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The fundamentals for Reproducing Kernel Hilbert Spaces (RKHS) regression methods are described in this chapter. We first point out the virtues of RKHS regression methods and why these methods are gaining a lot of acceptance in statistical machine learnin
We also benchmarked runtime and memory usage on an scRNA-seq dataset of 100,000 cells reprogramming from MEFs to iEPs49(Fig.5dand Supplementary Note2). It took CellRank about 33 s to compute macrostates from this large dataset (Supplementary Table1). For fate probabilities, the (generali...
the kernel returns its inner product of the vector spaces. That’s all we need from the higher vector space. And for any number of dimensions whatsoever, the inner product returns a scalar. Kernels, therefore, helps you calculate the inner product of the higher vector space without you knowin...
// sample length arma::mat X = arma::randn(n_samp,n_dim); arma::vec theta_0 = 1.0 + 3.0*arma::randu(n_dim,1); arma::vec mu = sigm(X*theta_0); arma::vec Y(n_samp); for (int i=0; i < n_samp; i++) { Y(i) = ( arma::as_scalar(arma::randu(1)) < mu(i...
have been developed in the statistical literature. The contribution of this paper is to focus on the study of the local linear nonparametric estimation of the quantile of a scalar response variable given a functional covariate. In fact, the covariate is a random variable taking values in a semi...
The constraints indicate that for every xj in the triplets, the distance to the closest point xi with the same label is less than the distance to xk with a different label. The scalar “1” on the right side is arbitrary because all elements in PA can be scaled up and down in exact ...
A crucial step in the training process is the generation of the training datasets which provide a representative sampling of the multidimensional space of interest. For most of the ML regression methods, the computational effort needed to achieve a certain accuracy strongly depends on the size of ...
Interpretation using predictions is more informative I think of regression coefficients as "nuisance parameters" 3. Methods of interpretation must be practical 4. margins makes hard things easy, very hard things merely hard 5. Hopefully, Stata 15 will make impossible things possible 84 / 87 ...