Optimize Regression Tree on Tall Array

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Optimize hyperparameters of a regression tree automatically using a tall array. The sample data set is the carsmall data set. This example converts the data set to a tall array and uses it to run the optimization procedure.

When you perform calculations on tall arrays, MATLAB® uses either a parallel pool (default if you have Parallel Computing Toolbox™) or the local MATLAB session. If you want to run the example using the local MATLAB session when you have Parallel Computing Toolbox, you can change the global execution environment by using the mapreducer function.

Load the carsmall data set. Consider Displacement, Horsepower, and Weight as predictors of the response MPG.

load carsmall
X = [Displacement Horsepower Weight];

Convert the in-memory arrays X and MPG to tall arrays.

tx = tall(X);
ty = tall(MPG);

Optimize hyperparameters automatically using the OptimizeHyperparameters name-value argument. Find the optimal MinLeafSize value that minimizes holdout cross-validation loss. (Specifying "auto" uses MinLeafSize.) For reproducibility, use the "expected-improvement-plus" acquisition function and set the seeds of the random number generators using rng and tallrng. The results can vary depending on the number of workers and the execution environment for the tall arrays. For details, see Control Where Your Code Runs.

rng("default") 
tallrng("default")
[Mdl,~,HyperparameterOptimizationResults] = fitrtree(tx,ty, ...
OptimizeHyperparameters="auto", ...
HyperparameterOptimizationOptions=struct(Holdout=0.3, ...
AcquisitionFunctionName="expected-improvement-plus"))

Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 24 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 1.9 sec
|======================================================================================|
| Iter | Eval   | Objective:  | Objective   | BestSoFar   | BestSoFar   |  MinLeafSize |
|      | result | log(1+loss) | runtime     | (observed)  | (estim.)    |              |
|======================================================================================|
|    1 | Best   |      3.2007 |      146.85 |      3.2007 |      3.2007 |            2 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 21 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 8.8 sec
Evaluation completed in 11 sec
|    2 | Error  |         NaN |      35.424 |         NaN |      3.2007 |           46 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 3.2 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 16 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.2 sec
Evaluation completed in 1.6 sec
|    3 | Best   |      3.1876 |      90.147 |      3.1876 |      3.1884 |           18 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 1.3 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 27 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 13 sec
Evaluation completed in 14 sec
|    4 | Best   |      2.9048 |      86.663 |      2.9048 |      2.9537 |            6 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 7.1 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 20 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 3.2 sec
|    5 | Accept |      3.2895 |      80.469 |      2.9048 |      2.9048 |           15 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 2.9 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 18 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 21 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 2.7 sec
|    6 | Accept |      3.1641 |      87.492 |      2.9048 |      3.1493 |            5 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 10 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.81 sec
Evaluation completed in 1.1 sec
|    7 | Accept |      2.9048 |      73.904 |      2.9048 |      2.9048 |            6 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 0.94 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 8.2 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 8.2 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 8.2 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 8.8 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 1.5 sec
|    8 | Accept |      2.9522 |        42.8 |      2.9048 |      2.9048 |            7 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 1.2 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 11 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 9.4 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 9.7 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 9.1 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.3 sec
Evaluation completed in 1.7 sec
|    9 | Accept |      2.9985 |       48.86 |      2.9048 |      2.9048 |            8 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 1.4 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 15 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 12 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 13 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 11 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.5 sec
|   10 | Accept |      3.0185 |       61.83 |      2.9048 |      2.9048 |           10 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 2.2 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 9.6 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 17 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.89 sec
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Evaluation completed in 16 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 5.1 sec
Evaluation completed in 5.7 sec
|   11 | Accept |      3.2895 |      55.453 |      2.9048 |      2.9048 |           14 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 3.6 sec
Evaluation completed in 4.6 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 6.5 sec
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- Pass 3 of 4: Completed in 9.6 sec
- Pass 4 of 4: Completed in 2 min 43 sec
Evaluation completed in 4 min 26 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 1 min 45 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.6 sec
Evaluation completed in 2.6 sec
|   12 | Accept |      3.4798 |      382.55 |      2.9048 |      2.9049 |           31 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 2.5 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 15 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 13 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 10 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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- Pass 4 of 4: Completed in 51 sec
Evaluation completed in 1 min 31 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 2 min 38 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 2 min 0 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 18 sec
Evaluation completed in 20 sec
|   13 | Accept |      3.2248 |      439.68 |      2.9048 |      2.9048 |            1 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 12 sec
Evaluation completed in 15 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 9.6 sec
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- Pass 4 of 4: Completed in 8.8 sec
Evaluation completed in 45 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 7 sec
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- Pass 3 of 4: Completed in 21 sec
- Pass 4 of 4: Completed in 39 sec
Evaluation completed in 1 min 35 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 17 sec
- Pass 2 of 4: Completed in 52 sec
- Pass 3 of 4: Completed in 24 sec
- Pass 4 of 4: Completed in 1 min 11 sec
Evaluation completed in 3 min 8 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 29 sec
- Pass 2 of 4: Completed in 8.4 sec
- Pass 3 of 4: Completed in 6.4 sec
- Pass 4 of 4: Completed in 7.5 sec
Evaluation completed in 59 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 20 sec
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Evaluation completed in 1 min 40 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 2.7 sec
Evaluation completed in 3.2 sec
