Anchor texts are useful complementary description for target pages, widely applied to improve search relevance. The benefits come from the additional information introduced into document representation and the intelligent ways of estimating their relative importance. Previous work on anchor importance estimation treated anchor text independently without considering its context. As a result, the lack of constraints from such context fails to guarantee a stable anchor text representation. We propose an anchor graph regularization approach to incorporate constraints from such context into anchor text weighting process, casting the task into a convex quadratic optimization problem. The constraints draw from the estimation of anchor-anchor, anchor-page, and page-page similarity. Based on any estimators, our approach operates as a post process of refining the estimated anchor weights, making it a plug and play component in search infrastructure. Comparable experiments on standard data sets (TREC 2009 and 2010) demonstrate the efficacy of our approach.

Recently, location-based social networks (LBSNs), such as Gowalla, Foursquare, Facebook, and Brightkite, etc., have attracted millions of users to share their social friendship and their locations via check-ins. The available check-in information makes it possible to mine users’ preference on locations and to provide favorite recommendations. Personalized Point-of-interest (POI) recommendation is a significant task in LBSNs since it can help targeted users explore their surroundings as well as help third-party developers to provide personalized services. To solve this task, matrix factorization is a promising tool due to its success in recommender systems. However, previously proposed matrix factorization (MF) methods do not explore geographical influence, e.g., multi-center check-in property, which yields suboptimal solutions for the recommendation. In this paper, to the best of our knowledge, we are the first to fuse MF with geographical and social influence for POI recommendation in LBSNs. We first capture the geographical influence via modeling the probability of a user’s check-in on a location as a Multi-center Gaussian Model (MGM). Next, we include social information and fuse the geographical influence into a generalized matrix factorization framework. Our solution to POI recommendation is efficient and scales linearly with the number of observations. Finally, we conduct thorough experiments on a large-scale real-world LBSNs dataset and demonstrate that the fused matrix factorization framework with MGM utilizes the distance information sufficiently and outperforms other state-of-the-art methods significantly.

SPARQL query containment under schema axioms is the problem of determining whether, for any RDF graph satisfying a given set of schema axioms, the answers to a query are contained in the answers of another query. This problem has major applications for verification and optimization of queries. In order to solve it, we rely on the mu-calculus. Firstly, we provide a mapping from RDF graphs into transition systems. Secondly, SPARQL queries and RDFS and SHI axioms are encoded into mu-calculus formulas. This allows us to reduce query containment and equivalence to satisfiability in the mu-calculus. Finally, we prove a double exponential upper bound for containment under SHI schema axioms.

Causal inference uses observations to infer the causal structure of the data generating system. We study a class of functional models that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual time series, whereas traditional methods like Granger causality exploit the variance of residuals. There are two main contributions: (1) Theoretical: By restricting the model class (e.g. to additive noise) we can provide a more general identifiability result than existing ones. This result incorporates lagged and instantaneous effects that can be nonlinear and do not need to be faithful, and non-instantaneous feedbacks between the time series. (2) Practical: If there are no feedback loops between time series, we propose an algorithm based on non-linear independence tests of time series. When the data are causally insufficient, or the data generating process does not satisfy the model assumptions, this algorithm may still give partial results, but mostly avoids incorrect answers. An extension to (non-instantaneous) feedbacks is possible, but not discussed. It outperforms existing methods on artificial and real data. Code can be provided upon request.

The constraints arising from DAG models with latent variables can be naturally represented by means of acyclic directed mixed graphs (ADMGs). Such graphs contain directed and bidirected arrows, and contain no directed cycles. DAGs with latent variables imply independence constraints in the distribution resulting from a 'fixing' operation, in which a joint distribution is divided by a conditional. This operation generalizes marginalizing and conditioning. Some of these constraints correspond to identifiable 'dormant' independence constraints, with the well known 'Verma constraint' as one example. Recently, models defined by a set of the constraints arising after fixing from a DAG with latents, were characterized via a recursive factorization and a nested Markov property. In addition, a parameterization was given in the discrete case. In this paper we use this parameterization to describe a parameter fitting algorithm, and a search and score structure learning algorithm for these nested Markov models. We apply our algorithms to a variety of datasets.

