Reduce(c, lapply(seq(nrow(dt)), function(i) grnn::guess(nn, as. Gn <- grnn::smooth(grnn::learn(df), sigma = 1) lower mean and higher variance.ĭf <- ame(y = Boston, scale(Boston)) With no surprise, the performance of simple Uniform Random remains the lowest, e.g. While both Latin Hypercube and Sobol Sequence generate similar averages of CV R-squares, the variance of CV R-squares for Latin Hypercube is much lower. In the example below, three types of random numbers are applied to the hyper-parameter optimization of General Regression Neural Network (GRNN) in the 1-dimension case. The points have spatial dimension M, and there the number of points in a dataset is denoted by N. Plot(sobol_2d(100, 2019), main = " SOBOL SEQUENCE", xlab = '', ylab = '', cex = 2, col = "red") LHS is a dataset directory which collects Latin Hypercube Sampling datasets. LHS can be incorporated into an existing Monte Carlo model fairly easily, and work with. The method commonly used to reduce the number or runs necessary for a Monte Carlo simulation to achieve a reasonably accurate random distribution. Plot(latin_2d(100, 2019), main = "LATIN HYPERCUBE", xlab = '', ylab = '', cex = 2, col = "blue") Latin hypercube sampling (LHS) is a form of stratified sampling that can be applied to multiple variables. Return(randtoolbox::sobol(n, dim = 2, scrambling = 3, seed = seed)) A comparison below shows how each of three looks like in the 2-dimension data space. On the other hand, LHS covers the data space more evenly in a way similar to the Quasi Random, such as Sobol Sequence. LHS is similar to the Uniform Random in the sense that the Uniform Random number is drawn within each equal-space interval. For the N-dimension LHS with N > 1, we just need to independently repeat the 1-dimension LHS for N times and then randomly combine these sequences into a list of N-tuples. We first partition the whole data space into 10 equal intervals and then randomly select a data point from each interval. Let’s assume that we’d like to perform LHS for 10 data points in the 1-dimension data space. Latin Hypercube Sampling (LHS) is another interesting way to generate near-random sequences with a very simple idea.
In my previous post, I’ve shown the difference between the uniform pseudo random and the quasi random number generators in the hyper-parameter optimization of machine learning.