This paper introduces a novel approach for learning to rank (LETOR) based on the notion of monotone retargeting. It involves minimizing a divergence between all monotonic increasing transformations of the training scores and a parameterized prediction function. The minimization is both over the transformations as well as over the parameters. It is applied to Bregman divergences, a large class of "distance like" functions that were recently shown to be the unique class that is statistically consistent with the normalized discounted gain (NDCG) criterion [19]. The algorithm uses alternating projection style updates, in which one set of simultaneous projections can be computed independent of the Bregman divergence and the other reduces to parameter estimation of a generalized linear model. This results in easily implemented, efficiently parallelizable algorithm for the LETOR task that enjoys global optimum guarantees under mild conditions. We present empirical results on benchmark datasets showing that this approach can outperform the state of the art NDCG consistent techniques.

A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y. For example, we might use a DPP to display a set of news headlines that are relevant to a user's interests while covering a variety of topics. Suppose, however, that we are asked to sequentially select multiple diverse sets of items, for example, displaying new headlines day-by-day. We might want these sets to be diverse not just individually but also through time, offering headlines today that are unlike the ones shown yesterday. In this paper, we construct a Markov DPP (M-DPP) that models a sequence of random sets {Yt}. The proposed M-DPP defines a stationary process that maintains DPP margins. Crucially, the induced union process Zt = Yt u Yt-1 is also marginally DPP-distributed. Jointly, these properties imply that the sequence of random sets are encouraged to be diverse both at a given time step as well as across time steps. We describe an exact, efficient sampling procedure, and a method for incrementally learning a quality measure over items in the base set Y based on external preferences. We apply the M-DPP to the task of sequentially displaying diverse and relevant news articles to a user with topic preferences.

Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from having not just a single solution, but the top M most probable solutions known as the M-Best MAP problem. In this paper, we propose an efficient message-passing based algorithm for solving the M-Best MAP problem. Specifically, our algorithm solves the recently proposed Linear Programming (LP) formulation of M-Best MAP [7], while being orders of magnitude faster than a generic LP-solver. Our approach relies on studying a particular partial Lagrangian relaxation of the M-Best MAP LP which exposes a natural combinatorial structure of the problem that we exploit.

This paper considers stochastic bandits with side observations, a model that accounts for both the exploration/exploitation dilemma and relationships between arms. In this setting, after pulling an arm i, the decision maker also observes the rewards for some other actions related to i. We will see that this model is suited to content recommendation in social networks, where users' reactions may be endorsed or not by their friends. We provide efficient algorithms based on upper confidence bounds (UCBs) to leverage this additional information and derive new bounds improving on standard regret guarantees. We also evaluate these policies in the context of movie recommendation in social networks: experiments on real datasets show substantial learning rate speedups ranging from 2.2x to 14x on dense networks.

This paper proposes a Hilbert space embedding for Dirichlet Process mixture models via a stick-breaking construction of Sethuraman. Although Bayesian nonparametrics offers a powerful approach to construct a prior that avoids the need to specify the model size/complexity explicitly, an exact inference is often intractable. On the other hand, frequentist approaches such as kernel machines, which suffer from the model selection/comparison problems, often benefit from efficient learning algorithms. This paper discusses the possibility to combine the best of both worlds by using the Dirichlet Process mixture model as a case study.

This paper introduces a novel, well-founded, betweenness measure, called the Bag-of-Paths (BoP) betweenness, as well as its extension, the BoP group betweenness, to tackle semisupervised classification problems on weighted directed graphs. The objective of semi-supervised classification is to assign a label to unlabeled nodes using the whole topology of the graph and the labeled nodes at our disposal. The BoP betweenness relies on a bag-of-paths framework assigning a Boltzmann distribution on the set of all possible paths through the network such that long (high-cost) paths have a low probability of being picked from the bag, while short (low-cost) paths have a high probability of being picked. Within that context, the BoP betweenness of node j is defined as the sum of the a posteriori probabilities that node j lies in-between two arbitrary nodes i, k, when picking a path starting in i and ending in k. Intuitively, a node typically receives a high betweenness if it has a large probability of appearing on paths connecting two arbitrary nodes of the network. This quantity can be computed in closed form by inverting a n x n matrix where n is the number of nodes. For the group betweenness, the paths are constrained to start and end in nodes within the same class, therefore defining a group betweenness for each class. Unlabeled nodes are then classified according to the class showing the highest group betweenness. Experiments on various real-world data sets show that BoP group betweenness outperforms all the tested state of-the-art methods. The benefit of the BoP betweenness is particularly noticeable when only a few labeled nodes are available.

We introduce a new discrepancy score between two distributions that gives an indication on their similarity. While much research has been done to determine if two samples come from exactly the same distribution, much less research considered the problem of determining if two finite samples come from similar distributions. The new score gives an intuitive interpretation of similarity; it optimally perturbs the distributions so that they best fit each other. The score is defined between distributions, and can be efficiently estimated from samples. We provide convergence bounds of the estimated score, and develop hypothesis testing procedures that test if two data sets come from similar distributions. The statistical power of this procedures is presented in simulations. We also compare the score's capacity to detect similarity with that of other known measures on real data.

This document demonstrates that the efficient approach for diagnosis of Petri nets via integer linear programming may be unable to detect a fault even if the system is diagnosable.

Nonparametric Bayesian modeling techniques, especially Dirichlet process mixture (DPM) models, have become very popular in statistics over the last few years, for performing nonparametric density estimation [1], [2], [3]. This theory is based on the observation that an infinite number of component distributions in an ordinary finite mixture model (clustering model) tends on the limit to a Dirichlet process (DP) prior [2], [4]. Eventually, the nonparametric Bayesian inference scheme induced by a DPM model yields a posterior distribution on the proper number of model component densities (inferred clusters) [5], rather than selecting a fixed number of mixture components. Hence, the obtained nonparametric Bayesian formulation eliminates the need of doing inference (or making arbitrary choices) on the number of mixture components (clusters) necessary to represent the modeled data. An interesting alternative to the Dirichlet process prior for nonparametric Bayesian modeling is the Pitman-Yor process (PYP) prior [6]. Pitman-Yor processes produce power-law distributions that allow for better modeling populations comprising a high number of clusters with low popularity and a low number of clusters with high popularity [7]. Indeed, the Pitman-Yor process prior can be viewed as a generalization of the Dirichlet process prior, and reduces to it for a specific selection of its parameter values. In [8], a Gaussian process-based coupled PYP method for joint segmentation of multiple images is proposed.

Generalized relational theories with null values in the sense of Reiter are first-order theories that provide a semantics for relational databases with incomplete information. In this paper we show that any such theory can be turned into an equivalent logic program, so that models of the theory can be generated using computational methods of answer set programming. As a step towards this goal, we develop a general method for calculating stable models under the domain closure assumption but without the unique name assumption.