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fitrauto
Automatically select regression model with optimized hyperparameters
Since R2020b
Syntax
Description
Given predictor and response data, fitrauto automatically
tries a selection of regression model types with different hyperparameter values. By default,
the function uses Bayesian optimization to select models and their hyperparameter values, and
computes the following for each model: log(1 + valLoss), where valLoss is the cross-validation mean squared error
(MSE). After the optimization is complete, fitrauto returns the model,
trained on the entire data set, that is expected to best predict the responses for new data.
You can use the predict and loss object functions of
the returned model to predict on new data and compute the test set MSE,
respectively.
Use fitrauto when you are uncertain which model types best suit your
data. For information on alternative methods for tuning hyperparameters of regression models,
see Alternative Functionality.
If your data contains over 10,000 observations, consider using an asynchronous successive
halving algorithm (ASHA) instead of Bayesian optimization when you run
fitrauto. ASHA optimization often finds good solutions faster than
Bayesian optimization for data sets with many observations.
Mdl = fitrauto(Tbl,ResponseVarName)Mdl with tuned hyperparameters. The table
Tbl contains the predictor variables and the response variable,
where ResponseVarName is the name of the response variable.
Mdl = fitrauto(___,Name,Value)HyperparameterOptimizationOptions name-value argument to specify
whether to use Bayesian optimization (default) or an asynchronous successive halving
algorithm (ASHA). To use ASHA optimization, specify
"HyperparameterOptimizationOptions",struct("Optimizer","asha"). You
can include additional fields in the structure to control other aspects of the
optimization.
[
also returns Mdl,OptimizationResults] = fitrauto(___)OptimizationResults, which contains the results of the
model selection and hyperparameter tuning process.
Examples
Automatically Select Regression Model Using Table Data
Use fitrauto to automatically select a regression model with optimized hyperparameters, given predictor and response data stored in a table.
Load Data
Load the carbig data set, which contains measurements of cars made in the 1970s and early 1980s.
load carbigCreate a table containing the predictor variables Acceleration, Displacement, and so on, as well as the response variable MPG.
cars = table(Acceleration,Displacement,Horsepower, ...
Model_Year,Origin,Weight,MPG);Remove rows of cars where the table has missing values.
cars = rmmissing(cars);
Categorize the cars based on whether they were made in the USA.
cars.Origin = categorical(cellstr(cars.Origin)); cars.Origin = mergecats(cars.Origin,["France","Japan",... "Germany","Sweden","Italy","England"],"NotUSA");
Partition Data
Partition the data into training and test sets. Use approximately 80% of the observations for the model selection and hyperparameter tuning process, and 20% of the observations to test the performance of the final model returned by fitrauto. Use cvpartition to partition the data.
rng("default") % For reproducibility of the data partition c = cvpartition(height(cars),"Holdout",0.2); trainingIdx = training(c); % Training set indices carsTrain = cars(trainingIdx,:); testIdx = test(c); % Test set indices carsTest = cars(testIdx,:);
Run fitrauto
Pass the training data to fitrauto. By default, fitrauto determines appropriate model types to try, uses Bayesian optimization to find good hyperparameter values, and returns a trained model Mdl with the best expected performance. Additionally, fitrauto provides a plot of the optimization and an iterative display of the optimization results. For more information on how to interpret these results, see Verbose Display.
Expect this process to take some time. To speed up the optimization process, consider running the optimization in parallel, if you have a Parallel Computing Toolbox™ license. To do so, pass "HyperparameterOptimizationOptions",struct("UseParallel",true) to fitrauto as a name-value argument.
Mdl = fitrauto(carsTrain,"MPG");Learner types to explore: ensemble, svm, tree Total iterations (MaxObjectiveEvaluations): 90 Total time (MaxTime): Inf |================================================================================================================================================| | Iter | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| validation loss | validation loss | | | |================================================================================================================================================| | 1 | Best | 3.3416 | 0.1617 | 3.3416 | 3.3416 | tree | MinLeafSize: 118 | | 2 | Accept | 4.1303 | 0.10689 | 3.3416 | 3.3416 | svm | BoxConstraint: 16.579 | | | | | | | | | KernelScale: 0.0045538 | | | | | | | | | Epsilon: 657.79 | | 3 | Best | 2.5197 | 0.077313 | 2.5197 | 2.6121 | tree | MinLeafSize: 2 | | 4 | Best | 2.3335 | 4.6922 | 2.3335 | 2.3335 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 291 | | | | | | | | | MinLeafSize: 9 | | 5 | Accept | 2.3398 | 3.1524 | 2.3335 | 2.3366 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 206 | | | | | | | | | MinLeafSize: 13 | | 6 | Best | 2.204 | 4.9207 | 2.204 | 2.2049 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 256 | | | | | | | | | MinLeafSize: 12 | | 7 | Accept | 4.1303 | 0.055823 | 2.204 | 2.2049 | svm | BoxConstraint: 0.0048178 | | | | | | | | | KernelScale: 0.011576 | | | | | | | | | Epsilon: 441.39 | | 8 | Accept | 2.4787 | 0.060431 | 2.204 | 2.2049 | tree | MinLeafSize: 9 | | 9 | Accept | 4.1303 | 0.03731 | 2.204 | 2.2049 | svm | BoxConstraint: 8.581 | | | | | | | | | KernelScale: 61.095 | | | | | | | | | Epsilon: 296.69 | | 10 | Accept | 4.1303 | 0.035203 | 2.204 | 2.2049 | svm | BoxConstraint: 140.96 | | | | | | | | | KernelScale: 0.012197 | | | | | | | | | Epsilon: 69.002 | | 11 | Accept | 2.9157 | 0.035004 | 2.204 | 2.2049 | tree | MinLeafSize: 32 | | 12 | Accept | 3.2199 | 0.033218 | 2.204 | 2.2049 | tree | MinLeafSize: 64 | | 13 | Accept | 2.4157 | 0.038466 | 2.204 | 2.2049 | tree | MinLeafSize: 4 | | 14 | Accept | 4.1303 | 0.039282 | 2.204 | 2.2049 | svm | BoxConstraint: 1.3859 | | | | | | | | | KernelScale: 71.061 | | | | | | | | | Epsilon: 181.44 | | 15 | Accept | 3.4156 | 0.032522 | 2.204 | 2.2049 | tree | MinLeafSize: 102 | | 16 | Accept | 2.5197 | 0.042514 | 2.204 | 2.2049 | tree | MinLeafSize: 2 | | 17 | Accept | 5.4306 | 23.255 | 2.204 | 2.2049 | svm | BoxConstraint: 0.0018102 | | | | | | | | | KernelScale: 0.016815 | | | | | | | | | Epsilon: 8.1687 | | 18 | Accept | 3.1121 | 4.0538 | 2.204 | 2.2042 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 288 | | | | | | | | | MinLeafSize: 106 | | 19 | Best | 2.1971 | 4.4769 | 2.1971 | 2.1972 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 227 | | | | | | | | | MinLeafSize: 2 | | 20 | Best | 2.1971 | 4.1893 | 2.1971 | 2.1972 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 223 | | | | | | | | | MinLeafSize: 2 | |================================================================================================================================================| | Iter | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| validation