Автоматически выберите регрессионую модель с оптимизированными гиперпараметрами
Данные предиктора и отклика, fitrauto автоматически пытается выбрать типы регрессионной модели с различными значениями гиперзначений параметров. Функция использует оптимизацию Байеса, чтобы выбрать модели и их значения гиперзначений параметров, и вычисляет следующее для каждой модели: логарифмическая ( 1 + valLoss), где valLoss является средней квадратичной невязкой перекрестной валидации (MSE). После завершения оптимизации ,fitrauto возвращает модель, обученную на целом наборе данных, которая, как ожидается, лучше всего спрогнозирует отклики для новых данных. Вы можете использовать predict и loss функции объекта возвращенной модели для предсказания новых данных и вычисления тестового набора MSE, соответственно.
Использовать fitrauto когда вы не уверены, какие типы модели лучше всего соответствуют вашим данным. Для получения информации об альтернативных методах настройки гиперпараметров регрессионых моделей, см. «Альтернативная функциональность».
Mdl = fitrauto(Tbl,ResponseVarName)Mdl с настроенными гиперпараметрами. Таблица Tbl содержит переменные предиктора и переменную отклика, где ResponseVarName - имя переменной отклика.
Mdl = fitrauto(___,Name,Value)HyperparameterOptimizationOptions аргумент пары "имя-значение", чтобы задать, как выполняется байесовская оптимизация.
[ дополнительно возвращается Mdl,OptimizationResults] = fitrauto(___)OptimizationResults, а BayesianOptimization объект, содержащий результаты выбора модели и процесса настройки гиперпараметра.
Использование fitrauto чтобы автоматически выбрать регрессионую модель с оптимизированными гиперпараметрами, данные предиктора и отклика, сохраненные в таблице.
Загрузка данных
Загрузите carbig набор данных, содержащий измерения автомобилей 1970-х и начала 1980-х годов.
load carbigСоздайте таблицу, содержащую переменные предиктора Acceleration, Displacement, и так далее, а также переменная отклика MPG.
cars = table(Acceleration,Displacement,Horsepower, ...
Model_Year,Origin,Weight,MPG);Данные о разделах
Разделите данные на обучающие и тестовые наборы. Используйте приблизительно 80% наблюдений для процесса выбора модели и настройки гиперпараметра и 20% наблюдений, чтобы проверить эффективность конечной модели, возвращенной fitrauto. Использование cvpartition для разбиения данных на разделы.
rng('default') % For reproducibility of the data partition c = cvpartition(length(MPG),'Holdout',0.2); trainingIdx = training(c); % Training set indices carsTrain = cars(trainingIdx,:); testIdx = test(c); % Test set indices carsTest = cars(testIdx,:);
Выполняйте fitrauto
Передайте обучающие данные в fitrauto. По умолчанию fitrauto определяет соответствующие типы модели, чтобы попробовать, использует байесовскую оптимизацию, чтобы найти хорошие значения гиперзначений параметров, и возвращает обученную модель Mdl с наилучшей ожидаемой эффективностью. Кроме того, fitrauto предоставляет график оптимизации и итерационное отображение результатов оптимизации. Для получения дополнительной информации о том, как интерпретировать эти результаты, смотрите Подробное отображение.
Ожидайте, что этот процесс займет некоторое время. Чтобы ускорить процесс оптимизации, рассмотрите параллельный запуск оптимизации, если у вас есть лицензия Parallel Computing Toolbox™. Для этого передайте 'HyperparameterOptimizationOptions',struct('UseParallel',true) на fitrauto как аргумент пары "имя-значение".
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)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 1 | Best | 2.5161 | 1.4197 | 2.5161 | 2.5161 | tree | MinLeafSize: 6 |
| 2 | Accept | 4.1439 | 0.68799 | 2.5161 | 2.5161 | svm | BoxConstraint: 336.91 | | | | | | | | | KernelScale: 0.0018275 | | | | | | | | | Epsilon: 0.1074 |
| 3 | Accept | 4.144 | 5.5942 | 2.5161 | 2.5161 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 257 | | | | | | | | | MinLeafSize: 156 |
| 4 | Accept | 3.1976 | 20.387 | 2.5161 | 2.5161 | svm | BoxConstraint: 0.033502 | | | | | | | | | KernelScale: 153.38 | | | | | | | | | Epsilon: 0.093672 |
| 5 | Best | 2.5041 | 0.13106 | 2.5041 | 2.5101 | tree | MinLeafSize: 5 |
| 6 | Best | 2.2096 | 7.0177 | 2.2096 | 2.5101 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | MinLeafSize: 1 |
| 7 | Accept | 2.7182 | 0.085053 | 2.2096 | 2.5057 | tree | MinLeafSize: 1 |
| 8 | Accept | 17.207 | 23.312 | 2.2096 | 2.5057 | svm | BoxConstraint: 196.73 | | | | | | | | | KernelScale: 34.789 | | | | | | | | | Epsilon: 0.03716 |
| 9 | Accept | 4.1439 | 0.057226 | 2.2096 | 2.5057 | svm | BoxConstraint: 346.92 | | | | | | | | | KernelScale: 0.032493 | | | | | | | | | Epsilon: 0.23974 |
| 10 | Best | 2.1916 | 6.4368 | 2.1916 | 2.5057 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 278 | | | | | | | | | MinLeafSize: 13 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 11 | Accept | 2.8889 | 0.1325 | 2.1916 | 2.5057 | svm | BoxConstraint: 0.033068 | | | | | | | | | KernelScale: 585.38 | | | | | | | | | Epsilon: 4.6993 |
| 12 | Accept | 4.1439 | 0.06362 | 2.1916 | 2.5057 | svm | BoxConstraint: 48.997 | | | | | | | | | KernelScale: 0.0045904 | | | | | | | | | Epsilon: 18.085 |
| 13 | Accept | 4.1439 | 0.048941 | 2.1916 | 2.5057 | svm | BoxConstraint: 985.69 | | | | | | | | | KernelScale: 0.0010988 | | | | | | | | | Epsilon: 449.48 |
| 14 | Accept | 2.2844 | 6.7538 | 2.1916 | 2.4806 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | MinLeafSize: 63 |
| 15 | Accept | 4.1439 | 0.054943 | 2.1916 | 2.4806 | svm | BoxConstraint: 0.010812 | | | | | | | | | KernelScale: 1.2015 | | | | | | | | | Epsilon: 0.034209 |
| 16 | Accept | 4.1439 | 0.055455 | 2.1916 | 2.4806 | svm | BoxConstraint: 0.0021787 | | | | | | | | | KernelScale: 0.018209 | | | | | | | | | Epsilon: 443.71 |
| 17 | Accept | 2.2075 | 6.7931 | 2.1916 | 2.1942 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | MinLeafSize: 17 |
| 18 | Accept | 2.6056 | 0.08425 | 2.1916 | 2.1942 | tree | MinLeafSize: 2 |
| 19 | Accept | 2.6056 | 0.087135 | 2.1916 | 2.1942 | tree | MinLeafSize: 2 |
| 20 | Accept | 2.7182 | 0.062848 | 2.1916 | 2.1942 | tree | MinLeafSize: 1 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 21 | Accept | 2.2402 | 6.8909 | 2.1916 | 2.2011 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 282 | | | | | | | | | MinLeafSize: 2 |
| 22 | Accept | 2.6056 | 0.059067 | 2.1916 | 2.2011 | tree | MinLeafSize: 2 |
| 23 | Accept | 2.3016 | 4.8177 | 2.1916 | 2.1911 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 202 | | | | | | | | | MinLeafSize: 9 |
| 24 | Accept | 4.1439 | 0.05258 | 2.1916 | 2.1911 | svm | BoxConstraint: 37.028 | | | | | | | | | KernelScale: 0.033731 | | | | | | | | | Epsilon: 0.2457 |