|   14 | Accept |      3.1498 |      514.07 |      2.9048 |      2.9048 |            3 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 2 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 10 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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- Pass 4 of 4: Completed in 3.1 sec
Evaluation completed in 13 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 1.9 sec
- Pass 2 of 4: Completed in 3.6 sec
- Pass 3 of 4: Completed in 6.6 sec
- Pass 4 of 4: Completed in 3.9 sec
Evaluation completed in 19 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 2.2 sec
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- Pass 3 of 4: Completed in 5.5 sec
- Pass 4 of 4: Completed in 4.9 sec
Evaluation completed in 18 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 4.6 sec
Evaluation completed in 5.1 sec
|   15 | Accept |      2.9048 |      73.371 |      2.9048 |      2.9048 |            6 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 4 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 15 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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- Pass 4 of 4: Completed in 3.6 sec
Evaluation completed in 15 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.89 sec
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Evaluation completed in 10 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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- Pass 4 of 4: Completed in 2.4 sec
Evaluation completed in 9.7 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.3 sec
Evaluation completed in 1.6 sec
|   16 | Accept |      2.9048 |       62.61 |      2.9048 |      2.9048 |            6 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.75 sec
Evaluation completed in 1.1 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.93 sec
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Evaluation completed in 10 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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- Pass 4 of 4: Completed in 3.3 sec
Evaluation completed in 14 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.5 sec
Evaluation completed in 2 sec
|   17 | Accept |      3.1847 |      30.961 |      2.9048 |      2.9048 |           23 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.2 sec
Evaluation completed in 1.6 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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- Pass 3 of 4: Completed in 3.6 sec
- Pass 4 of 4: Completed in 2.5 sec
Evaluation completed in 11 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.63 sec
- Pass 2 of 4: Completed in 1.9 sec
- Pass 3 of 4: Completed in 3.1 sec
- Pass 4 of 4: Completed in 1.7 sec
Evaluation completed in 8.4 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 1.3 sec
- Pass 2 of 4: Completed in 2 sec
- Pass 3 of 4: Completed in 2.6 sec
- Pass 4 of 4: Completed in 2 sec
Evaluation completed in 8.9 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.62 sec
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- Pass 3 of 4: Completed in 2.6 sec
- Pass 4 of 4: Completed in 1.7 sec
Evaluation completed in 7.5 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.67 sec
Evaluation completed in 0.97 sec
|   18 | Accept |      3.1817 |      45.083 |      2.9048 |      2.9048 |            4 |
Evaluating tall expression using the Parallel Pool 'Processes':
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Evaluation completed in 0.82 sec
Evaluating tall expression using the Parallel Pool 'Processes':
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- Pass 4 of 4: Completed in 2.7 sec
Evaluation completed in 8.4 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.73 sec
Evaluation completed in 1.1 sec
|   19 | Error  |         NaN |      12.301 |      2.9048 |      2.9048 |           38 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.49 sec
Evaluation completed in 0.84 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.69 sec
- Pass 2 of 4: Completed in 1.9 sec
- Pass 3 of 4: Completed in 3.5 sec
- Pass 4 of 4: Completed in 1.9 sec
Evaluation completed in 8.9 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.64 sec
- Pass 2 of 4: Completed in 1.6 sec
- Pass 3 of 4: Completed in 2.7 sec
- Pass 4 of 4: Completed in 1.9 sec
Evaluation completed in 7.9 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.81 sec
- Pass 2 of 4: Completed in 1.9 sec
- Pass 3 of 4: Completed in 2.6 sec
- Pass 4 of 4: Completed in 2.1 sec
Evaluation completed in 8.4 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.54 sec
- Pass 2 of 4: Completed in 1.8 sec
- Pass 3 of 4: Completed in 2.8 sec
- Pass 4 of 4: Completed in 1.8 sec
Evaluation completed in 8 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.78 sec
Evaluation completed in 1.1 sec
|   20 | Accept |      3.0628 |       42.12 |      2.9048 |      2.9048 |           12 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.61 sec
Evaluation completed in 1.1 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.62 sec
- Pass 2 of 4: Completed in 1.8 sec
- Pass 3 of 4: Completed in 2.9 sec
- Pass 4 of 4: Completed in 2.1 sec
Evaluation completed in 8.3 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 1 sec
- Pass 2 of 4: Completed in 1.6 sec
- Pass 3 of 4: Completed in 2.4 sec
- Pass 4 of 4: Completed in 1.6 sec
Evaluation completed in 7.6 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.58 sec
Evaluation completed in 0.86 sec
|======================================================================================|
| Iter | Eval   | Objective:  | Objective   | BestSoFar   | BestSoFar   |  MinLeafSize |
|      | result | log(1+loss) | runtime     | (observed)  | (estim.)    |              |
|======================================================================================|
|   21 | Accept |      3.1847 |      21.396 |      2.9048 |      2.9048 |           27 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.45 sec
Evaluation completed in 0.77 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.51 sec
- Pass 2 of 4: Completed in 1.5 sec
- Pass 3 of 4: Completed in 2.3 sec
- Pass 4 of 4: Completed in 1.6 sec
Evaluation completed in 6.7 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.52 sec
- Pass 2 of 4: Completed in 1.5 sec
- Pass 3 of 4: Completed in 2.4 sec
- Pass 4 of 4: Completed in 1.6 sec
Evaluation completed in 6.9 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.69 sec
- Pass 2 of 4: Completed in 1.5 sec
- Pass 3 of 4: Completed in 4 sec