loss | validation loss | | | |================================================================================================================================================| | 21 | Accept | 2.2314 | 5.0182 | 2.1971 | 2.1972 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 262 | | | | | | | | | MinLeafSize: 5 | | 22 | Accept | 2.5925 | 4.2399 | 2.1971 | 2.1972 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | MinLeafSize: 39 | | 23 | Accept | 2.1971 | 5.466 | 2.1971 | 2.1972 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 285 | | | | | | | | | MinLeafSize: 2 | | 24 | Accept | 2.3352 | 1.6689 | 2.1971 | 2.1972 | svm | BoxConstraint: 2.2648 | | | | | | | | | KernelScale: 0.92531 | | | | | | | | | Epsilon: 0.51865 | | 25 | Accept | 2.9882 | 3.4342 | 2.1971 | 2.1971 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 247 | | | | | | | | | MinLeafSize: 73 | | 26 | Accept | 2.3583 | 3.7169 | 2.1971 | 2.1971 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 255 | | | | | | | | | MinLeafSize: 12 | | 27 | Accept | 2.6476 | 0.052651 | 2.1971 | 2.1971 | tree | MinLeafSize: 28 | | 28 | Accept | 2.4016 | 0.045653 | 2.1971 | 2.1971 | tree | MinLeafSize: 6 | | 29 | Accept | 3.7573 | 0.054446 | 2.1971 | 2.1971 | svm | BoxConstraint: 9.4057 | | | | | | | | | KernelScale: 100.66 | | | | | | | | | Epsilon: 0.24447 | | 30 | Accept | 2.6046 | 0.038702 | 2.1971 | 2.1971 | tree | MinLeafSize: 24 | | 31 | Accept | 2.4157 | 0.038974 | 2.1971 | 2.1971 | tree | MinLeafSize: 4 | | 32 | Accept | 4.1303 | 0.034693 | 2.1971 | 2.1971 | svm | BoxConstraint: 303.85 | | | | | | | | | KernelScale: 0.0083624 | | | | | | | | | Epsilon: 39.54 | | 33 | Accept | 4.146 | 0.039632 | 2.1971 | 2.1971 | svm | BoxConstraint: 0.16546 | | | | | | | | | KernelScale: 248.79 | | | | | | | | | Epsilon: 1.1182 | | 34 | Accept | 3.0466 | 0.035622 | 2.1971 | 2.1971 | tree | MinLeafSize: 46 | | 35 | Accept | 2.3417 | 3.6854 | 2.1971 | 2.1971 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 246 | | | | | | | | | MinLeafSize: 12 | | 36 | Accept | 2.7264 | 5.237 | 2.1971 | 2.1972 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 274 | | | | | | | | | MinLeafSize: 105 | | 37 | Accept | 2.5457 | 3.608 | 2.1971 | 2.1972 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 257 | | | | | | | | | MinLeafSize: 33 | | 38 | Accept | 2.6603 | 0.057475 | 2.1971 | 2.1972 | tree | MinLeafSize: 1 | | 39 | Accept | 2.3589 | 2.9631 | 2.1971 | 2.1972 | svm | BoxConstraint: 56.509 | | | | | | | | | KernelScale: 1.509 | | | | | | | | | Epsilon: 0.5604 | | 40 | Accept | 4.1303 | 0.037567 | 2.1971 | 2.1972 | svm | BoxConstraint: 0.001484 | | | | | | | | | KernelScale: 0.0032176 | | | | | | | | | Epsilon: 22.445 | |================================================================================================================================================| | Iter | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| validation loss | validation loss | | | |================================================================================================================================================| | 41 | Accept | 2.5507 | 0.045858 | 2.1971 | 2.1972 | tree | MinLeafSize: 15 | | 42 | Best | 2.1945 | 5.5104 | 2.1945 | 2.1966 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 289 | | | | | | | | | MinLeafSize: 6 | | 43 | Accept | 3.9788 | 0.050732 | 2.1945 | 2.1966 | svm | BoxConstraint: 31.423 | | | | | | | | | KernelScale: 0.16609 | | | | | | | | | Epsilon: 14.619 | | 44 | Accept | 4.0639 | 0.040411 | 2.1945 | 2.1966 | svm | BoxConstraint: 42.958 | | | | | | | | | KernelScale: 459.03 | | | | | | | | | Epsilon: 0.98679 | | 45 | Accept | 2.5392 | 0.037327 | 2.1945 | 2.1966 | svm | BoxConstraint: 32.844 | | | | | | | | | KernelScale: 24.244 | | | | | | | | | Epsilon: 2.8938 | | 46 | Accept | 4.1222 | 0.039989 | 2.1945 | 2.1966 | svm | BoxConstraint: 0.001348 | | | | | | | | | KernelScale: 5.1158 | | | | | | | | | Epsilon: 2.4534 | | 47 | Best | 2.1523 | 0.054429 | 2.1523 | 2.1525 | svm | BoxConstraint: 145.8 | | | | | | | | | KernelScale: 6.9661 | | | | | | | | | Epsilon: 1.692 | | 48 | Best | 2.0991 | 0.043964 | 2.0991 | 2.0991 | svm | BoxConstraint: 11.118 | | | | | | | | | KernelScale: 4.5614 | | | | | | | | | Epsilon: 0.6909 | | 49 | Accept | 2.1321 | 0.048682 | 2.0991 | 2.0991 | svm | BoxConstraint: 12.625 | | | | | | | | | KernelScale: 3.7951 | | | | | | | | | Epsilon: 1.9243 | | 50 | Accept | 2.1155 | 0.065734 | 2.0991 | 2.0988 | svm | BoxConstraint: 2.9811 | | | | | | | | | KernelScale: 2.2304 | | | | | | | | | Epsilon: 0.11742 | | 51 | Accept | 2.1127 | 0.061163 | 2.0991 | 2.0991 | svm | BoxConstraint: 4.6122 | | | | | | | | | KernelScale: 2.5002 | | | | | | | | | Epsilon: 0.24122 | | 52 | Accept | 2.3111 | 2.183 | 2.0991 | 2.099 | svm | BoxConstraint: 13.002 | | | | | | | | | KernelScale: 1.2194 | | | | | | | | | Epsilon: 0.0097793 | | 53 | Accept | 2.1329 | 0.060156 | 2.0991 | 2.0987 | svm | BoxConstraint: 81.429 | | | | | | | | | KernelScale: 5.9963 | | | | | | | | | Epsilon: 0.040814 | | 54 | Accept | 2.1395 | 0.046864 | 2.0991 | 2.0991 | svm | BoxConstraint: 43.058 | | | | | | | | | KernelScale: 8.8124 | | | | | | | | | Epsilon: 0.31232 | | 55 | Accept | 2.1268 | 0.070321 | 2.0991 | 2.0993 | svm | BoxConstraint: 18.909 | | | | | | | | | KernelScale: 3.2821 | | | | | | | | | Epsilon: 0.049352 | | 56 | Accept | 2.2052 | 5.7654 | 2.0991 | 2.0993 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 299 | | | | | | | | | MinLeafSize: 1 | | 57 | Accept | 2.1528 | 0.15163 | 2.0991 | 2.0994 | svm | BoxConstraint: 930.08 | | | | | | | | | KernelScale: 7.7684 | | | | | | | | | Epsilon: 0.15953 | | 58 | Accept | 2.1402 | 0.075441 | 2.0991 | 2.0998 | svm | BoxConstraint: 90.458 | | | | | | | | | KernelScale: 4.8465 | | | | | | | | | Epsilon: 0.16486 | | 59 | Accept | 2.169 | 0.33792 | 2.0991 | 2.0998 | svm | BoxConstraint: 838.56 | | | | | | | | | KernelScale: 4.9126 | | | | | | | | | Epsilon: 0.010297 | | 60 | Accept | 2.1441 | 0.1108 | 2.0991 | 2.1 | svm | BoxConstraint: 977.44 | | | | | | | | | KernelScale: 9.5442 | | | | | | | | | Epsilon: 0.0096251 | |================================================================================================================================================| | Iter | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| validation loss | validation loss | | | |================================================================================================================================================| | 61 | Accept | 2.3548 | 3.0057 | 2.0991 | 2.1 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 201 | | | | | | | | | MinLeafSize: 1 | | 62 | Accept | 2.134 | 0.051302 | 2.0991 | 2.1 | svm | BoxConstraint: 7.3349 | | | | | | | | | KernelScale: 4.5654 | | | | | | | | | Epsilon: 0.010146 | | 63 | Accept | 2.1198 | 0.042744 | 2.0991 | 2.1015 | svm | BoxConstraint: 9.5959 | | | | | | | | | KernelScale: 4.8771 | | | | | | | | | Epsilon: 0.19667 | | 64 | Accept | 2.1389 | 0.058507 | 2.0991 | 2.1014 | svm | BoxConstraint: 948.83 | | | | | | | | | KernelScale: 16.462 | | | | | | | | | Epsilon: 0.47562 | | 65 | Accept | 2.1122 | 0.062182 | 2.0991 | 2.1017 | svm | BoxConstraint: 1.8061 | | | | | | | | | KernelScale: 2.0447 | | | | | | | | | Epsilon: 0.010408 | | 66 | Accept | 2.1239 | 0.053398 | 2.0991 | 2.102 | svm | BoxConstraint: 3.1375 | | | | | | | | | KernelScale: 2.5109 | | | | | | | | | Epsilon: 0.012724 | | 67 | Accept | 2.1168 | 0.051692 | 2.0991 | 2.104 | svm | BoxConstraint: 15.336 | | | | | | | | | KernelScale: 3.8639 | | | | | | | | | Epsilon: 0.35151 | | 68 | Accept | 2.1262 | 0.060441 | 2.0991 | 2.1042 | svm | BoxConstraint: 619.86 | | | | | | | | | KernelScale: 12.746 | | | | | | | | | Epsilon: 0.12944 | | 69 | Accept | 2.1288 | 0.041367 | 2.0991 | 2.1087 | svm | BoxConstraint: 14.346 | | | | | | | | | KernelScale: 5.6377 | | | | | | | | | Epsilon: 1.1115 | | 70 | Accept | 2.1075 | 0.046906 | 2.0991 | 2.1073 | svm | BoxConstraint: 6.3065 | | | | | | | | | KernelScale: 3.3652 | | | | | | | | | Epsilon: 0.37711 | | 71 | Accept | 2.1122 | 0.058036 | 2.0991 | 2.1071 | svm | BoxConstraint: 0.21669 | | | | | | | | | KernelScale: 1.3771 | | | | | | | | | Epsilon: 0.010668 | | 72 | Accept | 2.1086 | 0.057236 | 2.0991 | 2.1072 | svm | BoxConstraint: 0.6199 | | | | | | | | | KernelScale: 1.6673 | | | | | | | | | Epsilon: 0.02609 | | 73 | Accept | 2.2008 | 0.20609 | 2.0991 | 2.107 | svm | BoxConstraint: 0.74478 | | | | | | | | | KernelScale: 1.1364 | | | | | | | | | Epsilon: 0.0097464 | | 74 | Accept | 2.1274 | 0.045525 | 2.0991 | 2.1075 | svm | BoxConstraint: 0.24664 | | | | | | | | | KernelScale: 1.9581 | | | | | | | | | Epsilon: 0.0095196 | | 75 | Accept | 2.1194 | 0.062398 | 2.0991 | 2.1076 | svm | BoxConstraint: 0.84673 | | | | | | | | | KernelScale: 1.6712 | | | | | | | | | Epsilon: 0.38722 | | 76 | Accept | 2.339 | 3.0245 | 2.0991 | 2.1076 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 204 | | | | | | | | | MinLeafSize: 3 | | 77 | Accept | 4.1303 | 0.045681 | 2.0991 | 2.1046 | svm | BoxConstraint: 3.6938 | | | | | | | | | KernelScale: 1.3489 | | | | | | | | | Epsilon: 883.83 | | 78 | Accept | 2.1418 | 0.063846 | 2.0991 | 2.105 | svm | BoxConstraint: 53.966 | | | | | | | | | KernelScale: 4.7398 | | | | | | | | | Epsilon: 0.0098142 | | 79 | Accept | 2.1226 | 0.068867 | 2.0991 | 2.1052 | svm | BoxConstraint: 0.21684 | | | | | | | | | KernelScale: 1.2724 | | | | | | | | | Epsilon: 0.067508 | | 80 | Accept | 2.1215 | 0.071022 | 2.0991 | 2.1054 | svm | BoxConstraint: 0.89132 | | | | | | | | | KernelScale: 1.6131 | | | | | | | | | Epsilon: 0.080329 | |================================================================================================================================================| | Iter | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| validation loss | validation loss | | | |================================================================================================================================================| | 81 | Accept | 2.1109 | 0.049506 | 2.0991 | 2.1055 | svm | BoxConstraint: 1.8778 | | | | | | | | | KernelScale: 2.3249 | | | | | | | | | Epsilon: 0.40345 | | 82 | Accept | 2.1894 | 0.047319 | 2.0991 | 2.1052 | svm | BoxConstraint: 0.0080677 | | | | | | | | | KernelScale: 0.98345 | | | | | | | | | Epsilon: 0.0098795 | | 83 | Accept | 2.1159 | 0.055132 | 2.0991 | 2.1053 | svm | BoxConstraint: 0.097667 | | | | | | | | | KernelScale: 1.4607 | | | | | | | | | Epsilon: 0.029531 | | 84 | Accept | 2.1106 | 0.047832 | 2.0991 | 2.1064 | svm | BoxConstraint: 9.7081 | | | | | | | | | KernelScale: 3.5404 | | | | | | | | | Epsilon: 0.77633 | | 85 | Accept | 2.1338 | 0.052769 | 2.0991 | 2.1065 | svm | BoxConstraint: 328.02 | | | | | | | | | KernelScale: 11.996 | | | | | | | | | Epsilon: 0.63786 | | 86 | Accept | 2.1017 | 0.046959 | 2.0991 | 2.1033 | svm | BoxConstraint: 15.397 | | | | | | | | | KernelScale: 4.4256 | | | | | | | | | Epsilon: 0.7265 | | 87 | Accept | 4.1303 | 0.036522 | 2.0991 | 2.1033 | svm | BoxConstraint: 434.58 | | | | | | | | | KernelScale: 0.0010827 | | | | | | | | | Epsilon: 0.011393 | | 88 | Accept | 2.0996 | 0.046978 | 2.0991 | 2.1017 | svm | BoxConstraint: 24.978 | | | | | | | | | KernelScale: 4.7899 | | | | | | | | | Epsilon: 0.72324 | | 89 | Accept | 2.1053 | 0.046511 | 2.0991 | 2.1025 | svm | BoxConstraint: 18.777 | | | | | | | | | KernelScale: 4.5251 | | | | | | | | | Epsilon: 0.76878 | | 90 | Accept | 2.1034 | 0.047849 | 2.0991 | 2.1026 | svm | BoxConstraint: 19.098 | | | | | | | | | KernelScale: 4.5336 | | | | | | | | | Epsilon: 0.75174 | __________________________________________________________ Optimization completed. Total iterations: 90 Total elapsed time: 136.2822 seconds Total time for training and validation: 111.4242 seconds Best observed learner is an svm model with: Learner: svm BoxConstraint: 11.118 KernelScale: 4.5614 Epsilon: 0.6909 Observed log(1 + valLoss): 2.0991 Time for training and validation: 0.043964 seconds Best estimated learner (returned model) is an svm model with: Learner: svm BoxConstraint: 15.397 KernelScale: 4.4256 Epsilon: 0.7265 Estimated log(1 + valLoss): 2.1026 Estimated time for training and validation: 0.046399 seconds Documentation for fitrauto display
The final model returned by fitrauto corresponds to the best estimated learner. Before returning the model, the function retrains it using the entire training data (carsTrain), the listed Learner (or model) type, and the displayed hyperparameter values.
Evaluate Test Set Performance
Evaluate the performance of the model on the test set. testError is based on the test set mean squared error (MSE). Smaller MSE values indicate better performance.
testMSE = loss(Mdl,carsTest,"MPG");
testError = log(1 + testMSE)testError = 2.2000
Automatically Select Regression Model Using Matrix Data
Use fitrauto to automatically select a regression model with optimized hyperparameters, given predictor and response data stored in separate variables.
Load Data
Load the carbig data set, which contains measurements of cars made in the 1970s and early 1980s.
load carbigCreate a matrix X containing the predictor variables Acceleration, Cylinders, and so on. Store the response variable MPG in the variable Y.
X = [Acceleration Cylinders Displacement Weight]; Y = MPG;
Delete rows of X and Y where either array has missing values.
R = rmmissing([X Y]); X = R(:,1:end-1); Y = R(:,end);
Create a variable indicating which predictors are categorical. Cylinders is the only categorical variable in X.
categoricalVars = [false true false false];
Partition Data
Partition the data into training and test sets. Use approximately 80% of the observations for the model selection and hyperparameter tuning process, and 20% of the observations to test the performance of the final model returned by fitrauto. Use cvpartition to partition the data.
rng("default") % For reproducibility of the partition c = cvpartition(length(Y),"Holdout",0.20); trainingIdx = training(c); % Indices for the training set XTrain = X(trainingIdx,:); YTrain = Y(trainingIdx); testIdx = test(c); % Indices for the test set XTest = X(testIdx,:); YTest = Y(testIdx);
Run fitrauto
Pass the training data to fitrauto. By default, fitrauto determines appropriate model (or learner) types to try, uses Bayesian optimization to find good hyperparameter values for those models, and returns a trained model Mdl with the best expected performance. Specify the categorical predictors, and run the optimization in parallel (requires Parallel Computing Toolbox™). Return a second output OptimizationResults that contains the details of the Bayesian optimization.
