We consider the validation of prognostic diagnostic tests that predict two prognostic subgroups (high-risk vs low-risk) for a given disease or treatment. When comparing survival curves between two prognostic subgroups the possibility of misclassification arises, i.e. a patient predicted as high-risk might be de facto low-risk and vice versa. This is a fundamental difference from comparing survival curves between two populations (e.g. control vs treatment in RCT), where there is not an option of misclassification between members of populations. We show that there is a relationship between prognostic subgroups' survival estimates at a time point and positive and negative predictive values in the classification settings. Consequently, the prevalence needs to be taken into account when validating the survival of prognostic subgroups at a time point. Our findings question current methods of comparing survival curves between prognostic subgroups in the validation set because they do not take into account the survival rates of the population.

We consider the problem of estimating the class prior in an unlabeled dataset. Under the assumption that an additional labeled dataset is available, the class prior can be estimated by fitting a mixture of class-wise data distributions to the unlabeled data distribution. However, in practice, such an additional labeled dataset is often not available. In this paper, we show that, with additional samples coming only from the positive class, the class prior of the unlabeled dataset can be estimated correctly. Our key idea is to use properly penalized divergences for model fitting to cancel the error caused by the absence of negative samples. We further show that the use of the penalized $L_1$-distance gives a computationally efficient algorithm with an analytic solution. The consistency, stability, and estimation error are theoretically analyzed. Finally, we experimentally demonstrate the usefulness of the proposed method.

Although much progress has been made in classification with high-dimensional features \citep{Fan_Fan:2008, JGuo:2010, CaiSun:2014, PRXu:2014}, classification with ultrahigh-dimensional features, wherein the features much outnumber the sample size, defies most existing work. This paper introduces a novel and computationally feasible multivariate screening and classification method for ultrahigh-dimensional data. Leveraging inter-feature correlations, the proposed method enables detection of marginally weak and sparse signals and recovery of the true informative feature set, and achieves asymptotic optimal misclassification rates. We also show that the proposed procedure provides more powerful discovery boundaries compared to those in \citet{CaiSun:2014} and \citet{JJin:2009}. The performance of the proposed procedure is evaluated using simulation studies and demonstrated via classification of patients with different post-transplantation renal functional types.

Think of a regression model mapping a number of features onto a real number (potentially a probability). The resulting real number can then be mapped on one of two classes, depending on whether this predicted number is greater or lower than some choosable threshold. Let's take for example a logistic regression and data on the survivorship of the Titanic accident to introduce the relevant concepts which will lead naturally to the ROC (Receiver Operating Characteristic) and its AUC or AUROC (Area Under ROC Curve). Every record in the data set represents a passenger – providing information on her/his age, gender, class, number of siblings/spouses aboard (sibsp), number of parents/children aboard (parch) and, of course, whether s/he survived the accident. The logistic regression model is tested on batches of 10 cases with a model trained on the remaining N-10 cases – the test batches form a partition of the data. In short, Leave-10-out CV has been applied to arrive at more accurate estimation of the out-of-sample error rates.

Many machine learning algorithms require precise estimates of covariance matrices. The sample covariance matrix performs poorly in high-dimensional settings, which has stimulated the development of alternative methods, the majority based on factor models and shrinkage. Recent work of Ledoit and Wolf has extended the shrinkage framework to Nonlinear Shrinkage (NLS), a more powerful covariance estimator based on Random Matrix Theory. Our contribution shows that, contrary to claims in the literature, cross-validation based covariance matrix estimation (CVC) yields comparable performance at strongly reduced complexity and runtime. On two real world data sets, we show that the CVC estimator yields superior results than competing shrinkage and factor based methods.

Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in closed form just involving linear algebra operations. However, they are hampered by two important problems: the high computational cost involved, as two kernel matrices of the sample size have to be computed and stored, and the interpretability of the measure, which remains hidden behind the implicit feature map. We here address these two issues. We introduce the Sensitivity Maps (SMs) for the Hilbert-Schmidt independence criterion (HSIC). Sensitivity maps allow us to explicitly analyze and visualize the relative relevance of both examples and features on the dependence measure. We also present the randomized HSIC (RHSIC) and its corresponding sensitivity maps to cope with large scale problems. We build upon the framework of random features and the Bochner's theorem to approximate the involved kernels in the canonical HSIC. The power of the RHSIC measure scales favourably with the number of samples, and it approximates HSIC and the sensitivity maps efficiently. Convergence bounds of both the measure and the sensitivity map are also provided. Our proposal is illustrated in synthetic examples, and challenging real problems of dependence estimation, feature selection, and causal inference from empirical data.

Model-based collaborative filtering analyzes user-item interactions to infer latent factors that represent user preferences and item characteristics in order to predict future interactions. Most collaborative filtering algorithms assume that these latent factors are static, although it has been shown that user preferences and item perceptions drift over time. In this paper, we propose a conjugate and numerically stable dynamic matrix factorization (DCPF) based on compound Poisson matrix factorization that models the smoothly drifting latent factors using Gamma-Markov chains. We propose a numerically stable Gamma chain construction, and then present a stochastic variational inference approach to estimate the parameters of our model. We apply our model to time-stamped ratings data sets: Netflix, Yelp, and Last.fm,

In my previous post, we saw that R-squared can lead to a misleading interpretation of the quality of our regression fit, in terms of prediction power. One thing that R-squared offers no protection against is overfitting. On the other hand, cross validation, by allowing us to have cases in our testing set that are different from the cases in our training set, inherently offers protection against overfittting. In this type of validation, one case in our data set is used as the test set, while the remaining cases are used as the training set. We iterate through the data set, until all cases have served as the test set.

Extracting actionable intelligence from distributed, heterogeneous, correlated and high-dimensional data sources requires run-time processing and learning both locally and globally. In the last decade, a large number of meta-learning techniques have been proposed in which local learners make online predictions based on their locally-collected data instances, and feed these predictions to an ensemble learner, which fuses them and issues a global prediction. However, most of these works do not provide performance guarantees or, when they do, these guarantees are asymptotic. None of these existing works provide confidence estimates about the issued predictions or rate of learning guarantees for the ensemble learner. In this paper, we provide a systematic ensemble learning method called Hedged Bandits, which comes with both long run (asymptotic) and short run (rate of learning) performance guarantees. Moreover, our approach yields performance guarantees with respect to the optimal local prediction strategy, and is also able to adapt its predictions in a data-driven manner. We illustrate the performance of Hedged Bandits in the context of medical informatics and show that it outperforms numerous online and offline ensemble learning methods.

A recent Compliance Week story on how artificial intelligence could revolutionize compliance depicted how technology firms "are offering software platforms that promise to automate otherwise routine tasks and improve upon fraud detection audits, anti-money laundering protocols, and know-your-customer screening." With the advent of cyber-security attacks, developers of advanced artificial intelligence security monitoring solutions have also emerged. However, understanding when and how often monitoring solutions should be executed presents trade-offs to be considered. Legacy approaches to risk monitoring look for recognized threats by known signatures and pre-built event detection logic. Often these standby methods rest on technology confines and as a result are not aligned to business risk.