Kernel Regression Coefficients for Practical Significance

Quantitative researchers often use Student’s t-test (and its p-values) to claim that a particular regressor is important (statistically significantly) for explaining the variation in a response variable. A study is subject to the p-hacking problem when its author relies too much on formal statistical significance while ignoring the size of what is at stake. We suggest reporting estimates using nonlinear kernel regressions and the standardization of all variables to avoid p-hacking. We are filling an essential gap in the literature because p-hacking-related papers do not even mention kernel regressions or standardization. Although our methods have general applicability in all sciences, our illustrations refer to risk management for a cross-section of firms and financial management in macroeconomic time series. We estimate nonlinear, nonparametric kernel regressions for both examples to illustrate the computation of scale-free generalized partial correlation coefficients (GPCCs). We suggest supplementing the usual p-values by “practical significance” revealed by scale-free GPCCs. We show that GPCCs also yield new pseudo regression coefficients to measure each regressor’s relative (nonlinear) contribution in a kernel regression.

ROKET: Associating Somatic Mutation with Clinical Outcomes through Kernel Regression and Optimal Transport

Somatic mutations in cancer patients are inherently sparse and potentially high dimensional. Cancer patients may share the same set of deregulated biological processes perturbed by different sets of somatically mutated genes. Therefore, when assessing the associations between somatic mutations and clinical outcomes, gene-by-gene analyses is often under-powered because it does not capture the complex disease mechanisms shared across cancer patients. Rather than testing genes one by one, an intuitive approach is to aggregate somatic mutation data of multiple genes to assess the joint association. The challenge is how to aggregate such information. Building on the optimal transport method, we propose a principled approach to estimate the similarity of somatic mutation profiles of multiple genes between tumor samples, while accounting for gene-gene similarity defined by gene annotations or empirical mutational patterns. Using such similarities, we can assess the associations between somatic mutations and clinical outcomes by kernel regression. We have applied our method to analyze somatic mutation data of 17 cancer types and identified at least three cancer types harboring associations between somatic mutations and overall survival, progression-free interval or cytolytic activity.

Forecasting of Steam Coal Price Based on Robust Regularized Kernel Regression and Empirical Mode Decomposition

Aiming at the problem of difficulties in modeling the nonlinear relation in the steam coal dataset, this article proposes a forecasting method for the price of steam coal based on robust regularized kernel regression and empirical mode decomposition. By selecting the polynomial kernel function, the robust loss function and L2 regular term to construct a robust regularized kernel regression model are used. The polynomial kernel function does not depend on the kernel parameters and can mine the global rules in the dataset so that improves the forecasting stability of the kernel model. This method maps the features to the high-dimensional space by using the polynomial kernel function to transform the nonlinear law in the original feature space into linear law in the high-dimensional space and helps learn the linear law in the high-dimensional feature space by using the linear model. The Huber loss function is selected to reduce the influence of abnormal noise in the dataset on the model performance, and the L2 regular term is used to reduce the risk of model overfitting. We use the combined model based on empirical mode decomposition (EMD) and auto regressive integrated moving average (ARIMA) model to compensate for the error of robust regularized kernel regression model, thus making up for the limitations of the single forecasting model. Finally, we use the steam coal dataset to verify the proposed model and such model has an optimal evaluation index value compared to other contrast models after the model performance is evaluated as per the evaluation index such as RMSE, MAE, and mean absolute percentage error.

Kernel Regression Imputation in Manifolds via Bi-Linear Modeling: The Dynamic-MRI Case

<div>This paper introduces a non-parametric approximation framework for imputation-by-regression on data with missing entries. The proposed framework, coined kernel regression imputation in manifolds (KRIM), is built on the hypothesis that features, generated by the measured data, lie close to an unknown-to-the-user smooth manifold. The feature space, where the smooth manifold is embedded in, takes the form of a reproducing kernel Hilbert space (RKHS). Aiming at concise data descriptions, KRIM identifies a small number of ``landmark points'' to define approximating ``linear patches'' in the feature space which mimic tangent spaces to smooth manifolds. This geometric information is infused into the design through a novel bi-linear model that allows for multiple approximating RKHSs. To effect imputation-by-regression, a bi-linear inverse problem is solved by an iterative algorithm with guaranteed convergence to a stationary point of a non-convex loss function. To showcase KRIM's modularity, the application of KRIM to dynamic magnetic resonance imaging (dMRI) is detailed, where reconstruction of images from severely under-sampled dMRI data is desired. Extensive numerical tests on synthetic and real dMRI data demonstrate the superior performance of KRIM over state-of-the-art approaches under several metrics and with a small computational footprint.</div>

Detection of Outdated Sensors in Wireless Network via a New Protocol

A novel method is proposed using the nonlinear mapping with kernel functions to correctly locate the outdated sensors in a wireless sensor network (WSN). Such detection system used Cornell regression and solved via the vector support regression (VSR) plus multi-dimensional backup vector regression (MBVSR). The developed method was simplistic and effective without the need of any additional hardware for any measurement. It required only the vicinity and information of location from the anchor nodes to detect the outdated sensors. It was achieved in three stages including the measurements, kernel regression, and stepping stage. First step measured the proximity information from a given grid. The relationships between the proximity and geographic distance among the sensors’ nodes were generated in the kernel regression stage. For the stepping phase, every sensor node found its location in the distributed way via the kernel regression. Simulation results showed the robustness and high efficiency of the proposed scheme.