Expect this process to take some time. By default, fitrauto provides a plot of the optimization and an iterative display of the optimization results. For more information on how to interpret these results, see Verbose Display.
options = struct("UseParallel",true); [Mdl,OptimizationResults] = fitrauto(XTrain,YTrain, ... "CategoricalPredictors",categoricalVars, ... "HyperparameterOptimizationOptions",options);
Starting parallel pool (parpool) using the 'Processes' profile ... Connected to parallel pool with 8 workers. Copying objective function to workers... Done copying objective function to workers. Learner types to explore: ensemble, svm, tree Total iterations (MaxObjectiveEvaluations): 90 Total time (MaxTime): Inf |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 1 | 6 | Best | 3.1329 | 1.9788 | 3.1329 | 3.1329 | tree | MinLeafSize: 5 | | 2 | 6 | Accept | 3.1329 | 1.985 | 3.1329 | 3.1329 | tree | MinLeafSize: 5 | | 3 | 6 | Accept | 3.1539 | 1.9764 | 3.1329 | 3.1329 | tree | MinLeafSize: 9 | | 4 | 6 | Accept | 4.1701 | 2.1518 | 3.1329 | 3.1329 | svm | BoxConstraint: 0.033502 | | | | | | | | | | KernelScale: 153.38 | | | | | | | | | | Epsilon: 0.095234 | | 5 | 8 | Accept | 3.1684 | 0.72622 | 3.1329 | 3.147 | tree | MinLeafSize: 4 | | 6 | 8 | Best | 3.0322 | 0.20501 | 3.0322 | 3.0528 | svm | BoxConstraint: 0.010812 | | | | | | | | | | KernelScale: 1.2015 | | | | | | | | | | Epsilon: 0.034779 | | 7 | 8 | Accept | 3.2871 | 0.23632 | 3.0322 | 3.0528 | tree | MinLeafSize: 2 | | 8 | 8 | Accept | 4.1645 | 7.601 | 3.0322 | 3.0528 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 257 | | | | | | | | | | MinLeafSize: 154 | | 9 | 8 | Accept | 3.2871 | 0.50364 | 3.0322 | 3.0528 | tree | MinLeafSize: 2 | | 10 | 8 | Best | 2.9469 | 10.828 | 2.9469 | 2.9628 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | | MinLeafSize: 1 | | 11 | 8 | Best | 2.9388 | 10.949 | 2.9388 | 2.9413 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 288 | | | | | | | | | | MinLeafSize: 3 | | 12 | 8 | Accept | 2.9581 | 10.32 | 2.9388 | 2.9404 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | | MinLeafSize: 62 | | 13 | 7 | Accept | 2.9581 | 10.584 | 2.9388 | 2.9403 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | | MinLeafSize: 62 | | 14 | 7 | Accept | 2.9581 | 10.626 | 2.9388 | 2.9403 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | | MinLeafSize: 62 | | 15 | 8 | Accept | 3.6004 | 0.36596 | 2.9388 | 2.9403 | tree | MinLeafSize: 120 | | 16 | 8 | Accept | 3.6004 | 0.41888 | 2.9388 | 2.9403 | tree | MinLeafSize: 120 | | 17 | 8 | Accept | 3.1539 | 0.14494 | 2.9388 | 2.9403 | tree | MinLeafSize: 9 | | 18 | 7 | Best | 2.9287 | 11.356 | 2.9287 | 2.9403 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | | MinLeafSize: 16 | | 19 | 7 | Accept | 4.1645 | 1.9545 | 2.9287 | 2.9403 | svm | BoxConstraint: 159.44 | | | | | | | | | | KernelScale: 34.732 | | | | | | | | | | Epsilon: 412.2 | | 20 | 7 | Accept | 4.1862 | 0.1901 | 2.9287 | 2.9403 | svm | BoxConstraint: 7.487 | | | | | | | | | | KernelScale: 81.753 | | | | | | | | | | Epsilon: 12.782 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 21 | 7 | Accept | 4.1645 | 0.19246 | 2.9287 | 2.9403 | svm | BoxConstraint: 2.1296 | | | | | | | | | | KernelScale: 3.2623 | | | | | | | | | | Epsilon: 609.61 | | 22 | 6 | Accept | 3.9011 | 1.5706 | 2.9287 | 2.9403 | svm | BoxConstraint: 9.4057 | | | | | | | | | | KernelScale: 100.66 | | | | | | | | | | Epsilon: 0.2386 | | 23 | 6 | Accept | 3.1593 | 0.18031 | 2.9287 | 2.9403 | tree | MinLeafSize: 8 | | 24 | 7 | Accept | 2.9494 | 0.3265 | 2.9287 | 2.9403 | svm | BoxConstraint: 746.54 | | | | | | | | | | KernelScale: 5.6788 | | | | | | | | | | Epsilon: 1.0177 | | 25 | 7 | Accept | 2.9494 | 0.26551 | 2.9287 | 2.9403 | svm | BoxConstraint: 746.54 | | | | | | | | | | KernelScale: 5.6788 | | | | | | | | | | Epsilon: 1.0177 | | 26 | 7 | Accept | 9.5074 | 20.334 | 2.9287 | 2.9403 | svm | BoxConstraint: 336.91 | | | | | | | | | | KernelScale: 0.0018275 | | | | | | | | | | Epsilon: 0.10919 | | 27 | 7 | Accept | 2.9494 | 0.79583 | 2.9287 | 2.9403 | svm | BoxConstraint: 746.54 | | | | | | | | | | KernelScale: 5.6788 | | | | | | | | | | Epsilon: 1.0177 | | 28 | 6 | Best | 2.9287 | 11.352 | 2.9287 | 2.9403 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 262 | | | | | | | | | | MinLeafSize: 5 | | 29 | 6 | Accept | 3.6021 | 0.45991 | 2.9287 | 2.9403 | tree | MinLeafSize: 1 | | 30 | 5 | Accept | 3.1697 | 8.5532 | 2.9287 | 2.9403 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 247 | | | | | | | | | | MinLeafSize: 74 | | 31 | 5 | Accept | 3.1014 | 1.3678 | 2.9287 | 2.9403 | tree | MinLeafSize: 13 | | 32 | 8 | Accept | 2.9806 | 0.26062 | 2.9287 | 2.9403 | svm | BoxConstraint: 5.2568 | | | | | | | | | | KernelScale: 10.811 | | | | | | | | | | Epsilon: 0.074584 | | 33 | 8 | Accept | 4.165 | 0.13934 | 2.9287 | 2.9403 | svm | BoxConstraint: 0.18243 | | | | | | | | | | KernelScale: 128.12 | | | | | | | | | | Epsilon: 5.0924 | | 34 | 8 | Accept | 2.9351 | 11.473 | 2.9287 | 2.9288 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 282 | | | | | | | | | | MinLeafSize: 2 | | 35 | 7 | Accept | 2.9423 | 5.5429 | 2.9287 | 2.9288 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 202 | | | | | | | | | | MinLeafSize: 50 | | 36 | 7 | Accept | 3.4421 | 0.51292 | 2.9287 | 2.9288 | tree | MinLeafSize: 76 | | 37 | 8 | Accept | 2.9423 | 6.4536 | 2.9287 | 2.927 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 239 | | | | | | | | | | MinLeafSize: 50 | | 38 | 4 | Accept | 3.1708 | 10.551 | 2.8874 | 2.8928 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 274 | | | | | | | | | | MinLeafSize: 106 | | 39 | 4 | Accept | 2.9338 | 9.5391 | 2.8874 | 2.8928 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 280 | | | | | | | | | | MinLeafSize: 45 | | 40 | 4 | Accept | 2.9351 | 6.3776 | 2.8874 | 2.8928 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 233 | | | | | | | | | | MinLeafSize: 2 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 41 | 4 | Best | 2.8874 | 6.3082 | 2.8874 | 2.8928 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 271 | | | | | | | | | | MinLeafSize: 1 | | 42 | 4 | Accept | 2.8981 | 7.7345 | 2.8874 | 2.8928 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 271 | | | | | | | | | | MinLeafSize: 1 | | 43 | 8 | Accept | 3.2678 | 0.19997 | 2.8874 | 2.8928 | tree | MinLeafSize: 65 | | 44 | 5 | Best | 2.8796 | 4.3397 | 2.8796 | 2.8796 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 209 | | | | | | | | | | MinLeafSize: 4 | | 45 | 5 | Accept | 2.8803 | 5.559 | 2.8796 | 2.8796 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 250 | | | | | | | | | | MinLeafSize: 10 | | 46 | 5 | Accept | 3.2871 | 0.40833 | 2.8796 | 2.8796 | tree | MinLeafSize: 2 | | 47 | 5 | Accept | 2.9099 | 5.7828 | 2.8796 | 2.8796 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 213 | | | | | | | | | | MinLeafSize: 10 | | 48 | 8 | Accept | 2.9351 | 7.025 | 2.8796 | 2.8796 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 265 | | | | | | | | | | MinLeafSize: 2 | | 49 | 6 | Accept | 5.4316 | 20.005 | 2.8796 | 2.8796 | svm | BoxConstraint: 28.808 | | | | | | | | | | KernelScale: 0.3219 | | | | | | | | | | Epsilon: 0.13762 | | 50 | 6 | Accept | 3.1177 | 0.68844 | 2.8796 | 2.8796 | svm | BoxConstraint: 127.48 | | | | | | | | | | KernelScale: 105 | | | | | | | | | | Epsilon: 