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Empirical investigation of multi-source cross-validation in clinical machine learning
Mar 22, 2024
Traditionally, machine learning-based clinical prediction models have been trained and evaluated on patient data from a single source, such as a hospital. Cross-validation methods can be used to estimate the accuracy of such models on new patients originating from the same source, by repeated random splitting of the data. However, such estimates tend to be highly overoptimistic when compared to accuracy obtained from deploying models to sources not represented in the dataset, such as a new hospital. The increasing availability of multi-source medical datasets provides new opportunities for obtaining more comprehensive and realistic evaluations of expected accuracy through source-level cross-validation designs. In this study, we present a systematic empirical evaluation of standard K-fold cross-validation and leave-source-out cross-validation methods in a multi-source setting. We consider the task of electrocardiogram based cardiovascular disease classification, combining and harmonizing the openly available PhysioNet CinC Challenge 2021 and the Shandong Provincial Hospital datasets for our study. Our results show that K-fold cross-validation, both on single-source and multi-source data, systemically overestimates prediction performance when the end goal is to generalize to new sources. Leave-source-out cross-validation provides more reliable performance estimates, having close to zero bias though larger variability. The evaluation highlights the dangers of obtaining misleading cross-validation results on medical data and demonstrates how these issues can be mitigated when having access to multi-source data.
Does Differentially Private Synthetic Data Lead to Synthetic Discoveries?
Mar 20, 2024
Background: Synthetic data has been proposed as a solution for sharing anonymized versions of sensitive biomedical datasets. Ideally, synthetic data should preserve the structure and statistical properties of the original data, while protecting the privacy of the individual subjects. Differential privacy (DP) is currently considered the gold standard approach for balancing this trade-off. Objectives: The aim of this study is to evaluate the Mann-Whitney U test on DP-synthetic biomedical data in terms of Type I and Type II errors, in order to establish whether statistical hypothesis testing performed on privacy preserving synthetic data is likely to lead to loss of test's validity or decreased power. Methods: We evaluate the Mann-Whitney U test on DP-synthetic data generated from real-world data, including a prostate cancer dataset (n=500) and a cardiovascular dataset (n=70 000), as well as on data drawn from two Gaussian distributions. Five different DP-synthetic data generation methods are evaluated, including two basic DP histogram release methods and MWEM, Private-PGM, and DP GAN algorithms. Conclusion: Most of the tested DP-synthetic data generation methods showed inflated Type I error, especially at privacy budget levels of $\epsilon\leq 1$. This result calls for caution when releasing and analyzing DP-synthetic data: low p-values may be obtained in statistical tests simply as a byproduct of the noise added to protect privacy. A DP smoothed histogram-based synthetic data generation method was shown to produce valid Type I error for all privacy levels tested but required a large original dataset size and a modest privacy budget ($\epsilon\geq 5$) in order to have reasonable Type II error levels.
Training neural networks with synthetic electrocardiograms
Nov 11, 2021
We present a method for training neural networks with synthetic electrocardiograms that mimic signals produced by a wearable single lead electrocardiogram monitor. We use domain randomization where the synthetic signal properties such as the waveform shape, RR-intervals and noise are varied for every training example. Models trained with synthetic data are compared to their counterparts trained with real data. Detection of r-waves in electrocardiograms recorded during different physical activities and in atrial fibrillation is used to compare the models. By allowing the randomization to increase beyond what is typically observed in the real-world data the performance is on par or superseding the performance of networks trained with real data. Experiments show robust performance with different seeds and training examples on different test sets without any test set specific tuning. The method makes possible to train neural networks using practically free-to-collect data with accurate labels without the need for manual annotations and it opens up the possibility of extending the use of synthetic data on cardiac disease classification when disease specific a priori information is used in the electrocardiogram generation. Additionally the distribution of data can be controlled eliminating class imbalances that are typically observed in health related data and additionally the generated data is inherently private.
A Link between Coding Theory and Cross-Validation with Applications
Mar 22, 2021
We study the combinatorics of cross-validation based AUC estimation under the null hypothesis that the binary class labels are exchangeable, that is, the data are randomly assigned into two classes given a fixed class proportion. In particular, we study how the estimators based on leave-pair-out cross-validation (LPOCV), in which every possible pair of data with different class labels is held out from the training set at a time, behave under the null without any prior assumptions of the learning algorithm or the data. It is shown that the maximal number of different fixed proportion label assignments on a sample of data, for which a learning algorithm can achieve zero LPOCV error, is the maximal size of a constant weight error correcting code, whose length is the sample size, weight is the number of data labeled with one, and the Hamming distance between code words is four. We then introduce the concept of a light constant weight code and show similar results for nonzero LPOCV errors. We also prove both upper and lower bounds on the maximal sizes of the light constant weight codes that are similar to the classical results for contant weight codes. These results pave the way towards the design of new LPOCV based statistical tests for the learning algorithms ability of distinguishing two classes from each other that are analogous to the classical Wilcoxon-Mann-Whitney U test for fixed functions. Behavior of some representative examples of learning algorithms and data are simulated in an experimental case study.
