In many recommendation applications such as news recommendation, the items that can be rec- ommended come and go at a very fast pace. This is a challenge for recommender systems (RS) to face this setting. Online learning algorithms seem to be the most straight forward solution. The contextual bandit framework was introduced for that very purpose. In general the evaluation of a RS is a critical issue. Live evaluation is of- ten avoided due to the potential loss of revenue, hence the need for offline evaluation methods. Two options are available. Model based meth- ods are biased by nature and are thus difficult to trust when used alone. Data driven methods are therefore what we consider here. Evaluat- ing online learning algorithms with past data is not simple but some methods exist in the litera- ture. Nonetheless their accuracy is not satisfac- tory mainly due to their mechanism of data re- jection that only allow the exploitation of a small fraction of the data. We precisely address this issue in this paper. After highlighting the limita- tions of the previous methods, we present a new method, based on bootstrapping techniques. This new method comes with two important improve- ments: it is much more accurate and it provides a measure of quality of its estimation. The latter is a highly desirable property in order to minimize the risks entailed by putting online a RS for the first time. We provide both theoretical and ex- perimental proofs of its superiority compared to state-of-the-art methods, as well as an analysis of the convergence of the measure of quality.

Several methods have been recently proposed for estimating sparse Gaussian graphical models using $\ell_{1}$ regularization on the inverse covariance matrix. Despite recent advances, contemporary applications require methods that are even faster in order to handle ill-conditioned high dimensional modern day datasets. In this paper, we propose a new method, G-AMA, to solve the sparse inverse covariance estimation problem using Alternating Minimization Algorithm (AMA), that effectively works as a proximal gradient algorithm on the dual problem. Our approach has several novel advantages over existing methods. First, we demonstrate that G-AMA is faster than the previous best algorithms by many orders of magnitude and is thus an ideal approach for modern high throughput applications. Second, global linear convergence of G-AMA is demonstrated rigorously, underscoring its good theoretical properties. Third, the dual algorithm operates on the covariance matrix, and thus easily facilitates incorporating additional constraints on pairwise/marginal relationships between feature pairs based on domain specific knowledge. Over and above estimating a sparse inverse covariance matrix, we also illustrate how to (1) incorporate constraints on the (bivariate) correlations and, (2) incorporate equality (equisparsity) or linear constraints between individual inverse covariance elements. Fourth, we also show that G-AMA is better adept at handling extremely ill-conditioned problems, as is often the case with real data. The methodology is demonstrated on both simulated and real datasets to illustrate its superior performance over recently proposed methods.

We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This type of problems have recently attracted a great deal of interest, mainly due to their omnipresence in top-notch applications. Under this \emph{locally} Lipschitz continuous gradient setting, we analyze the convergence behavior of proximal Newton schemes with the added twist of a probable presence of inexact evaluations. We prove attractive convergence rate guarantees and enhance state-of-the-art optimization schemes to accommodate such developments. Experimental results on sparse covariance estimation show the merits of our algorithm, both in terms of recovery efficiency and complexity.

In online advertising, display ads are increasingly being placed based on real-time auctions where the advertiser who wins gets to serve the ad. This is called real-time bidding (RTB). In RTB, auctions have very tight time constraints on the order of 100ms. Therefore mechanisms for bidding intelligently such as clickthrough rate prediction need to be sufficiently fast. In this work, we propose to use dimensionality reduction of the user-website interaction graph in order to produce simplified features of users and websites that can be used as predictors of clickthrough rate. We demonstrate that the Infinite Relational Model (IRM) as a dimensionality reduction offers comparable predictive performance to conventional dimensionality reduction schemes, while achieving the most economical usage of features and fastest computations at run-time. For applications such as real-time bidding, where fast database I/O and few computations are key to success, we thus recommend using IRM based features as predictors to exploit the recommender effects from bipartite graphs.

