Many applications concern sparse signals, for example, detecting anomalies from the differences between consecutive images taken by surveillance cameras. This paper focuses on the problem of recovering a K-sparse signal x in N dimensions. In the mainstream framework of compressed sensing (CS), the vector x is recovered from M non-adaptive linear measurements y = xS, where S (of size N x M) is typically a Gaussian (or Gaussian-like) design matrix, through some optimization procedure such as linear programming (LP). In our proposed method, the design matrix S is generated from an $\alpha$-stable distribution with $\alpha\approx 0$. Our decoding algorithm mainly requires one linear scan of the coordinates, followed by a few iterations on a small number of coordinates which are "undetermined" in the previous iteration. Comparisons with two strong baselines, linear programming (LP) and orthogonal matching pursuit (OMP), demonstrate that our algorithm can be significantly faster in decoding speed and more accurate in recovery quality, for the task of exact spare recovery. Our procedure is robust against measurement noise. Even when there are no sufficient measurements, our algorithm can still reliably recover a significant portion of the nonzero coordinates. To provide the intuition for understanding our method, we also analyze the procedure by assuming an idealistic setting. Interestingly, when K=2, the "idealized" algorithm achieves exact recovery with merely 3 measurements, regardless of N. For general K, the required sample size of the "idealized" algorithm is about 5K.

Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of structural network properties. The present paper advocates a graph embedding approach with centrality considerations to comply with node hierarchy. The problem is formulated as one of constrained multi-dimensional scaling (MDS), and it is solved via block coordinate descent iterations with successive approximations and guaranteed convergence to a KKT point. In addition, a regularization term enforcing graph smoothness is incorporated with the goal of reducing edge crossings. Experimental results demonstrate that the algorithm converges, and can be used to efficiently embed large graphs on the order of thousands of nodes.

This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to express the remaining features. More precisely, given a data matrix X, the algorithm identifies a matrix C such that X approximately equals CX and some linear constraints. The constraints are chosen to ensure that the matrix C selects features; these features can then be used to find a low-rank NMF of X. A theoretical analysis demonstrates that this approach has guarantees similar to those of the recent NMF algorithm of Arora et al. (2012). In contrast with this earlier work, the proposed method extends to more general noise models and leads to efficient, scalable algorithms. Experiments with synthetic and real datasets provide evidence that the new approach is also superior in practice. An optimized C++ implementation can factor a multigigabyte matrix in a matter of minutes.

In this paper, we study the problem of sparse multiple kernel learning (MKL), where the goal is to efficiently learn a combination of a fixed small number of kernels from a large pool that could lead to a kernel classifier with a small prediction error. We develop an efficient algorithm based on the greedy coordinate descent algorithm, that is able to achieve a geometric convergence rate under appropriate conditions. The convergence rate is achieved by measuring the size of functional gradients by an empirical $\ell_2$ norm that depends on the empirical data distribution. This is in contrast to previous algorithms that use a functional norm to measure the size of gradients, which is independent from the data samples. We also establish a generalization error bound of the learned sparse kernel classifier using the technique of local Rademacher complexity.

'Distribution regression' refers to the situation where a response Y depends on a covariate P where P is a probability distribution. The model is Y f(P) µ where f is an unknown regression function and µ is a random error. Typically, we do not observe P directly, but rather, we observe a sample from P. In this paper we develop theory and methods for distribution-free versions of distribution regression. This means that we do not make distributional assumptions about the error term µ and covariate P. We prove that when the effective dimension is small enough (as measured by the doubling dimension), then the excess prediction risk converges to zero with a polynomial rate.

Class algebra provides a natural framework for sharing of ISA hierarchies between users that may be unaware of each other's definitions. This permits data from relational databases, object-oriented databases, and tagged XML documents to be unioned into one distributed ontology, sharable by all users without the need for prior negotiation or the development of a "standard" ontology for each field. Moreover, class algebra produces a functional correspondence between a class's class algebraic definition (i.e. its "intent") and the set of all instances which satisfy the expression (i.e. its "extent"). The framework thus provides assistance in quickly locating examples and counterexamples of various definitions. This kind of information is very valuable when developing models of the real world, and serves as an invaluable tool assisting in the proof of theorems concerning these class algebra expressions. Finally, the relative frequencies of objects in the ISA hierarchy can produce a useful Boolean algebra of probabilities. The probabilities can be used by traditional information-theoretic classification methodologies to obtain optimal ways of classifying objects in the database.