| 25 | Accept | 3.352 | 0.043391 | 2.1916 | 2.1911 | tree | MinLeafSize: 122 |
| 26 | Accept | 4.1439 | 0.062799 | 2.1916 | 2.1911 | svm | BoxConstraint: 0.01045 | | | | | | | | | KernelScale: 0.0024261 | | | | | | | | | Epsilon: 12.355 |
| 27 | Accept | 2.3188 | 5.1633 | 2.1916 | 2.1884 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 212 | | | | | | | | | MinLeafSize: 2 |
| 28 | Accept | 2.4271 | 5.8444 | 2.1916 | 2.1908 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 247 | | | | | | | | | MinLeafSize: 83 |
| 29 | Accept | 2.6056 | 0.05574 | 2.1916 | 2.1908 | tree | MinLeafSize: 2 |
| 30 | Accept | 4.1439 | 0.054692 | 2.1916 | 2.1908 | svm | BoxConstraint: 2.1296 | | | | | | | | | KernelScale: 3.2623 | | | | | | | | | Epsilon: 599.62 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 31 | Accept | 2.5241 | 0.051793 | 2.1916 | 2.1908 | tree | MinLeafSize: 8 |
| 32 | Accept | 2.6443 | 5.2572 | 2.1916 | 2.1969 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 229 | | | | | | | | | MinLeafSize: 52 |
| 33 | Accept | 2.2537 | 5.641 | 2.1916 | 2.1931 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 235 | | | | | | | | | MinLeafSize: 26 |
| 34 | Accept | 2.5448 | 0.053688 | 2.1916 | 2.1931 | tree | MinLeafSize: 19 |
| 35 | Accept | 2.4438 | 0.045817 | 2.1916 | 2.1931 | tree | MinLeafSize: 13 |
| 36 | Accept | 2.7182 | 0.062646 | 2.1916 | 2.1931 | tree | MinLeafSize: 1 |
| 37 | Accept | 2.4749 | 0.048072 | 2.1916 | 2.1931 | tree | MinLeafSize: 9 |
| 38 | Accept | 13.083 | 31.488 | 2.1916 | 2.1931 | svm | BoxConstraint: 5.2568 | | | | | | | | | KernelScale: 10.811 | | | | | | | | | Epsilon: 0.073361 |
| 39 | Accept | 2.2446 | 5.2866 | 2.1916 | 2.1952 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 214 | | | | | | | | | MinLeafSize: 4 |
| 40 | Accept | 3.0919 | 0.040315 | 2.1916 | 2.1952 | tree | MinLeafSize: 62 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 41 | Accept | 2.6335 | 6.4626 | 2.1916 | 2.1926 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 280 | | | | | | | | | MinLeafSize: 45 |
| 42 | Accept | 4.1439 | 0.048186 | 2.1916 | 2.1926 | svm | BoxConstraint: 0.093799 | | | | | | | | | KernelScale: 0.0053728 | | | | | | | | | Epsilon: 17.332 |
| 43 | Accept | 2.8766 | 0.075435 | 2.1916 | 2.1926 | svm | BoxConstraint: 0.20553 | | | | | | | | | KernelScale: 880.29 | | | | | | | | | Epsilon: 4.5637 |
| 44 | Accept | 2.2402 | 5.6507 | 2.1916 | 2.1944 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 233 | | | | | | | | | MinLeafSize: 2 |
| 45 | Accept | 2.4576 | 5.4632 | 2.1916 | 2.1928 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 232 | | | | | | | | | MinLeafSize: 27 |
| 46 | Accept | 3.003 | 0.069043 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.0010563 | | | | | | | | | KernelScale: 527.21 | | | | | | | | | Epsilon: 0.010074 |
| 47 | Accept | 4.1439 | 0.05544 | 2.1916 | 2.1928 | svm | BoxConstraint: 1.6452 | | | | | | | | | KernelScale: 880.96 | | | | | | | | | Epsilon: 656.96 |
| 48 | Accept | 11.118 | 31.888 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.001029 | | | | | | | | | KernelScale: 25.502 | | | | | | | | | Epsilon: 0.22713 |
| 49 | Accept | 3.0019 | 0.064077 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.012054 | | | | | | | | | KernelScale: 976.62 | | | | | | | | | Epsilon: 0.013474 |
| 50 | Accept | 4.1439 | 0.069826 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.045381 | | | | | | | | | KernelScale: 0.030659 | | | | | | | | | Epsilon: 0.021441 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 51 | Accept | 4.1439 | 0.050005 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.090287 | | | | | | | | | KernelScale: 69.941 | | | | | | | | | Epsilon: 125.56 |
| 52 | Accept | 4.1439 | 0.054745 | 2.1916 | 2.1928 | svm | BoxConstraint: 285.67 | | | | | | | | | KernelScale: 0.14938 | | | | | | | | | Epsilon: 764.19 |
| 53 | Accept | 2.8779 | 0.11876 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.064002 | | | | | | | | | KernelScale: 969.91 | | | | | | | | | Epsilon: 0.46473 |
| 54 | Accept | 12.921 | 18.315 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.019899 | | | | | | | | | KernelScale: 50.528 | | | | | | | | | Epsilon: 0.0091628 |
| 55 | Accept | 2.9117 | 0.076534 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.028436 | | | | | | | | | KernelScale: 919.02 | | | | | | | | | Epsilon: 1.2395 |
| 56 | Accept | 3.0276 | 0.064801 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.0073097 | | | | | | | | | KernelScale: 898.72 | | | | | | | | | Epsilon: 0.088715 |
| 57 | Accept | 7.1555 | 20.87 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.07913 | | | | | | | | | KernelScale: 100.43 | | | | | | | | | Epsilon: 0.78937 |
| 58 | Accept | 2.9075 | 0.077548 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.03913 | | | | | | | | | KernelScale: 956.28 | | | | | | | | | Epsilon: 1.1315 |
| 59 | Accept | 2.9168 | 0.068648 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.033583 | | | | | | | | | KernelScale: 973.75 | | | | | | | | | Epsilon: 2.1404 |
| 60 | Accept | 4.1439 | 0.053635 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.1278 | | | | | | | | | KernelScale: 899.12 | | | | | | | | | Epsilon: 36.993 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 61 | Accept | 2.9456 | 0.073895 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.022705 | | | | | | | | | KernelScale: 995.04 | | | | | | | | | Epsilon: 0.21977 |
| 62 | Accept | 4.1439 | 0.04979 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.0047868 | | | | | | | | | KernelScale: 0.1518 | | | | | | | | | Epsilon: 0.042601 |
| 63 | Accept | 2.9095 | 0.065115 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.033402 | | | | | | | | | KernelScale: 989.34 | | | | | | | | | Epsilon: 0.3073 |
| 64 | Accept | 4.1439 | 0.065248 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.056303 | | | | | | | | | KernelScale: 0.29988 | | | | | | | | | Epsilon: 0.10313 |
| 65 | Accept | 4.1439 | 0.050181 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.0040769 | | | | | | | | | KernelScale: 238.59 | | | | | | | | | Epsilon: 32.573 |
| 66 | Accept | 2.6802 | 2.1221 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.11739 | | | | | | | | | KernelScale: 555.21 | | | | | | | | | Epsilon: 0.048956 |
| 67 | Accept | 4.1439 | 0.055315 | 2.1916 | 2.1928 | svm | BoxConstraint: 772.51 | | | | | | | | | KernelScale: 0.016887 | | | | | | | | | Epsilon: 72.705 |
| 68 | Accept | 4.1439 | 0.063152 | 2.1916 | 2.1928 | svm | BoxConstraint: 63.153 | | | | | | | | | KernelScale: 0.0080065 | | | | | | | | | Epsilon: 481.39 |
