#LATIN HYPERCUBE SAMPLING HOW TO#

There are 20 sample points displayed as dots, and each axis draws 20 grid lines to show its subintervals. To check the sampling result, I created a plot to show all sample points. Run latinHyperCubeSamp(0, 20, designTable, 'lhsExampleResult1') The last parameter is the table name where to save the sampling result.Įxample 1 - Draw sample from two parameters. The third parameter is the table name of your design table. The second parameter is the size of the sample. The first parameter is random seed and its default value is 0, which uses the clock time as the seed. Enter Latin Hypercube sampling, which arises as a generalization of the Latin Square to n-th dimensional space: by splitting an Nth-dimensional problem into M probabilistically equivalent subsets of N-space and filling those spaces with M samples, a near-random distribution across the space is possible. LatinHyperCubeSamp(seed=0, sampleSize, designTable, resultTable) The function latinHyperCubeSamp has four parameters. %latinHyperCubeSamp run latinHyperCubeSamp ( 0, 20, designTable, 'lhsExampleResult1') Column minValue saves minimum and column maxValue saves maximum.Ģ) Add the following two lines to your IML Proc code. In this example table, there are 5 hyperparameters. SelectedFlag = 1 /* refrain j from further consideration */Ĭall TableWriteToDataSet( tbl, resultTable) ġ) Create a design table to specify the name, minimum and maximum of each hyperparameter. SelectedFlag = j(dimension, sampleSize, 0) Intervals = do(minValue, maxValue, (maxValue-minValue)/sampleSize) Įta= intervals + uniform(seed)*(maxValue-minValue)/sampleSize Start latinHyperCubeSamp( seed= 0, sampleSize, designTable, resultTable) SAS Implementation %macro latinHyperCubeSamp This gives us a Latin hypercube sample that we label as x(1). Increase i by 1 and repeat step 3 until all the Eta(i) are considered. Now, refrain j from further consideration. Pick an integer j at random such that 1 <= j <= T and let x(i) = (Eta(i), Nu(j)) be the first point in the Latin hypercube sample. Call them Eta(i) and Nu(i) when they are sampled from the interval(i), that is from [(i-1)/T, i/T).ģ. Randomly sample two points Eta and Nu within each subinterval. Divide the interval of each dimension into T equally spaced subintervals.Ģ. In order to obtain a Latin hypercube sample of size T from the two-dimensional space, we devise the following algorithm:ġ.

To illustrate the algorithm, here we use a two-dimensional data’s sampling as an example. The algorithm I used is from the paper Bayes Factors for Variance Components in the Mixed Linear Model, but in my implementation, I extended the algorithm to support any-dimensional data’s sampling, and the value space of hyperparameters does not limit to unit space.

#LATIN HYPERCUBE SAMPLING HOW TO#

In this article, I will show you how to implement the Latin Hypercube sampling method with SAS/IML. Some research shows that Latin Hypercube sampling performs better than random search and SAS Visual Data Mining and Machine Learning uses Latin Hypercube sampling to generate the initial set of hyperparameters configurations. There are several ways to solve the cold start problem, and mostly often used methods include random search and Latin Hypercube sampling. However, Bayesian optimization has an issue of determining the initial samples in order to kick off the optimization process, and we call this issue “code start”. This funding is gratefully acknowledged.In my previous post “ Bayesian Optimization”, I demonstrated the optimization procedure based on Bayesian method. The project has been funded by Pacific Institute for Climate Solutions, Natural Resources Canada and Natural Sciences and Engineering Research Council of Canada. This submission is developed for 2060 Project at the Institute for Integrated Energy Systems at the University of Victoria, Canada. Please subscribe to my signal processing channel to see more tutorials: Random Sampling - Tutorial 5 - Monte Carlo Vs. This work examines state-of-the-art sampling schemes categorized in space-filling-optimal designs such as Latin Hypercube sampling and L1-optical sampling and compares their empirical performance against standard random sampling to observe strong differences in the convergence properties of the methods. Random Sampling - Tutorial 4 - Latin Hypercube Sampling Random Sampling - Tutorial 3 - Monte Carlo Example Random Sampling - Tutorial 2 - Monte Carlo Random Sampling - Tutorial 1 - Introduction Please watch the following short tutorials to quickly learn random sampling (Monte Carlo Vs. To learn more about this function, please watch the following tutorial: This function is developed to generate different realizations of correlated random variables using Latin hypercube sampling method.