- Pass 4 of 4: Completed in 1.6 sec
Evaluation completed in 8.5 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.51 sec
- Pass 2 of 4: Completed in 1.5 sec
- Pass 3 of 4: Completed in 2.4 sec
- Pass 4 of 4: Completed in 1.6 sec
Evaluation completed in 6.8 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.68 sec
Evaluation completed in 0.96 sec
|   22 | Accept |      3.0185 |      36.679 |      2.9048 |      2.9048 |            9 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.42 sec
Evaluation completed in 0.74 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.56 sec
- Pass 2 of 4: Completed in 1.4 sec
- Pass 3 of 4: Completed in 2.7 sec
- Pass 4 of 4: Completed in 2.1 sec
Evaluation completed in 7.6 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.63 sec
- Pass 2 of 4: Completed in 2.9 sec
- Pass 3 of 4: Completed in 2.6 sec
- Pass 4 of 4: Completed in 1.7 sec
Evaluation completed in 8.7 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.54 sec
- Pass 2 of 4: Completed in 1.5 sec
- Pass 3 of 4: Completed in 2.5 sec
- Pass 4 of 4: Completed in 2 sec
Evaluation completed in 7.3 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.67 sec
Evaluation completed in 0.99 sec
|   23 | Accept |      3.0749 |        30.6 |      2.9048 |      2.9048 |           20 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.49 sec
Evaluation completed in 0.85 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.61 sec
- Pass 2 of 4: Completed in 1.6 sec
- Pass 3 of 4: Completed in 2.5 sec
- Pass 4 of 4: Completed in 1.7 sec
Evaluation completed in 7.3 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.55 sec
- Pass 2 of 4: Completed in 1.7 sec
- Pass 3 of 4: Completed in 2.7 sec
- Pass 4 of 4: Completed in 2 sec
Evaluation completed in 7.8 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.53 sec
- Pass 2 of 4: Completed in 1.6 sec
- Pass 3 of 4: Completed in 2.5 sec
- Pass 4 of 4: Completed in 1.6 sec
Evaluation completed in 7 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.49 sec
- Pass 2 of 4: Completed in 1.4 sec
- Pass 3 of 4: Completed in 2.5 sec
- Pass 4 of 4: Completed in 1.6 sec
Evaluation completed in 6.8 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.63 sec
Evaluation completed in 0.92 sec
|   24 | Accept |      3.0628 |      37.276 |      2.9048 |      2.9048 |           11 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.48 sec
Evaluation completed in 0.81 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.5 sec
- Pass 2 of 4: Completed in 1.5 sec
- Pass 3 of 4: Completed in 2.4 sec
- Pass 4 of 4: Completed in 1.7 sec
Evaluation completed in 6.9 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.3 sec
Evaluation completed in 1.6 sec
|   25 | Error  |         NaN |      11.244 |      2.9048 |      2.9048 |           34 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.69 sec
Evaluation completed in 1.3 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.49 sec
- Pass 2 of 4: Completed in 2.6 sec
- Pass 3 of 4: Completed in 2.6 sec
- Pass 4 of 4: Completed in 2 sec
Evaluation completed in 9.2 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 1 sec
- Pass 2 of 4: Completed in 1.6 sec
- Pass 3 of 4: Completed in 2.7 sec
- Pass 4 of 4: Completed in 1.8 sec
Evaluation completed in 8.3 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.6 sec
|   26 | Accept |      3.1847 |      24.908 |      2.9048 |      2.9048 |           25 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.88 sec
Evaluation completed in 1.3 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.89 sec
- Pass 2 of 4: Completed in 2.4 sec
- Pass 3 of 4: Completed in 3.2 sec
- Pass 4 of 4: Completed in 2.1 sec
Evaluation completed in 9.9 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.71 sec
- Pass 2 of 4: Completed in 1.5 sec
- Pass 3 of 4: Completed in 3 sec
- Pass 4 of 4: Completed in 2.8 sec
Evaluation completed in 9.9 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.51 sec
- Pass 2 of 4: Completed in 1.4 sec
- Pass 3 of 4: Completed in 2.4 sec
- Pass 4 of 4: Completed in 1.7 sec
Evaluation completed in 6.9 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.72 sec
Evaluation completed in 0.99 sec
|   27 | Accept |      3.2895 |      35.461 |      2.9048 |      2.9048 |           16 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.45 sec
Evaluation completed in 0.76 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.79 sec
- Pass 2 of 4: Completed in 1.5 sec
- Pass 3 of 4: Completed in 3.3 sec
- Pass 4 of 4: Completed in 1.7 sec
Evaluation completed in 8.2 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.7 sec
- Pass 2 of 4: Completed in 1.7 sec
- Pass 3 of 4: Completed in 4 sec
- Pass 4 of 4: Completed in 2.8 sec
Evaluation completed in 10 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.78 sec
- Pass 2 of 4: Completed in 3.1 sec
- Pass 3 of 4: Completed in 2.3 sec
- Pass 4 of 4: Completed in 1.7 sec
Evaluation completed in 8.8 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.77 sec
Evaluation completed in 1 sec
|   28 | Accept |      3.2135 |      35.324 |      2.9048 |      2.9048 |           13 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.64 sec
Evaluation completed in 1 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.62 sec
- Pass 2 of 4: Completed in 2 sec
- Pass 3 of 4: Completed in 3.7 sec
- Pass 4 of 4: Completed in 2.3 sec
Evaluation completed in 9.4 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 1.1 sec
- Pass 2 of 4: Completed in 2 sec
- Pass 3 of 4: Completed in 3.3 sec
- Pass 4 of 4: Completed in 1.7 sec
Evaluation completed in 9 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.68 sec
Evaluation completed in 0.96 sec
|   29 | Accept |      3.1847 |      23.879 |      2.9048 |      2.9048 |           21 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.5 sec
Evaluation completed in 1.5 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.58 sec
- Pass 2 of 4: Completed in 2.9 sec
- Pass 3 of 4: Completed in 2.5 sec
- Pass 4 of 4: Completed in 1.6 sec
Evaluation completed in 8.5 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 4: Completed in 0.56 sec
- Pass 2 of 4: Completed in 2.5 sec
- Pass 3 of 4: Completed in 2.5 sec
- Pass 4 of 4: Completed in 3.2 sec
Evaluation completed in 9.7 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1 sec
Evaluation completed in 1.3 sec
|   30 | Accept |      3.1827 |      24.406 |      2.9048 |      2.9122 |           29 |

