In this paper, we consider asymptotic properties of the support vector machine (SVM) in high-dimension, low-sample-size (HDLSS) settings. We show that the hard-margin linear SVM holds a consistency property in which misclassification rates tend to zero as the dimension goes to infinity under certain severe conditions. We show that the SVM is very biased in HDLSS settings and its performance is affected by the bias directly. In order to overcome such difficulties, we propose a bias-corrected SVM (BC-SVM). We show that the BC-SVM gives preferable performances in HDLSS settings. We also discuss the SVMs in multiclass HDLSS settings. Finally, we check the performance of the classifiers in actual data analyses.
Given a supervised machine learning problem where the training set has been subject to a known sampling bias, how can a model be trained to fit the original dataset? We achieve this through the Bayesian inference framework by altering the posterior distribution to account for the sampling function. We then apply this solution to binary logistic regression, and discuss scenarios where a dataset might be subject to intentional sample bias such as label imbalance. This technique is widely applicable for statistical inference on big data, from the medical sciences to image recognition to marketing…
A Systematic Bias of Machine Learning Regression Models and Its Correction: an Application to Imaging-based Brain Age Prediction
University of Maryland（马里兰大学）；School of Medicine（医学院）；Maryland Psychiatric Research Center（马里兰精神病研究中心）；The University of Maryland Institute for Health Computing (UM-IHC)（马里兰大学健康计算研究所）
Computer Vision Lab, ETH Zürich（苏黎世联邦理工学院计算机视觉实验室）
Undersampling the k-space in MRI allows saving precious acquisition time, yet results in an ill-posed inversion problem. Recently, many deep learning techniques have been developed, addressing this issue of recovering the fully sampled MR image from the undersampled data. However, these learning based schemes are susceptible to differences between the training data and the image to be reconstructed at test time. One such difference can be attributed to the bias field present in MR images, caused by field inhomogeneities and coil sensitivities. In this work, we address the sensitivity of the re…
Physen-Noise2Noise: Physics-Guided Self-Supervised Defocus Deblurring with Bias Correction under Low-Light Conditions
School of Mathematics and Statistics, Central South University（数学与统计学学院，中南大学）；Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education, Hunan Provincial Key Laboratory of Low-Dimensional Structural Physics and Devices, School of Physics and Electronics, Hunan University（教育部微/纳米光电器件重点实验室，湖南省低维结构物理与器件重点实验室，物理与电子学院，湖南大学）
Varying domains and biased datasets can lead to differences between the training and the target distributions, known as covariate shift. Current approaches for alleviating this often rely on estimating the ratio of training and target probability density functions. These techniques require parameter tuning and can be unstable across different datasets. We present a new method for handling covariate shift using the empirical cumulative distribution function estimates of the target distribution by a rigorous generalization of a recent idea proposed by Vapnik and Izmailov. Further, we show experi…
This article reviews bias-correction models for measurement error of exposure variables in the field of nutritional epidemiology. Measurement error usually attenuates estimated slope towards zero. Due to the influence of measurement error, inference of parameter estimate is conservative and confidence interval of the slope parameter is too narrow. Bias-correction in estimators and confidence intervals are of primary interest. We review the following bias-correction models: regression calibration methods, likelihood based models, missing data models, simulation based methods, nonparametric mode…
Imperial College London（帝国理工学院）；King’s College London（伦敦国王学院）；University College London（伦敦大学学院）
We derive a family of loss functions to train models in the presence of sampling bias. Examples are when the prevalence of a pathology differs from its sampling rate in the training dataset, or when a machine learning practioner rebalances their training dataset. Sampling bias causes large discrepancies between model performance in the lab and in more realistic settings. It is omnipresent in medical imaging applications, yet is often overlooked at training time or addressed on an ad-hoc basis. Our approach is based on Bayesian risk minimization. For arbitrary likelihood models we derive the as…
