A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively applies binary splits to divide the set of classes into two subsets, and trains a binary classifier for each split. Although ensembles of nested dichotomies with random structure have been shown to perform well in practice, using a more sophisticated class subset selection method can be used to improve classification accuracy. We investigate an approach to this problem called random-pair selection, and evaluate its effectiveness compared to other published methods of subset selection. We show that our method outperforms other methods in many cases when forming ensembles of nested dichotomies, and is at least on par in all other cases.

We study the residual bootstrap (RB) method in the context of high-dimensional linear regression. Specifically, we analyze the distributional approximation of linear contrasts $c^{\top} (\hat{\beta}_{\rho}-\beta)$, where $\hat{\beta}_{\rho}$ is a ridge-regression estimator. When regression coefficients are estimated via least squares, classical results show that RB consistently approximates the laws of contrasts, provided that $p\ll n$, where the design matrix is of size $n\times p$. Up to now, relatively little work has considered how additional structure in the linear model may extend the validity of RB to the setting where $p/n\asymp 1$. In this setting, we propose a version of RB that resamples residuals obtained from ridge regression. Our main structural assumption on the design matrix is that it is nearly low rank --- in the sense that its singular values decay according to a power-law profile. Under a few extra technical assumptions, we derive a simple criterion for ensuring that RB consistently approximates the law of a given contrast. We then specialize this result to study confidence intervals for mean response values $X_i^{\top} \beta$, where $X_i^{\top}$ is the $i$th row of the design. More precisely, we show that conditionally on a Gaussian design with near low-rank structure, RB simultaneously approximates all of the laws $X_i^{\top}(\hat{\beta}_{\rho}-\beta)$, $i=1,\dots,n$. This result is also notable as it imposes no sparsity assumptions on $\beta$. Furthermore, since our consistency results are formulated in terms of the Mallows (Kantorovich) metric, the existence of a limiting distribution is not required.

We propose a novel methodology, forest floor, to visualize and interpret random forest (RF) models. RF is a popular and useful tool for non-linear multi-variate classification and regression, which yields a good trade-off between robustness (low variance) and adaptiveness (low bias). Direct interpretation of a RF model is difficult, as the explicit ensemble model of hundreds of deep trees is complex. Nonetheless, it is possible to visualize a RF model fit by its mapping from feature space to prediction space. Hereby the user is first presented with the overall geometrical shape of the model structure, and when needed one can zoom in on local details. Dimensional reduction by projection is used to visualize high dimensional shapes. The traditional method to visualize RF model structure, partial dependence plots, achieve this by averaging multiple parallel projections. We suggest to first use feature contributions, a method to decompose trees by splitting features, and then subsequently perform projections. The advantages of forest floor over partial dependence plots is that interactions are not masked by averaging. As a consequence, it is possible to locate interactions, which are not visualized in a given projection. Furthermore, we introduce: a goodness-of-visualization measure, use of colour gradients to identify interactions and an out-of-bag cross validated variant of feature contributions.

Abstract--Disagreement between two classifiers regarding the class membership of an observation in pattern recognition can be indicative of an anomaly and its nuance. As in general classifiers base their decision on class aposteriori probabilities, the most natural approach to detecting classifier incongruence is to use divergence. However, existing divergences are not particularly suitable to gauge classifier incongruence. In this paper, we postulate the properties that a divergence measure should satisfy and propose a novel divergence measure, referred to as Delta divergence. In contrast to existing measures, it is decision cognizant. The focus in Delta divergence on the dominant hypotheses has a clutter reducing property, the significance of which grows with increasing number of classes. The proposed measure satisfies other important properties such as symmetry, and independence of classifier confidence. The relationship of the proposed divergence to some baseline measures is demonstrated experimentally, showing its superiority. Divergence in information theory has been intensively studied and researched over the last six decades. On one hand the massive interest in the subject has been driven by the diversity of applications where divergence plays the key role as an objective function. On the other hand the investigation of the underlying theoretical properties of divergence has motivated the discovery of new measures with tailor made characteristics that are fine tuned for specific applications.