This volume contains the papers presented at CICLOPS'12: 12th International Colloquium on Implementation of Constraint and LOgic Programming Systems held on Tueseday September 4th, 2012 in Budapest. The program included 1 invited talk, 9 technical presentations and a panel discussion on Prolog open standards (open.pl). Each programme paper was reviewed by 3 reviewers. CICLOPS'12 continues a tradition of successful workshops on Implementations of Logic Programming Systems, previously held in Budapest (1993) and Ithaca (1994), the Compulog Net workshops on Parallelism and Implementation Technologies held in Madrid (1993 and 1994), Utrecht (1995) and Bonn (1996), the Workshop on Parallelism and Implementation Technology for (Constraint) Logic Programming Languages held in Port Jefferson (1997), Manchester (1998), Las Cruces (1999), and London (2000), and more recently the Colloquium on Implementation of Constraint and LOgic Programming Systems in Paphos (2001), Copenhagen (2002), Mumbai (2003), Saint Malo (2004), Sitges (2005), Seattle (2006), Porto (2007), Udine (2008), Pasadena (2009), Edinburgh (2010) - together with WLPE, Lexington (2011). We would like to thank all the authors, Tom Schrijvers for his invited talk, the programme committee members, and the ICLP 2012 organisers. We would like to also thank arXiv.org for providing permanent hosting.

We present a model for aggregation of product review snippets by joint aspect identification and sentiment analysis. Our model simultaneously identifies an underlying set of ratable aspects presented in the reviews of a product (e.g., sushi and miso for a Japanese restaurant) and determines the corresponding sentiment of each aspect. This approach directly enables discovery of highly-rated or inconsistent aspects of a product. Our generative model admits an efficient variational mean-field inference algorithm. It is also easily extensible, and we describe several modifications and their effects on model structure and inference. We test our model on two tasks, joint aspect identification and sentiment analysis on a set of Yelp reviews and aspect identification alone on a set of medical summaries. We evaluate the performance of the model on aspect identification, sentiment analysis, and per-word labeling accuracy. We demonstrate that our model outperforms applicable baselines by a considerable margin, yielding up to 32% relative error reduction on aspect identification and up to 20% relative error reduction on sentiment analysis.

The family of Groves mechanisms, which includes the well-known VCG mechanism (also known as the Clarke mechanism), is a family of efficient and strategy-proof mechanisms. Unfortunately, the Groves mechanisms are generally not budget balanced. That is, under such mechanisms, payments may flow into or out of the system of the agents, resulting in deficits or reduced utilities for the agents. We consider the following problem: within the family of Groves mechanisms, we want to identify mechanisms that give the agents the highest utilities, under the constraint that these mechanisms must never incur deficits. We adopt a prior-free approach. We introduce two general measures for comparing mechanisms in prior-free settings. We say that a non-deficit Groves mechanism M individually dominates another non-deficit Groves mechanism M' if for every type profile, every agent's utility under M is no less than that under M', and this holds with strict inequality for at least one type profile and one agent. We say that a non-deficit Groves mechanism M collectively dominates another non-deficit Groves mechanism M' if for every type profile, the agents' total utility under M is no less than that under M', and this holds with strict inequality for at least one type profile. The above definitions induce two partial orders on non-deficit Groves mechanisms. We study the maximal elements corresponding to these two partial orders, which we call the individually undominated mechanisms and the collectively undominated mechanisms, respectively.

A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and prediction capabilities. This probabilistic approach can naturally accommodate general models for the data distribution, lending itself to various fitting criteria that yield optimum estimates in the maximum-a-posteriori sense. In particular, two algorithms are devised for Gaussian- and Poisson-distributed data, that minimize the rank-regularized least-squares error and Kullback-Leibler divergence, respectively. The proposed technique is able to recover the "ground-truth'' tensor rank when tested on synthetic data, and to complete brain imaging and yeast gene expression datasets with 50% and 15% of missing entries respectively, resulting in recovery errors at -10dB and -15dB.