| 69 | Accept | 4.1439 | 0.054083 | 2.1916 | 2.1928 | svm | BoxConstraint: 4.117 | | | | | | | | | KernelScale: 73.496 | | | | | | | | | Epsilon: 121.74 |
| 70 | Accept | 4.1439 | 0.05377 | 2.1916 | 2.1928 | svm | BoxConstraint: 30.398 | | | | | | | | | KernelScale: 0.12159 | | | | | | | | | Epsilon: 64.06 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 71 | Accept | 4.1439 | 0.053553 | 2.1916 | 2.1928 | svm | BoxConstraint: 3.9304 | | | | | | | | | KernelScale: 871.88 | | | | | | | | | Epsilon: 23.7 |
| 72 | Accept | 4.1439 | 0.050525 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.031734 | | | | | | | | | KernelScale: 0.28247 | | | | | | | | | Epsilon: 0.0097239 |
| 73 | Accept | 4.1439 | 0.068567 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.021528 | | | | | | | | | KernelScale: 0.001858 | | | | | | | | | Epsilon: 283.71 |
| 74 | Accept | 4.1439 | 0.055336 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.024702 | | | | | | | | | KernelScale: 0.055101 | | | | | | | | | Epsilon: 84.374 |
| 75 | Accept | 2.8707 | 0.095257 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.070484 | | | | | | | | | KernelScale: 928.16 | | | | | | | | | Epsilon: 0.11681 |
| 76 | Accept | 4.1439 | 0.059476 | 2.1916 | 2.1928 | svm | BoxConstraint: 636.13 | | | | | | | | | KernelScale: 0.0020368 | | | | | | | | | Epsilon: 2.0625 |
| 77 | Accept | 2.8682 | 0.10867 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.059284 | | | | | | | | | KernelScale: 888.99 | | | | | | | | | Epsilon: 0.1389 |
| 78 | Accept | 2.7111 | 0.59286 | 2.1916 | 2.1928 | svm | BoxConstraint: 2.4776 | | | | | | | | | KernelScale: 998.2 | | | | | | | | | Epsilon: 1.5291 |
| 79 | Accept | 2.7625 | 0.45668 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.91288 | | | | | | | | | KernelScale: 996.35 | | | | | | | | | Epsilon: 0.16968 |
| 80 | Accept | 3.2211 | 0.058812 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.0011498 | | | | | | | | | KernelScale: 989.38 | | | | | | | | | Epsilon: 0.0091368 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 81 | Accept | 4.1439 | 0.05754 | 2.1916 | 2.1928 | svm | BoxConstraint: 26.543 | | | | | | | | | KernelScale: 0.0016089 | | | | | | | | | Epsilon: 0.68659 |
| 82 | Accept | 4.1439 | 0.055356 | 2.1916 | 2.1928 | svm | BoxConstraint: 129.11 | | | | | | | | | KernelScale: 0.044504 | | | | | | | | | Epsilon: 3.7911 |
| 83 | Accept | 2.7643 | 0.51644 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.82852 | | | | | | | | | KernelScale: 990.02 | | | | | | | | | Epsilon: 0.013169 |
| 84 | Accept | 4.1439 | 0.05615 | 2.1916 | 2.1928 | svm | BoxConstraint: 53.003 | | | | | | | | | KernelScale: 3.9941 | | | | | | | | | Epsilon: 318.78 |
| 85 | Accept | 4.1439 | 0.054645 | 2.1916 | 2.1928 | svm | BoxConstraint: 10.848 | | | | | | | | | KernelScale: 0.2138 | | | | | | | | | Epsilon: 876.72 |
| 86 | Accept | 2.8797 | 0.077707 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.063788 | | | | | | | | | KernelScale: 999.56 | | | | | | | | | Epsilon: 0.24966 |
| 87 | Accept | 4.1439 | 0.056472 | 2.1916 | 2.1928 | svm | BoxConstraint: 29.921 | | | | | | | | | KernelScale: 300.51 | | | | | | | | | Epsilon: 872.64 |
| 88 | Accept | 4.1439 | 0.053269 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.5701 | | | | | | | | | KernelScale: 0.020421 | | | | | | | | | Epsilon: 282.76 |
| 89 | Accept | 4.1439 | 0.054778 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.60472 | | | | | | | | | KernelScale: 0.0052641 | | | | | | | | | Epsilon: 0.11831 |
| 90 | Accept | 2.8676 | 0.097394 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.11411 | | | | | | | | | KernelScale: 977.02 | | | | | | | | | Epsilon: 0.090725 |
__________________________________________________________ Optimization completed. Total iterations: 90 Total elapsed time: 589.6892 seconds Total time for training and validation: 245.2123 seconds Best observed learner is an ensemble model with: Method: LSBoost NumLearningCycles: 278 MinLeafSize: 13 Observed log(1 + valLoss): 2.1916 Time for training and validation: 6.4368 seconds Best estimated learner (returned model) is an ensemble model with: Method: LSBoost NumLearningCycles: 278 MinLeafSize: 13 Estimated log(1 + valLoss): 2.1928 Estimated time for training and validation: 5.8977 seconds Documentation for fitrauto display
Конечная модель, возвращенная fitrauto соответствует лучшему оцененному ученику. Перед возвращением модели функция переобучает ее, используя все обучающие данные (carsTrain), перечисленные Learner (или модель) тип и отображенные значения гиперзначений параметров.
Оценка эффективности тестового набора
Оцените эффективность модели на тестовом наборе. testError основан на средней квадратичной невязке тестового набора (MSE). Меньшие значения MSE указывают на лучшую эффективность.
testMSE = loss(Mdl,carsTest,'MPG');
testError = log(1 + testMSE)testError = 2.3194
Использование fitrauto чтобы автоматически выбрать регрессионую модель с оптимизированными гиперпараметрами, данные предиктора и отклика, сохраненные в отдельных переменных.
Загрузка данных
Загрузите carbig набор данных, содержащий измерения автомобилей 1970-х и начала 1980-х годов.
load carbigСоздайте матрицу X содержащие переменные предиктора Acceleration, Cylindersи так далее. Сохраните переменную отклика MPG в переменной Y.
X = [Acceleration Cylinders Displacement Weight]; Y = MPG;
Создайте переменную, указывающую, какие предикторы являются категориальными. Cylinders является единственной категориальной переменной в X.
categoricalVars = [false true false false];
Данные о разделах
Разделите данные на обучающие и тестовые наборы. Используйте приблизительно 80% наблюдений для процесса выбора модели и настройки гиперпараметра и 20% наблюдений, чтобы проверить эффективность конечной модели, возвращенной fitrauto. Использование cvpartition для разбиения данных на разделы.
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);
Выполняйте fitrauto
Передайте обучающие данные в fitrauto. По умолчанию fitrauto определяет соответствующие типы моделей (или учащихся), чтобы попробовать, использует байесовскую оптимизацию, чтобы найти хорошие значения гиперзначений параметров для этих моделей, и возвращает обученную модель Mdl с наилучшей ожидаемой эффективностью. Задайте категориальные предикторы и запустите оптимизацию параллельно (требует Parallel Computing Toolbox™). Верните второй выход OptimizationResults который содержит детали байесовской оптимизации.
Ожидайте, что этот процесс займет некоторое время. По умолчанию fitrauto предоставляет график оптимизации и итерационное отображение результатов оптимизации. Для получения дополнительной информации о том, как интерпретировать эти результаты, смотрите Подробное отображение.
