A new dimension reduction method based on Gaussian finite mixtures is proposed as an extension to sliced inverse regression (SIR). The model-based SIR (MSIR) approach allows the main limitation of SIR to be overcome, i.e., failure in the presence of regression symmetric relationships, without the need to impose further assumptions. Extensive numerical studies are presented to compare the new method with some of most popular dimension reduction methods, such as SIR, sliced average variance estimation, principal Hessian direction, and directional regression. MSIR appears sufficiently flexible to accommodate various regression functions, and its performance is comparable with or better, particularly as sample size grows, than other available methods. Lastly, MSIR is illustrated with two real data examples about ozone concentration regression, and hand-written digit classification.

This paper discusses several problems in dynamical systems and control, where methods from learning theory are used in the state space of linear systems. This is in contrast to previous approaches in the frequency domain [19, 6]. We refer to [6] for a general survey on applications of machine learning to system identification. Basically, learning theory allows to deal with problems when only data from a given system are given. Reproducing Kernel Hilbert Spaces (RKHS) allow to work in a very large dimensional space in order to simplify the underlying problem.

Decision analytics commonly focuses on the text mining of financial news sources in order to provide managerial decision support and to predict stock market movements. Existing predictive frameworks almost exclusively apply traditional machine learning methods, whereas recent research indicates that traditional machine learning methods are not sufficiently capable of extracting suitable features and capturing the non-linear nature of complex tasks. As a remedy, novel deep learning models aim to overcome this issue by extending traditional neural network models with additional hidden layers. Indeed, deep learning has been shown to outperform traditional methods in terms of predictive performance. In this paper, we adapt the novel deep learning technique to financial decision support. In this instance, we aim to predict the direction of stock movements following financial disclosures. As a result, we show how deep learning can outperform the accuracy of random forests as a benchmark for machine learning by 5.66%.

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shift-invariant kernel functions (e.g., Gaussian kernel). In this paper, we propose to use Quasi-Monte Carlo (QMC) approximations instead, where the relevant integrands are evaluated on a low-discrepancy sequence of points as opposed to random point sets as in the Monte Carlo approach. We derive a new discrepancy measure called box discrepancy based on theoretical characterizations of the integration error with respect to a given sequence. We then propose to learn QMC sequences adapted to our setting based on explicit box discrepancy minimization. Our theoretical analyses are complemented with empirical results that demonstrate the effectiveness of classical and adaptive QMC techniques for this problem.

It has recently been found that Bell scenarios are only a small subclass of interesting setups for studying the nonclassical features of quantum theory within spacetime. We find that it is possible to talk about classical correlations, quantum correlations and other kinds of correlations on any directed acyclic graph, and this captures various extensions of Bell scenarios which have been considered in the literature. From a conceptual point of view, the main feature of our approach is its high level of unification: while the notions of source, choice of setting and measurement play all seemingly different roles in a Bell scenario, our formalism shows that they are all instances of the same concept of "event". Our work can also be understood as a contribution to the subject of causal inference with latent variables. Among other things, we introduce hidden Bayesian networks as a generalization of hidden Markov models. Contents 1. Introduction 2 2. What is causal structure?

This paper focuses on finding spatial and temporal criminal hotspots. It analyses two different real-world crimes datasets for Denver, CO and Los Angeles, CA and provides a comparison between the two datasets through a statistical analysis supported by several graphs. Then, it clarifies how we conducted Apriori algorithm to produce interesting frequent patterns for criminal hotspots. In addition, the paper shows how we used Decision Tree classifier and Naive Bayesian classifier in order to predict potential crime types. To further analyse crimes datasets, the paper introduces an analysis study by combining our findings of Denver crimes dataset with its demographics information in order to capture the factors that might affect the safety of neighborhoods. The results of this solution could be used to raise awareness regarding the dangerous locations and to help agencies to predict future crimes in a specific location within a particular time.

This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. We investigate the spectral convergence of both unnormalized and normalized graph Laplacians towards the appropriate operators in the continuum domain. We obtain sharp conditions on how the connectivity radius can be scaled with respect to the number of sample points for the spectral convergence to hold. We also show that the discrete clusters obtained via spectral clustering converge towards a continuum partition of the ground truth measure. Such continuum partition minimizes a functional describing the continuum analogue of the graph-based spectral partitioning. Our approach, based on variational convergence, is general and flexible.

Random forests are a learning algorithm proposed by Breiman [Mach. Learn. 45 (2001) 5--32] that combines several randomized decision trees and aggregates their predictions by averaging. Despite its wide usage and outstanding practical performance, little is known about the mathematical properties of the procedure. This disparity between theory and practice originates in the difficulty to simultaneously analyze both the randomization process and the highly data-dependent tree structure. In the present paper, we take a step forward in forest exploration by proving a consistency result for Breiman's [Mach. Learn. 45 (2001) 5--32] original algorithm in the context of additive regression models. Our analysis also sheds an interesting light on how random forests can nicely adapt to sparsity. 1. Introduction. Random forests are an ensemble learning method for classification and regression that constructs a number of randomized decision trees during the training phase and predicts by averaging the results. Since its publication in the seminal paper of Breiman (2001), the procedure has become a major data analysis tool, that performs well in practice in comparison with many standard methods. What has greatly contributed to the popularity of forests is the fact that they can be applied to a wide range of prediction problems and have few parameters to tune. Aside from being simple to use, the method is generally recognized for its accuracy and its ability to deal with small sample sizes, high-dimensional feature spaces and complex data structures. The random forest methodology has been successfully involved in many practical problems, including air quality prediction (winning code of the EMC data science global hackathon in 2012, see http://www.kaggle.com/c/dsg-hackathon), chemoinformatics [Svetnik et al. (2003)], ecology [Prasad, Iverson and Liaw (2006), Cutler et al. (2007)], 3D

Variable selection techniques aim at identifying such relevant covariates (for a review see Guyon, 2006). Usually, variable selection aims at one of two goals: to identify informative covariates in order to get scientific insight into the data and the process that generated the outcome; or to use the covariates identified as relevant in order to predict the outcome. In this work we primarily focus on the identification of informative covariates but also consider prediction results using real data. We consider variable selection (also called feature selection in computer science-related communities) as a part of the broader field of dimensionality reduction. Many variable selection methods share the common drawback of being unstable with respect to small changes of the data: if one estimates the set of relevant covariates on different sets of observations coming from the same source, the result can vary significantly.

Since its introduction in [15], spectral analysis of various matrices associated to groups has become one of the most widely used clustering techniques in statistics and machine learning. In the context of unlabeled graphs, a number of methods, all of which come under the broad heading of spectral clustering have been proposed. These methods based on spectral analysis of adjacency matrices or some derived matrix such as one of the Laplacians ([31], [28], [23], [29], [32]) have been studied in connection with their effectiveness in identifying members of blocks in exchangeable graph block models. In this paper after introducing the methods and models, we intend to review some of the literature.