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.

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.

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.

Recidivism prediction instruments 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.

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.

In this paper, we propose a general framework to learn a robust large-margin binary classifier when corrupt measurements, called anomalies, caused by sensor failure might be present in the training set. The goal is to minimize the generalization error of the classifier on non-corrupted measurements while controlling the false alarm rate associated with anomalous samples. By incorporating a non-parametric regularizer based on an empirical entropy estimator, we propose a Geometric-Entropy-Minimization regularized Maximum Entropy Discrimination (GEM-MED) method to learn to classify and detect anomalies in a joint manner. We demonstrate using simulated data and a real multimodal data set. Our GEM-MED method can yield improved performance over previous robust classification methods in terms of both classification accuracy and anomaly detection rate.

We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of sparsity across precision matrices. It gives sparse estimates of interactions and produces interpretable models. Inspired by the connected-components structure of the estimated precision matrices, we propose the community Bayes model, which partitions features into several conditional independent communities and splits the classification problem into separate smaller ones. The community Bayes idea is quite general and can be applied to non-Gaussian data and likelihood-based classifiers.

We investigate metric learning in the context of dynamic time warping (DTW), the by far most popular dissimilarity measure used for the comparison and analysis of motion capture data. While metric learning enables a problem-adapted representation of data, the majority of meth- ods has been proposed for vectorial data only. In this contribution, we extend the popular principle offered by the large margin nearest neighbours learner (LMNN) to DTW by treating the resulting component-wise dissimilarity values as features. We demonstrate, that this principle greatly enhances the classification accuracy in several benchmarks. Further, we show that recent auxiliary concepts such as metric regularisation can be transferred from the vectorial case to component-wise DTW in a similar way. We illustrate, that metric regularisation constitutes a crucial prerequisite for the interpretation of the resulting relevance profiles.

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.

Machine learning is a fashionable buzzword right now in infosec, and is often referenced as the key to next-gen, signature-less security. But along with all of the hype and buzz, there also is a mind-blowing amount of misunderstanding surrounding machine learning in infosec. Machine learning isn't a silver bullet for all information security problems, and in fact can be detrimental if misinterpreted. For example, company X claims to block 99% of all malware, or company Y's intrusion detection will stop 99% of all attacks, yet customers see an overwhelming number of false positives. What do the accuracy numbers really mean? In fact, these simple statistics lose meaning without the proper context.