options = struct('UseParallel',true); [Mdl,OptimizationResults] = fitrauto(XTrain,YTrain, ... 'CategoricalPredictors',categoricalVars, ... 'HyperparameterOptimizationOptions',options);
Starting parallel pool (parpool) using the 'local' profile ... Connected to the parallel pool (number of workers: 6). 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)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 1 | 5 | Best | 3.0205 | 1.7491 | 3.0205 | 3.0329 | tree | MinLeafSize: 6 | | 2 | 5 | Accept | 3.0453 | 1.6641 | 3.0205 | 3.0329 | tree | MinLeafSize: 5 |
| 3 | 4 | Accept | 4.143 | 2.6491 | 3.0205 | 3.0329 | svm | BoxConstraint: 336.91 | | | | | | | | | | KernelScale: 0.0018275 | | | | | | | | | | Epsilon: 0.1074 | | 4 | 4 | Accept | 4.1434 | 7.5491 | 3.0205 | 3.0329 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 257 | | | | | | | | | | MinLeafSize: 156 |
| 5 | 3 | Best | 2.9188 | 8.6194 | 2.9188 | 3.0329 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | | MinLeafSize: 1 | | 6 | 3 | Accept | 4.143 | 0.83485 | 2.9188 | 3.0329 | svm | BoxConstraint: 346.92 | | | | | | | | | | KernelScale: 0.032493 | | | | | | | | | | Epsilon: 0.23974 |
| 7 | 6 | Accept | 2.9275 | 0.19147 | 2.9188 | 2.9276 | svm | BoxConstraint: 0.033068 | | | | | | | | | | KernelScale: 585.38 | | | | | | | | | | Epsilon: 4.6993 |
| 8 | 4 | Accept | 4.143 | 0.09353 | 2.9188 | 2.9276 | svm | BoxConstraint: 985.69 | | | | | | | | | | KernelScale: 0.0010988 | | | | | | | | | | Epsilon: 449.48 | | 9 | 4 | Accept | 4.143 | 0.62222 | 2.9188 | 2.9276 | svm | BoxConstraint: 0.04588 | | | | | | | | | | KernelScale: 0.33917 | | | | | | | | | | Epsilon: 0.073755 | | 10 | 4 | Accept | 3.0205 | 0.21301 | 2.9188 | 2.9276 | tree | MinLeafSize: 6 |
|===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 11 | 6 | Best | 2.9167 | 7.3685 | 2.9167 | 2.9276 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | | MinLeafSize: 63 |
| 12 | 4 | Accept | 3.6673 | 22.826 | 2.8696 | 2.8697 | svm | BoxConstraint: 0.033502 | | | | | | | | | | KernelScale: 153.38 | | | | | | | | | | Epsilon: 0.093672 | | 13 | 4 | Best | 2.8696 | 8.0371 | 2.8696 | 2.8697 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | | MinLeafSize: 17 | | 14 | 4 | Accept | 2.8696 | 7.6155 | 2.8696 | 2.8697 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | | MinLeafSize: 17 |
| 15 | 3 | Accept | 2.8696 | 8.2039 | 2.8696 | 2.8697 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | | MinLeafSize: 17 | | 16 | 3 | Accept | 3.1971 | 0.1933 | 2.8696 | 2.8697 | tree | MinLeafSize: 2 |
| 17 | 6 | Accept | 3.0139 | 0.12079 | 2.8696 | 2.8697 | tree | MinLeafSize: 34 |
| 18 | 5 | Accept | 4.143 | 0.23444 | 2.8696 | 2.8697 | svm | BoxConstraint: 0.0023916 | | | | | | | | | | KernelScale: 0.0049969 | | | | | | | | | | Epsilon: 3.0552 | | 19 | 5 | Accept | 3.3225 | 0.19712 | 2.8696 | 2.8697 | tree | MinLeafSize: 122 |
| 20 | 3 | Accept | 2.8717 | 5.5602 | 2.8217 | 2.8697 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 282 | | | | | | | | | | MinLeafSize: 2 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 21 | 3 | Best | 2.8217 | 4.2702 | 2.8217 | 2.8697 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 202 | | | | | | | | | | MinLeafSize: 9 | | 22 | 3 | Accept | 4.143 | 0.11628 | 2.8217 | 2.8697 | svm | BoxConstraint: 37.028 | | | | | | | | | | KernelScale: 0.033731 | | | | | | | | | | Epsilon: 0.2457 |
| 23 | 6 | Accept | 4.143 | 0.067367 | 2.8217 | 2.8697 | svm | BoxConstraint: 0.01045 | | | | | | | | | | KernelScale: 0.0024261 | | | | | | | | | | Epsilon: 12.355 |
| 24 | 5 | Accept | 3.1971 | 0.094668 | 2.8217 | 2.8697 | tree | MinLeafSize: 2 | | 25 | 5 | Accept | 4.143 | 0.10279 | 2.8217 | 2.8697 | svm | BoxConstraint: 308.5 | | | | | | | | | | KernelScale: 0.015174 | | | | | | | | | | Epsilon: 0.53501 |
| 26 | 5 | Accept | 4.143 | 0.07812 | 2.8217 | 2.8697 | svm | BoxConstraint: 2.1296 | | | | | | | | | | KernelScale: 3.2623 | | | | | | | | | | Epsilon: 599.62 |
| 27 | 6 | Accept | 11.41 | 32.991 | 2.8217 | 2.8697 | svm | BoxConstraint: 0.0054638 | | | | | | | | | | KernelScale: 45.011 | | | | | | | | | | Epsilon: 5.0385 |
| 28 | 6 | Accept | 2.8657 | 5.3498 | 2.8217 | 2.8221 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 229 | | | | | | | | | | MinLeafSize: 52 |
| 29 | 3 | Accept | 2.8689 | 6.3959 | 2.8217 | 2.8221 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 235 | | | | | | | | | | MinLeafSize: 26 | | 30 | 3 | Accept | 2.8689 | 5.5649 | 2.8217 | 2.8221 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 235 | | | | | | | | | | MinLeafSize: 26 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 31 | 3 | Accept | 2.9197 | 0.043492 | 2.8217 | 2.8221 | tree | MinLeafSize: 19 | | 32 | 3 | Accept | 2.9403 | 0.050907 | 2.8217 | 2.8221 | tree | MinLeafSize: 13 |
| 33 | 6 | Accept | 4.143 | 0.1117 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0013002 | | | | | | | | | | KernelScale: 365.07 | | | | | | | | | | Epsilon: 533.39 |
| 34 | 5 | Accept | 4.1924 | 16.905 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0057208 | | | | | | | | | | KernelScale: 143.79 | | | | | | | | | | Epsilon: 4.0917 | | 35 | 5 | Accept | 2.9804 | 0.16413 | 2.8217 | 2.8221 | tree | MinLeafSize: 8 |
| 36 | 4 | Accept | 2.8842 | 4.4972 | 2.8217 | 2.8221 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 214 | | | | | | | | | | MinLeafSize: 4 | | 37 | 4 | Accept | 3.112 | 0.40292 | 2.8217 | 2.8221 | tree | MinLeafSize: 62 |
| 38 | 3 | Accept | 2.8686 | 5.942 | 2.8217 | 2.8221 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 285 | | | | | | | | | | MinLeafSize: 45 | | 39 | 3 | Accept | 4.143 | 0.048389 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.093799 | | | | | | | | | | KernelScale: 0.0053728 | | | | | | | | | | Epsilon: 17.332 |
| 40 | 6 | Accept | 2.9487 | 0.053171 | 2.8217 | 2.8221 | tree | MinLeafSize: 27 |
|===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 41 | 3 | Accept | 12.196 | 29.49 | 2.8217 | 2.8221 | svm | BoxConstraint: 86.083 | | | | | | | | | | KernelScale: 52.727 | | | | | | | | | | Epsilon: 8.3179 | | 42 | 3 | Accept | 2.8717 | 4.5788 | 2.8217 | 2.8221 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 233 | | | | | | | | | | MinLeafSize: 2 | | 43 | 3 | Accept | 2.9093 | 0.24973 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.034974 | | | | | | | | | | KernelScale: 588.77 | | | | | | | | | | Epsilon: 3.8683 | | 44 | 3 | Accept | 2.9804 | 0.18263 | 2.8217 | 2.8221 | tree | MinLeafSize: 8 |
| 45 | 6 | Accept | 4.143 | 0.10875 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.084355 | | | | | | | | | | KernelScale: 0.052988 | | | | | | | | | | Epsilon: 76.921 |
| 46 | 5 | Accept | 2.8478 | 4.7428 | 2.8217 | 2.8221 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 229 | | | | | | | | | | MinLeafSize: 8 | | 47 | 5 | Accept | 4.143 | 1.2887 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0036358 | | | | | | | | | | KernelScale: 4.7627 | | | | | | | | | | Epsilon: 20.208 |
| 48 | 4 | Accept | 3.2214 | 16.267 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.069952 | | | | | | | | | | KernelScale: 207.68 | | | | | | | | | | Epsilon: 0.092526 | | 49 | 4 | Accept | 2.924 | 0.18896 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0095751 | | | | | | | | | | KernelScale: 358.95 | | | | | | | | | | Epsilon: 4.7526 |
| 50 | 3 | Accept | 3.1542 | 15.88 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.028095 | | | | | | | | | | KernelScale: 184.52 | | | | | | | | | | Epsilon: 0.09847 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 51 | 3 | Accept | 2.9143 | 3.0279 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0033005 | | | | | | | | | | KernelScale: 252.81 | | | | | | | | | | Epsilon: 2.6159 |
