Thomas Insel left Verily, a health-science spin-off formed by Google's parent company, to co-found a start-up called Mindstrong Health this year. In early 2015, I testified with several other National Institutes of Health (NIH) directors at an annual hearing held by the US Senate. It was my 13th and final year as director of the US National Institute of Mental Health (NIMH) in Bethesda, Maryland. What struck me most was how the harsh fiscal reality tempered the passionate bipartisan support for the NIH. As one senator noted, with a federal deficit of nearly US$500 billion, there was little hope of any significant increase in funding. Six months after that hearing, I left the NIH for Silicon Valley, first working at Verily in South San Francisco, California, a health-science spin-off formed by Google's parent company Alphabet.

In classification problems, sampling bias between training data and testing data is critical to the ranking performance of classification scores. Such bias can be both unintentionally introduced by data collection and intentionally introduced by the algorithm, such as under-sampling or weighting techniques applied to imbalanced data. When such sampling bias exists, using the raw classification score to rank observations in the testing data can lead to suboptimal results. In this paper, I investigate the optimal calibration strategy in general settings, and develop a practical solution for one specific sampling bias case, where the sampling bias is introduced by stratified sampling. The optimal solution is developed by analytically solving the problem of optimizing the ROC curve. For practical data, I propose a ranking algorithm for general classification models with stratified data. Numerical experiments demonstrate that the proposed algorithm effectively addresses the stratified sampling bias issue. Interestingly, the proposed method shows its potential applicability in two other machine learning areas: unsupervised learning and model ensembling, which can be future research topics.

We consider classifiers for high-dimensional data under the strongly spiked eigenvalue (SSE) model. We first show that high-dimensional data often have the SSE model. We consider a distance-based classifier using eigenstructures for the SSE model. We apply the noise reduction methodology to estimation of the eigenvalues and eigenvectors in the SSE model. We create a new distance-based classifier by transforming data from the SSE model to the non-SSE model. We give simulation studies and discuss the performance of the new classifier. Finally, we demonstrate the new classifier by using microarray data sets.

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, overfitting is typically mitigated by adding regularization terms to the objective that penalize hypothesis complexity. In this paper we introduce new regularization techniques using ideas from distributionally robust optimization, and we give new probabilistic interpretations to existing techniques. Specifically, we propose to minimize the worst-case expected loss, where the worst case is taken over the ball of all (continuous or discrete) distributions that have a bounded transportation distance from the (discrete) empirical distribution. By choosing the radius of this ball judiciously, we can guarantee that the worst-case expected loss provides an upper confidence bound on the loss on test data, thus offering new generalization bounds. We prove that the resulting regularized learning problems are tractable and can be tractably kernelized for many popular loss functions. We validate our theoretical out-of-sample guarantees through simulated and empirical experiments.

We propose a probabilistic framework for domain adaptation that blends both generative and discriminative modeling in a principled way. Under this framework, generative and discriminative models correspond to specific choices of the prior over parameters. This provides us a very general way to interpolate between generative and discriminative extremes through different choices of priors. By maximizing both the marginal and the conditional log-likelihoods, models derived from this framework can use both labeled instances from the source domain as well as unlabeled instances from both source and target domains. Under this framework, we show that the popular reconstruction loss of autoencoder corresponds to an upper bound of the negative marginal log-likelihoods of unlabeled instances, where marginal distributions are given by proper kernel density estimations. This provides a way to interpret the empirical success of autoencoders in domain adaptation and semi-supervised learning. We instantiate our framework using neural networks, and build a concrete model, DAuto. Empirically, we demonstrate the effectiveness of DAuto on text, image and speech datasets, showing that it outperforms related competitors when domain adaptation is possible.

