Simplifying expressions is important to make numerical integration of large expressions from High Energy Physics tractable. To this end, Horner's method can be used. Finding suitable Horner schemes is assumed to be hard, due to the lack of local heuristics. Recently, MCTS was reported to be able to find near optimal schemes. However, several parameters had to be fine-tuned manually. In this work, we investigate the state space properties of Horner schemes and find that the domain is relatively flat and contains only a few local minima. As a result, the Horner space is appropriate to be explored by Stochastic Local Search (SLS), which has only two parameters: the number of iterations (computation time) and the neighborhood structure. We found a suitable neighborhood structure, leaving only the allowed computation time as a parameter. We performed a range of experiments. The results obtained by SLS are similar or better than those obtained by MCTS. Furthermore, we show that SLS obtains the good results at least 10 times faster. Using SLS, we can speed up numerical integration of many real-world large expressions by at least a factor of 24. For High Energy Physics this means that numerical integrations that took weeks can now be done in hours.

Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the so-called regularized kernel estimate. We show that such an estimate can be characterized as simply applying a constant amount of shrinkage to all observed pairwise distances. This fact allows us to establish risk bounds for the estimate implying that the true distances can be estimated consistently in an average sense as the number of objects increases. In addition, such a characterization suggests an efficient algorithm to compute the distance matrix estimator, as an alternative to the usual second order cone programming known not to scale well for large problems. Numerical experiments and an application in visualizing the diversity of Vpu protein sequences from a recent HIV-1 study further demonstrate the practical merits of the proposed method.

These are notes from the lecture of Devavrat Shah given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithms", that took place in Les Houches, France from Monday September 30th, 2013, till Friday October 11th, 2013. The school was organized by Florent Krzakala from UPMC & ENS Paris, Federico Ricci-Tersenghi from La Sapienza Roma, Lenka Zdeborova from CEA Saclay & CNRS, and Riccardo Zecchina from Politecnico Torino. This lecture of Devavrat Shah (MIT) covers the basics of inference and learning. It explains how inference problems are represented within structures known as graphical models. The theoretical basis of the belief propagation algorithm is then explained and derived. This lecture sets the stage for generalizations and applications of message passing algorithms.

This paper introduces a multi-period inspector scheduling problem (MPISP), which is a new variant of the multi-trip vehicle routing problem with time windows (VRPTW). In the MPISP, each inspector is scheduled to perform a route in a given multi-period planning horizon. At the end of each period, each inspector is not required to return to the depot but has to stay at one of the vertices for recuperation. If the remaining time of the current period is insufficient for an inspector to travel from his/her current vertex $A$ to a certain vertex B, he/she can choose either waiting at vertex A until the start of the next period or traveling to a vertex C that is closer to vertex B. Therefore, the shortest transit time between any vertex pair is affected by the length of the period and the departure time. We first describe an approach of computing the shortest transit time between any pair of vertices with an arbitrary departure time. To solve the MPISP, we then propose several local search operators adapted from classical operators for the VRPTW and integrate them into a tabu search framework. In addition, we present a constrained knapsack model that is able to produce an upper bound for the problem. Finally, we evaluate the effectiveness of our algorithm with extensive experiments based on a set of test instances. Our computational results indicate that our approach generates high-quality solutions.

We propose and evaluate alternative ensemble schemes for a new instance based learning classifier, the Randomised Sphere Cover (RSC) classifier. RSC fuses instances into spheres, then bases classification on distance to spheres rather than distance to instances. The randomised nature of RSC makes it ideal for use in ensembles. We propose two ensemble methods tailored to the RSC classifier; $\alpha \beta$RSE, an ensemble based on instance resampling and $\alpha$RSSE, a subspace ensemble. We compare $\alpha \beta$RSE and $\alpha$RSSE to tree based ensembles on a set of UCI datasets and demonstrates that RSC ensembles perform significantly better than some of these ensembles, and not significantly worse than the others. We demonstrate via a case study on six gene expression data sets that $\alpha$RSSE can outperform other subspace ensemble methods on high dimensional data when used in conjunction with an attribute filter. Finally, we perform a set of Bias/Variance decomposition experiments to analyse the source of improvement in comparison to a base classifier.

