We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrices to have equal entries and also encourage zeros in the precision matrix. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze an EEG dataset to demonstrate our method's interpretability and classification accuracy.

My colleague Amy Nicholson is the UK expert on Azure Machine Learning, the following blog post is after a quizzing session to get understand how to get started with Azure Machine Learning" Each student receives $100 of Azure credit per month, for 6 months. The Faculty member receives $250 per month, for 12 months. The Azure machine learning team provided a very nice walkthrough tutorial which covers a lot of the basics. This tutorial is really useful as it takes you through the entire process of creating an AzureML workspace, uploading data, creating an experiment to predict someone's credit risk, building, training, and evaluating the models, publishing your best model as a web service, and calling that web service. Now you need to learn how to import a data set into Azure Machine Learning, and where to find interesting data to build something amazing.

There's only one WWE pay-per-view scheduled until Survivor Series in November, and it's set for Sunday night in Boston. Hell in a Cell 2016, a "Monday Night Raw" PPV, will feature three matches inside of the cage, including a first for WWE. While WWE is calling the three matches a "triple main event," the women's championship match might close the show. Sasha Banks defends her title against Charlotte in what should be the conclusion of their long-running feud, and it's the first time ever that women will compete in Hell in a Cell. Roman Reigns and Rusev will fight inside of the cell, as well, in a United States Championship match. Bayley vs. Dana Brooke could potentially be added to the card before the end of the week, but only six matches are officially scheduled for Hell in a Cell following "Monday Night Raw."

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.

Discussion[Discussion] How Gaussian naïve Bayes forms a non-linear decision boundary? Also, please explain decision boundary for decision trees. If the two gaussians are non isotropic you can derive that the bound is quadratic/elliptic curve.

Recidivism prediction instruments (RPI's) provide decision makers with an assessment of the likelihood that a criminal defendant will reoffend at a future point in time. While such instruments are gaining increasing popularity across the country, their use is attracting tremendous controversy. Much of the controversy concerns potential discriminatory bias in the risk assessments that are produced. This paper discusses a fairness criterion originating in the field of educational and psychological testing that has recently been applied to assess the fairness of recidivism prediction instruments. We demonstrate how adherence to the criterion may lead to considerable disparate impact when recidivism prevalence differs across groups.

Methods for unsupervised anomaly detection suffer from the fact that the data is unlabeled, making it difficult to assess the optimality of detection algorithms. Ensemble learning has shown exceptional results in classification and clustering problems, but has not seen as much research in the context of outlier detection. Existing methods focus on combining output scores of individual detectors, but this leads to outputs that are not easily interpretable. In this paper, we introduce a theoretical foundation for combining individual detectors with Bayesian classifier combination. Not only are posterior distributions easily interpreted as the probability distribution of anomalies, but bias, variance, and individual error rates of detectors are all easily obtained. Performance on real-world datasets shows high accuracy across varied types of time series data.

Trying to discern drug smugglers passing through customs presents exactly the same problem as trying to discern security threats passing through our networks. Machine learning has been applied to both with varying degrees of success, but ultimately the technology reaches the same limitations. Machine learning has two basic elements: feature vectors and classification exemplars -- the data that is gathered and the corresponding classification examples. In the case of drug smugglers, we might observe number of travelers, point of origin, point of destination, number of bags, length of stay and weight of the bags. We might also flag any traveler or pair of travelers with two or more bags whose combined weight is greater than 150 pounds, whose stay is less than a week and who originated from a climate conducive to poppies.

Large margin classifiers, such as the support vector machine (SVM) [1] and the maximum entropy discrimination (MED) classifier [2], have enjoyed great popularity in the signal processing and machine learning communities due to their broad applicability, robust performance, and the availability of fast software implementations. When the training data is representative of the test data, the performance of MED/SVM has theoretical guarantees that have been validated in practice [1], [3], [4]. Moreover, since the decision boundary of the MED/SVM is solely defined by a few support vectors, the algorithm can tolerate random feature distortions and perturbations. However, in many real applications, anomalous measurements are inherent to the data set due to strong environmental noise or possible sensor failures. Such anomalies arise in industrial process monitoring, video surveillance, tactical multimodal sensing, robust spectrum sensing [5], [6], and, more generally, any application that involves unattended sensors in difficult environments (Figure 1).

We propose a novel stacked generalization (stacking) method as a dynamic ensemble technique using a pool of heterogeneous classifiers for node label classification on networks. The proposed method assigns component models a set of functional coefficients, which can vary smoothly with certain topological features of a node. Compared to the traditional stacking model, the proposed method can dynamically adjust the weights of individual models as we move across the graph and provide a more versatile and significantly more accurate stacking model for label prediction on a network. We demonstrate the benefits of the proposed model using both a simulation study and real data analysis.