We present an algorithm for classification tasks on big data. Experiments conducted as part of this study indicate that the algorithm can be as accurate as ensemble methods such as random forests or gradient boosted trees. Unlike ensemble methods, the models produced by the algorithm can be easily interpreted. The algorithm is based on a divide and conquer strategy and consists of two steps. The first step consists of using a decision tree to segment the large dataset. By construction, decision trees attempt to create homogeneous class distributions in their leaf nodes. However, non-homogeneous leaf nodes are usually produced. The second step of the algorithm consists of using a suitable classifier to determine the class labels for the non-homogeneous leaf nodes. The decision tree segment provides a coarse segment profile while the leaf level classifier can provide information about the attributes that affect the label within a segment.

The original problem of supervised classification considers the task of automatically assigning objects to their respective classes on the basis of numerical measurements derived from these objects. Classifiers are the tools that implement the actual functional mapping from these measurements---also called features or inputs---to the so-called class label---or output. The fields of pattern recognition and machine learning study ways of constructing such classifiers. The main idea behind supervised methods is that of learning from examples: given a number of example input-output relations, to what extent can the general mapping be learned that takes any new and unseen feature vector to its correct class? This chapter provides a basic introduction to the underlying ideas of how to come to a supervised classification problem. In addition, it provides an overview of some specific classification techniques, delves into the issues of object representation and classifier evaluation, and (very) briefly covers some variations on the basic supervised classification task that may also be of interest to the practitioner.

Building classification models is an intrinsically practical exercise that requires many design decisions prior to deployment. We aim to provide some guidance in this decision making process. Specifically, given a classification problem with real valued attributes, we consider which classifier or family of classifiers should one use. Strong contenders are tree based homogeneous ensembles, support vector machines or deep neural networks. All three families of model could claim to be state-of-the-art, and yet it is not clear when one is preferable to the others. Our extensive experiments with over 200 data sets from two distinct archives demonstrate that, rather than choose a single family and expend computing resources on optimising that model, it is significantly better to build simpler versions of classifiers from each family and ensemble. We show that the Heterogeneous Ensembles of Standard Classification Algorithms (HESCA), which ensembles based on error estimates formed on the train data, is significantly better (in terms of error, balanced error, negative log likelihood and area under the ROC curve) than its individual components, picking the component that is best on train data, and a support vector machine tuned over 1089 different parameter configurations. We demonstrate HESCA+, which contains a deep neural network, a support vector machine and two decision tree forests, is significantly better than its components, picking the best component, and HESCA. We analyse the results further and find that HESCA and HESCA+ are of particular value when the train set size is relatively small and the problem has multiple classes. HESCA is a fast approach that is, on average, as good as state-of-the-art classifiers, whereas HESCA+ is significantly better than average and represents a strong benchmark for future research.

In this paper we present a technique for using the bootstrap to estimate the operating characteristics and their variability for certain types of ensemble methods. Bootstrapping a model can require a huge amount of work if the training data set is large. Fortunately in many cases the technique lets us determine the effect of infinite resampling without actually refitting a single model. We apply the technique to the study of meta-parameter selection for random forests. We demonstrate that alternatives to bootstrap aggregation and to considering \sqrt{d} features to split each node, where d is the number of features, can produce improvements in predictive accuracy.

Binary classification is highly used in credit scoring in the estimation of probability of default. The validation of such predictive models is based both on rank ability, and also on calibration (i.e. how accurately the probabilities output by the model map to the observed probabilities). In this study we cover the current best practices regarding calibration for binary classification, and explore how different approaches yield different results on real world credit scoring data. The limitations of evaluating credit scoring models using only rank ability metrics are explored. A benchmark is run on 18 real world datasets, and results compared. The calibration techniques used are Platt Scaling and Isotonic Regression. Also, different machine learning models are used: Logistic Regression, Random Forest Classifiers, and Gradient Boosting Classifiers. Results show that when the dataset is treated as a time series, the use of re-calibration with Isotonic Regression is able to improve the long term calibration better than the alternative methods. Using re-calibration, the non-parametric models are able to outperform the Logistic Regression on Brier Score Loss.