0.58941 | | 51 | 6 | Accept | 7.8524 | 0.68066 | 2.8796 | 2.8796 | svm | BoxConstraint: 3.2128 | | | | | | | | | | KernelScale: 0.0015524 | | | | | | | | | | Epsilon: 0.11513 | | 52 | 7 | Accept | 3.1329 | 0.068468 | 2.8796 | 2.8796 | tree | MinLeafSize: 5 | | 53 | 7 | Accept | 2.9597 | 0.088717 | 2.8796 | 2.8796 | svm | BoxConstraint: 990.41 | | | | | | | | | | KernelScale: 29.533 | | | | | | | | | | Epsilon: 0.015011 | | 54 | 8 | Accept | 2.9076 | 5.4054 | 2.8796 | 2.8796 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 248 | | | | | | | | | | MinLeafSize: 13 | | 55 | 8 | Accept | 4.1645 | 0.07993 | 2.8796 | 2.8796 | svm | BoxConstraint: 1.246 | | | | | | | | | | KernelScale: 0.048145 | | | | | | | | | | Epsilon: 337.42 | | 56 | 4 | Accept | 4.8948 | 27.255 | 2.8796 | 2.8796 | svm | BoxConstraint: 0.093799 | | | | | | | | | | KernelScale: 0.0053728 | | | | | | | | | | Epsilon: 17.621 | | 57 | 4 | Accept | 2.9227 | 8.5858 | 2.8796 | 2.8796 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 360 | | | | | | | | | | MinLeafSize: 9 | | 58 | 4 | Accept | 2.8934 | 5.1523 | 2.8796 | 2.8796 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 298 | | | | | | | | | | MinLeafSize: 2 | | 59 | 4 | Accept | 2.8877 | 5.7141 | 2.8796 | 2.8796 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 299 | | | | | | | | | | MinLeafSize: 2 | | 60 | 4 | Accept | 2.8982 | 5.5545 | 2.8796 | 2.8796 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 320 | | | | | | | | | | MinLeafSize: 1 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 61 | 8 | Accept | 3.0945 | 0.065636 | 2.8796 | 2.8796 | tree | MinLeafSize: 11 | | 62 | 6 | Accept | 2.8818 | 5.1985 | 2.8796 | 2.8796 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 298 | | | | | | | | | | MinLeafSize: 2 | | 63 | 6 | Accept | 4.1645 | 0.17235 | 2.8796 | 2.8796 | svm | BoxConstraint: 0.0010273 | | | | | | | | | | KernelScale: 0.24074 | | | | | | | | | | Epsilon: 280.24 | | 64 | 6 | Accept | 4.1645 | 0.069883 | 2.8796 | 2.8796 | svm | BoxConstraint: 2.4541 | | | | | | | | | | KernelScale: 5.0059 | | | | | | | | | | Epsilon: 29.021 | | 65 | 6 | Best | 2.8788 | 3.2047 | 2.8788 | 2.8785 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 223 | | | | | | | | | | MinLeafSize: 5 | | 66 | 6 | Accept | 3.1966 | 4.5298 | 2.8788 | 2.8785 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 243 | | | | | | | | | | MinLeafSize: 109 | | 67 | 6 | Accept | 4.2278 | 0.075829 | 2.8788 | 2.8785 | svm | BoxConstraint: 0.49855 | | | | | | | | | | KernelScale: 822.57 | | | | | | | | | | Epsilon: 13.604 | | 68 | 7 | Accept | 3.4183 | 0.040748 | 2.8788 | 2.8785 | tree | MinLeafSize: 93 | | 69 | 7 | Accept | 2.9682 | 0.089978 | 2.8788 | 2.8785 | svm | BoxConstraint: 990.82 | | | | | | | | | | KernelScale: 32.258 | | | | | | | | | | Epsilon: 0.65013 | | 70 | 7 | Accept | 17.606 | 16.61 | 2.8788 | 2.8785 | svm | BoxConstraint: 244.81 | | | | | | | | | | KernelScale: 0.029911 | | | | | | | | | | Epsilon: 1.3663 | | 71 | 7 | Accept | 3.2871 | 0.12707 | 2.8788 | 2.8785 | tree | MinLeafSize: 2 | | 72 | 6 | Accept | 2.8957 | 2.8051 | 2.8788 | 2.8785 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 203 | | | | | | | | | | MinLeafSize: 21 | | 73 | 6 | Accept | 4.1645 | 0.049095 | 2.8788 | 2.8785 | svm | BoxConstraint: 0.0023954 | | | | | | | | | | KernelScale: 0.0017894 | | | | | | | | | | Epsilon: 779.82 | | 74 | 7 | Accept | 4.1645 | 0.073002 | 2.8788 | 2.8785 | svm | BoxConstraint: 0.0022454 | | | | | | | | | | KernelScale: 1.2218 | | | | | | | | | | Epsilon: 1223.3 | | 75 | 6 | Accept | 3.0324 | 7.4797 | 2.8788 | 2.878 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 386 | | | | | | | | | | MinLeafSize: 74 | | 76 | 6 | Accept | 2.8964 | 3.1304 | 2.8788 | 2.878 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 222 | | | | | | | | | | MinLeafSize: 21 | | 77 | 6 | Accept | 3.1637 | 0.054723 | 2.8788 | 2.878 | tree | MinLeafSize: 6 | | 78 | 5 | Accept | 2.8986 | 2.8386 | 2.8788 | 2.878 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 204 | | | | | | | | | | MinLeafSize: 21 | | 79 | 5 | Accept | 4.1645 | 0.04896 | 2.8788 | 2.878 | svm | BoxConstraint: 0.0012664 | | | | | | | | | | KernelScale: 0.0010838 | | | | | | | | | | Epsilon: 54.909 | | 80 | 7 | Accept | 16.812 | 11.246 | 2.8788 | 2.8778 | svm | BoxConstraint: 0.071974 | | | | | | | | | | KernelScale: 0.030156 | | | | | | | | | | Epsilon: 1.0328 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 81 | 7 | Accept | 2.9388 | 7.0653 | 2.8788 | 2.8778 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 375 | | | | | | | | | | MinLeafSize: 3 | | 82 | 4 | Accept | 2.9194 | 0.056852 | 2.8788 | 2.8778 | svm | BoxConstraint: 0.49279 | | | | | | | | | | KernelScale: 1.837 | | | | | | | | | | Epsilon: 0.028024 | | 83 | 4 | Accept | 3.6021 | 0.073288 | 2.8788 | 2.8778 | tree | MinLeafSize: 1 | | 84 | 4 | Accept | 4.1645 | 0.043986 | 2.8788 | 2.8778 | svm | BoxConstraint: 0.0010569 | | | | | | | | | | KernelScale: 0.05901 | | | | | | | | | | Epsilon: 154.61 | | 85 | 4 | Accept | 4.0662 | 0.051015 | 2.8788 | 2.8778 | svm | BoxConstraint: 0.65745 | | | | | | | | | | KernelScale: 42.989 | | | | | | | | | | Epsilon: 0.018275 | | 86 | 8 | Accept | 2.8973 | 2.9559 | 2.8788 | 2.8778 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 200 | | | | | | | | | | MinLeafSize: 21 | | 87 | 6 | Accept | 3.1593 | 0.030722 | 2.8788 | 2.8778 | tree | MinLeafSize: 8 | | 88 | 6 | Accept | 4.1645 | 0.1004 | 2.8788 | 2.8778 | svm | BoxConstraint: 0.026752 | | | | | | | | | | KernelScale: 0.0090205 | | | | | | | | | | Epsilon: 234.51 | | 89 | 6 | Accept | 4.1645 | 0.085556 | 2.8788 | 2.8778 | svm | BoxConstraint: 701.89 | | | | | | | | | | KernelScale: 0.014432 | | | | | | | | | | Epsilon: 823.78 | | 90 | 7 | Accept | 3.0786 | 0.058939 | 2.8788 | 2.8778 | tree | MinLeafSize: 12 |
__________________________________________________________ Optimization completed. Total iterations: 90 Total elapsed time: 70.4919 seconds Total time for training and validation: 366.4178 seconds Best observed learner is an ensemble model with: Learner: ensemble Method: Bag NumLearningCycles: 223 MinLeafSize: 5 Observed log(1 + valLoss): 2.8788 Time for training and validation: 3.2047 seconds Best estimated learner (returned model) is an ensemble model with: Learner: ensemble Method: Bag NumLearningCycles: 223 MinLeafSize: 5 Estimated log(1 + valLoss): 2.8778 Estimated time for training and validation: 3.6185 seconds Documentation for fitrauto display
The final model returned by fitrauto corresponds to the best estimated learner. Before returning the model, the function retrains it using the entire training data (XTrain and YTrain), the listed Learner (or model) type, and the displayed hyperparameter values.
Evaluate Test Set Performance
Evaluate the performance of the model on the test set. testError is based on the test set mean squared error (MSE). Smaller MSE values indicate better performance.
testMSE = loss(Mdl,XTest,YTest); testError = log(1 + testMSE)
testError = 2.6223
Compare Optimized and Simple Linear Regression Model
Use fitrauto to automatically select a regression model with optimized hyperparameters, given predictor and response data stored in a table. Compare the performance of the resulting regression model to the performance of a simple linear regression model created with fitlm.
