We introduce a method to learn a mixture of submodular "shells" in a large-margin setting. A submodular shell is an abstract submodular function that can be instantiated with a ground set and a set of parameters to produce a submodular function. A mixture of such shells can then also be so instantiated to produce a more complex submodular function. What our algorithm learns are the mixture weights over such shells. We provide a risk bound guarantee when learning in a large-margin structured-prediction setting using a projected subgradient method when only approximate submodular optimization is possible (such as with submodular function maximization). We apply this method to the problem of multi-document summarization and produce the best results reported so far on the widely used NIST DUC-05 through DUC-07 document summarization corpora.

Cardinality potentials are a generally useful class of high order potential that affect probabilities based on how many of D binary variables are active. Maximum a posteriori (MAP) inference for cardinality potential models is well-understood, with efficient computations taking O(DlogD) time. Yet efficient marginalization and sampling have not been addressed as thoroughly in the machine learning community. We show that there exists a simple algorithm for computing marginal probabilities and drawing exact joint samples that runs in O(Dlog2 D) time, and we show how to frame the algorithm as efficient belief propagation in a low order tree-structured model that includes additional auxiliary variables. We then develop a new, more general class of models, termed Recursive Cardinality models, which take advantage of this efficiency. Finally, we show how to do efficient exact inference in models composed of a tree structure and a cardinality potential. We explore the expressive power of Recursive Cardinality models and empirically demonstrate their utility.

Hierarchical beta process has found interesting applications in recent years. In this paper we present a modified hierarchical beta process prior with applications to hierarchical modeling of multiple data sources. The novel use of the prior over a hierarchical factor model allows factors to be shared across different sources. We derive a slice sampler for this model, enabling tractable inference even when the likelihood and the prior over parameters are non-conjugate. This allows the application of the model in much wider contexts without restrictions. We present two different data generative models a linear GaussianGaussian model for real valued data and a linear Poisson-gamma model for count data. Encouraging transfer learning results are shown for two real world applications text modeling and content based image retrieval.

We consider the problem of Probably Approximate Correct (PAC) learning of a binary classifier from noisy labeled examples acquired from multiple annotators (each characterized by a respective classification noise rate). First, we consider the complete information scenario, where the learner knows the noise rates of all the annotators. For this scenario, we derive sample complexity bound for the Minimum Disagreement Algorithm (MDA) on the number of labeled examples to be obtained from each annotator. Next, we consider the incomplete information scenario, where each annotator is strategic and holds the respective noise rate as a private information. For this scenario, we design a cost optimal procurement auction mechanism along the lines of Myerson's optimal auction design framework in a non-trivial manner. This mechanism satisfies incentive compatibility property, thereby facilitating the learner to elicit true noise rates of all the annotators.

Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing some particular network properties (such as degree distribution or clustering coefficient), or they are aimed at estimating joint probability distributions, which is often intractable in large-scale networks. In this paper, we first propose a novel network statistic, based on the Laplacian spectrum of graphs, which allows to dispense with any parametric assumption concerning the modeled network properties. Second, we use the defined statistic to develop the Fiedler random graph model, switching the focus from the estimation of joint probability distributions to a more tractable conditional estimation setting. After analyzing the dependence structure characterizing Fiedler random graphs, we evaluate them experimentally in edge prediction over several real-world networks, showing that they allow to reach a much higher prediction accuracy than various alternative statistical models.

We describe theoretical bounds and a practical algorithm for teaching a model by demonstration in a sequential decision making environment. Unlike previous efforts that have optimized learners that watch a teacher demonstrate a static policy, we focus on the teacher as a decision maker who can dynamically choose different policies to teach different parts of the environment. We develop several teaching frameworks based on previously defined supervised protocols, such as Teaching Dimension, extending them to handle noise and sequences of inputs encountered in an MDP.We provide theoretical bounds on the learnability of several important model classes in this setting and suggest a practical algorithm for dynamic teaching.

Previous work on recommender systems mainly focus on fitting the ratings provided by users. However, the response patterns, i.e., some items are rated while others not, are generally ignored. We argue that failing to observe such response patterns can lead to biased parameter estimation and sub-optimal model performance. Although several pieces of work have tried to model users' response patterns, they miss the effectiveness and interpretability of the successful matrix factorization collaborative filtering approaches. To bridge the gap, in this paper, we unify explicit response models and PMF to establish the Response Aware Probabilistic Matrix Factorization (RAPMF) framework. We show that RAPMF subsumes PMF as a special case. Empirically we demonstrate the merits of RAPMF from various aspects.

In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a convex program to tighten them. To solve these programs effectively for general region graphs we utilize the entropy barrier method, thus decomposing the original programs by their dual programs and solve them with dual block optimization scheme. The entropy barrier method provides an elegant framework to generalize the message-passing scheme to high-order region graph, as well as to solve the block dual steps in closed-form. This is a key for computational relevancy for large problems with thousands of regions.

Recently, Petrik et al. demonstrated that L1Regularized Approximate Linear Programming (RALP) could produce value functions and policies which compared favorably to established linear value function approximation techniques like LSPI. RALP's success primarily stems from the ability to solve the feature selection and value function approximation steps simultaneously. RALP's performance guarantees become looser if sampled next states are used. For very noisy domains, RALP requires an accurate model rather than samples, which can be unrealistic in some practical scenarios. In this paper, we demonstrate this weakness, and then introduce Locally Smoothed L1-Regularized Approximate Linear Programming (LS-RALP). We demonstrate that LS-RALP mitigates inaccuracies stemming from noise even without an accurate model. We show that, given some smoothness assumptions, as the number of samples increases, error from noise approaches zero, and provide experimental examples of LS-RALP's success on common reinforcement learning benchmark problems.

Multi-modal data collections, such as corpora of paired images and text snippets, require analysis methods beyond single-view component and topic models. For continuous observations the current dominant approach is based on extensions of canonical correlation analysis, factorizing the variation into components shared by the different modalities and those private to each of them. For count data, multiple variants of topic models attempting to tie the modalities together have been presented. All of these, however, lack the ability to learn components private to one modality, and consequently will try to force dependencies even between minimally correlating modalities. In this work we combine the two approaches by presenting a novel HDP-based topic model that automatically learns both shared and private topics. The model is shown to be especially useful for querying the contents of one domain given samples of the other.