| 52 | 6 | Accept | 10.06 | 18.169 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.043122 | | | | | | | | | | KernelScale: 74.674 | | | | | | | | | | Epsilon: 0.071781 |
| 53 | 2 | Accept | 2.8989 | 7.2493 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.014817 | | | | | | | | | | KernelScale: 247.68 | | | | | | | | | | Epsilon: 2.5942 | | 54 | 2 | Accept | 2.9049 | 0.55744 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.033022 | | | | | | | | | | KernelScale: 505.18 | | | | | | | | | | Epsilon: 0.1266 | | 55 | 2 | Accept | 2.9804 | 0.066427 | 2.8217 | 2.8221 | tree | MinLeafSize: 8 | | 56 | 2 | Accept | 2.9032 | 0.17339 | 2.8217 | 2.8221 | tree | MinLeafSize: 17 | | 57 | 2 | Accept | 4.143 | 0.058535 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0011341 | | | | | | | | | | KernelScale: 0.0017464 | | | | | | | | | | Epsilon: 0.012532 |
| 58 | 6 | Accept | 2.9268 | 0.13315 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0042653 | | | | | | | | | | KernelScale: 319.4 | | | | | | | | | | Epsilon: 4.5985 |
| 59 | 4 | Accept | 2.9081 | 1.8508 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0012679 | | | | | | | | | | KernelScale: 229.31 | | | | | | | | | | Epsilon: 0.075286 | | 60 | 4 | Accept | 4.143 | 0.059851 | 2.8217 | 2.8227 | svm | BoxConstraint: 275.76 | | | | | | | | | | KernelScale: 0.034549 | | | | | | | | | | Epsilon: 6.2312 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 61 | 4 | Accept | 2.8335 | 4.6933 | 2.8217 | 2.8227 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 219 | | | | | | | | | | MinLeafSize: 26 |
| 62 | 5 | Accept | 2.9049 | 1.902 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0071219 | | | | | | | | | | KernelScale: 278.65 | | | | | | | | | | Epsilon: 2.7464 |
| 63 | 3 | Accept | 2.8816 | 15.271 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.044779 | | | | | | | | | | KernelScale: 253.31 | | | | | | | | | | Epsilon: 0.15109 | | 64 | 3 | Accept | 2.8773 | 9.1951 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.042581 | | | | | | | | | | KernelScale: 336.99 | | | | | | | | | | Epsilon: 0.072146 | | 65 | 3 | Accept | 2.9573 | 3.597 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.035397 | | | | | | | | | | KernelScale: 251.22 | | | | | | | | | | Epsilon: 5.8103 |
| 66 | 6 | Accept | 2.9045 | 0.8479 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0017256 | | | | | | | | | | KernelScale: 280.49 | | | | | | | | | | Epsilon: 0.17061 |
| 67 | 5 | Accept | 3.1507 | 0.089958 | 2.8217 | 2.8227 | tree | MinLeafSize: 3 | | 68 | 5 | Accept | 3.1971 | 0.14914 | 2.8217 | 2.8227 | tree | MinLeafSize: 2 |
| 69 | 5 | Accept | 4.143 | 30.354 | 2.8217 | 2.8227 | svm | BoxConstraint: 1.3468 | | | | | | | | | | KernelScale: 9.6762 | | | | | | | | | | Epsilon: 0.023868 |
| 70 | 5 | Accept | 2.9037 | 1.2103 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0030905 | | | | | | | | | | KernelScale: 288.83 | | | | | | | | | | Epsilon: 0.089541 |
|===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 71 | 4 | Accept | 6.6283 | 17.347 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0017058 | | | | | | | | | | KernelScale: 104.21 | | | | | | | | | | Epsilon: 0.065687 | | 72 | 4 | Accept | 2.9655 | 15.866 | 2.8217 | 2.8227 | svm | BoxConstraint: 16.694 | | | | | | | | | | KernelScale: 563.25 | | | | | | | | | | Epsilon: 0.82854 |
| 73 | 4 | Accept | 3.0653 | 0.064937 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0014988 | | | | | | | | | | KernelScale: 637.21 | | | | | | | | | | Epsilon: 0.082183 |
| 74 | 2 | Accept | 5.9041 | 19.341 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0015248 | | | | | | | | | | KernelScale: 115.07 | | | | | | | | | | Epsilon: 0.14178 | | 75 | 2 | Accept | 2.874 | 14.077 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.049938 | | | | | | | | | | KernelScale: 249.2 | | | | | | | | | | Epsilon: 2.3027 | | 76 | 2 | Accept | 2.9116 | 0.1932 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0015667 | | | | | | | | | | KernelScale: 364.11 | | | | | | | | | | Epsilon: 0.046357 |
| 77 | 6 | Accept | 2.9266 | 0.089378 | 2.8217 | 2.8203 | svm | BoxConstraint: 0.008711 | | | | | | | | | | KernelScale: 689.75 | | | | | | | | | | Epsilon: 0.11038 |
| 78 | 3 | Accept | 2.9134 | 0.2501 | 2.8217 | 2.7031 | svm | BoxConstraint: 0.0013447 | | | | | | | | | | KernelScale: 362.68 | | | | | | | | | | Epsilon: 0.096474 | | 79 | 3 | Accept | 4.143 | 0.086465 | 2.8217 | 2.7031 | svm | BoxConstraint: 37.006 | | | | | | | | | | KernelScale: 0.031201 | | | | | | | | | | Epsilon: 8.5325 | | 80 | 3 | Accept | 2.9804 | 0.070321 | 2.8217 | 2.7031 | tree | MinLeafSize: 8 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 81 | 3 | Accept | 4.143 | 0.057551 | 2.8217 | 2.7031 | svm | BoxConstraint: 8.2928 | | | | | | | | | | KernelScale: 0.22318 | | | | | | | | | | Epsilon: 0.35272 |
| 82 | 6 | Accept | 2.905 | 0.35685 | 2.8217 | 2.6899 | svm | BoxConstraint: 0.0049863 | | | | | | | | | | KernelScale: 405.18 | | | | | | | | | | Epsilon: 0.20248 |
| 83 | 4 | Accept | 4.143 | 0.057428 | 2.8217 | 2.6899 | svm | BoxConstraint: 0.0035019 | | | | | | | | | | KernelScale: 10.124 | | | | | | | | | | Epsilon: 22.114 | | 84 | 4 | Accept | 2.9968 | 0.053485 | 2.8217 | 2.6899 | tree | MinLeafSize: 31 | | 85 | 4 | Accept | 2.9487 | 0.067551 | 2.8217 | 2.6899 | tree | MinLeafSize: 27 |
| 86 | 2 | Accept | 11.192 | 19.605 | 2.8217 | 2.7382 | svm | BoxConstraint: 86.675 | | | | | | | | | | KernelScale: 92.212 | | | | | | | | | | Epsilon: 2.4057 | | 87 | 2 | Accept | 2.8848 | 6.0635 | 2.8217 | 2.7382 | svm | BoxConstraint: 0.015422 | | | | | | | | | | KernelScale: 295.63 | | | | | | | | | | Epsilon: 0.10658 | | 88 | 2 | Accept | 2.8919 | 2.8002 | 2.8217 | 2.7382 | svm | BoxConstraint: 0.013027 | | | | | | | | | | KernelScale: 316.74 | | | | | | | | | | Epsilon: 0.1048 |
| 89 | 6 | Accept | 2.9712 | 0.073966 | 2.8217 | 2.7363 | svm | BoxConstraint: 0.00197 | | | | | | | | | | KernelScale: 560.31 | | | | | | | | | | Epsilon: 0.42707 |
| 90 | 5 | Accept | 3.0045 | 0.1149 | 2.8217 | 2.7363 | tree | MinLeafSize: 45 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 91 | 5 | Accept | 3.031 | 0.041383 | 2.8217 | 2.7363 | tree | MinLeafSize: 61 |
__________________________________________________________ Optimization completed. Total iterations: 91 Total elapsed time: 201.923 seconds Total time for training and validation: 436.1019 seconds Best observed learner is an ensemble model with: Method: Bag NumLearningCycles: 202 MinLeafSize: 9 Observed log(1 + valLoss): 2.8217 Time for training and validation: 4.2702 seconds Best estimated learner (returned model) is an svm model with: BoxConstraint: 0.0013447 KernelScale: 362.68 Epsilon: 0.096474 Estimated log(1 + valLoss): 2.7363 Estimated time for training and validation: 0.29514 seconds Documentation for fitrauto display
Конечная модель, возвращенная fitrauto соответствует лучшему оцененному ученику. Перед возвращением модели функция переобучает ее, используя все обучающие данные (XTrain и YTrain), перечисленные Learner (или модель) тип и отображенные значения гиперзначений параметров.
Оценка эффективности тестового набора
Оцените эффективность модели на тестовом наборе. testError основан на средней квадратичной невязке тестового набора (MSE). Меньшие значения MSE указывают на лучшую эффективность.
testMSE = loss(Mdl,XTest,YTest); testError = log(1 + testMSE)
testError = 2.9873
Использование fitrauto чтобы автоматически выбрать регрессионую модель с оптимизированными гиперпараметрами, данные предиктора и отклика, сохраненные в таблице. Сравните эффективность полученной регрессионной модели с эффективностью простой линейной регрессионой, созданной с помощью fitlm.
