We study the stability vis a vis adversarial noise of matrix factorization algorithm for matrix completion. In particular, our results include: (I) we bound the gap between the solution matrix of the factorization method and the ground truth in terms of root mean square error; (II) we treat the matrix factorization as a subspace fitting problem and analyze the difference between the solution subspace and the ground truth; (III) we analyze the prediction error of individual users based on the subspace stability. We apply these results to the problem of collaborative filtering under manipulator attack, which leads to useful insights and guidelines for collaborative filtering system design.

This paper considers the multi-task learning problem and in the setting where some relevant features could be shared across few related tasks. Most of the existing methods assume the extent to which the given tasks are related or share a common feature space to be known apriori. In real-world applications however, it is desirable to automatically discover the groups of related tasks that share a feature space. In this paper we aim at searching the exponentially large space of all possible groups of tasks that may share a feature space. The main contribution is a convex formulation that employs a graph-based regularizer and simultaneously discovers few groups of related tasks, having close-by task parameters, as well as the feature space shared within each group. The regularizer encodes an important structure among the groups of tasks leading to an efficient algorithm for solving it: if there is no feature space under which a group of tasks has close-by task parameters, then there does not exist such a feature space for any of its supersets. An efficient active set algorithm that exploits this simplification and performs a clever search in the exponentially large space is presented. The algorithm is guaranteed to solve the proposed formulation (within some precision) in a time polynomial in the number of groups of related tasks discovered. Empirical results on benchmark datasets show that the proposed formulation achieves good generalization and outperforms state-of-the-art multi-task learning algorithms in some cases.

We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore the implications. We also show how the separation of concerns afforded by using this composite representation allows for the design of families of losses with the same Bayes risk.

Oriental ink painting, called Sumi-e, is one of the most appealing painting styles that has attracted artists around the world. Major challenges in computer-based Sumi-e simulation are to abstract complex scene information and draw smooth and natural brush strokes. To automatically find such strokes, we propose to model the brush as a reinforcement learning agent, and learn desired brush-trajectories by maximizing the sum of rewards in the policy search framework. We also provide elaborate design of actions, states, and rewards tailored for a Sumi-e agent. The effectiveness of our proposed approach is demonstrated through simulated Sumi-e experiments.

Inference problems in graphical models can be represented as a constrained optimization of a free energy function. It is known that when the Bethe free energy is used, the fixedpoints of the belief propagation (BP) algorithm correspond to the local minima of the free energy. However BP fails to converge in many cases of interest. Moreover, the Bethe free energy is non-convex for graphical models with cycles thus introducing great difficulty in deriving efficient algorithms for finding local minima of the free energy for general graphs. In this paper we introduce two efficient BP-like algorithms, one sequential and the other parallel, that are guaranteed to converge to the global minimum, for any graph, over the class of energies known as "convex free energies". In addition, we propose an efficient heuristic for setting the parameters of the convex free energy based on the structure of the graph.

Latent topic models have been successfully applied as an unsupervised topic discovery technique in large document collections. With the proliferation of hypertext document collection such as the Internet, there has also been great interest in extending these approaches to hypertext [6, 9]. These approaches typically model links in an analogous fashion to how they model words - the document-link co-occurrence matrix is modeled in the same way that the document-word co-occurrence matrix is modeled in standard topic models. In this paper we present a probabilistic generative model for hypertext document collections that explicitly models the generation of links. Specifically, links from a word w to a document d depend directly on how frequent the topic of w is in d, in addition to the in-degree of d. We show how to perform EM learning on this model efficiently. By not modeling links as analogous to words, we end up using far fewer free parameters and obtain better link prediction results.

Assume that cause-effect relationships between variables can be described as a directed acyclic graph and the corresponding linear structural equation model.We consider the identification problem of total effects in the presence of latent variables and selection bias between a treatment variable and a response variable. Pearl and his colleagues provided the back door criterion, the front door criterion (Pearl, 2000) and the conditional instrumental variable method (Brito and Pearl, 2002) as identifiability criteria for total effects in the presence of latent variables, but not in the presence of selection bias. In order to solve this problem, we propose new graphical identifiability criteria for total effects based on the identifiable factor models. The results of this paper are useful to identify total effects in observational studies and provide a new viewpoint to the identification conditions of factor models.

The Liner Shipping Fleet Repositioning Problem (LSFRP) poses a large financial burden on liner shipping firms. During repositioning, vessels are moved between services in a liner shipping network. The LSFRP is characterized by chains of interacting activities, many of which have costs that are a function of their duration; for example, sailing slowly between two ports is cheaper than sailing quickly. Despite its great industrial importance, the LSFRP has received little attention in the literature. We show how the LSFRP can be solved sub-optimally using the planner POPF and optimally with a mixed-integer program (MIP) and a novel method called Temporal Optimization Planning (TOP). We evaluate the performance of each of these techniques on a dataset of real-world instances from our industrial collaborator, and show that automated planning scales to the size of problems faced by industry.

The paper illustrates a novel approach to conformant planning using classical planners. The approach relies on two core ideas developed to deal with incomplete information in the initial situation: the use of a classical planner to solve non-classical planning problems, and the reduction of the size of the initial belief state. Differently from previous uses of classical planners to solve non-classical planning problems, the approach proposed in this paper creates a valid plan from a possible plan---by inserting actions into the possible plan and maintaining only one level of non-deterministic choice (i.e., the initial plan being modified). The algorithm can be instantiated with different classical planners---the paper presents the GC[LAMA] implementation, whose classical planner is LAMA. We investigate properties of the approach, including conditions for completeness. GC[LAMA] is empirically evaluated against state-of-the-art conformant planners, using benchmarks from the literature. The experimental results show that GC[LAMA] is superior to other planners, in both performance and scalability. GC[LAMA] is the only planner that can solve the largest instances from several domains. The paper investigates the reasons behind the good performance and the challenges encountered in GC[LAMA].

Many important problems are too difficult to solve optimally. A traditional approach to such problems is bounded suboptimal search, which guarantees solution costs within a user-specified factor of optimal. Recently, a complementary approach has been proposed: bounded-cost search, where solution cost is required to be below a user-specified absolute bound. In this paper, we show how bounded-cost search can incorporate inadmissible estimates of solution cost and solution length. This information has previously been shown to improve bounded suboptimal search and, in an empirical evaluation over five benchmark domains, we find that our new algorithms surpass the state-of-the-art in bounded-cost search as well, particularly for domains where action costs differ.