In the supervised learning setting termed Multiple-Instance Learning (MIL), the examples are bags of instances, and the bag label is a function of the labels of its instances. Typically, this function is the Boolean OR. The learner observes a sample of bags and the bag labels, but not the instance labels that determine the bag labels. The learner is then required to emit a classification rule for bags based on the sample. MIL has numerous applications, and many heuristic algorithms have been used successfully on this problem, each adapted to specific settings or applications. In this work we provide a unified theoretical analysis for MIL, which holds for any underlying hypothesis class, regardless of a specific application or problem domain. We show that the sample complexity of MIL is only poly-logarithmically dependent on the size of the bag, for any underlying hypothesis class. In addition, we introduce a new PAC-learning algorithm for MIL, which uses a regular supervised learning algorithm as an oracle. We prove that efficient PAC-learning for MIL can be generated from any efficient non-MIL supervised learning algorithm that handles one-sided error. The computational complexity of the resulting algorithm is only polynomially dependent on the bag size.

The early classifications of the computational complexity of planning under various restrictions in STRIPS (Bylander) and SAS+ (Baeckstroem and Nebel) have influenced following research in planning in many ways. We go back and reanalyse their subclasses, but this time using the more modern tool of parameterized complexity analysis. This provides new results that together with the old results give a more detailed picture of the complexity landscape. We demonstrate separation results not possible with standard complexity theory, which contributes to explaining why certain cases of planning have seemed simpler in practice than theory has predicted. In particular, we show that certain restrictions of practical interest are tractable in the parameterized sense of the term, and that a simple heuristic is sufficient to make a well-known partial-order planner exploit this fact.

In this paper, we propose a framework to study a general class of strategic behavior in voting, which we call vote operations. We prove the following theorem: if we fix the number of alternatives, generate $n$ votes i.i.d. according to a distribution $\pi$, and let $n$ go to infinity, then for any $\epsilon >0$, with probability at least $1-\epsilon$, the minimum number of operations that are needed for the strategic individual to achieve her goal falls into one of the following four categories: (1) 0, (2) $\Theta(\sqrt n)$, (3) $\Theta(n)$, and (4) $\infty$. This theorem holds for any set of vote operations, any individual vote distribution $\pi$, and any integer generalized scoring rule, which includes (but is not limited to) almost all commonly studied voting rules, e.g., approval voting, all positional scoring rules (including Borda, plurality, and veto), plurality with runoff, Bucklin, Copeland, maximin, STV, and ranked pairs. We also show that many well-studied types of strategic behavior fall under our framework, including (but not limited to) constructive/destructive manipulation, bribery, and control by adding/deleting votes, margin of victory, and minimum manipulation coalition size. Therefore, our main theorem naturally applies to these problems.

We examine a fundamental problem that models various active sampling setups, such as network tomography. We analyze sampling of a multivariate normal distribution with an unknown expectation that needs to be estimated: in our setup it is possible to sample the distribution from a given set of linear functionals, and the difficulty addressed is how to optimally select the combinations to achieve low estimation error. Although this problem is in the heart of the field of optimal design, no efficient solutions for the case with many functionals exist. We present some bounds and an efficient sub-optimal solution for this problem for more structured sets such as binary functionals that are induced by graph walks.

A concrete formal understanding of how concepts combine is vital to significant progress in many fields including psychology, linguistics, and cognitive science. However, concepts have been resistant to mathematical description because people use conjunctions and disjunctions of concepts in ways that violate the rules of classical logic; i.e., concepts interact in ways that are non-compositional [4]. This is true also with respect to properties (e.g., although people do not rate talks as a characteristic property of Pet or Bird, they rate it as characteristic of Pet Bird) and exemplar typicalities (e.g., although people do not rate Guppy as a typical Pet, nor a typical Fish, they rate it as a highly typical Pet Fish [5]). This has come to be known as the Pet Fish Problem, and the general phenomenon wherein the typicality of an exemplar for a conjunctively combined concept is greater than that for either of the constituent concepts has come to be called the Guppy Effect, although further investigation revealed that the Pet Fish Problem is not a particularly good example of the Guppy Effect, and that other concept combinations exhibit this effect more strongly [6]. One can refer to the situation wherein people estimate the typicality of an exemplar of the concept combination as more extreme than it is for one of the constituent concepts in a conjunctive combination as overextension.

