In my previous post “ Bayesian Optimization”, I demonstrated the optimization procedure based on Bayesian method. 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”. There are several ways to solve the cold start problem, and mostly often used methods include random search and Latin Hypercube sampling. 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. In this article, I will show you how to implement the Latin Hypercube sampling method with SAS/IML. 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. To illustrate the algorithm, here we use a two-dimensional data’s sampling as an example. In order to obtain a Latin hypercube sample of size T from the two-dimensional space, we devise the following algorithm:ġ. Divide the interval of each dimension into T equally spaced subintervals.Ģ. Latin hypercube sampling is suggested as a tool to improve the efficiency of different importance sampling methods for structural reliability analysis. Randomly sample two points Eta and Nu within each subinterval. Call them Eta(i) and Nu(i) when they are sampled from the interval(i), that is from [(i-1)/T, i/T).ģ. 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. Now, refrain j from further consideration. Increase i by 1 and repeat step 3 until all the Eta(i) are considered. 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). 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. In this example table, there are 5 hyperparameters. %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. LatinHyperCubeSamp(seed=0, sampleSize, designTable, resultTable) The function latinHyperCubeSamp has four parameters. The first parameter is random seed and its default value is 0, which uses the clock time as the seed. The second parameter is the size of the sample. The third parameter is the table name of your design table. 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. To check the sampling result, I created a plot to show all sample points. How to Convert Date of Birth to Age in Excel (With Examples) January 17, 2023. Excel Google Sheets MongoDB Python R SAS SPSS Stata TI-84 All. There are 20 sample points displayed as dots, and each axis draws 20 grid lines to show its subintervals. Latin hypercube sampling is a method that can be used to sample random numbers in which samples are distributed evenly over a sample space. #LATIN HYPERCUBE SAMPLING EXCEL HOW TO#Īutomate from Excel: Deterministic Analysis.Bolt Properties in a Probabilistic Analysis.From the figure, we can see that each subinterval has one sample point only.Used for budgeting, allocation, scheduling, and more. Combines Monte Carlo simulation with sophisticated optimization techniques to find optimal solutions to uncertain problems.
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