We consider the link prediction problem in a partially observed network, where the objective is to make predictions in the unobserved portion of the network. Many existing methods reduce link prediction to binary classification problem. However, the dominance of absent links in real world networks makes misclassification error a poor performance metric. Instead, researchers have argued for using ranking performance measures, like AUC, AP and NDCG, for evaluation. Our main contribution is to recast the link prediction problem as a learning to rank problem and use effective learning to rank techniques directly during training. This is in contrast to existing work that uses ranking measures only during evaluation. Our approach is able to deal with the class imbalance problem by using effective, scalable learning to rank techniques during training. Furthermore, our approach allows us to combine network topology and node features. As a demonstration of our general approach, we develop a link prediction method by optimizing the cross-entropy surrogate, originally used in the popular ListNet ranking algorithm. We conduct extensive experiments on publicly available co-authorship, citation and metabolic networks to demonstrate the merits of our method.

We provide theoretical and empirical evidence for a type of asymmetry between causes and effects that is present when these are related via linear models contaminated with additive non-Gaussian noise. Assuming that the causes and the effects have the same distribution, we show that the distribution of the residuals of a linear fit in the anti-causal direction is closer to a Gaussian than the distribution of the residuals in the causal direction. This Gaussianization effect is characterized by reduction of the magnitude of the high-order cumulants and by an increment of the differential entropy of the residuals. The problem of non-linear causal inference is addressed by performing an embedding in an expanded feature space, in which the relation between causes and effects can be assumed to be linear. The effectiveness of a method to discriminate between causes and effects based on this type of asymmetry is illustrated in a variety of experiments using different measures of Gaussianity. The proposed method is shown to be competitive with state-of-the-art techniques for causal inference.

To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise ratios, limited measurements, prior information, and computational tractability requirements? How can we combine prior information with measurements to achieve these limits? Classical statistics gives incisive answers to these questions as the measurement density $\alpha = \frac{N}{P}\rightarrow \infty$. However, these classical results are not relevant to modern high-dimensional inference problems, which instead occur at finite $\alpha$. We formulate and analyze high-dimensional inference as a problem in the statistical physics of quenched disorder. Our analysis uncovers fundamental limits on the accuracy of inference in high dimensions, and reveals that widely cherished inference algorithms like maximum likelihood (ML) and maximum-a posteriori (MAP) inference cannot achieve these limits. We further find optimal, computationally tractable algorithms that can achieve these limits. Intriguingly, in high dimensions, these optimal algorithms become computationally simpler than MAP and ML, while still outperforming them. For example, such optimal algorithms can lead to as much as a 20% reduction in the amount of data to achieve the same performance relative to MAP. Moreover, our analysis reveals simple relations between optimal high dimensional inference and low dimensional scalar Bayesian inference, insights into the nature of generalization and predictive power in high dimensions, information theoretic limits on compressed sensing, phase transitions in quadratic inference, and connections to central mathematical objects in convex optimization theory and random matrix theory.

Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity Similarity Optimization (PSO) model represents - at the moment - the climax of this theory. It suggests that the trade-off between node popularity and similarity is a mechanism to explain how complex network topologies emerge - as discrete samples - from the continuous world of hyperbolic geometry. The hyperbolic space seems appropriate to represent real complex networks. In fact, it preserves many of their fundamental topological properties, and can be exploited for real applications such as, among others, link prediction and community detection. Here, we observe for the first time that a topological-based machine learning class of algorithms - for nonlinear unsupervised dimensionality reduction - can directly approximate the network's node angular coordinates of the hyperbolic model into a two-dimensional space, according to a similar topological organization that we named angular coalescence. On the basis of this phenomenon, we propose a new class of algorithms that offers fast and accurate coalescent embedding of networks in the hyperbolic space even for graphs with thousands of nodes.

Studies on computational neuroscience through functional magnetic resonance imaging (fMRI) and following biological inspired system stated that human action recognition in the brain of mammalian leads two distinct pathways in the model, which are specialized for analysis of motion (optic flow) and form information. Principally, we have defined a novel and robust form features applying active basis model as form extractor in form pathway in the biological inspired model. An unbalanced synergetic neural net-work classifies shapes and structures of human objects along with tuning its attention parameter by quantum particle swarm optimization (QPSO) via initiation of Centroidal Voronoi Tessellations. These tools utilized and justified as strong tools for following biological system model in form pathway. But the final decision has done by combination of ultimate outcomes of both pathways via fuzzy inference which increases novality of proposed model. Combination of these two brain pathways is done by considering each feature sets in Gaussian membership functions with fuzzy product inference method. Two configurations have been proposed for form pathway: applying multi-prototype human action templates using two time synergetic neural network for obtaining uniform template regarding each actions, and second scenario that it uses abstracting human action in four key-frames. Experimental results showed promising accuracy performance on different datasets (KTH and Weizmann).