Wireless sensor networks are composed of distributed sensors that can be used for signal detection or classification. The likelihood functions of the hypotheses are often not known in advance, and decision rules have to be learned via supervised learning. A specific such algorithm is Fisher discriminant analysis (FDA), the classification accuracy of which has been previously studied in the context of wireless sensor networks. Previous work, however, does not take into account the communication protocol or battery lifetime of the sensor networks; in this paper we extend the existing studies by proposing a model that captures the relationship between battery lifetime and classification accuracy. In order to do so we combine the FDA with a model that captures the dynamics of the Carrier-Sense Multiple-Access (CSMA) algorithm, the random-access algorithm used to regulate communications in sensor networks. This allows us to study the interaction between the classification accuracy, battery lifetime and effort put towards learning, as well as the impact of the back-off rates of CSMA on the accuracy. We characterize the tradeoff between the length of the training stage and accuracy, and show that accuracy is non-monotone in the back-off rate due to changes in the training sample size and overfitting.

This paper presents a novel fuzzy logic based Adaptive Super-twisting Sliding Mode Controller for the control of dynamic uncertain systems. The proposed controller combines the advantages of Second order Sliding Mode Control, Fuzzy Logic Control and Adaptive Control. The reaching conditions, stability and robustness of the system with the proposed controller are guaranteed. In addition, the proposed controller is well suited for simple design and implementation. The effectiveness of the proposed controller over the first order Sliding Mode Fuzzy Logic controller is illustrated by Matlab based simulations performed on a DC-DC Buck converter. Based on this comparison, the proposed controller is shown to obtain the desired transient response without causing chattering and error under steady-state conditions. The proposed controller is able to give robust performance in terms of rejection to input voltage variations and load variations.

Inferring probabilistic networks from data is a notoriously difficult task. Under various goodness-of-fit measures, finding an optimal network is NP-hard, even if restricted to polytrees of bounded in-degree. Polynomial-time algorithms are known only for rare special cases, perhaps most notably for branchings, that is, polytrees in which the in-degree of every node is at most one. Here, we study the complexity of finding an optimal polytree that can be turned into a branching by deleting some number of arcs or nodes, treated as a parameter. We show that the problem can be solved via a matroid intersection formulation in polynomial time if the number of deleted arcs is bounded by a constant. The order of the polynomial time bound depends on this constant, hence the algorithm does not establish fixed-parameter tractability when parameterized by the number of deleted arcs. We show that a restricted version of the problem allows fixed-parameter tractability and hence scales well with the parameter. We contrast this positive result by showing that if we parameterize by the number of deleted nodes, a somewhat more powerful parameter, the problem is not fixed-parameter tractable, subject to a complexity-theoretic assumption.

Game tree search algorithms such as minimax have been used with enormous success in turn-based adversarial games such as Chess or Checkers. However, such algorithms cannot be directly applied to real-time strategy (RTS) games because a number of reasons. For example, minimax assumes a turn-taking game mechanics, not present in RTS games. In this paper we present RTMM, a real-time variant of the standard minimax algorithm, and discuss its applicability in the context of RTS games. We discuss its strengths and weaknesses, and evaluate it in two real-time games.

The graphical lasso \citep{FHT2007a} is an algorithm for learning the structure in an undirected Gaussian graphical model, using $\ell_1$ regularization to control the number of zeros in the precision matrix ${\B\Theta}={\B\Sigma}^{-1}$ \citep{BGA2008,yuan_lin_07}. The {\texttt R} package \GL\ \citep{FHT2007a} is popular, fast, and allows one to efficiently build a path of models for different values of the tuning parameter. Convergence of \GL\ can be tricky; the converged precision matrix might not be the inverse of the estimated covariance, and occasionally it fails to converge with warm starts. In this paper we explain this behavior, and propose new algorithms that appear to outperform \GL. By studying the "normal equations" we see that, \GL\ is solving the {\em dual} of the graphical lasso penalized likelihood, by block coordinate ascent; a result which can also be found in \cite{BGA2008}. In this dual, the target of estimation is $\B\Sigma$, the covariance matrix, rather than the precision matrix $\B\Theta$. We propose similar primal algorithms \PGL\ and \DPGL, that also operate by block-coordinate descent, where $\B\Theta$ is the optimization target. We study all of these algorithms, and in particular different approaches to solving their coordinate sub-problems. We conclude that \DPGL\ is superior from several points of view.