Sentence examples for exceeds sample size from inspiring English sources

Many modern genomic data analyses require implementing regressions where the number of parameters (p, e.g., the number of marker effects) exceeds sample size (n).

However, to produce stable and high-quality outputs, variable selection methods are highly recommended, when the number of markers vastly exceeds sample size.

However, when the marker matrix X was fed into the ANN, so the number of features greatly exceeded sample size, Pearson's correlation coefficients in the cross-validation runs depended tightly on the number of neurons used in the hidden layer of the network.

In this article, we consider testing problems in high-dimensional MANOVA where the number of variables exceeds the sample size.

Often the number of response variables vastly exceeds the sample size and well-established techniques such as multivariate analysis of variance (MANOVA) cannot be used to analyze the data.

In particular, the square root loss function facilitates the choice of regularization parameters based on the noise level that is critically difficult to estimate as the number of variables increases; the nonconvex penalty is shown to be superior over the convex penalty in terms of selection consistency especially when the number of variables exceeds the sample size.

Such an estimator can handle multicollinear or singular design matrices even when the number of covariates exceeds the sample size, and can shrink the coefficient estimates of irrelevant covariates towards zero, which makes it useful for nonlinear regressions via basis expansions.

We consider a high-dimensional model where the number of regressors potentially exceeds the sample size but a subset of them suffices to construct a reasonable approximation to the conditional quantile function.

These methods allow to estimate α0 at the root-n rate when the total number p of other regressors, called controls, potentially exceeds the sample size n using sparsity assumptions.

The approach addresses the case where the number of variables p largely exceeds the sample size n ((p gg n)), which is common in the Big Data context.

Standard linear regression is not applicable for microarray gene expression data where the number of covariates far exceeds the sample size.