Recent work in scalable approximate Gaussian process regression has discussed a bias-variance-computation trade-off when estimating the log marginal likelihood. We suggest a method that adaptively selects the amount of computation to use when estimating the log marginal likelihood so that the bias of the objective function is guaranteed to be small. While simple in principle, our current implementation of the method is not competitive computationally with existing approximations.
Shanghai Jiao Tong University（上海交通大学）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；University of the Chinese Academy of Sciences（中国科学院大学）；Key Lab for Astrophysics（天体物理重点实验室）
The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm retains the attractive properties of the standard GP as a nonparametric and flexible regression method, it can greatly improve the model accuracy for contaminated data even in the presence of extreme or abundant outliers. It is also easier to implement compared with previous robust GP variants that rely on approximate inference. Applied to a wide range of expe…
Robust Gaussian Process Regression with a Bias Model
Florida State University（佛罗里达州立大学）；University of Dayton Research Institute（代顿大学研究院）；Air Force Research Laboratory（空军研究实验室）；Luna Innovations Incorporated（露娜创新公司）
Double logistic regression approach to biased positive-unlabeled data
University of Life Sciences, Warsaw（华沙生命科学大学）；Polish Academy of Sciences（波兰科学院）；Warsaw University of Technology（华沙理工大学）；Nicolaus Copernicus University（哥白尼大学）
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）
Regression Analysis of Dependent Binary Data for Estimating Disease Etiology from Case-Control Studies
在大规模疾病病因学研究中，流行病学家经常需要使用未观察到的疾病原因的多个二元指标，这些指标并不完全敏感或特异，以估计病因特异性病例分数，称为“群体病因分数”（PEF）。尽管最近的方法的进步，科学需要纳入控制数据，以估计解释变量的影响后的PEFs，但是，仍然没有得到满足。在本文中，我们建立并扩展了嵌套部分潜在类模型（npLCMs，Wu et al.，2017）为病例对照研究中病因学回归分析的一般框架。来自对照组的数据提供了有关测量特异性和协变的必要信息，用于正确分配每个病例的特定原因概率。我们通过一个单独的回归模型估计控制的诊断措施的协变量的分布和先验鼓励更简单的条件依赖结构。我们使用马尔可夫链蒙特卡罗的后验推断的PEF功能，案件的潜在类别和政策利益的整体PEF。我们说明了回归分析与模拟，并显示出更少的偏差估计和更有效的推断比npLCM分析省略协变量的整体PEFs。一项对儿童肺炎研究中心数据的回归分析揭示了肺炎病因对季节、年龄、疾病严重程度和HIV状态的依赖性。
Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed covariates modeling the mean of the response are correlated with the spatial random effect. As a result, estimates for regression coefficients of the covariates can be severely biased and interpretation of these is no longer valid. Recent literature has shown that typical solutions for reducing spatial confounding can lead to misleading and counterintuitive …
Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cases where the target functions to be approximated exhibit high-frequency or multi-scale features. In this work we investigate this limitation through the lens of Neural Tangent Kernel (NTK) theory and elucidate how PINNs are biased towards learning functions along the dominant eigen-directions of their limiting NTK. Using this observation, we construct novel architectures that employ spatio-temporal and multi-scale ra…
Kyoto University（京都大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；The Institute of Statistical Mathematics（统计数学研究所）；NOMURA Asset Management Co., Ltd.（野村资产管理株式会社）
For supervised classification problems, this paper considers estimating the query's label probability through local regression using observed covariates. Well-known nonparametric kernel smoother and $k$-nearest neighbor ($k$-NN) estimator, which take label average over a ball around the query, are consistent but asymptotically biased particularly for a large radius of the ball. To eradicate such bias, local polynomial regression (LPoR) and multiscale $k$-NN (MS-$k$-NN) learn the bias term by local regression around the query and extrapolate it to the query itself. However, their theoretical op…
A data set sampled from a certain population is biased if the subgroups of the population are sampled at proportions that are significantly different from their underlying proportions. Training machine learning models on biased data sets requires correction techniques to compensate for the bias. We consider two commonly-used techniques, resampling and reweighting, that rebalance the proportions of the subgroups to maintain the desired objective function. Though statistically equivalent, it has been observed that resampling outperforms reweighting when combined with stochastic gradient algorith…
Analysis of overfitting in the regularized Cox model
Institute for Mathematical and Molecular Biomedicine, King’s College London（伦敦国王学院数学与分子生物医学研究所）；King’s College London（伦敦国王学院）；Saddle Point Science Ltd（鞍点科学有限公司）