Загрузка и разбиение данных
Загрузите carbig набор данных, содержащий измерения автомобилей 1970-х и начала 1980-х годов. Преобразуйте Cylinders переменная к categorical переменная. Создайте таблицу, содержащую переменные предиктора Acceleration, Cylinders, Displacement, и так далее, а также переменная отклика MPG.
load carbig Cylinders = categorical(Cylinders); cars = table(Acceleration,Cylinders,Displacement, ... Horsepower,Model_Year,Origin,Weight,MPG);
Разделите данные на обучающие и тестовые наборы. Используйте приблизительно 80% наблюдений для обучения и 20% наблюдений для проверки. Использование cvpartition для разбиения данных на разделы.
rng('default') % For reproducibility of the data partition c = cvpartition(length(MPG),'Holdout',0.2); trainingIdx = training(c); % Training set indices carsTrain = cars(trainingIdx,:); testIdx = test(c); % Test set indices carsTest = cars(testIdx,:);
Выполняйте fitrauto
Передайте обучающие данные в fitrauto. По умолчанию fitrauto определяет соответствующие типы модели, чтобы попробовать, использует байесовскую оптимизацию, чтобы найти хорошие значения гиперзначений параметров, и возвращает обученную модель autoMdl с наилучшей ожидаемой эффективностью. Задайте, чтобы оптимизировать по всем оптимизируемым гиперпараметрам и запустить оптимизацию параллельно (требует Parallel Computing Toolbox™).
Ожидайте, что этот процесс займет некоторое время. По умолчанию fitrauto предоставляет график оптимизации и итерационное отображение результатов оптимизации. Для получения дополнительной информации о том, как интерпретировать эти результаты, смотрите Подробное отображение.
options = struct('UseParallel',true); autoMdl = fitrauto(carsTrain,'MPG','OptimizeHyperparameters','all', ... 'HyperparameterOptimizationOptions',options);
Starting parallel pool (parpool) using the 'local' profile ... Connected to the parallel pool (number of workers: 6). 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)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 1 | 4 | Accept | 3.5168 | 2.3522 | 2.6193 | 2.6197 | tree | MinLeafSize: 38 | | | | | | | | | | MaxNumSplits: 2 | | | | | | | | | | NumVariablesToSample: 1 | | 2 | 4 | Accept | 2.6633 | 2.3211 | 2.6193 | 2.6197 | tree | MinLeafSize: 1 | | | | | | | | | | MaxNumSplits: 44 | | | | | | | | | | NumVariablesToSample: 4 | | 3 | 4 | Best | 2.6193 | 2.3426 | 2.6193 | 2.6197 | tree | MinLeafSize: 29 | | | | | | | | | | MaxNumSplits: 52 | | | | | | | | | | NumVariablesToSample: 6 | | 4 | 4 | Accept | 4.1439 | 3.798 | 2.6193 | 2.6197 | svm | BoxConstraint: 0.010718 | | | | | | | | | | KernelScale: 1.7547 | | | | | | | | | | Epsilon: 182.6 | | 5 | 2 | Accept | 2.3998 | 8.4115 | 2.2082 | 2.6197 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.64294 | | | | | | | | | | MinLeafSize: 39 | | | | | | | | | | NumVariablesToSample: NaN | | 6 | 2 | Best | 2.2082 | 9.4573 | 2.2082 | 2.6197 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.033855 | | | | | | | | | | MinLeafSize: 6 | | | | | | | | | | NumVariablesToSample: NaN | | 7 | 2 | Accept | 4.1439 | 0.37564 | 2.2082 | 2.6197 | svm | BoxConstraint: 0.012677 | | | | | | | | | | KernelScale: 351.81 | | | | | | | | | | Epsilon: 140.99 | | 8 | 6 | Accept | 4.1439 | 1.1014 | 2.2082 | 2.6197 | svm | BoxConstraint: 37.191 | | | | | | | | | | KernelScale: 21.113 | | | | | | | | | | Epsilon: 33.874 | | 9 | 6 | Accept | 2.7394 | 1.8778 | 2.2082 | 2.6197 | svm | BoxConstraint: 0.057859 | | | | | | | | | | KernelScale: 448.87 | | | | | | | | | | Epsilon: 4.2169 | | 10 | 3 | Accept | 2.5987 | 6.4235 | 2.2082 | 2.4798 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.89898 | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: NaN | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 11 | 3 | Accept | 3.2336 | 6.93 | 2.2082 | 2.4798 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.56281 | | | | | | | | | | MinLeafSize: 123 | | | | | | | | | | NumVariablesToSample: NaN | | 12 | 3 | Accept | 2.682 | 6.4489 | 2.2082 | 2.4798 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 51 | | | | | | | | | | NumVariablesToSample: 2 | | 13 | 3 | Accept | 2.4795 | 0.40654 | 2.2082 | 2.4798 | tree | MinLeafSize: 6 | | | | | | | | | | MaxNumSplits: 32 | | | | | | | | | | NumVariablesToSample: 5 | | 14 | 5 | Accept | 4.1439 | 0.28349 | 2.2082 | 2.4798 | svm | BoxConstraint: 297.35 | | | | | | | | | | KernelScale: 0.87756 | | | | | | | | | | Epsilon: 0.043798 | | 15 | 5 | Accept | 2.845 | 0.3422 | 2.2082 | 2.4798 | svm | BoxConstraint: 0.0027083 | | | | | | | | | | KernelScale: 413.17 | | | | | | | | | | Epsilon: 0.13572 | | 16 | 5 | Accept | 2.7106 | 5.6397 | 2.2082 | 2.3735 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.74839 | | | | | | | | | | MinLeafSize: 88 | | | | | | | | | | NumVariablesToSample: NaN | | 17 | 3 | Accept | 6.0492 | 4.8396 | 2.2082 | 2.3735 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0010498 | | | | | | | | | | MinLeafSize: 130 | | | | | | | | | | NumVariablesToSample: NaN | | 18 | 3 | Accept | 2.2932 | 5.4011 | 2.2082 | 2.3735 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.10542 | | | | | | | | | | MinLeafSize: 57 | | | | | | | | | | NumVariablesToSample: NaN | | 19 | 3 | Accept | 2.6686 | 0.22924 | 2.2082 | 2.3735 | tree | MinLeafSize: 5 | | | | | | | | | | MaxNumSplits: 7 | | | | | | | | | | NumVariablesToSample: 5 | | 20 | 6 | Accept | 4.1439 | 1.5528 | 2.2082 | 2.3735 | svm | BoxConstraint: 0.07294 | | | | | | | | | | KernelScale: 761.22 | | | | | | | | | | Epsilon: 31.544 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 21 | 4 | Accept | 4.143 | 0.10249 | 2.2082 | 2.3735 | tree | MinLeafSize: 132 | | | | | | | | | | MaxNumSplits: 8 | | | | | | | | | | NumVariablesToSample: 5 | | 22 | 4 | Accept | 4.143 | 0.31889 | 2.2082 | 2.3735 | tree | MinLeafSize: 138 | | | | | | | | | | MaxNumSplits: 3 | | | | | | | | | | NumVariablesToSample: 7 | | 23 | 4 | Accept | 3.5024 | 0.16777 | 2.2082 | 2.3735 | tree | MinLeafSize: 83 | | | | | | | | | | MaxNumSplits: 41 | | | | | | | | | | NumVariablesToSample: 2 | | 24 | 2 | Accept | 4.1439 | 33.887 | 2.2082 | 2.3735 | svm | BoxConstraint: 0.15265 | | | | | | | | | | KernelScale: 1.4893 | | | | | | | | | | Epsilon: 0.44287 | | 25 | 2 | Accept | 2.3583 | 5.6469 | 2.2082 | 2.3735 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: 2 | | 26 | 2 | Accept | 4.1439 | 0.08045 | 2.2082 | 2.3735 | svm | BoxConstraint: 0.0050384 | | | | | | | | | | KernelScale: 0.18651 | | | | | | | | | | Epsilon: 11.818 | | 27 | 6 | Accept | 4.1439 | 0.11643 | 2.2082 | 2.3735 | svm | BoxConstraint: 0.19519 | | | | | | | | | | KernelScale: 0.48473 | | | | | | | | | | Epsilon: 0.02267 | | 28 | 6 | Accept | 2.6334 | 0.69581 | 2.2082 | 2.3735 | tree | MinLeafSize: 6 | | | | | | | | | | MaxNumSplits: 43 | | | | | | | | | | NumVariablesToSample: 2 | | 29 | 2 | Accept | 5.9862 | 5.4794 | 2.2082 | 2.3735 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.001143 | | | | | | | | | | MinLeafSize: 104 | | | | | | | | | | NumVariablesToSample: NaN | | 30 | 2 | Accept | 2.2456 | 7.9201 | 2.2082 | 2.3735 