The residual plot above shows the prediction error of the test dataset plotted against a selected feature. We built this model just before the wild-card round of the NFL playoffs, and we wanted to test the model against 10 previous games. Of our 10 predictions, seven were correct, and two of the three incorrect predictions were very close to margin (50 percent), as seen in the table below. So, we were comfortable with this model. Next, our model correctly predicted the outcome of three out of four playoff games.

Dr. Anil Maheshwari has done a great job in taking a complex, highly important subject area and making it accessible to everyone. The book begins by simply connecting to what you know, and then bang - you've suddenly found out about Decision Trees, Regression Models and Artificial Neural Networks, not to mention cluster analysis, mining and Big Data. It takes real experience and authority, as well as a great generosity of spirit to be able to write like this. For instance in Chapter 12 on Big Data, Dr. Maheshwari presents "The Big Data Landscape" that gives you a great overview on a single page. I also much appreciated the way the Primer sections are made available, for beginners, and there is also a way for more advanced readers to get to stuff that is useful to take them to the next level.

We present a fast variational Bayesian algorithm for performing non-negative matrix factorisation and tri-factorisation. We show that our approach achieves faster convergence per iteration and timestep (wall-clock) than Gibbs sampling and non-probabilistic approaches, and do not require additional samples to estimate the posterior. We show that in particular for matrix tri-factorisation convergence is difficult, but our variational Bayesian approach offers a fast solution, allowing the tri-factorisation approach to be used more effectively.

Predictive modeling is increasingly being employed to assist human decision-makers. One purported advantage of replacing human judgment with computer models in high stakes settings-- such as sentencing, hiring, policing, college admissions, and parole decisions-- is the perceived "neutrality" of computers. It is argued that because computer models do not hold personal prejudice, the predictions they produce will be equally free from prejudice. There is growing recognition that employing algorithms does not remove the potential for bias, and can even amplify it, since training data were inevitably generated by a process that is itself biased. In this paper, we provide a probabilistic definition of algorithmic bias. We propose a method to remove bias from predictive models by removing all information regarding protected variables from the permitted training data. Unlike previous work in this area, our framework is general enough to accommodate arbitrary data types, e.g. binary, continuous, etc. Motivated by models currently in use in the criminal justice system that inform decisions on pre-trial release and paroling, we apply our proposed method to a dataset on the criminal histories of individuals at the time of sentencing to produce "race-neutral" predictions of re-arrest. In the process, we demonstrate that the most common approach to creating "race-neutral" models-- omitting race as a covariate-- still results in racially disparate predictions. We then demonstrate that the application of our proposed method to these data removes racial disparities from predictions with minimal impact on predictive accuracy.

Abstract--In this paper we investigate a link between state-space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state-space models are transformed into continuous time form and corresponding Gaussian Process kernels are derived. Experimental results demonstrate that the derived GP kernels are correct and appropriate for Gaussian Process Regression. An experiment with a real world dataset shows that the modeling is identical with state-space models and with the proposed GP kernels. The considered connection allows the researchers to look at their models from a different angle and facilitate sharing ideas between these two different modeling approaches. I NTRODUCTION ANDM OTIVATION Time series modeling and prediction is one of oldest topics in statistics. The very first statisticians already dealt with time dependent data. For example, Beveridge wheat price (years 1500 to 1869) or Wolfer's sunspot number (years 1610-1960) [1] are examples of very early time series. Nowadays time series analysis and forecasting is ubiquitous in many fields of science and engineering. Econometricians, physicists, statisticians, biologists, climatologists etc. encounter time dependent data in their daily work. Since this problem is very old and very widespread, different fields of science developed their own sets of methods for analysis and forecasting of time series. For instance, in statistics and econometrics domains the most common models are state-space (SS) models [2], [3]. In the physics domain the dominating class of models constitute nonlinear dynamical models [4].

Cross-validation (CV) is a technique for evaluating the ability of statistical models/learning systems based on a given data set. Despite its wide applicability, the rather heavy computational cost can prevent its use as the system size grows. To resolve this difficulty in the case of Bayesian linear regression, we develop a formula for evaluating the leave-one-out CV error approximately without actually performing CV. The usefulness of the developed formula is tested by statistical mechanical analysis for a synthetic model. This is confirmed by application to a real-world supernova data set as well.

This paper studies how to capture dependency graph structures from real data which may not be multivariate Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we use an additive over-parametrization with shrinkage to incorporate variable dependencies into the criterion. An iterative Gaussian graph learning algorithm is proposed with ease in implementation. Statistical analysis shows that with the error measured in terms of a proper Bregman divergence, the estimators have fast rate of convergence. Real-life examples in different settings are given to demonstrate the efficacy of the proposed methodology.

In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with supervision. We proceed by first proposing improvements of the recently-introduced convolutional kernel networks (CKNs) in the context of unsupervised learning; then, we derive backpropagation rules to take advantage of labeled training data. The resulting model is a new type of convolutional neural network, where optimizing the filters at each layer is equivalent to learning a linear subspace in a reproducing kernel Hilbert space (RKHS). We show that our method achieves reasonably competitive performance for image classification on some standard "deep learning" datasets such as CIFAR-10 and SVHN, and also for image super-resolution, demonstrating the applicability of our approach to a large variety of image-related tasks.

We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset of input features. The proposed estimators enjoy sharp oracle inequalities, and with a predictive information criterion for model selection, they adapt to unknown sparsity by controlling both rank and row support of the coefficient matrix. A class of algorithms is developed that can accommodate various convex and nonconvex sparsity-inducing penalties, and can be used for rank-constrained variable screening in high-dimensional multivariate data. The paper also showcases applications in macroeconomics and computer vision to demonstrate how low-dimensional data structures can be effectively captured by joint variable selection and projection.

An artificial intelligence system designed to predict the outcomes of cases at the European Court of Human Rights would side with the human judges 79 percent of the time. Researchers at University College London and the University of Sheffield in the U.K., and the University of Pennsylvania in the U.S., described the system in a paper published Monday by the Peer Journal of Computer Science. "We formulated a binary classification task where the input of our classifiers is the textual content extracted from a case and the target output is the actual judgment as to whether there has been a violation of an article of the convention of human rights," wrote the paper's authors, Nikolaos Aletras, Dimitrios Tsarapatsanis, Daniel Preo?iuc-Pietro and Vasileios Lampos. The system examined public court documents relating to 584 cases of violations of articles 3 (prohibiting torture), 6 (right to a fair trial) and 8 (respect for private life) of the European Convention on Human Rights, which has been ratified by 47 European countries. The court documents have a distinctive structure, discussing first the procedure by which the case reached the court, the facts and circumstances of the case, relevant law, and the legal arguments applied.