An answer to a query has a well-defined lineage expression (alternatively called how-provenance) that explains how the answer was derived. Recent work has also shown how to compute the lineage of a non-answer to a query. However, the cause of an answer or non-answer is a more subtle notion and consists, in general, of only a fragment of the lineage. In this paper, we adapt Halpern, Pearl, and Chockler's recent definitions of causality and responsibility to define the causes of answers and non-answers to queries, and their degree of responsibility. Responsibility captures the notion of degree of causality and serves to rank potentially many causes by their relative contributions to the effect. Then, we study the complexity of computing causes and responsibilities for conjunctive queries. It is known that computing causes is NP-complete in general. Our first main result shows that all causes to conjunctive queries can be computed by a relational query which may involve negation. Thus, causality can be computed in PTIME, and very efficiently so. Next, we study computing responsibility. Here, we prove that the complexity depends on the conjunctive query and demonstrate a dichotomy between PTIME and NP-complete cases. For the PTIME cases, we give a non-trivial algorithm, consisting of a reduction to the max-flow computation problem. Finally, we prove that, even when it is in PTIME, responsibility is complete for LOGSPACE, implying that, unlike causality, it cannot be computed by a relational query.

Voting is a simple mechanism to combine together the preferences of multiple agents. Unfortunately, agents may try to manipulate the result by mis-reporting their preferences. One barrier that might exist to such manipulation is computational complexity. In particular, it has been shown that it is NP-hard to compute how to manipulate a number of different voting rules. How- ever, NP-hardness only bounds the worst-case complexity. Recent theoretical results suggest that manipulation may often be easy in practice. In this paper, we show that empirical studies are useful in improving our understanding of this issue. We consider two settings which represent the two types of complexity results that have been identified in this area: manipulation with un-weighted votes by a single agent, and manipulation with weighted votes by a coalition of agents. In the first case, we consider Single Transferable Voting (STV), and in the second case, we consider veto voting. STV is one of the few voting rules used in practice where it is NP-hard to compute how a single agent can manipulate the result when votes are unweighted. It also appears one of the harder voting rules to manipulate since it involves multiple rounds. On the other hand, veto voting is one of the simplest representatives of voting rules where it is NP-hard to compute how a coalition of weighted agents can manipulate the result. In our experiments, we sample a number of distributions of votes including uniform, correlated and real world elections. In many of the elections in our experiments, it was easy to compute how to manipulate the result or to prove that manipulation was impossible. Even when we were able to identify a situation in which manipulation was hard to compute (e.g. when votes are highly correlated and the election is hung), we found that the computational difficulty of computing manipulations was somewhat precarious (e.g. with such hung elections, even a single uncorrelated voter was enough to make manipulation easy to compute).

Robust low-rank matrix estimation is a topic of increasing interest, with promising applications in a variety of fields, from computer vision to data mining and recommender systems. Recent theoretical results establish the ability of such data models to recover the true underlying low-rank matrix when a large portion of the measured matrix is either missing or arbitrarily corrupted. However, if low rank is not a hypothesis about the true nature of the data, but a device for extracting regularity from it, no current guidelines exist for choosing the rank of the estimated matrix. In this work we address this problem by means of the Minimum Description Length (MDL) principle -- a well established information-theoretic approach to statistical inference -- as a guideline for selecting a model for the data at hand. We demonstrate the practical usefulness of our formal approach with results for complex background extraction in video sequences.

Kernel methods have long provided powerful tools for generalizing linear statistical approaches to nonlinear settings, through an embedding of the sample to a high dimensional feature space, namely a reproducing kernel Hilbert space (RKHS) [18, 28]. Examples include support vector machines, kernel PCA, and kernel CCA, among others. In these cases, data are mapped via a canonical feature map to a reproducing kernel Hilbert space (of high or even infinite dimension), in which the linear operations that define the algorithms are implemented. The inner product between feature mappings need never be computed explicitly, but is given by a positive definite kernel function unique to the RKHS: this permits efficient computation without the need to deal explicitly with the feature representation. The mappings of individual points to a feature space may be generalized to mappings of probability measures[e.g. 3, Chapter 4]. We call such mappings the kernel means of the underlying random variables.

We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R^D given a noisy sample from the manifold. We assume that the manifold satisfies a smoothness condition and that the noise distribution has compact support. We show that the optimal rate of convergence is n^{-2/(2+d)}. Thus, the minimax rate depends only on the dimension of the manifold, not on the dimension of the space in which M is embedded.

User preferences for items can be inferred from either explicit feedback, such as item ratings, or implicit feedback, such as rental histories. Research in collaborative filtering has concentrated on explicit feedback, resulting in the development of accurate and scalable models. However, since explicit feedback is often difficult to collect it is important to develop effective models that take advantage of the more widely available implicit feedback. We introduce a probabilistic approach to collaborative filtering with implicit feedback based on modelling the user's item selection process. In the interests of scalability, we restrict our attention to tree-structured distributions over items and develop a principled and efficient algorithm for learning item trees from data. We also identify a problem with a widely used protocol for evaluating implicit feedback models and propose a way of addressing it using a small quantity of explicit feedback data.

