This paper gives optimal algorithms for determining realvalued univariate unimodal regressions, that is, for determining the optimal regression which is increasing and then decreasing. Such regressions arise in a wide variety of applications. They are shape-constrained nonparametric regressions, closely related to isotonic regression. For unimodal regression on weighted points our algorithm for...

Abstract Twin neural network regression (TNNR) is trained to predict differences between the target values of two different data points rather than targets themselves. By ensembling predicted an unseen point and all training points, it possible obtain a very accurate prediction for original problem. Since any loop should sum zero, loops can be supplied data, even if themselves within are unlabe...

The mode of a distribution provides an important summary of data and is often estimated based on some non-parametric kernel density estimator. This article develops a new data analysis tool called modal linear regression in order to explore highdimensional data. Modal linear regression models the conditional mode of a response Y given a set of predictors x as a linear function of x. Modal linea...

Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the upper and lower tails. This paper develops a theory of quantile regression in the tails. Specifically , it obtains the large sample properties of extremal (ext...