A key aspect of word of mouth marketing are emotions. Emotions in texts help propagating messages in conventional advertising. In word of mouth scenarios, emotions help to engage consumers and incite to propagate the message further. While the function of emotions in offline marketing in general and word of mouth marketing in particular is rather well understood, online marketing can only offer a limited view on the function of emotions. In this contribution we seek to close this gap. We therefore investigate how emotions function in social media. To do so, we collected more than 30,000 brand marketing messages from the Google+ social networking site. Using state of the art computational linguistics classifiers, we compute the sentiment of these messages. Starting out with Poisson regression-based baseline models, we seek to replicate earlier findings using this large data set. We extend upon earlier research by computing multi-level mixed effects models that compare the function of emotions across different industries. We find that while the well known notion of activating emotions propagating messages holds in general for our data as well. But there are significant differences between the observed industries.

The Infinite Relational Model (IRM) is a probabilistic model for relational data clustering that partitions objects into clusters based on observed relationships. This paper presents Averaged CVB (ACVB) solutions for IRM, convergence-guaranteed and practically useful fast Collapsed Variational Bayes (CVB) inferences. We first derive ordinary CVB and CVB0 for IRM based on the lower bound maximization. CVB solutions yield deterministic iterative procedures for inferring IRM given the truncated number of clusters. Our proposal includes CVB0 updates of hyperparameters including the concentration parameter of the Dirichlet Process, which has not been studied in the literature. To make the CVB more practically useful, we further study the CVB inference in two aspects. First, we study the convergence issues and develop a convergence-guaranteed algorithm for any CVB-based inferences called ACVB, which enables automatic convergence detection and frees non-expert practitioners from difficult and costly manual monitoring of inference processes. Second, we present a few techniques for speeding up IRM inferences. In particular, we describe the linear time inference of CVB0, allowing the IRM for larger relational data uses. The ACVB solutions of IRM showed comparable or better performance compared to existing inference methods in experiments, and provide deterministic, faster, and easier convergence detection.

Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, $F$ measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures simultaneously. For example, error is the sum of false positives and false negatives and a univariate test on error cannot make a distinction between these two sources, but a 2-variate test can. Similarly, instead of combining precision and recall in $F$ measure, we can have a 2-variate test on (precision, recall). We use Hotelling's multivariate $T^2$ test for comparing two algorithms, and when we have three or more algorithms we use the multivariate analysis of variance (MANOVA) followed by pairwise post hoc tests. In our experiments, we see that multivariate tests have higher power than univariate tests, that is, they can detect differences that univariate tests cannot. We also discuss how multivariate analysis allows us to automatically extract performance measures that best distinguish the behavior of multiple algorithms.

Automatic anomaly detection is a major issue in various areas. Beyond mere detection, the identification of the origin of the problem that produced the anomaly is also essential. This paper introduces a general methodology that can assist human operators who aim at classifying monitoring signals. The main idea is to leverage expert knowledge by generating a very large number of indicators. A feature selection method is used to keep only the most discriminant indicators which are used as inputs of a Naive Bayes classifier. The parameters of the classifier have been optimized indirectly by the selection process. Simulated data designed to reproduce some of the anomaly types observed in real world engines.

Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyperspectral unmixing. This problem is referred to as near-separable NMF and requires that there exists a cone spanned by a small subset of the columns of the input nonnegative matrix approximately containing all columns. In this paper, we propose a preconditioning based on semidefinite programming making the input matrix well-conditioned. This in turn can improve significantly the performance of near-separable NMF algorithms which is illustrated on the popular successive projection algorithm (SPA). The new preconditioned SPA is provably more robust to noise, and outperforms SPA on several synthetic data sets. We also show how an active-set method allow us to apply the preconditioning on large-scale real-world hyperspectral images.