Let G=(V,E) be an undirected graph, lambda_k be the k-th smallest eigenvalue of the normalized laplacian matrix of G. There is a basic fact in algebraic graph theory that lambda_k > 0 if and only if G has at most k-1 connected components. We prove a robust version of this fact. If lambda_k>0, then for some 1\leq \ell\leq k-1, V can be {\em partitioned} into l sets P_1,\ldots,P_l such that each P_i is a low-conductance set in G and induces a high conductance induced subgraph. In particular, \phi(P_i)=O(l^3\sqrt{\lambda_l}) and \phi(G[P_i]) >= \lambda_k/k^2). We make our results algorithmic by designing a simple polynomial time spectral algorithm to find such partitioning of G with a quadratic loss in the inside conductance of P_i's. Unlike the recent results on higher order Cheeger's inequality [LOT12,LRTV12], our algorithmic results do not use higher order eigenfunctions of G. If there is a sufficiently large gap between lambda_k and lambda_{k+1}, more precisely, if \lambda_{k+1} >= \poly(k) lambda_{k}^{1/4} then our algorithm finds a k partitioning of V into sets P_1,...,P_k such that the induced subgraph G[P_i] has a significantly larger conductance than the conductance of P_i in G. Such a partitioning may represent the best k clustering of G. Our algorithm is a simple local search that only uses the Spectral Partitioning algorithm as a subroutine. We expect to see further applications of this simple algorithm in clustering applications.

Chebyshev Greedy Algorithm is a generalization of the well known Orthogonal Matching Pursuit defined in a Hilbert space to the case of Banach spaces. We apply this algorithm for constructing sparse approximate solutions (with respect to a given dictionary) to convex optimization problems. Rate of convergence results in a style of the Lebesgue-type inequalities are proved.

Reconstructing transcriptional regulatory networks is an important task in functional genomics. Data obtained from experiments that perturb genes by knockouts or RNA interference contain useful information for addressing this reconstruction problem. However, such data can be limited in size and/or are expensive to acquire. On the other hand, observational data of the organism in steady state (e.g. wild-type) are more readily available, but their informational content is inadequate for the task at hand. We develop a computational approach to appropriately utilize both data sources for estimating a regulatory network. The proposed approach is based on a three-step algorithm to estimate the underlying directed but cyclic network, that uses as input both perturbation screens and steady state gene expression data. In the first step, the algorithm determines causal orderings of the genes that are consistent with the perturbation data, by combining an exhaustive search method with a fast heuristic that in turn couples a Monte Carlo technique with a fast search algorithm. In the second step, for each obtained causal ordering, a regulatory network is estimated using a penalized likelihood based method, while in the third step a consensus network is constructed from the highest scored ones. Extensive computational experiments show that the algorithm performs well in reconstructing the underlying network and clearly outperforms competing approaches that rely only on a single data source. Further, it is established that the algorithm produces a consistent estimate of the regulatory network.

Bayesian planning is a formally elegant approach to learning optimal behaviour under model uncertainty, trading off exploration and exploitation in an ideal way. Unfortunately, planning optimally in the face of uncertainty is notoriously taxing, since the search space is enormous. In this paper we introduce a tractable, sample-based method for approximate Bayes-optimal planning which exploits Monte-Carlo tree search. Our approach avoids expensive applications of Bayes rule within the search tree by sampling models from current beliefs, and furthermore performs this sampling in a lazy manner. This enables it to outperform previous Bayesian model-based reinforcement learning algorithms by a significant margin on several well-known benchmark problems. As we show, our approach can even work in problems with an infinite state space that lie qualitatively out of reach of almost all previous work in Bayesian exploration.

This article considers the performance of the MOA* multiobjective search algorithm with heuristic information. It is shown that in certain cases blind search can be more efficient than perfectly informed search, in terms of both node and label expansions. A class of simple graph search problems is defined for which the number of nodes grows linearly with problem size and the number of nondominated labels grows quadratically. It is proved that for these problems the number of node expansions performed by blind MOA* grows linearly with problem size, while the number of such expansions performed with a perfectly informed heuristic grows quadratically. It is also proved that the number of label expansions grows quadratically in the blind case and cubically in the informed case.

Algorithmic composition is the partial or total automation of the process of music composition by using computers. Since the 1950s, different computational techniques related to Artificial Intelligence have been used for algorithmic composition, including grammatical representations, probabilistic methods, neural networks, symbolic rule-based systems, constraint programming and evolutionary algorithms. This survey aims to be a comprehensive account of research on algorithmic composition, presenting a thorough view of the field for researchers in Artificial Intelligence.

In order to automatically generate high-quality game levels, one needs to be able to automatically verify that the levels are playable. The simulation-based approach to playability testing uses an artificial agent to play through the level, but building such an agent is not always an easy task and such an agent is not always readily available. We discuss this prob- lem in the context of the physics-based puzzle game Cut the Rope, which features continuous time and state space, mak- ing several approaches such as exhaustive search and reactive agents inefficient. We show that a deliberative Prolog-based agent can be used to suggest all sensible moves at each state, which allows us to restrict the search space so that depth-first search for solutions become viable. This agent is successfully used to test playability in Ropossum, a level generator based on grammatical evolution. The method proposed in this paper is likely to be useful for a large variety of games with similar characteristics.

Monte Carlo Tree Search (MCTS) has produced many recent breakthroughs in game AI research, particularly in computer Go. In this paper we consider how MCTS can be applied to create engaging AI for a popular commercial mobile phone game: Spades by AI Factory, which has been downloaded more than 2.5 million times. In particular, we show how MCTS can be integrated with knowledge-based methods to create an interesting, fun and strong player which makes far fewer plays that could be perceived by human observers as blunders than MCTS without the injection of knowledge. These blunders are particularly noticeable for Spades, where a human player must co-operate with an AI partner. MCTS gives objectively stronger play than the knowledge-based approach used in previous versions of the game and offers the flexibility to customise behaviour whilst maintaining a reusable core, with a reduced development cycle compared to purely knowledge-based techniques.

Search is a recognized technique for procedural content generation and game design, and it has been used successfully as part of commercial and academic games. In this context, search has almost always referred to selective search, as opposed to larger brute-force searches. The argument against brute-force search is that the state spaces of the games are almost always too large to be amenable for brute-force search. We believe, however, that brute-force search should not be too quickly dismissed. State spaces with trillions or tens of trillions states can now be exhaustively searched with relative ease, and growth in parallelism and computational power is expected to continue to scale this trend. We believe that this, combined with appropriate abstraction, will allow exhaustive search to be applied to many problems once thought to be prohibitively large. We explore this argument in the context of a game called "Fling!," available for mobile devices, showing a system for interactively designing and analyzing puzzles.

Planning-based techniques are a very powerful tool for automated story generation. However, as the number of possible actions increases, traditional planning techniques suffer from a combinatorial explosion due to large branching factors. In this work, we apply Monte Carlo Tree Search (MCTS) techniques to generate stories in domains with large numbers of possible actions (100+). Our approach employs a Bayesian story evaluation method to guide the planning towards believable stories that reach a user defined goal. We generate stories in a novel domain with different type of story goals. Our approach shows an order of magnitude improvement in performance over traditional search techniques.