Clever sampling methods can be used to improve the handling of big data and increase its usefulness. The subject of this study is remote sensing, specifically airborne laser scanning point clouds representing different classes of ground cover. The aim is to derive a supervised learning model for the classification using CARTs. In order to measure the effect of different sampling methods on the classification accuracy, various experiments with varying types of sampling methods, sample sizes, and accuracy metrics have been designed. Numerical results for a subset of a large surveying project covering the lower Rhine area in Germany are shown. General conclusions regarding sampling design are drawn and presented.

Dynamic geometry systems (DGS) have become basic tools in many areas of geometry as, for example, in education. Geometry Automated Theorem Provers (GATP) are an active area of research and are considered as being basic tools in future enhanced educational software as well as in a next generation of mechanized mathematics assistants. Recently emerged Web repositories of geometric knowledge, like TGTP and Intergeo, are an attempt to make the already vast data set of geometric knowledge widely available. Considering the large amount of geometric information already available, we face the need of a query mechanism for descriptions of geometric constructions. In this paper we discuss two approaches for describing geometric figures (declarative and procedural), and present algorithms for querying geometric figures in declaratively and procedurally described corpora, by using a DGS or a dedicated controlled natural language for queries.

Existing work in multi-agent collision prediction and avoidance typically assumes discrete-time trajectories with Gaussian uncertainty or that are completely deterministic. We propose an approach that allows detection of collisions even between continuous, stochastic trajectories with the only restriction that means and variances can be computed. To this end, we employ probabilistic bounds to derive criterion functions whose negative sign provably is indicative of probable collisions. For criterion functions that are Lipschitz, an algorithm is provided to rapidly find negative values or prove their absence. We propose an iterative policy-search approach that avoids prior discretisations and yields collision-free trajectories with adjustably high certainty. We test our method with both fixed-priority and auction-based protocols for coordinating the iterative planning process. Results are provided in collision-avoidance simulations of feedback controlled plants.

In this paper, we present a novel two-stage metric learning algorithm. We first map each learning instance to a probability distribution by computing its similarities to a set of fixed anchor points. Then, we define the distance in the input data space as the Fisher information distance on the associated statistical manifold. This induces in the input data space a new family of distance metric with unique properties. Unlike kernelized metric learning, we do not require the similarity measure to be positive semi-definite. Moreover, it can also be interpreted as a local metric learning algorithm with well defined distance approximation. We evaluate its performance on a number of datasets. It outperforms significantly other metric learning methods and SVM.

We consider nonparametric estimation of $L_2$, Renyi-$\alpha$ and Tsallis-$\alpha$ divergences between continuous distributions. Our approach is to construct estimators for particular integral functionals of two densities and translate them into divergence estimators. For the integral functionals, our estimators are based on corrections of a preliminary plug-in estimator. We show that these estimators achieve the parametric convergence rate of $n^{-1/2}$ when the densities' smoothness, $s$, are both at least $d/4$ where $d$ is the dimension. We also derive minimax lower bounds for this problem which confirm that $s > d/4$ is necessary to achieve the $n^{-1/2}$ rate of convergence. We validate our theoretical guarantees with a number of simulations.

A neuron is a basic physiological and computational unit of the brain. While much is known about the physiological properties of a neuron, its computational role is poorly understood. Here we propose to view a neuron as a signal processing device that represents the incoming streaming data matrix as a sparse vector of synaptic weights scaled by an outgoing sparse activity vector. Formally, a neuron minimizes a cost function comprising a cumulative squared representation error and regularization terms. We derive an online algorithm that minimizes such cost function by alternating between the minimization with respect to activity and with respect to synaptic weights. The steps of this algorithm reproduce well-known physiological properties of a neuron, such as weighted summation and leaky integration of synaptic inputs, as well as an Oja-like, but parameter-free, synaptic learning rule. Our theoretical framework makes several predictions, some of which can be verified by the existing data, others require further experiments. Such framework should allow modeling the function of neuronal circuits without necessarily measuring all the microscopic biophysical parameters, as well as facilitate the design of neuromorphic electronics.