The problem to accurately and parsimoniously characterize random series of events (RSEs) present in the Web, such as e-mail conversations or Twitter hashtags, is not trivial. Reports found in the literature reveal two apparent conflicting visions of how RSEs should be modeled. From one side, the Poissonian processes, of which consecutive events follow each other at a relatively regular time and should not be correlated. On the other side, the self-exciting processes, which are able to generate bursts of correlated events and periods of inactivities. The existence of many and sometimes conflicting approaches to model RSEs is a consequence of the unpredictability of the aggregated dynamics of our individual and routine activities, which sometimes show simple patterns, but sometimes results in irregular rising and falling trends. In this paper we propose a highly parsimonious way to characterize general RSEs, namely the Burstiness Scale (BuSca) model. BuSca views each RSE as a mix of two independent process: a Poissonian and a self-exciting one. Here we describe a fast method to extract the two parameters of BuSca that, together, gives the burstyness scale, which represents how much of the RSE is due to bursty and viral effects. We validated our method in eight diverse and large datasets containing real random series of events seen in Twitter, Yelp, e-mail conversations, Digg, and online forums. Results showed that, even using only two parameters, BuSca is able to accurately describe RSEs seen in these diverse systems, what can leverage many applications.

We introduce a wavelet-domain functional analysis of variance (fANOVA) method based on a Bayesian hierarchical model. The factor effects are modeled through a spike-and-slab mixture at each location-scale combination along with a normal-inverse-Gamma (NIG) conjugate setup for the coefficients and errors. A graphical model called the Markov grove (MG) is designed to jointly model the spike-and-slab statuses at all location-scale combinations, which incorporates the clustering of each factor effect in the wavelet-domain thereby allowing borrowing of strength across location and scale. The posterior of this NIG-MG model is analytically available through a pyramid algorithm of the same computational complexity as Mallat's pyramid algorithm for discrete wavelet transform, i.e., linear in both the number of observations and the number of locations. Posterior probabilities of factor contributions can also be computed through pyramid recursion, and exact samples from the posterior can be drawn without MCMC. We investigate the performance of our method through extensive simulation and show that it outperforms existing wavelet-domain fANOVA methods in a variety of common settings. We apply the method to analyzing the orthosis data.

We suppose that f has no special structural properties, e.g., concavity, or linearity, that we can exploit to solve this problem, making it a "black blox." We also suppose that evaluating f is costly or time-consuming, making these evaluations "expensive", severely limiting the number of evaluations we may perform. This typically occurs because each evaluation requires running a complex PDE-based or discrete-event simulation, or requires training a machine learning algorithm on a large dataset. When f comes from a discrete-event simulation, this problem is also called "simulation optimization." Bayesian optimization is a popular class of techniques for solving this problem, originating with the seminal paper (Kushner, 1964), and enjoying early contributions from (Mockus et al., 1978; Mockus, 1989). This class of techniques was popularized in the 1990s by the introduction in (Jones et al., 1998) of the most well-known Bayesian optimization method, Efficient Global Optimization (EGO), relying on earlier ideas from (Mockus, 1989). Recently the machine learning community has devoted considerable attention to Bayesian optimization for its applications to tuning computationally intensive machine learning models, as in, e.g., (Snoek et al., 2012). Textbooks and surveys on Bayesian optimization include (Forrester et al., 2008; Brochu et al., 2010). Most work on Bayesian optimization assumes we can observe the objective function directly without noise, but a substantial number of papers, e.g.

Bayesian optimization techniques have been successfully applied to robotics, planning, sensor placement, recommendation, advertising, intelligent user interfaces and automatic algorithm configuration. Despite these successes, the approach is restricted to problems of moderate dimension, and several workshops on Bayesian optimization have identified its scaling to high-dimensions as one of the holy grails of the field. In this paper, we introduce a novel random embedding idea to attack this problem. The resulting Random EMbedding Bayesian Optimization (REMBO) algorithm is very simple, has important invariance properties, and applies to domains with both categorical and continuous variables. We present a thorough theoretical analysis of REMBO. Empirical results confirm that REMBO can effectively solve problems with billions of dimensions, provided the intrinsic dimensionality is low. They also show that REMBO achieves state-of-the-art performance in optimizing the 47 discrete parameters of a popular mixed integer linear programming solver.

Understanding the demographics of users of online social networks has important applications for health, marketing, and public messaging. Whereas most prior approaches rely on a supervised learning approach, in which individual users are labeled with demographics for training, we instead create a distantly labeled dataset by collecting audience measurement data for 1,500 websites (e.g., 50% of visitors to gizmodo.com are estimated to have a bachelor's degree). We then fit a regression model to predict these demographics from information about the followers of each website on Twitter. Using patterns derived both from textual content and the social network of each user, our final model produces an average held-out correlation of .77 across seven different variables (age, gender, education, ethnicity, income, parental status, and political preference). We then apply this model to classify individual Twitter users by ethnicity, gender, and political preference, finding performance that is surprisingly competitive with a fully supervised approach.