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 12 | | | | | | | | | | NumVariablesToSample: 7 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 31 | 2 | Accept | 2.9745 | 7.6297 | 2.2082 | 2.3735 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.010155 | | | | | | | | | | MinLeafSize: 13 | | | | | | | | | | NumVariablesToSample: NaN | | 32 | 2 | Accept | 2.6819 | 6.0671 | 2.2082 | 2.3735 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 57 | | | | | | | | | | NumVariablesToSample: 5 | | 33 | 2 | Accept | 2.927 | 0.11096 | 2.2082 | 2.3735 | tree | MinLeafSize: 1 | | | | | | | | | | MaxNumSplits: 123 | | | | | | | | | | NumVariablesToSample: 2 | | 34 | 4 | Accept | 4.1439 | 0.11416 | 2.2082 | 2.3735 | svm | BoxConstraint: 2.1967 | | | | | | | | | | KernelScale: 0.02117 | | | | | | | | | | Epsilon: 0.20631 | | 35 | 4 | Accept | 2.9904 | 0.096707 | 2.2082 | 2.3735 | tree | MinLeafSize: 44 | | | | | | | | | | MaxNumSplits: 265 | | | | | | | | | | NumVariablesToSample: 2 | | 36 | 4 | Accept | 2.6513 | 0.10209 | 2.2082 | 2.3735 | tree | MinLeafSize: 1 | | | | | | | | | | MaxNumSplits: 90 | | | | | | | | | | NumVariablesToSample: 2 | | 37 | 4 | Accept | 2.2442 | 7.3117 | 2.2082 | 2.2083 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: 6 | | 38 | 4 | Accept | 2.345 | 5.3353 | 2.2082 | 2.2083 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 3 | | | | | | | | | | NumVariablesToSample: 2 | | 39 | 3 | Accept | 3.1314 | 4.9709 | 2.2082 | 2.2083 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 82 | | | | | | | | | | NumVariablesToSample: 5 | | 40 | 3 | Accept | 4.1439 | 0.076184 | 2.2082 | 2.2083 | svm | BoxConstraint: 488.75 | | | | | | | | | | KernelScale: 0.047261 | | | | | | | | | | Epsilon: 0.019147 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 41 | 5 | Accept | 2.611 | 15.327 | 2.2082 | 2.2083 | svm | BoxConstraint: 0.0057698 | | | | | | | | | | KernelScale: 199.91 | | | | | | | | | | Epsilon: 1.094 | | 42 | 5 | Accept | 4.1439 | 0.11014 | 2.2082 | 2.2083 | svm | BoxConstraint: 347.06 | | | | | | | | | | KernelScale: 0.024995 | | | | | | | | | | Epsilon: 0.012891 | | 43 | 3 | Best | 2.1839 | 5.4291 | 2.1839 | 2.2083 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.079786 | | | | | | | | | | MinLeafSize: 16 | | | | | | | | | | NumVariablesToSample: NaN | | 44 | 3 | Accept | 2.9934 | 0.080707 | 2.1839 | 2.2083 | tree | MinLeafSize: 37 | | | | | | | | | | MaxNumSplits: 171 | | | | | | | | | | NumVariablesToSample: 4 | | 45 | 3 | Accept | 4.1439 | 0.090101 | 2.1839 | 2.2083 | svm | BoxConstraint: 0.24707 | | | | | | | | | | KernelScale: 0.0040563 | | | | | | | | | | Epsilon: 0.75695 | | 46 | 6 | Accept | 2.2144 | 5.1987 | 2.1839 | 2.1982 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.078839 | | | | | | | | | | MinLeafSize: 16 | | | | | | | | | | NumVariablesToSample: NaN | | 47 | 4 | Accept | 2.2877 | 5.9143 | 2.1839 | 2.1129 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 15 | | | | | | | | | | NumVariablesToSample: 5 | | 48 | 4 | Accept | 3.0763 | 0.13281 | 2.1839 | 2.1129 | tree | MinLeafSize: 12 | | | | | | | | | | MaxNumSplits: 2 | | | | | | | | | | NumVariablesToSample: 3 | | 49 | 4 | Accept | 4.1439 | 1.3244 | 2.1839 | 2.1129 | svm | BoxConstraint: 6.6689 | | | | | | | | | | KernelScale: 0.048705 | | | | | | | | | | Epsilon: 59.545 | | 50 | 3 | Accept | 4.1439 | 30.675 | 2.1839 | 2.1984 | svm | BoxConstraint: 13.655 | | | | | | | | | | KernelScale: 4.3086 | | | | | | | | | | Epsilon: 6.9116 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 51 | 3 | Accept | 2.2728 | 5.7106 | 2.1839 | 2.1984 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 14 | | | | | | | | | | NumVariablesToSample: 5 | | 52 | 6 | Accept | 2.4156 | 4.7264 | 2.1839 | 2.1984 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 24 | | | | | | | | | | NumVariablesToSample: 3 | | 53 | 4 | Accept | 4.1439 | 0.07497 | 2.1839 | 2.1984 | svm | BoxConstraint: 424.87 | | | | | | | | | | KernelScale: 0.41352 | | | | | | | | | | Epsilon: 0.74479 | | 54 | 4 | Accept | 2.3527 | 5.0415 | 2.1839 | 2.1984 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.62721 | | | | | | | | | | MinLeafSize: 3 | | | | | | | | | | NumVariablesToSample: NaN | | 55 | 4 | Accept | 2.5975 | 0.086879 | 2.1839 | 2.1984 | tree | MinLeafSize: 2 | | | | | | | | | | MaxNumSplits: 12 | | | | | | | | | | NumVariablesToSample: 6 | | 56 | 3 | Accept | 4.1439 | 30.921 | 2.1839 | 2.1983 | svm | BoxConstraint: 0.0044643 | | | | | | | | | | KernelScale: 4.2576 | | | | | | | | | | Epsilon: 0.066941 | | 57 | 3 | Accept | 2.2488 | 6.5278 | 2.1839 | 2.1983 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 4 | | | | | | | | | | NumVariablesToSample: 6 | | 58 | 5 | Accept | 2.2375 | 6.3071 | 2.1839 | 2.1982 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 4 | | | | | | | | | | NumVariablesToSample: 6 | | 59 | 5 | Accept | 2.2145 | 5.1044 | 2.1839 | 2.1982 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.13809 | | | | | | | | | | MinLeafSize: 5 | | | | | | | | | | NumVariablesToSample: NaN | | 60 | 2 | Accept | 2.2771 | 5.7956 | 2.1839 | 2.1953 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: 4 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 61 | 2 | Accept | 2.4755 | 4.7265 | 2.1839 | 2.1953 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 5 | | | | | | | | | | NumVariablesToSample: 1 | | 62 | 2 | Accept | 2.6456 | 0.082657 | 2.1839 | 2.1953 | tree | MinLeafSize: 2 | | | | | | | | | | MaxNumSplits: 36 | | | | | | | | | | NumVariablesToSample: 4 | | 63 | 2 | Accept | 2.5294 | 5.4057 | 2.1839 | 2.1953 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 35 | | | | | | | | | | NumVariablesToSample: 5 | | 64 | 6 | Accept | 2.3409 | 5.5648 | 2.1839 | 2.0591 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 25 | | | | | | | | | | NumVariablesToSample: 6 | | 65 | 2 | Accept | 2.3209 | 7.4037 | 2.1839 | 2.0591 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.016875 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 66 | 2 | Accept | 2.5782 | 5.5342 | 2.1839 | 2.0591 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.015531 | | | | | | | | | | MinLeafSize: 76 | | | | | | | | | | NumVariablesToSample: NaN | | 67 | 2 | Accept | 2.2537 | 7.2619 | 2.1839 | 2.0591 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 6 | | | | | | | | | | NumVariablesToSample: 7 | | 68 | 2 | Accept | 4.1426 | 4.7455 | 2.1839 | 2.0591 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 134 | | | | | | | | | | NumVariablesToSample: 2 | | 69 | 2 | Accept | 2.9366 | 0.094426 | 2.1839 | 2.0591 | tree | MinLeafSize: 8 | | | | | | | | | | MaxNumSplits: 37 | | | | | | | | | | NumVariablesToSample: 1 | | 70 | 6 | Accept | 2.2338 | 5.1862 | 2.1839 | 2.1934 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.17516 | | | | | | | | | | MinLeafSize: 9 | | | | | | | | | | NumVariablesToSample: NaN | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 71 | 3 | Accept | 4.143 | 4.4939 | 2.1839 | 2.1968 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.038144 | | | | | | | | | | MinLeafSize: 