Generalized vec trick for fast learning of pairwise kernel models
Sep 02, 2020
Pairwise learning corresponds to the supervised learning setting where the goal is to make predictions for pairs of objects. Prominent applications include predicting drug-target or protein-protein interactions, or customer-product preferences. Several kernel functions have been proposed for incorporating prior knowledge about the relationship between the objects, when training kernel based learning methods. However, the number of training pairs n is often very large, making O(n^2) cost of constructing the pairwise kernel matrix infeasible. If each training pair x= (d,t) consists of drug d and target t, let m and q denote the number of unique drugs and targets appearing in the training pairs. In many real-world applications m,q << n, which can be used to develop computational shortcuts. Recently, a O(nm+nq) time algorithm we refer to as the generalized vec trick was introduced for training kernel methods with the Kronecker kernel. In this work, we show that a large class of pairwise kernels can be expressed as a sum of product matrices, which generalizes the result to the most commonly used pairwise kernels. This includes symmetric and anti-symmetric, metric-learning, Cartesian, ranking, as well as linear, polynomial and Gaussian kernels. In the experiments, we demonstrate how the introduced approach allows scaling pairwise kernels to much larger data sets than previously feasible, and compare the kernels on a number of biological interaction prediction tasks.
A Comparative Study of Pairwise Learning Methods based on Kernel Ridge Regression
Mar 05, 2018Many machine learning problems can be formulated as predicting labels for a pair of objects. Problems of that kind are often referred to as pairwise learning, dyadic prediction or network inference problems. During the last decade kernel methods have played a dominant role in pairwise learning. They still obtain a state-of-the-art predictive performance, but a theoretical analysis of their behavior has been underexplored in the machine learning literature. In this work we review and unify existing kernel-based algorithms that are commonly used in different pairwise learning settings, ranging from matrix filtering to zero-shot learning. To this end, we focus on closed-form efficient instantiations of Kronecker kernel ridge regression. We show that independent task kernel ridge regression, two-step kernel ridge regression and a linear matrix filter arise naturally as a special case of Kronecker kernel ridge regression, implying that all these methods implicitly minimize a squared loss. In addition, we analyze universality, consistency and spectral filtering properties. Our theoretical results provide valuable insights in assessing the advantages and limitations of existing pairwise learning methods.
Tournament Leave-pair-out Cross-validation for Receiver Operating Characteristic (ROC) Analysis
Jan 29, 2018
Receiver operating characteristic (ROC) analysis is widely used for evaluating diagnostic systems. Recent studies have shown that estimating an area under ROC curve (AUC) with standard cross-validation methods suffers from a large bias. The leave-pair-out (LPO) cross-validation has been shown to correct this bias. However, while LPO produces an almost unbiased estimate of AUC, it does not provide a ranking of the data needed for plotting and analyzing the ROC curve. In this study, we propose a new method called tournament leave-pair-out (TLPO) cross-validation. This method extends LPO by creating a tournament from pair comparisons to produce a ranking for the data. TLPO preserves the advantage of LPO for estimating AUC, while it also allows performing ROC analysis. We have shown using both synthetic and real world data that TLPO is as reliable as LPO for AUC estimation and confirmed the bias in leave-one-out cross-validation on low-dimensional data.
Fast Kronecker product kernel methods via generalized vec trick
Apr 19, 2017
Kronecker product kernel provides the standard approach in the kernel methods literature for learning from graph data, where edges are labeled and both start and end vertices have their own feature representations. The methods allow generalization to such new edges, whose start and end vertices do not appear in the training data, a setting known as zero-shot or zero-data learning. Such a setting occurs in numerous applications, including drug-target interaction prediction, collaborative filtering and information retrieval. Efficient training algorithms based on the so-called vec trick, that makes use of the special structure of the Kronecker product, are known for the case where the training data is a complete bipartite graph. In this work we generalize these results to non-complete training graphs. This allows us to derive a general framework for training Kronecker product kernel methods, as specific examples we implement Kronecker ridge regression and support vector machine algorithms. Experimental results demonstrate that the proposed approach leads to accurate models, while allowing order of magnitude improvements in training and prediction time.
Playtime Measurement with Survival Analysis
Jan 04, 2017
Maximizing product use is a central goal of many businesses, which makes retention and monetization two central analytics metrics in games. Player retention may refer to various duration variables quantifying product use: total playtime or session playtime are popular research targets, and active playtime is well-suited for subscription games. Such research often has the goal of increasing player retention or conversely decreasing player churn. Survival analysis is a framework of powerful tools well suited for retention type data. This paper contributes new methods to game analytics on how playtime can be analyzed using survival analysis without covariates. Survival and hazard estimates provide both a visual and an analytic interpretation of the playtime phenomena as a funnel type nonparametric estimate. Metrics based on the survival curve can be used to aggregate this playtime information into a single statistic. Comparison of survival curves between cohorts provides a scientific AB-test. All these methods work on censored data and enable computation of confidence intervals. This is especially important in time and sample limited data which occurs during game development. Throughout this paper, we illustrate the application of these methods to real world game development problems on the Hipster Sheep mobile game.
Efficient Pairwise Learning Using Kernel Ridge Regression: an Exact Two-Step Method
Jun 14, 2016
Pairwise learning or dyadic prediction concerns the prediction of properties for pairs of objects. It can be seen as an umbrella covering various machine learning problems such as matrix completion, collaborative filtering, multi-task learning, transfer learning, network prediction and zero-shot learning. In this work we analyze kernel-based methods for pairwise learning, with a particular focus on a recently-suggested two-step method. We show that this method offers an appealing alternative for commonly-applied Kronecker-based methods that model dyads by means of pairwise feature representations and pairwise kernels. In a series of theoretical results, we establish correspondences between the two types of methods in terms of linear algebra and spectral filtering, and we analyze their statistical consistency. In addition, the two-step method allows us to establish novel algorithmic shortcuts for efficient training and validation on very large datasets. Putting those properties together, we believe that this simple, yet powerful method can become a standard tool for many problems. Extensive experimental results for a range of practical settings are reported.