Автоматически выберите модель регрессии оптимизированными гиперпараметрами
Учитывая предиктор и данные об ответе, fitrauto автоматически пробует выбор типов модели регрессии с различными гиперзначениями параметров. По умолчанию функция использует Байесовую оптимизацию, чтобы выбрать модели и их гиперзначения параметров, и вычисляет следующее для каждой модели: журнал (1 + valLoss), где valLoss является среднеквадратической ошибкой (MSE) перекрестной проверки. После того, как оптимизация завершена, fitrauto возвращает модель, обученную на целом наборе данных, который, как ожидают, лучше всего предскажет ответы для новых данных. Можно использовать predict и loss объектные функции возвращенной модели, чтобы предсказать на новых данных и вычислить набор тестов MSE, соответственно.
Использование fitrauto когда вы не уверены, какие типы модели лучше всего удовлетворяют вашим данным. Для получения информации об альтернативных методах для настройки гиперпараметров моделей регрессии см. альтернативную функциональность.
Если ваши данные содержат более чем 10 000 наблюдений, рассмотрите использование асинхронного последовательного алгоритма сокращения вдвое (ASHA) вместо Байесовой оптимизации, когда вы запускаетесь fitrauto. Оптимизация ASHA часто находит хорошие решения быстрее, чем Байесова оптимизация для наборов данных со многими наблюдениями.
Mdl = fitrauto(Tbl,ResponseVarName)Mdl регрессии настроенными гиперпараметрами. Таблица Tbl содержит переменные предикторы и переменную отклика, где ResponseVarName имя переменной отклика.
Mdl = fitrauto(___,Name,Value)HyperparameterOptimizationOptions аргумент значения имени, чтобы задать, использовать ли Байесовую оптимизацию (значение по умолчанию) или асинхронный последовательный алгоритм сокращения вдвое (ASHA). Чтобы использовать оптимизацию ASHA, задайте "HyperparameterOptimizationOptions",struct("Optimizer","asha"). Можно включать дополнительные поля в структуру, чтобы управлять другими аспектами оптимизации.
[ также возвращает Mdl,OptimizationResults] = fitrauto(___)OptimizationResults, который содержит результаты выбора модели и настраивающего процесса гиперпараметра. Этим выходом является BayesianOptimization возразите, когда вы используете Байесовую оптимизацию и таблицу, когда вы используете оптимизацию ASHA.
Используйте fitrauto автоматически выбрать модель регрессии оптимизированными гиперпараметрами, учитывая предиктор и данные об ответе, хранимые в таблице.
Загрузка данных
Загрузите carbig набор данных, который содержит измерения автомобилей, сделанных в 1970-х и в начале 1980-х.
load carbigСоставьте таблицу, содержащую переменные предикторы Acceleration, Displacement, и так далее, а также переменная отклика MPG.
cars = table(Acceleration,Displacement,Horsepower, ...
Model_Year,Origin,Weight,MPG);Данные о разделе
Разделите данные в наборы обучающих данных и наборы тестов. Используйте приблизительно 80% наблюдений для выбора модели и настраивающего процесса гиперпараметра, и 20% наблюдений, чтобы проверить производительность итоговой модели, возвращенной fitrauto. Используйте cvpartition разделить данные.
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,:);
Запустите fitrauto
Передайте обучающие данные fitrauto. По умолчанию, fitrauto определяет соответствующие типы модели, чтобы попробовать, использует Байесовую оптимизацию, чтобы найти хорошие гиперзначения параметров и возвращает обученную модель Mdl с лучшей ожидаемой эффективностью. Кроме того, fitrauto предоставляет график оптимизации и итеративное отображение результатов оптимизации. Для получения дополнительной информации о том, как интерпретировать эти результаты, смотрите Многословное Отображение.
Ожидайте, что этот процесс займет время. Чтобы ускорить процесс оптимизации, рассмотрите выполнение оптимизации параллельно, если у вас есть лицензия Parallel Computing Toolbox™. Для этого передайте "HyperparameterOptimizationOptions",struct("UseParallel",true) к fitrauto в качестве аргумента значения имени.