Load and Partition Data
Load the carbig data set, which contains measurements of cars made in the 1970s and early 1980s. Convert the Cylinders variable to a categorical variable. Create a table containing the predictor variables Acceleration, Cylinders, Displacement, and so on, as well as the response variable MPG.
load carbig Cylinders = categorical(Cylinders); cars = table(Acceleration,Cylinders,Displacement, ... Horsepower,Model_Year,Origin,Weight,MPG);
Delete rows of cars where the table has missing values.
cars = rmmissing(cars);
Categorize the cars based on whether they were made in the USA.
cars.Origin = categorical(cellstr(cars.Origin)); cars.Origin = mergecats(cars.Origin,["France","Japan",... "Germany","Sweden","Italy","England"],"NotUSA");
Partition the data into training and test sets. Use approximately 80% of the observations for training, and 20% of the observations for testing. Use cvpartition to partition the data.
rng("default") % For reproducibility of the data partition c = cvpartition(height(cars),"Holdout",0.2); trainingIdx = training(c); % Training set indices carsTrain = cars(trainingIdx,:); testIdx = test(c); % Test set indices carsTest = cars(testIdx,:);
Run fitrauto
Pass the training data to fitrauto. By default, fitrauto determines appropriate model types to try, uses Bayesian optimization to find good hyperparameter values, and returns a trained model autoMdl with the best expected performance. Specify to optimize over all optimizable hyperparameters and run the optimization in parallel (requires Parallel Computing Toolbox™).
Expect this process to take some time. By default, fitrauto provides a plot of the optimization and an iterative display of the optimization results. For more information on how to interpret these results, see Verbose Display.
options = struct("UseParallel",true); autoMdl = fitrauto(carsTrain,"MPG","OptimizeHyperparameters","all", ... "HyperparameterOptimizationOptions",options);
Starting parallel pool (parpool) using the 'Processes' profile ... Connected to parallel pool with 6 workers. Copying objective function to workers... Done copying objective function to workers. Learner types to explore: ensemble, svm, tree Total iterations (MaxObjectiveEvaluations): 90 Total time (MaxTime): Inf |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 1 | 6 | Best | 4.1303 | 3.4475 | 4.1303 | 4.1303 | svm | BoxConstraint: 0.0010671 | | | | | | | | | | KernelScale: 19.242 | | | | | | | | | | Epsilon: 44.847 | | 2 | 6 | Best | 3.1459 | 3.8766 | 3.1459 | 3.1459 | tree | MinLeafSize: 5 | | | | | | | | | | MaxNumSplits: 2 | | | | | | | | | | NumVariablesToSample: 3 | | 3 | 6 | Accept | 4.1303 | 1.4169 | 3.1459 | 3.1459 | svm | BoxConstraint: 0.73976 | | | | | | | | | | KernelScale: 2.7037 | | | | | | | | | | Epsilon: 38.421 | | 4 | 6 | Best | 2.5639 | 1.2712 | 2.5639 | 2.7048 | tree | MinLeafSize: 9 | | | | | | | | | | MaxNumSplits: 199 | | | | | | | | | | NumVariablesToSample: 5 | | 5 | 6 | Accept | 3.3002 | 0.33561 | 2.5639 | 2.564 | tree | MinLeafSize: 13 | | | | | | | | | | MaxNumSplits: 1 | | | | | | | | | | NumVariablesToSample: 4 | | 6 | 6 | Accept | 4.1303 | 0.21087 | 2.5639 | 2.564 | svm | BoxConstraint: 0.01028 | | | | | | | | | | KernelScale: 0.0032203 | | | | | | | | | | Epsilon: 36.299 | | 7 | 6 | Accept | 2.5852 | 0.41237 | 2.5639 | 2.564 | tree | MinLeafSize: 2 | | | | | | | | | | MaxNumSplits: 120 | | | | | | | | | | NumVariablesToSample: 7 | | 8 | 5 | Accept | 4.7998 | 13.852 | 2.5639 | 2.564 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0042702 | | | | | | | | | | MinLeafSize: 31 | | | | | | | | | | NumVariablesToSample: NaN | | 9 | 5 | Accept | 4.5891 | 11.084 | 2.5639 | 2.564 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0051188 | | | | | | | | | | MinLeafSize: 83 | | | | | | | | | | NumVariablesToSample: NaN | | 10 | 5 | Accept | 4.6825 | 11.581 | 2.5639 | 2.564 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0045559 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 11 | 6 | Accept | 2.6585 | 0.63223 | 2.5639 | 2.5633 | tree | MinLeafSize: 5 | | | | | | | | | | MaxNumSplits: 61 | | | | | | | | | | NumVariablesToSample: 2 | | 12 | 6 | Accept | 2.5733 | 0.69096 | 2.5639 | 2.5653 | tree | MinLeafSize: 5 | | | | | | | | | | MaxNumSplits: 61 | | | | | | | | | | NumVariablesToSample: 2 | | 13 | 6 | Best | 2.2945 | 9.4664 | 2.2945 | 2.2956 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: 4 | | 14 | 6 | Accept | 4.1303 | 0.23153 | 2.2945 | 2.2956 | svm | BoxConstraint: 27.717 | | | | | | | | | | KernelScale: 21.172 | | | | | | | | | | Epsilon: 390.93 | | 15 | 6 | Accept | 2.6405 | 7.1727 | 2.2945 | 2.2988 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 45 | | | | | | | | | | NumVariablesToSample: 6 | | 16 | 5 | Accept | 2.3432 | 7.1757 | 2.2945 | 2.1873 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: 3 | | 17 | 5 | Accept | 2.8316 | 0.32852 | 2.2945 | 2.1873 | svm | BoxConstraint: 0.038615 | | | | | | | | | | KernelScale: 0.26266 | | | | | | | | | | Epsilon: 5.8807 | | 18 | 6 | Accept | 4.1551 | 6.261 | 2.2945 | 2.3249 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.014547 | | | | | | | | | | MinLeafSize: 145 | | | | | | | | | | NumVariablesToSample: NaN | | 19 | 6 | Accept | 2.3708 | 7.183 | 2.2945 | 2.3532 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 26 | | | | | | | | | | NumVariablesToSample: 6 | | 20 | 6 | Accept | 2.5191 | 7.6483 | 2.2945 | 2.3519 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.9913 | | | | | | | | | | MinLeafSize: 4 | | | | | | | | | | NumVariablesToSample: NaN | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 21 | 5 | Accept | 2.5191 | 7.4956 | 2.2945 | 2.2937 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.9913 | | | | | | | | | | MinLeafSize: 4 | | | | | | | | | | NumVariablesToSample: NaN | | 22 | 5 | Accept | 3.1622 | 7.0091 | 2.2945 | 2.2937 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 116 | | | | | | | | | | NumVariablesToSample: 6 | | 23 | 5 | Accept | 2.6846 | 0.2699 | 2.2945 | 2.2937 | tree | MinLeafSize: 1 | | | | | | | | | | MaxNumSplits: 248 | | | | | | | | | | NumVariablesToSample: 7 | | 24 | 5 | Accept | 3.0009 | 0.13263 | 2.2945 | 2.2937 | tree | MinLeafSize: 30 | | | | | | | | | | MaxNumSplits: 21 | | | | | | | | | | NumVariablesToSample: 2 | | 25 | 5 | Accept | 2.9014 | 0.056488 | 2.2945 | 2.2937 | tree | MinLeafSize: 2 | | | | | | | | | | MaxNumSplits: 4 | | | | | | | | | | NumVariablesToSample: 4 | | 26 | 6 | Accept | 2.5073 | 4.9712 | 2.2945 | 2.2937 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 29 | | | | | | | | | | NumVariablesToSample: 3 | | 27 | 6 | Accept | 2.4723 | 0.42317 | 2.2945 | 2.2937 | tree | MinLeafSize: 9 | | | | | | | | | | MaxNumSplits: 157 | | | | | | | | | | NumVariablesToSample: 6 | | 28 | 6 | Accept | 2.5015 | 4.7606 | 2.2945 | 2.294 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 11 | | | | | | | | | | NumVariablesToSample: 1 | | 29 | 6 | Accept | 2.499 | 5.0657 | 2.2945 | 2.294 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 11 | | | | | | | | | | NumVariablesToSample: 1 | | 30 | 6 | Accept | 4.1303 | 0.16935 | 2.2945 | 2.294 | svm | BoxConstraint: 0.0011506 | | | | | | | | | | KernelScale: 352.85 | | | | | | | | | | Epsilon: 163.49 | | 31 | 5 | Accept | 2.3265 | 6.3484 | 2.2945 | 2.294 