142 | | | | | | | | | | NumVariablesToSample: NaN | | 72 | 3 | Accept | 4.1439 | 0.076138 | 2.1839 | 2.1968 | svm | BoxConstraint: 131.74 | | | | | | | | | | KernelScale: 0.0031145 | | | | | | | | | | Epsilon: 0.028465 | | 73 | 3 | Accept | 4.143 | 0.074774 | 2.1839 | 2.1968 | tree | MinLeafSize: 156 | | | | | | | | | | MaxNumSplits: 1 | | | | | | | | | | NumVariablesToSample: 5 | | 74 | 3 | Accept | 2.3197 | 5.1527 | 2.1839 | 2.1968 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 9 | | | | | | | | | | NumVariablesToSample: 3 | | 75 | 6 | Accept | 2.5309 | 4.7886 | 2.1839 | 2.1969 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.97421 | | | | | | | | | | MinLeafSize: 13 | | | | | | | | | | NumVariablesToSample: NaN | | 76 | 3 | Accept | 2.2935 | 5.3774 | 2.1839 | 2.1983 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.16149 | | | | | | | | | | MinLeafSize: 30 | | | | | | | | | | NumVariablesToSample: NaN | | 77 | 3 | Accept | 2.3649 | 4.9029 | 2.1839 | 2.1983 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: 2 | | 78 | 3 | Accept | 3.3541 | 0.065977 | 2.1839 | 2.1983 | tree | MinLeafSize: 79 | | | | | | | | | | MaxNumSplits: 65 | | | | | | | | | | NumVariablesToSample: 3 | | 79 | 3 | Accept | 2.3592 | 5.0572 | 2.1839 | 2.1983 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: 2 | | 80 | 6 | Accept | 2.4009 | 4.5836 | 2.1839 | 2.1983 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 18 | | | | | | | | | | NumVariablesToSample: 2 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 81 | 2 | Accept | 10.894 | 31.052 | 2.1839 | 2.1983 | svm | BoxConstraint: 0.05924 | | | | | | | | | | KernelScale: 16.477 | | | | | | | | | | Epsilon: 1.204 | | 82 | 2 | Accept | 2.216 | 5.8077 | 2.1839 | 2.1983 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.038621 | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: NaN | | 83 | 2 | Accept | 2.2547 | 5.6201 | 2.1839 | 2.1983 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 4 | | | | | | | | | | NumVariablesToSample: 5 | | 84 | 2 | Accept | 4.1439 | 0.11346 | 2.1839 | 2.1983 | svm | BoxConstraint: 230.13 | | | | | | | | | | KernelScale: 15.715 | | | | | | | | | | Epsilon: 425.18 | | 85 | 2 | Accept | 4.1439 | 0.10597 | 2.1839 | 2.1983 | svm | BoxConstraint: 10.758 | | | | | | | | | | KernelScale: 0.020507 | | | | | | | | | | Epsilon: 4.9755 | | 86 | 6 | Accept | 2.219 | 6.1221 | 2.1839 | 2.1981 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.038658 | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: NaN | | 87 | 2 | Accept | 2.8447 | 0.17007 | 2.1839 | 2.1981 | svm | BoxConstraint: 0.013729 | | | | | | | | | | KernelScale: 535.02 | | | | | | | | | | Epsilon: 2.1063 | | 88 | 2 | Accept | 4.1439 | 0.079667 | 2.1839 | 2.1981 | svm | BoxConstraint: 0.32731 | | | | | | | | | | KernelScale: 22.615 | | | | | | | | | | Epsilon: 41.604 | | 89 | 2 | Accept | 2.2928 | 4.9488 | 2.1839 | 2.1981 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.26144 | | | | | | | | | | MinLeafSize: 33 | | | | | | | | | | NumVariablesToSample: NaN | | 90 | 2 | Accept | 2.4525 | 0.12704 | 2.1839 | 2.1981 | tree | MinLeafSize: 4 | | | | | | | | | | MaxNumSplits: 92 | | | | | | | | | | NumVariablesToSample: 7 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 91 | 2 | Accept | 4.1439 | 0.093014 | 2.1839 | 2.1981 | svm | BoxConstraint: 0.0021134 | | | | | | | | | | KernelScale: 0.001228 | | | | | | | | | | Epsilon: 6.4785 | __________________________________________________________ Optimization completed. Total iterations: 91 Total elapsed time: 235.4082 seconds Total time for training and validation: 426.1606 seconds Best observed learner is an ensemble model with: Method: LSBoost LearnRate: 0.079786 MinLeafSize: 16 NumVariablesToSample: NaN Observed log(1 + valLoss): 2.1839 Time for training and validation: 5.4291 seconds Best estimated learner (returned model) is an ensemble model with: Method: LSBoost LearnRate: 0.079786 MinLeafSize: 16 NumVariablesToSample: NaN Estimated log(1 + valLoss): 2.1981 Estimated time for training and validation: 5.3328 seconds Documentation for fitrauto display
Конечная модель, возвращенная fitrauto соответствует лучшему оцененному ученику. Перед возвращением модели функция переобучает ее, используя все обучающие данные (carsTrain), перечисленные Learner (или модель) тип и отображенные значения гиперзначений параметров.
Создайте простую модель
Создайте простую линейную регрессионую модель linearMdl при помощи fitlm функция.
linearMdl = fitlm(carsTrain);
Хотя и linearMdl объект не имеет точно таких же свойств и методов, как autoMdl объект, можно использовать обе модели, чтобы предсказать значения отклика для новых данных при помощи predict функция объекта.
Сравнение эффективности тестового набора моделей
Сравнение эффективности linearMdl и autoMdl модели на наборе тестовых данных. Для каждой модели вычислите среднюю квадратичную невязку (MSE) тестового набора. Меньшие значения MSE указывают на лучшую эффективность.
ypred = predict(linearMdl,carsTest);
linearMSE = mean((carsTest.MPG-ypred).^2,'omitnan')linearMSE = 11.0981
autoMSE = loss(autoMdl,carsTest,'MPG')autoMSE = 8.8024
The autoMdl модель, по-видимому, превосходит linearMdl модель.
В зависимости от размера ваших данных и количества учащихся, которые вы задаете, fitrauto может занять некоторое время, чтобы запустить. Если у вас есть лицензия Parallel Computing Toolbox, можно ускорить расчеты, запустив оптимизацию параллельно. Для этого задайте 'HyperparameterOptimizationOptions',struct('UseParallel',true). Можно включать другие поля в структуру для управления другими аспектами оптимизации. См. HyperparameterOptimizationOptions.
Если вы не уверены, какие модели работают лучше всего для вашего набора данных, можно также использовать приложение Regression Learner. Используя приложение, можно выполнить настройку гиперпараметра для различных моделей и выбрать оптимизированную модель, которая работает лучше всего. Несмотря на то, что перед настройкой гиперпараметров модели необходимо выбрать конкретную модель, Regression Learner обеспечивает большую гибкость для выбора оптимизируемых гиперпараметров и настройки значений гиперзначений параметров. Приложение также позволяет вам обучать различные линейные регрессионые модели (см. Линейные регрессионые модели). Однако вы не можете оптимизировать параллельно, выберите 'linear' или 'kernel' учащиеся, или укажите веса наблюдений в приложении. Для получения дополнительной информации см. «Оптимизация гипероптимизации параметров управления» в приложении Regression Learner.
Если вы знаете, какие модели могут удовлетворить вашим данным, можно также использовать соответствующие функции подгонки модели и задать 'OptimizeHyperparameters' аргумент пары "имя-значение" для настройки гиперпараметров. Можно сравнить результаты по моделям, чтобы выбрать лучшую регрессионую модель. Для примера этого процесса, примененного к классификационным моделям, смотрите Движение к Автоматизации Выбора Модели Используя Байесову Оптимизацию.
fitrensemble | fitrgp | fitrkernel | fitrlinear | fitrsvm | fitrtree