positive definite link function $\kappa$, provided that the latent positions are i.i.d. from some distribution F. We then consider the exploitation task of vertex classification where the link function $\kappa$ belongs to the class of universal kernels and class labels are observed for a number of vertices tending to infinity and that the remaining vertices are to be classified. We show that minimization of the empirical $\varphi$-risk for some convex surrogate $\varphi$ of 0-1 loss over a class of linear classifiers with increasing complexities yields a universally consistent classifier, that is, a classification rule with error converging to Bayes optimal for any distribution F.

The recent proliferation of smart-phones and other wearable devices has lead to a surge of new mobile applications. Partially observable Markov decision processes provide a natural framework to design applications that continuously make decisions based on noisy sensor measurements. However, given the limited battery life, there is a need to minimize the amount of online computation. This can be achieved by compiling a policy into a finite state controller since there is no need for belief monitoring or online search. In this paper, we propose a new branch and bound technique to search for a good controller. In contrast to many existing algorithms for controllers, our search technique is not subject to local optima. We also show how to reduce the amount of search by avoiding the enumeration of isomorphic controllers and by taking advantage of suitable upper and lower bounds. The approach is demonstrated on several benchmark problems as well as a smart-phone application to assist persons with Alzheimer's to wayfind.

We present an efficient algorithm for simultaneously training sparse generalized linear models across many related problems, which may arise from bootstrapping, cross-validation and nonparametric permutation testing. Our approach leverages the redundancies across problems to obtain significant computational improvements relative to solving the problems sequentially by a conventional algorithm. We demonstrate our fast simultaneous training of generalized linear models (FaSTGLZ) algorithm on a number of real-world datasets, and we run otherwise computationally intensive bootstrapping and permutation test analyses that are typically necessary for obtaining statistically rigorous classification results and meaningful interpretation. Code is freely available at http://liinc.bme.columbia.edu/fastglz.

The level set tree approach of Hartigan (1975) provides a probabilistically based and highly interpretable encoding of the clustering behavior of a dataset. By representing the hierarchy of data modes as a dendrogram of the level sets of a density estimator, this approach offers many advantages for exploratory analysis and clustering, especially for complex and high-dimensional data. Several R packages exist for level set tree estimation, but their practical usefulness is limited by computational inefficiency, absence of interactive graphical capabilities and, from a theoretical perspective, reliance on asymptotic approximations. To make it easier for practitioners to capture the advantages of level set trees, we have written the Python package DeBaCl for DEnsity-BAsed CLustering. In this article we illustrate how DeBaCl's level set tree estimates can be used for difficult clustering tasks and interactive graphical data analysis. The package is intended to promote the practical use of level set trees through improvements in computational efficiency and a high degree of user customization. In addition, the flexible algorithms implemented in DeBaCl enjoy finite sample accuracy, as demonstrated in recent literature on density clustering. Finally, we show the level set tree framework can be easily extended to deal with functional data.

Artificial Intelligence began as a field probing some of the most fundamental questions of science - the nature of intelligence and the design of intelligent artifacts. But it has grown into a discipline that is deeply entwined with commerce and society. Today's AI technology, such as expert systems and intelligent assistants, pose some difficult questions of risk, trust and accountability. In this paper, we present these concerns, examining them in the context of historical developments that have shaped the nature and direction of AI research. We also suggest the exploration and further development of two paradigms, human intelligence-machine cooperation, and a sociological view of intelligence, which might help address some of these concerns.

The crucial importance of metrics in machine learning algorithms has led to an increasing interest in optimizing distance and similarity functions, an area of research known as metric learning. When data consist of feature vectors, a large body of work has focused on learning a Mahalanobis distance. Less work has been devoted to metric learning from structured objects (such as strings or trees), most of it focusing on optimizing a notion of edit distance. We identify two important limitations of current metric learning approaches. First, they allow to improve the performance of local algorithms such as k-nearest neighbors, but metric learning for global algorithms (such as linear classifiers) has not been studied so far. Second, the question of the generalization ability of metric learning methods has been largely ignored. In this thesis, we propose theoretical and algorithmic contributions that address these limitations. Our first contribution is the derivation of a new kernel function built from learned edit probabilities. Our second contribution is a novel framework for learning string and tree edit similarities inspired by the recent theory of (e,g,t)-good similarity functions. Using uniform stability arguments, we establish theoretical guarantees for the learned similarity that give a bound on the generalization error of a linear classifier built from that similarity. In our third contribution, we extend these ideas to metric learning from feature vectors by proposing a bilinear similarity learning method that efficiently optimizes the (e,g,t)-goodness. Generalization guarantees are derived for our approach, highlighting that our method minimizes a tighter bound on the generalization error of the classifier. Our last contribution is a framework for establishing generalization bounds for a large class of existing metric learning algorithms based on a notion of algorithmic robustness.

We investigate two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe. Both systems assign a representative to each voter so that the "sum of misrepresentations" is minimized. The winner determination problem for both systems is known to be NP-hard, hence this work aims at investigating whether there are variants of the proposed rules and/or specific electorates for which these problems can be solved efficiently. As a variation of these rules, instead of minimizing the sum of misrepresentations, we considered minimizing the maximal misrepresentation introducing effectively two new rules. In the general case these "minimax" versions of classical rules appeared to be still NP-hard. We investigated the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters. Here we have a mixture of positive and negative results: e.g., we proved fixed-parameter tractability for the parameter the number of candidates but fixed-parameter intractability for the number of winners. For single-peaked electorates our results are overwhelmingly positive: we provide polynomial-time algorithms for most of the considered problems. The only rule that remains NP-hard for single-peaked electorates is the classical Monroe rule.

List of conference committees for AAAI-13, IAAI-13, and the EAAI-13 symposium.