In this paper we aim to develop a general, model free, method for analyzing current status data using machine learning techniques. In particular, we propose a support vector machine (SVM) learning method for estimation of the failure time expectation for current status data. SVM was originally introduced by Vapnik in the 1990's and is firmly related to statistical learning theory (Vapnik, 1999). The choice of SVMs for current status data is motivated by the fact that SVMs can be implemented easily, have fast training speed, produce decision functions that have a strong generalization ability and can guarantee convergence to the optimal solution, under some weak assumptions (Shivaswamy et al., 2007). Current status data is a data format where the failure timeT is restricted to knowledge of whether or notT exceeds a random monitoring timeC . This data format is quite common and includes examples from various fields. Jewell and van der Laan (2004) mention a few examples including: studying the distribution of the age of a child at weaning given observation points; when conducting a partner study of HIV infection over a number of clinic visits; and when a tumor under investigation is occult and an animal is sacrificed at a certain time point in order to determine presence or absence of the tumor.

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, $k$-means, $k$-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features. We propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.

Using geometric data analysis, our objective is the analysis of narrative, with narrative of emotion being the focus in this work. The following two principles for analysis of emotion inform our work. Firstly, emotion is revealed not as a quality in its own right but rather through interaction. We study the 2-way relationship of Ilsa and Rick in the movie Casablanca, and the 3-way relationship of Emma, Charles and Rodolphe in the novel {\em Madame Bovary}. Secondly, emotion, that is expression of states of mind of subjects, is formed and evolves within the narrative that expresses external events and (personal, social, physical) context. In addition to the analysis methodology with key aspects that are innovative, the input data used is crucial. We use, firstly, dialogue, and secondly, broad and general description that incorporates dialogue. In a follow-on study, we apply our unsupervised narrative mapping to data streams with very low emotional expression. We map the narrative of Twitter streams. Thus we demonstrate map analysis of general narratives.

We investigate the difference between using an $\ell_1$ penalty versus an $\ell_1$ constraint in generalized eigenvalue problems, such as principal component analysis and discriminant analysis. Our main finding is that an $\ell_1$ penalty may fail to provide very sparse solutions; a severe disadvantage for variable selection that can be remedied by using an $\ell_1$ constraint. Our claims are supported both by empirical evidence and theoretical analysis. Finally, we illustrate the advantages of an $\ell_1$ constraint in the context of discriminant analysis and principal component analysis.

Most models of Stackelberg security games assume that the attacker only knows the defender's mixed strategy, but is not able to observe (even partially) the instantiated pure strategy. Such partial observation of the deployed pure strategy -- an issue we refer to as information leakage -- is a significant concern in practical applications. While previous research on patrolling games has considered the attacker's real-time surveillance, our settings, therefore models and techniques, are fundamentally different. More specifically, after describing the information leakage model, we start with an LP formulation to compute the defender's optimal strategy in the presence of leakage. Perhaps surprisingly, we show that a key subproblem to solve this LP (more precisely, the defender oracle) is NP-hard even for the simplest of security game models. We then approach the problem from three possible directions: efficient algorithms for restricted cases, approximation algorithms, and heuristic algorithms for sampling that improves upon the status quo. Our experiments confirm the necessity of handling information leakage and the advantage of our algorithms.

This paper studies the form and complexity of inference in graphical models using the abstraction offered by algebraic structures. In particular, we broadly formalize inference problems in graphical models by viewing them as a sequence of operations based on commutative semigroups. We then study the computational complexity of inference by organizing various problems into an "inference hierarchy". When the underlying structure of an inference problem is a commutative semiring -- i.e. a combination of two commutative semigroups with the distributive law -- a message passing procedure called belief propagation can leverage this distributive law to perform polynomial-time inference for certain problems. After establishing the NP-hardness of inference in any commutative semiring, we investigate the relation between algebraic properties in this setting and further show that polynomial-time inference using distributive law does not (trivially) extend to inference problems that are expressed using more than two commutative semigroups. We then extend the algebraic treatment of message passing procedures to survey propagation, providing a novel perspective using a combination of two commutative semirings. This formulation generalizes the application of survey propagation to new settings.

