This article considers the problem of sparse estimation of canonical vectors in linear discriminant analysis when $p\gg N$. Several methods have been proposed in the literature that estimate one canonical vector in the two-group case. However, $G-1$ canonical vectors can be considered if the number of groups is $G$. In the multi-group context, it is common to estimate canonical vectors in a sequential fashion. Moreover, separate prior estimation of the covariance structure is often required. We propose a novel methodology for direct estimation of canonical vectors. In contrast to existing techniques, the proposed method estimates all canonical vectors at once, performs variable selection across all the vectors and comes with theoretical guarantees on the variable selection and classification consistency. First, we highlight the fact that in the $N>p$ setting the canonical vectors can be expressed in a closed form up to an orthogonal transformation. Secondly, we propose an extension of this form to the $p\gg N$ setting and achieve feature selection by using a group penalty. The resulting optimization problem is convex and can be solved using a block-coordinate descent algorithm. The practical performance of the method is evaluated through simulation studies as well as real data applications.

Early diagnosis is important for type 2 diabetes (T2D) to improve patient prognosis, prevent complications and reduce long-term treatment costs. We present a novel risk profiling approach based exclusively on health expenditure data that is available to Belgian mutual health insurers. We used expenditure data related to drug purchases and medical provisions to construct models that predict whether a patient will start glucose-lowering pharmacotherapy in the coming years, based on that patient's recent medical expenditure history. The design and implementation of the modeling strategy are discussed in detail and several learning methods are benchmarked for our application. Our best performing model obtains between 74.9% and 76.8% area under the ROC curve, which is comparable to state-of-the-art risk prediction approaches for T2D based on questionnaires. In contrast to other methods, our approach can be implemented on a population-wide scale at virtually no extra operational cost. Possibly, our approach can be further improved by additional information about some risk factors of T2D that is unavailable in health expenditure data.

We propose an optimum mechanism for providing monetary incentives to the data sources of a statistical estimator such as linear regression, so that high quality data is provided at low cost, in the sense that the sum of payments and estimation error is minimized. The mechanism applies to a broad range of estimators, including linear and polynomial regression, kernel regression, and, under some additional assumptions, ridge regression. It also generalizes to several objectives, including minimizing estimation error subject to budget constraints. Besides our concrete results for regression problems, we contribute a mechanism design framework through which to design and analyze statistical estimators whose examples are supplied by workers with cost for labeling said examples.

Within the natural language processing (NLP) community, active learning has been widely investigated and applied in order to alleviate the annotation bottleneck faced by developers of new NLP systems and technologies. This paper presents the first theoretical analysis of stopping active learning based on stabilizing predictions (SP). The analysis has revealed three elements that are central to the success of the SP method: (1) bounds on Cohen's Kappa agreement between successively trained models impose bounds on differences in F-measure performance of the models; (2) since the stop set does not have to be labeled, it can be made large in practice, helping to guarantee that the results transfer to previously unseen streams of examples at test/application time; and (3) good (low variance) sample estimates of Kappa between successive models can be obtained. Proofs of relationships between the level of Kappa agreement and the difference in performance between consecutive models are presented. Specifically, if the Kappa agreement between two models exceeds a threshold T (where $T>0$), then the difference in F-measure performance between those models is bounded above by $\frac{4(1-T)}{T}$ in all cases. If precision of the positive conjunction of the models is assumed to be $p$, then the bound can be tightened to $\frac{4(1-T)}{(p+1)T}$.

The paper briefly introduces multiple classifier systems and describes a new algorithm, which improves classification accuracy by means of recommendation of a proper algorithm to an object classification. This recommendation is done assuming that a classifier is likely to predict the label of the object correctly if it has correctly classified its neighbors. The process of assigning a classifier to each object is based on Formal Concept Analysis. We explain the idea of the algorithm with a toy example and describe our first experiments with real-world datasets.

This work presents a novel modeling and analysis framework for graph sequences which addresses the challenge of detecting and contextualizing anomalies in labelled, streaming graph data. We introduce a generalization of the BTER model of Seshadhri et al. by adding flexibility to community structure, and use this model to perform multi-scale graph anomaly detection. Specifically, probability models describing coarse subgraphs are built by aggregating probabilities at finer levels, and these closely related hierarchical models simultaneously detect deviations from expectation. This technique provides insight into a graph's structure and internal context that may shed light on a detected event. Additionally, this multi-scale analysis facilitates intuitive visualizations by allowing users to narrow focus from an anomalous graph to particular subgraphs or nodes causing the anomaly. For evaluation, two hierarchical anomaly detectors are tested against a baseline Gaussian method on a series of sampled graphs. We demonstrate that our graph statistics-based approach outperforms both a distribution-based detector and the baseline in a labeled setting with community structure, and it accurately detects anomalies in synthetic and real-world datasets at the node, subgraph, and graph levels. To illustrate the accessibility of information made possible via this technique, the anomaly detector and an associated interactive visualization tool are tested on NCAA football data, where teams and conferences that moved within the league are identified with perfect recall, and precision greater than 0.786.

Over the last decade there has been increasing concern about the biases embodied in traditional evaluation methods for Natural Language Processing/Learning, particularly methods borrowed from Information Retrieval. Without knowledge of the Bias and Prevalence of the contingency being tested, or equivalently the expectation due to chance, the simple conditional probabilities Recall, Precision and Accuracy are not meaningful as evaluation measures, either individually or in combinations such as F-factor. The existence of bias in NLP measures leads to the 'improvement' of systems by increasing their bias, such as the practice of improving tagging and parsing scores by using most common value (e.g. water is always a Noun) rather than the attempting to discover the correct one. The measures Cohen Kappa and Powers Informedness are discussed as unbiased alternative to Recall and related to the psychologically significant measure DeltaP. In this paper we will analyze both biased and unbiased measures theoretically, characterizing the precise relationship between all these measures as well as evaluating the evaluation measures themselves empirically using a Monte Carlo simulation.

The F-measure or F-score is one of the most commonly used single number measures in Information Retrieval, Natural Language Processing and Machine Learning, but it is based on a mistake, and the flawed assumptions render it unsuitable for use in most contexts! Fortunately, there are better alternatives.

In medical domain, data features often contain missing values. This can create serious bias in the predictive modeling. Typical standard data mining methods often produce poor performance measures. In this paper, we propose a new method to simultaneously classify large datasets and reduce the effects of missing values. The proposed method is based on a multilevel framework of the cost-sensitive SVM and the expected maximization imputation method for missing values, which relies on iterated regression analyses. We compare classification results of multilevel SVM-based algorithms on public benchmark datasets with imbalanced classes and missing values as well as real data in health applications, and show that our multilevel SVM-based method produces fast, and more accurate and robust classification results.

Existing MAP inference algorithms for determinantal point processes (DPPs) need to calculate determinants or conduct eigenvalue decomposition generally at the scale of the full kernel, which presents a great challenge for real-world applications. In this paper, we introduce a class of DPPs, called BwDPPs, that are characterized by an almost block diagonal kernel matrix and thus can allow efficient block-wise MAP inference. Furthermore, BwDPPs are successfully applied to address the difficulty of selecting change-points in the problem of change-point detection (CPD), which results in a new BwDPP-based CPD method, named BwDppCpd. In BwDppCpd, a preliminary set of change-point candidates is first created based on existing well-studied metrics. Then, these change-point candidates are treated as DPP items, and DPP-based subset selection is conducted to give the final estimate of the change-points that favours both quality and diversity. The effectiveness of BwDppCpd is demonstrated through extensive experiments on five real-world datasets.