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.

The graphics processing unit (GPU) has emerged as a powerful and cost effective processor for general performance computing. GPUs are capable of an order of magnitude more floating-point operations per second as compared to modern central processing units (CPUs), and thus provide a great deal of promise for computationally intensive statistical applications. Fitting complex statistical models with a large number of parameters and/or for large datasets is often very computationally expensive. In this study, we focus on Gaussian process (GP) models -- statistical models commonly used for emulating expensive computer simulators. We demonstrate that the computational cost of implementing GP models can be significantly reduced by using a CPU+GPU heterogeneous computing system over an analogous implementation on a traditional computing system with no GPU acceleration. Our small study suggests that GP models are fertile ground for further implementation on CPU+GPU systems.

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.

A number of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov random field. Belief propagation, an iterative message-passing algorithm, computes exactly such marginals when the underlying graph is a tree. But it has gained its popularity as an efficient way to approximate them in the more general case, even if it can exhibits multiple fixed points and is not guaranteed to converge. In this paper, we express a new sufficient condition for local stability of a belief propagation fixed point in terms of the graph structure and the beliefs values at the fixed point. This gives credence to the usual understanding that Belief Propagation performs better on sparse graphs.

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.