We consider learning, from strictly behavioral data, the structure and parameters of linear influence games (LIGs), a class of parametric graphical games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic inference (CSI): Making inferences from causal interventions on stable behavior in strategic settings. Applications include the identification of the most influential individuals in large (social) networks. Such tasks can also support policy-making analysis. Motivated by the computational work on LIGs, we cast the learning problem as maximum-likelihood estimation (MLE) of a generative model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation uncovers the fundamental interplay between goodness-of-fit and model complexity: good models capture equilibrium behavior within the data while controlling the true number of equilibria, including those unobserved. We provide a generalization bound establishing the sample complexity for MLE in our framework. We propose several algorithms including convex loss minimization (CLM) and sigmoidal approximations. We prove that the number of exact PSNE in LIGs is small, with high probability; thus, CLM is sound. We illustrate our approach on synthetic data and real-world U.S. congressional voting records. We briefly discuss our learning framework's generality and potential applicability to general graphical games.

In this chapter we review the main literature related to kernel spectral clustering (KSC), an approach to clustering cast within a kernel-based optimization setting. KSC represents a least-squares support vector machine based formulation of spectral clustering described by a weighted kernel PCA objective. Just as in the classifier case, the binary clustering model is expressed by a hyperplane in a high dimensional space induced by a kernel. In addition, the multi-way clustering can be obtained by combining a set of binary decision functions via an Error Correcting Output Codes (ECOC) encoding scheme. Because of its model-based nature, the KSC method encompasses three main steps: training, validation, testing. In the validation stage model selection is performed to obtain tuning parameters, like the number of clusters present in the data. This is a major advantage compared to classical spectral clustering where the determination of the clustering parameters is unclear and relies on heuristics. Once a KSC model is trained on a small subset of the entire data, it is able to generalize well to unseen test points. Beyond the basic formulation, sparse KSC algorithms based on the Incomplete Cholesky Decomposition (ICD) and $L_0$, $L_1, L_0 + L_1$, Group Lasso regularization are reviewed. In that respect, we show how it is possible to handle large scale data. Also, two possible ways to perform hierarchical clustering and a soft clustering method are presented. Finally, real-world applications such as image segmentation, power load time-series clustering, document clustering and big data learning are considered.

In biospectroscopy, suitably annotated and statistically independent samples (e. g. patients, batches, etc.) for classifier training and testing are scarce and costly. Learning curves show the model performance as function of the training sample size and can help to determine the sample size needed to train good classifiers. However, building a good model is actually not enough: the performance must also be proven. We discuss learning curves for typical small sample size situations with 5 - 25 independent samples per class. Although the classification models achieve acceptable performance, the learning curve can be completely masked by the random testing uncertainty due to the equally limited test sample size. In consequence, we determine test sample sizes necessary to achieve reasonable precision in the validation and find that 75 - 100 samples will usually be needed to test a good but not perfect classifier. Such a data set will then allow refined sample size planning on the basis of the achieved performance. We also demonstrate how to calculate necessary sample sizes in order to show the superiority of one classifier over another: this often requires hundreds of statistically independent test samples or is even theoretically impossible. We demonstrate our findings with a data set of ca. 2550 Raman spectra of single cells (five classes: erythrocytes, leukocytes and three tumour cell lines BT-20, MCF-7 and OCI-AML3) as well as by an extensive simulation that allows precise determination of the actual performance of the models in question.

It's official, Microsoft has killed off Internet Explorer, its new browser will be Microsoft Edge although you'll be forgiven for thinking nothing has changed if you're looking at the logo. The browser, formally known as Project Spartan after the protagonist of Microsoft's Halo game series, is completely new according to the company. It announced the new name as part of its Windows 10 presentation at its Build developers conference in San Francisco. Edge is meant to give Microsoft a clean break from the negative connotations attached to the Internet Explorer brand by millions of people forced to use old, decrepit versions on work computers. It will live on for many of Microsoft's customers as the centrepiece of much software as a services packages, often required by administrative applications and point of sale.