Community-based Question Answering (CQA) sites play an important role in addressing health information needs. However, a significant number of posted questions remain unanswered. Automatically answering the posted questions can provide a useful source of information for online health communities. In this study, we developed an algorithm to automatically answer health-related questions based on past questions and answers (QA). We also aimed to understand information embedded within online health content that are good features in identifying valid answers. Our proposed algorithm uses information retrieval techniques to identify candidate answers from resolved QA. In order to rank these candidates, we implemented a semi-supervised leaning algorithm that extracts the best answer to a question. We assessed this approach on a curated corpus from Yahoo! Answers and compared against a rule-based string similarity baseline. On our dataset, the semi-supervised learning algorithm has an accuracy of 86.2%. UMLS-based (health-related) features used in the model enhance the algorithm's performance by proximately 8 %. A reasonably high rate of accuracy is obtained given that the data is considerably noisy. Important features distinguishing a valid answer from an invalid answer include text length, number of stop words contained in a test question, a distance between the test question and other questions in the corpus as well as a number of overlapping health-related terms between questions. Overall, our automated QA system based on historical QA pairs is shown to be effective according to the data set in this case study. It is developed for general use in the health care domain which can also be applied to other CQA sites.

Early diagnosis, playing an important role in preventing progress and treating the Alzheimer's disease (AD), is based on classification of features extracted from brain images. The features have to accurately capture main AD-related variations of anatomical brain structures, such as, e.g., ventricles size, hippocampus shape, cortical thickness, and brain volume. This paper proposes to predict the AD with a deep 3D convolutional neural network (3D-CNN), which can learn generic features capturing AD biomarkers and adapt to different domain datasets. The 3D-CNN is built upon a 3D convolutional autoencoder, which is pre-trained to capture anatomical shape variations in structural brain MRI scans. Fully connected upper layers of the 3D-CNN are then fine-tuned for each task-specific AD classification. Experiments on the \emph{ADNI} MRI dataset with no skull-stripping preprocessing have shown our 3D-CNN outperforms several conventional classifiers by accuracy and robustness. Abilities of the 3D-CNN to generalize the features learnt and adapt to other domains have been validated on the \emph{CADDementia} dataset.

Brain networks in fMRI are typically identified using spatial independent component analysis (ICA), yet mathematical constraints such as sparse coding and positivity both provide alternate biologically-plausible frameworks for generating brain networks. Non-negative Matrix Factorization (NMF) would suppress negative BOLD signal by enforcing positivity. Spatial sparse coding algorithms ($L1$ Regularized Learning and K-SVD) would impose local specialization and a discouragement of multitasking, where the total observed activity in a single voxel originates from a restricted number of possible brain networks. The assumptions of independence, positivity, and sparsity to encode task-related brain networks are compared; the resulting brain networks for different constraints are used as basis functions to encode the observed functional activity at a given time point. These encodings are decoded using machine learning to compare both the algorithms and their assumptions, using the time series weights to predict whether a subject is viewing a video, listening to an audio cue, or at rest, in 304 fMRI scans from 51 subjects. For classifying cognitive activity, the sparse coding algorithm of $L1$ Regularized Learning consistently outperformed 4 variations of ICA across different numbers of networks and noise levels (p$<$0.001). The NMF algorithms, which suppressed negative BOLD signal, had the poorest accuracy. Within each algorithm, encodings using sparser spatial networks (containing more zero-valued voxels) had higher classification accuracy (p$<$0.001). The success of sparse coding algorithms may suggest that algorithms which enforce sparse coding, discourage multitasking, and promote local specialization may capture better the underlying source processes than those which allow inexhaustible local processes such as ICA.

We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein's identity with the reproducing kernel Hilbert space theory. We apply our result to test how well a probabilistic model fits a set of observations, and derive a new class of powerful goodness-of-fit tests that are widely applicable for complex and high dimensional distributions, even for those with computationally intractable normalization constants. Both theoretical and empirical properties of our methods are studied thoroughly.

In relation to Bayesian statistics, the sensitivity and specificity are the conditional probabilities, the prevalence is the prior, and the positive/negative predicted values are the posterior probabilities.

Manufacturers often have to deal with up to 800 hours of downtime annually. On average an automotive manufacturer's TDC is 22,000 per minute; that is 1.3M per month! With the advance of predictive analytics, TDC can easily be reduced however only 14% of the manufacturing industry is taking advantage of its big data, according to a recent survey from MESA. Predictive maintenance is realized through the application of sophisticated machine learning techniques to equipment condition data collected in real-time or near real-time. It is now the new standard for reducing cost, risk and lost production in manufacturing facilities.