__________________________________________________________
Optimization completed.
MaxObjectiveEvaluations of 30 reached.
Total function evaluations: 30
Total elapsed time: 2708.2381 seconds
Total objective function evaluation time: 2693.8057

Best observed feasible point:
    MinLeafSize
    ___________

         6     

Observed objective function value = 2.9048
Estimated objective function value = 2.9122
Function evaluation time = 86.6631

Best estimated feasible point (according to models):
    MinLeafSize
    ___________

         6     

Estimated objective function value = 2.9122
Estimated function evaluation time = 70.1641

Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 2: Completed in 4.5 sec
- Pass 2 of 2: Completed in 5.6 sec
Evaluation completed in 15 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 7: Completed in 4.9 sec
- Pass 2 of 7: Completed in 3.2 sec
- Pass 3 of 7: Completed in 6.5 sec
- Pass 4 of 7: Completed in 1.1 sec
- Pass 5 of 7: Completed in 1.1 sec
- Pass 6 of 7: Completed in 1.6 sec
- Pass 7 of 7: Completed in 1.6 sec
Evaluation completed in 27 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 7: Completed in 0.36 sec
- Pass 2 of 7: Completed in 0.28 sec
- Pass 3 of 7: Completed in 0.64 sec
- Pass 4 of 7: Completed in 0.9 sec
- Pass 5 of 7: Completed in 1.7 sec
- Pass 6 of 7: Completed in 4.5 sec
- Pass 7 of 7: Completed in 22 sec
Evaluation completed in 40 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 7: Completed in 5.3 sec
- Pass 2 of 7: Completed in 0.29 sec
- Pass 3 of 7: Completed in 0.68 sec
- Pass 4 of 7: Completed in 0.93 sec
- Pass 5 of 7: Completed in 1 sec
- Pass 6 of 7: Completed in 1.9 sec
- Pass 7 of 7: Completed in 2.1 sec
Evaluation completed in 13 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 7: Completed in 0.32 sec
- Pass 2 of 7: Completed in 0.25 sec
- Pass 3 of 7: Completed in 0.77 sec
- Pass 4 of 7: Completed in 0.99 sec
- Pass 5 of 7: Completed in 2.2 sec
- Pass 6 of 7: Completed in 4.2 sec
- Pass 7 of 7: Completed in 1.8 sec
Evaluation completed in 11 sec
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 7: Completed in 0.33 sec
- Pass 2 of 7: Completed in 0.26 sec
- Pass 3 of 7: Completed in 0.74 sec
- Pass 4 of 7: Completed in 0.98 sec
- Pass 5 of 7: Completed in 1.3 sec
- Pass 6 of 7: Completed in 1.7 sec
- Pass 7 of 7: Completed in 1.6 sec
Evaluation completed in 7.9 sec

Figure contains an axes object. The axes object with title Min objective vs. Number of function evaluations, xlabel Function evaluations, ylabel Min objective contains 2 objects of type line. These objects represent Min observed objective, Estimated min objective.

Figure contains an axes object. The axes object with title Objective function model, xlabel MinLeafSize, ylabel Estimated objective function value contains 8 objects of type line. One or more of the lines displays its values using only markers These objects represent Observed points, Model mean, Model error bars, Noise error bars, Next point, Model minimum feasible.

Mdl = 
  CompactRegressionTree
             ResponseName: 'Y'
    CategoricalPredictors: []
        ResponseTransform: 'none'


  Properties, Methods

HyperparameterOptimizationResults = 
  SupervisedLearningBayesianOptimization
                      ObjectiveFcn: @createObjFcn/tallObjFcn
              VariableDescriptions: [3×1 optimizableVariable]
                           Options: [1×1 struct]
                      MinObjective: 2.9048
                   XAtMinObjective: [1×1 table]
             MinEstimatedObjective: 2.9122
          XAtMinEstimatedObjective: [1×1 table]
           NumObjectiveEvaluations: 30
                  TotalElapsedTime: 2.7082e+03
                         NextPoint: [1×1 table]
                            XTrace: [30×1 table]
                    ObjectiveTrace: [30×1 double]
                           LossFun: 'mse'
                         LossTrace: [30×1 double]
                  ConstraintsTrace: []
                     UserDataTrace: {30×1 cell}
      ObjectiveEvaluationTimeTrace: [30×1 double]
                IterationTimeTrace: [30×1 double]
                        ErrorTrace: [30×1 double]
                  FeasibilityTrace: [30×1 logical]
       FeasibilityProbabilityTrace: [30×1 double]
               IndexOfMinimumTrace: [30×1 double]
             ObjectiveMinimumTrace: [30×1 double]
    EstimatedObjectiveMinimumTrace: [30×1 double]

The trained model Mdl corresponds to the best estimated feasible point and uses the same MinLeafSize hyperparameter value.

Find the hyperparameter value used to train Mdl by using the bestPoint function. By default, bestPoint uses the same best point criterion used by fitrtree during the hyperparameter optimization ("min-visited-upper-confidence-interval"). In general, fit functions determine the best hyperparameter values based on the "min-visited-upper-confidence-interval" criterion (instead of the "min-observed" criterion) to avoid overfitting to noise in the data set.

bestEstimatedPoint = bestPoint(HyperparameterOptimizationResults)

bestEstimatedPoint=table
    MinLeafSize
    ___________

         6

Optimize Regression Tree on Tall Array

See Also

Topics