We provide an overview of the organization and results of the deterministic part of the 4th International Planning Competition, i.e., of the part concerned with evaluating systems doing deterministic planning. IPC-4 attracted even more competing systems than its already large predecessors, and the competition event was revised in several important respects. After giving an introduction to the IPC, we briefly explain the main differences between the deterministic part of IPC-4 and its predecessors. We then introduce formally the language used, called PDDL2.2 that extends PDDL2.1 by derived predicates and timed initial literals. We list the competing systems and overview the results of the competition. The entire set of data is far too large to be presented in full. We provide a detailed summary; the complete data is available in an online appendix. We explain how we awarded the competition prizes.

Between 1998 and 2004, the planning community has seen vast progress in terms of the sizes of benchmark examples that domain-independent planners can tackle successfully. The key technique behind this progress is the use of heuristic functions based on relaxing the planning task at hand, where the relaxation is to assume that all delete lists are empty. The unprecedented success of such methods, in many commonly used benchmark examples, calls for an understanding of what classes of domains these methods are well suited for. In the investigation at hand, we derive a formal background to such an understanding. We perform a case study covering a range of 30 commonly used STRIPS and ADL benchmark domains, including all examples used in the first four international planning competitions. We *prove* connections between domain structure and local search topology -- heuristic cost surface properties -- under an idealized version of the heuristic functions used in modern planners. The idealized heuristic function is called h^+, and differs from the practically used functions in that it returns the length of an *optimal* relaxed plan, which is NP-hard to compute. We identify several key characteristics of the topology under h^+, concerning the existence/non-existence of unrecognized dead ends, as well as the existence/non-existence of constant upper bounds on the difficulty of escaping local minima and benches. These distinctions divide the (set of all) planning domains into a taxonomy of classes of varying h^+ topology. As it turns out, many of the 30 investigated domains lie in classes with a relatively easy topology. Most particularly, 12 of the domains lie in classes where FFs search algorithm, provided with h^+, is a polynomial solving mechanism. We also present results relating h^+ to its approximation as implemented in FF. The behavior regarding dead ends is provably the same. We summarize the results of an empirical investigation showing that, in many domains, the topological qualities of h^+ are largely inherited by the approximation. The overall investigation gives a rare example of a successful analysis of the connections between typical-case problem structure, and search performance. The theoretical investigation also gives hints on how the topological phenomena might be automatically recognizable by domain analysis techniques. We outline some preliminary steps we made into that direction.

In many scientific disciplines structures in high-dimensional data have to be found, e.g., in stellar spectra, in genome data, or in face recognition tasks. In this work we present a novel approach to non-linear dimensionality reduction. It is based on fitting K-nearest neighbor regression to the unsupervised regression framework for learning of low-dimensional manifolds. Similar to related approaches that are mostly based on kernel methods, unsupervised K-nearest neighbor (UNN) regression optimizes latent variables w.r.t. the data space reconstruction error employing the K-nearest neighbor heuristic. The problem of optimizing latent neighborhoods is difficult to solve, but the UNN formulation allows the design of efficient strategies that iteratively embed latent points to fixed neighborhood topologies. UNN is well appropriate for sorting of high-dimensional data. The iterative variants are analyzed experimentally.

The hm admissible heuristics for (sequential and temporal) regression planning are defined by a parameterized relaxation of the optimal cost function in the regression search space, where the parameter m offers a trade-off between the accuracy and computational cost of theheuristic. Existing methods for computing the hm heuristic require time exponential in m, limiting them to small values (m andlt= 2). The hm heuristic can also be viewed as the optimal cost function in a relaxation of the search space: this paper presents relaxed search, a method for computing this function partially by searching in the relaxed space. The relaxed search method, because it computes hm only partially, is computationally cheaper and therefore usable for higher values of m. The (complete) hm heuristic is combined with partial hm heuristics, for m = 3,..., computed by relaxed search, resulting in a more accurate heuristic. This use of the relaxed search method to improve on the hm heuristic is evaluated by comparing two optimal temporal planners: TP4, which does not use it, and HSP*a, which uses it but is otherwise identical to TP4. The comparison is made on the domains used in the 2004 International Planning Competition, in which both planners participated. Relaxed search is found to be cost effective in some of these domains, but not all. Analysis reveals a characterization of the domains in which relaxed search can be expected to be cost effective, in terms of two measures on the original and relaxed search spaces. In the domains where relaxed search is cost effective, expanding small states is computationally cheaper than expanding large states and small states tend to have small successor states.