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.11482 | | | | | | | | | | MinLeafSize: 54 | | | | | | | | | | NumVariablesToSample: NaN | | 32 | 5 | Accept | 2.6676 | 0.14033 | 2.2945 | 2.294 | tree | MinLeafSize: 1 | | | | | | | | | | MaxNumSplits: 12 | | | | | | | | | | NumVariablesToSample: 4 | | 33 | 4 | Accept | 2.6931 | 1.5523 | 2.2945 | 2.294 | svm | BoxConstraint: 8.3226 | | | | | | | | | | KernelScale: 22.717 | | | | | | | | | | Epsilon: 3.2417 | | 34 | 4 | Accept | 3.3292 | 0.069533 | 2.2945 | 2.294 | tree | MinLeafSize: 72 | | | | | | | | | | MaxNumSplits: 251 | | | | | | | | | | NumVariablesToSample: 2 | | 35 | 4 | Accept | 2.7867 | 0.070147 | 2.2945 | 2.294 | tree | MinLeafSize: 4 | | | | | | | | | | MaxNumSplits: 5 | | | | | | | | | | NumVariablesToSample: 6 | | 36 | 4 | Accept | 4.1448 | 0.10004 | 2.2945 | 2.294 | svm | BoxConstraint: 1.8227 | | | | | | | | | | KernelScale: 977.3 | | | | | | | | | | Epsilon: 2.0809 | | 37 | 4 | Accept | 2.7305 | 0.071273 | 2.2945 | 2.294 | tree | MinLeafSize: 1 | | | | | | | | | | MaxNumSplits: 31 | | | | | | | | | | NumVariablesToSample: 4 | | 38 | 6 | Best | 2.1806 | 0.33042 | 2.1806 | 2.1808 | svm | BoxConstraint: 197.52 | | | | | | | | | | KernelScale: 4.7757 | | | | | | | | | | Epsilon: 0.029282 | | 39 | 6 | Accept | 2.1806 | 0.29825 | 2.1806 | 2.1807 | svm | BoxConstraint: 197.52 | | | | | | | | | | KernelScale: 4.7757 | | | | | | | | | | Epsilon: 0.029282 | | 40 | 5 | Accept | 2.1806 | 1.1365 | 2.1806 | 2.1807 | svm | BoxConstraint: 197.52 | | | | | | | | | | KernelScale: 4.7757 | | | | | | | | | | Epsilon: 0.029282 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 41 | 5 | Accept | 2.5404 | 0.11739 | 2.1806 | 2.1807 | tree | MinLeafSize: 2 | | | | | | | | | | MaxNumSplits: 257 | | | | | | | | | | NumVariablesToSample: 4 | | 42 | 6 | Accept | 2.7214 | 0.12168 | 2.1806 | 2.1807 | tree | MinLeafSize: 13 | | | | | | | | | | MaxNumSplits: 167 | | | | | | | | | | NumVariablesToSample: 3 | | 43 | 6 | Accept | 2.5848 | 0.060058 | 2.1806 | 2.1807 | tree | MinLeafSize: 17 | | | | | | | | | | MaxNumSplits: 12 | | | | | | | | | | NumVariablesToSample: 6 | | 44 | 6 | Best | 2.1759 | 0.11488 | 2.1759 | 2.1759 | svm | BoxConstraint: 0.19712 | | | | | | | | | | KernelScale: 2.8803 | | | | | | | | | | Epsilon: 0.07079 | | 45 | 6 | Accept | 4.1303 | 0.099786 | 2.1759 | 2.1758 | svm | BoxConstraint: 216.26 | | | | | | | | | | KernelScale: 0.0026892 | | | | | | | | | | Epsilon: 19.364 | | 46 | 6 | Accept | 3.2037 | 5.4636 | 2.1759 | 2.1758 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.96271 | | | | | | | | | | MinLeafSize: 116 | | | | | | | | | | NumVariablesToSample: NaN | | 47 | 6 | Accept | 4.1303 | 0.10162 | 2.1759 | 2.1759 | svm | BoxConstraint: 0.0026925 | | | | | | | | | | KernelScale: 7.0869 | | | | | | | | | | Epsilon: 24.319 | | 48 | 6 | Accept | 2.3346 | 6.1175 | 2.1759 | 2.1759 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 22 | | | | | | | | | | NumVariablesToSample: 6 | | 49 | 6 | Accept | 3.1417 | 0.056998 | 2.1759 | 2.1759 | tree | MinLeafSize: 17 | | | | | | | | | | MaxNumSplits: 5 | | | | | | | | | | NumVariablesToSample: 1 | | 50 | 6 | Accept | 2.2905 | 0.15188 | 2.1759 | 2.1763 | svm | BoxConstraint: 0.43806 | | | | | | | | | | KernelScale: 4.5798 | | | | | | | | | | Epsilon: 0.054809 | | 51 | 6 | Accept | 4.1303 | 0.060906 | 2.1759 | 2.1766 | svm | BoxConstraint: 0.0017279 | | | | | | | | | | KernelScale: 0.59584 | | | | | | | | | | Epsilon: 49.918 | | 52 | 6 | Accept | 2.2872 | 5.7381 | 2.1759 | 2.1766 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 13 | | | | | | | | | | NumVariablesToSample: 4 | | 53 | 6 | Accept | 3.0447 | 0.074364 | 2.1759 | 2.1766 | tree | MinLeafSize: 45 | | | | | | | | | | MaxNumSplits: 13 | | | | | | | | | | NumVariablesToSample: 4 | | 54 | 6 | Accept | 4.1303 | 0.085215 | 2.1759 | 2.1766 | svm | BoxConstraint: 11.673 | | | | | | | | | | KernelScale: 0.43927 | | | | | | | | | | Epsilon: 22.967 | | 55 | 6 | Accept | 4.1303 | 0.09175 | 2.1759 | 2.1762 | svm | BoxConstraint: 2.5552 | | | | | | | | | | KernelScale: 0.0026113 | | | | | | | | | | Epsilon: 997.73 | | 56 | 6 | Accept | 4.1303 | 0.061439 | 2.1759 | 2.1768 | svm | BoxConstraint: 0.057299 | | | | | | | | | | KernelScale: 55.001 | | | | | | | | | | Epsilon: 715.72 | | 57 | 6 | Accept | 2.2057 | 6.0594 | 2.1759 | 2.1768 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.22715 | | | | | | | | | | MinLeafSize: 5 | | | | | | | | | | NumVariablesToSample: NaN | | 58 | 6 | Accept | 2.1825 | 5.5939 | 2.1759 | 2.1768 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.22153 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 59 | 6 | Accept | 4.1303 | 0.071138 | 2.1759 | 2.1768 | tree | MinLeafSize: 132 | | | | | | | | | | MaxNumSplits: 17 | | | | | | | | | | NumVariablesToSample: 1 | | 60 | 6 | Accept | 4.1303 | 0.092724 | 2.1759 | 2.1763 | svm | BoxConstraint: 958.92 | | | | | | | | | | KernelScale: 0.70563 | | | | | | | | | | Epsilon: 537.94 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 61 | 5 | Accept | 5.2259 | 58.51 | 2.1759 | 2.1764 | svm | BoxConstraint: 0.95481 | | | | | | | | | | KernelScale: 0.0033698 | | | | | | | | | | Epsilon: 0.060804 | | 62 | 5 | Accept | 16.058 | 44.447 | 2.1759 | 2.1764 | svm | BoxConstraint: 0.87942 | | | | | | | | | | KernelScale: 0.042698 | | | | | | | | | | Epsilon: 4.1252 | | 63 | 5 | Accept | 2.8565 | 0.076866 | 2.1759 | 2.1764 | tree | MinLeafSize: 9 | | | | | | | | | | MaxNumSplits: 44 | | | | | | | | | | NumVariablesToSample: 2 | | 64 | 6 | Accept | 2.1905 | 6.0033 | 2.1759 | 2.1764 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.086539 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 65 | 6 | Accept | 4.1435 | 0.41502 | 2.1759 | 2.176 | svm | BoxConstraint: 0.0014713 | | | | | | | | | | KernelScale: 24.291 | | | | | | | | | | Epsilon: 0.0080531 | | 66 | 6 | Accept | 4.1303 | 0.06148 | 2.1759 | 2.176 | svm | BoxConstraint: 1004.8 | | | | | | | | | | KernelScale: 1.0362 | | | | | | | | | | Epsilon: 57.277 | | 67 | 6 | Accept | 2.2057 | 6.1759 | 2.1759 | 2.176 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.065318 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 68 | 6 | Accept | 2.6213 | 1.631 | 2.1759 | 2.176 | tree | MinLeafSize: 2 | | | | | | | | | | MaxNumSplits: 41 | | | | | | | | | | NumVariablesToSample: 5 | | 69 | 6 | Accept | 2.195 | 6.4848 | 2.1759 | 2.176 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.064514 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 70 | 5 | Best | 2.1681 | 5.6457 | 2.1681 | 2.1644 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.1184 | | | | | | | | | | MinLeafSize: 4 | | | | | | | | | | NumVariablesToSample: NaN | | 71 | 5 | Accept | 2.1814 | 0.33738 | 2.1681 | 2.1644 | svm | BoxConstraint: 1066.5 | | | | | | | | | | KernelScale: 21.451 | | | | | | | | | | Epsilon: 1.5466 | | 72 | 6 | Accept | 6.622 | 32.752 | 2.1681 | 2.1644 | svm | BoxConstraint: 154.74 | | | | | | | | | | KernelScale: 0.43817 | | | | | | | | | | Epsilon: 0.069304 | | 73 | 6 | Accept | 2.1846 | 5.7951 | 2.1681 | 2.1682 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.10013 | | | | | | | | | | MinLeafSize: 6 | | | | | | | | | | NumVariablesToSample: NaN | | 74 | 6 | Best | 2.1674 | 5.5415 | 2.1674 | 2.1681 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.095942 | | | | | | | | | | MinLeafSize: 6 | | | | | | | | | | NumVariablesToSample: NaN | | 75 | 6 | Accept | 2.2257 | 5.8925 | 2.1674 | 2.1657 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.082236 | | | | | | | | | | MinLeafSize: 7 | | | | | | | | | | NumVariablesToSample: NaN | | 76 | 6 | Accept | 2.6476 | 0.17979 | 2.1674 | 2.1657 | tree | MinLeafSize: 28 | | | | | | | | | | MaxNumSplits: 129 | | | | | | | | | | NumVariablesToSample: 7 | | 77 | 6 | Accept | 4.1303 | 0.20025 | 2.1674 | 2.1657 | svm | BoxConstraint: 88.122 | | | | | | | | | | KernelScale: 0.00080559 | | | | | | | | | | Epsilon: 80.763 | | 78 | 6 | Accept | 2.4686 | 0.08985 | 2.1674 | 2.1657 | tree | MinLeafSize: 11 | | | | | | | | | | MaxNumSplits: 185 | | | | | | | | | | NumVariablesToSample: 6 | | 79 | 6 | Accept | 6.0666 | 8.1575 | 2.1674 | 2.1655 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.00091284 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 80 | 6 | Accept | 3.2165 | 0.056294 | 2.1674 | 2.1655 | tree | MinLeafSize: 14 | | | | | | | | | | MaxNumSplits: 6 | | | | | | | | | | NumVariablesToSample: 1 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 81 | 6 | Accept | 2.245 | 7.6163 | 2.1674 | 2.1655 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: 7 | | 82 | 6 | Accept | 3.0936 | 5.5248 | 2.1674 | 2.1687 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.011017 | | | | | | | | | | MinLeafSize: 76 | | | | | | | | | | NumVariablesToSample: NaN | | 83 | 6 | Accept | 4.5354 | 11.561 | 2.1674 | 2.1687 | svm | BoxConstraint: 0.022073 | | | | | | | | | | KernelScale: 0.0034124 | | | | | | | | | | Epsilon: 2.9088 | | 84 | 6 | Accept | 3.0342 | 0.062138 | 2.1674 | 2.1687 | tree | MinLeafSize: 19 | | | | | | | | | | MaxNumSplits: 3 | | | | | | | | | | NumVariablesToSample: 5 | | 85 | 6 | Accept | 4.13 | 4.1837 | 2.1674 | 2.1673 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 174 | | | | | | | | | | NumVariablesToSample: 5 | | 86 | 5 | Accept | 2.8788 | 4.5181 | 2.1674 | 2.1673 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 63 | | | | | | | | | | NumVariablesToSample: 3 | | 87 | 5 | Accept | 3.2232 | 0.083182 | 2.1674 | 2.1673 | tree | MinLeafSize: 66 | | | | | | | | | | MaxNumSplits: 75 | | | | | | | | | | NumVariablesToSample: 4 | | 88 | 6 | Accept | 2.7458 | 0.062397 | 2.1674 | 2.1673 | tree | MinLeafSize: 27 | | | | | | | | | | MaxNumSplits: 9 | | | | | | | | | | NumVariablesToSample: 5 | | 89 | 6 | Accept | 4.1483 | 0.084711 | 2.1674 | 2.1673 | svm | BoxConstraint: 0.10441 | | | | | | | | | | KernelScale: 1191.6 | | | | | | | | | | Epsilon: 0.80681 | | 90 | 6 | Accept | 2.5444 | 0.063012 | 2.1674 | 2.1673 | tree | MinLeafSize: 17 | | | | | | | | | | MaxNumSplits: 81 | | | | | | | | | | NumVariablesToSample: 6 |
__________________________________________________________ Optimization completed. Total iterations: 90 Total elapsed time: 94.9921 seconds Total time for training and validation: 387.2946 seconds Best observed learner is an ensemble model with: Learner: ensemble Method: LSBoost LearnRate: 0.095942 MinLeafSize: 6 NumVariablesToSample: NaN Observed log(1 + valLoss): 2.1674 Time for training and validation: 5.5415 seconds Best estimated learner (returned model) is an ensemble model with: Learner: ensemble Method: LSBoost LearnRate: 0.1184 MinLeafSize: 4 NumVariablesToSample: NaN Estimated log(1 + valLoss): 2.1673 Estimated time for training and validation: 5.6503 seconds Documentation for fitrauto display
The final model returned by fitrauto corresponds to the best estimated learner. Before returning the model, the function retrains it using the entire training data (carsTrain), the listed Learner (or model) type, and the displayed hyperparameter values.
Create Simple Model
Create a simple linear regression model linearMdl by using the fitlm function.
linearMdl = fitlm(carsTrain);
Although the linearMdl object does not have the exact same properties and methods as the autoMdl object, you can use both models to predict response values for new data by using the predict object function.
Compare Test Set Performance of Models
Compare the performance of the linearMdl and autoMdl models on the test data set. For each model, compute the test set mean squared error (MSE). Smaller MSE values indicate better performance.
ypred = predict(linearMdl,carsTest);
linearMSE = mean((carsTest.MPG-ypred).^2,"omitnan")linearMSE = 10.0558
autoMSE = loss(autoMdl,carsTest,"MPG")autoMSE = 6.9868
The autoMdl model seems to outperform the linearMdl model.
Input Arguments
Output Arguments
More About
Tips
Depending on the size of your data set, the number of learners you specify, and the optimization method you choose,
fitrautocan take some time to run.If you have a Parallel Computing Toolbox license, you can speed up computations by running the optimization in parallel. To do so, specify
"HyperparameterOptimizationOptions",struct("UseParallel",true). You can include additional fields in the structure to control other aspects of the optimization. SeeHyperparameterOptimizationOptions.If
fitrautowith Bayesian optimization takes a long time to run because of the number of observations in your training set (for example, over 10,000), consider usingfitrautowith ASHA optimization instead. ASHA optimization often finds good solutions faster than Bayesian optimization for data sets with many observations. To use ASHA optimization, specify"HyperparameterOptimizationOptions",struct("Optimizer","asha"). You can include additional fields in the structure to control additional aspects of the optimization. In particular, if you have a time constraint, specify theMaxTimefield of theHyperparameterOptimizationOptionsstructure to limit the number of secondsfitrautoruns.
Algorithms
Alternative Functionality
If you are unsure which models work best for your data set, you can alternatively use the Regression Learner app. Using the app, you can perform hyperparameter tuning for different models, and choose the optimized model that performs best. Although you must select a specific model before you can tune the model hyperparameters, Regression Learner provides greater flexibility for selecting optimizable hyperparameters and setting hyperparameter values. The app also allows you to train a variety of linear regression models (see Linear Regression Models). However, you cannot optimize in parallel, specify observation weights, or use ASHA optimization in the app. For more information, see Hyperparameter Optimization in Regression Learner App.
If you know which models might suit your data, you can alternatively use the corresponding model fit functions and specify the
OptimizeHyperparametersname-value argument to tune hyperparameters. You can compare the results across the models to select the best regression model. For an example of this process applied to classification models, see Moving Towards Automating Model Selection Using Bayesian Optimization.
References
[1] Li, Liam, Kevin Jamieson, Afshin Rostamizadeh, Ekaterina Gonina, Moritz Hardt, Benjamin Recht, and Ameet Talwalkar. “A System for Massively Parallel Hyperparameter Tuning.” ArXiv:1810.05934v5 [Cs], March 16, 2020. https://arxiv.org/abs/1810.05934v5.
Extended Capabilities
Version History
Introduced in R2020b
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