Local polynomial fitting for univariate data has been widely studied and discussed, but up until now the multivariate equivalent has often been deemed impractical, due to the so-called curse of dimensionality. Here, rather than discounting it completely, we use density as a threshold to determine where over a data range reliable multivariate smoothing is possible, whilst accepting that in large...

The multivariate multi-response (MVMR) linear regression problem is investigated, in which design matrices are Gaussian with covariance matrices Σ = ( Σ, . . . ,Σ ) for K linear regressions. The support union of K p-dimensional regression vectors (collected as columns of matrix B∗) are recovered using l1/l2-regularized Lasso. Sufficient and necessary conditions to guarantee successful recovery ...

We propose a boosting method, multivariate L2Boosting, for multivariate linear regression based on some squared error loss for multivariate data. It can be applied to multivariate linear regression with continuous responses and to vector autoregressive time series. We prove, for i.i.d. as well as time series data, that multivariate L2Boosting can consistently recover sparse high-dimensional mul...

The percentage of patients hospitalized due to hyponatremia is getting higher. Hyponatremia the deficiency sodium electrolyte in human serum. This might indulge adverse effects and also associated with longer hospital stay or mortality, if it wasnt actively treated managed. work predicts futuristic levels based on their history health problems using multilayer perceptron multivariate linear reg...