Classical approaches to probabilistic inference - an area now reasonably well understood - have traditionally exploited low tree-width and sparsity of the graphical model for efficient exact and approximate inference. A more recent approach known as lifted inference [2, 12, 6, 7] has demonstrated the possibility to perform very efficient inference in highly-connected, but symmetric models such as those arising in the context of relational (or first-order) probabilistic models. While it is clear that symmetry is the essential element in lifted inference, there is currently no formally defined notion of symmetry of a probabilistic model, and thus no formal account of what "exploiting symmetry" means in lifted inference. The mathematical formulation of symmetry of an object is typically defined via a set of transformations that preserve the object of interest. Since this set forms a mathematical group (so-called the automorphism group of that object), the theory of groups and group action are essential in the study of symmetry. In this paper, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the notion of symmetry of a general graphical model. This automorphism group provides a precise mathematical framework for lifted inference in graphical models.

The problem of hierarchical clustering items from pairwise similarities is found across various scientific disciplines, from biology to networking. Often, applications of clustering techniques are limited by the cost of obtaining similarities between pairs of items. While prior work has been developed to reconstruct clustering using a significantly reduced set of pairwise similarities via adaptive measurements, these techniques are only applicable when choice of similarities are available to the user. In this paper, we examine reconstructing hierarchical clustering under similarity observations at-random. We derive precise bounds which show that a significant fraction of the hierarchical clustering can be recovered using fewer than all the pairwise similarities. We find that the correct hierarchical clustering down to a constant fraction of the total number of items (i.e., clusters sized O(N)) can be found using only O(N log N) randomly selected pairwise similarities in expectation.

Case vs control comparisons have been the classical approach to the study of neurological diseases. However, most patients will not fall cleanly into either group. Instead, clinicians will typically find patients that cannot be classified as having clearly progressed into the disease state. For those subjects, very little can be said about their brain function on the basis of analyses of group differences. To describe the intermediate brain function requires models that interpolate between the disease states. We have chosen Gaussian Processes (GP) regression to obtain a continuous spectrum of brain activation and to extract the unknown disease progression profile. Our models incorporate spatial distribution of measures of activation, e.g. the correlation of an fMRI trace with an input stimulus, and so constitute ultra-high multi-variate GP regressors. We applied GPs to model fMRI image phenotypes across Alzheimer's Disease (AD) behavioural measures, e.g. MMSE, ACE etc. scores, and obtained predictions at non-observed MMSE/ACE values. The overall model confirmed the known reduction in the spatial extent of activity in response to reading versus false-font stimulation. The predictive uncertainty indicated the worsening confidence intervals at behavioural scores distance from those used for GP training. Thus, the model indicated the type of patient (what behavioural score) that would need to included in the training data to improve models predictions.

A lot of effort has been invested into characterizing the convergence rates of gradient based algorithms for non-linear convex optimization. Recently, motivated by large datasets and problems in machine learning, the interest has shifted towards distributed optimization. In this work we present a distributed algorithm for strongly convex constrained optimization. Each node in a network of n computers converges to the optimum of a strongly convex, L-Lipchitz continuous, separable objective at a rate O(log (sqrt(n) T) / T) where T is the number of iterations. This rate is achieved in the online setting where the data is revealed one at a time to the nodes, and in the batch setting where each node has access to its full local dataset from the start. The same convergence rate is achieved in expectation when the subgradients used at each node are corrupted with additive zero-mean noise.

Stochastic optimization algorithms have many desirable features for large-scale machine learning, and accordingly have been the focus of renewed and intensive study in the last several years (e.g., see the papers [26, 4, 10, 30] and references therein). The empirical efficiency of these methods is backed with strong theoretical guarantees, providing sharp bounds on their convergence rates. These convergence rates are known to depend on the structure of the underlying objective function, with faster rates being possible for objective functions that are smooth and/or (strongly) convex, or optima that have desirable features such as sparsity. More precisely, for an objective function that is strongly convex, stochastic gradient descent enjoys a convergence rate ranging from O(1/T), when features vectors are extremely sparse, to O(d/T) when feature vectors are dense [11, 19, 12]. Such results are of significant interest, because the strong convexity condition is satisfied for many common machine learning problems, including boosting, least squares regression, support vector machines and generalized linear models, among other examples. A complementary type of condition is that of sparsity, either exact or approximate, in the optimal solution.