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 | 0.42811 | 2.5161 | 2.5161 | tree | MinLeafSize: 6 | | 2 | Accept | 4.1439 | 0.31653 | 2.5161 | 2.5161 | svm | BoxConstraint: 336.91 | | | | | | | | | KernelScale: 0.0018275 | | | | | | | | | Epsilon: 0.1074 | | 3 | Accept | 4.144 | 6.1354 | 2.5161 | 2.5161 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 257 | | | | | | | | | MinLeafSize: 156 | | 4 | Accept | 3.1976 | 21.572 | 2.5161 | 2.5161 | svm | BoxConstraint: 0.033502 | | | | | | | | | KernelScale: 153.38 | | | | | | | | | Epsilon: 0.093672 | | 5 | Best | 2.5041 | 0.098707 | 2.5041 | 2.5101 | tree | MinLeafSize: 5 | | 6 | Best | 2.173 | 8.434 | 2.173 | 2.2138 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | MinLeafSize: 1 | | 7 | Accept | 2.7182 | 0.10727 | 2.173 | 2.2138 | tree | MinLeafSize: 1 | | 8 | Accept | 17.207 | 24.418 | 2.173 | 2.2138 | svm | BoxConstraint: 196.73 | | | | | | | | | KernelScale: 34.789 | | | | | | | | | Epsilon: 0.03716 | | 9 | Accept | 4.1439 | 0.08053 | 2.173 | 2.2138 | svm | BoxConstraint: 346.92 | | | | | | | | | KernelScale: 0.032493 | | | | | | | | | Epsilon: 0.23974 | | 10 | Accept | 2.2139 | 7.9036 | 2.173 | 2.1945 | 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 | 0.10655 | 2.173 | 2.1945 | svm | BoxConstraint: 0.033068 | | | | | | | | | KernelScale: 585.38 | | | | | | | | | Epsilon: 4.6993 | | 12 | Accept | 4.1439 | 0.060722 | 2.173 | 2.1945 | svm | BoxConstraint: 48.997 | | | | | | | | | KernelScale: 0.0045904 | | | | | | | | | Epsilon: 18.085 | | 13 | Accept | 4.1439 | 0.079298 | 2.173 | 2.1945 | svm | BoxConstraint: 985.69 | | | | | | | | | KernelScale: 0.0010988 | | | | | | | | | Epsilon: 449.48 | | 14 | Accept | 2.2801 | 8.2142 | 2.173 | 2.1824 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | MinLeafSize: 63 | | 15 | Accept | 4.1439 | 0.075809 | 2.173 | 2.1824 | svm | BoxConstraint: 0.010812 | | | | | | | | | KernelScale: 1.2015 | | | | | | | | | Epsilon: 0.034209 | | 16 | Accept | 4.1439 | 0.061902 | 2.173 | 2.1824 | svm | BoxConstraint: 0.0021787 | | | | | | | | | KernelScale: 0.018209 | | | | | | | | | Epsilon: 443.71 | | 17 | Accept | 2.2159 | 7.9406 | 2.173 | 2.1777 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | MinLeafSize: 17 | | 18 | Accept | 2.6056 | 0.091476 | 2.173 | 2.1777 | tree | MinLeafSize: 2 | | 19 | Accept | 2.6056 | 0.13203 | 2.173 | 2.1777 | tree | MinLeafSize: 2 | | 20 | Accept | 2.7182 | 0.087514 | 2.173 | 2.1777 | 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 | 2.1763 | 7.9262 | 2.173 | 2.17 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 282 | | | | | | | | | MinLeafSize: 2 | | 22 | Accept | 2.6056 | 0.077927 | 2.173 | 2.17 | tree | MinLeafSize: 2 | | 23 | Accept | 2.3016 | 5.2336 | 2.173 | 2.1774 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 202 | | | | | | | | | MinLeafSize: 9 | | 24 | Accept | 4.1439 | 0.073168 | 2.173 | 2.1774 | svm | BoxConstraint: 37.028 | | | | | | | | | KernelScale: 0.033731 | | | | | | | | | Epsilon: 0.2457 | | 25 | Accept | 3.352 | 0.049267 | 2.173 | 2.1774 | tree | MinLeafSize: 122 | | 26 | Accept | 4.1439 | 0.060427 | 2.173 | 2.1774 | svm | BoxConstraint: 0.01045 | | | | | | | | | KernelScale: 0.0024261 | | | | | | | | | Epsilon: 12.355 | | 27 | Accept | 2.3188 | 5.9728 | 2.173 | 2.1761 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 212 | | | | | | | | | MinLeafSize: 2 | | 28 | Accept | 2.4075 | 5.8104 | 2.173 | 2.1765 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 247 | | | | | | | | | MinLeafSize: 83 | | 29 | Accept | 2.6056 | 0.098163 | 2.173 | 2.1765 | tree | MinLeafSize: 2 | | 30 | Accept | 4.1439 | 0.070094 | 2.173 | 2.1765 | 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 | 0.049706 | 2.173 | 2.1765 | tree | MinLeafSize: 8 | | 32 | Accept | 2.6443 | 4.9903 | 2.173 | 2.1764 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 229 | | | | | | | | | MinLeafSize: 52 | | 33 | Accept | 2.241 | 5.9324 | 2.173 | 2.175 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 235 | | | | | | | | | MinLeafSize: 26 | | 34 | Accept | 2.5448 | 0.046743 | 2.173 | 2.175 | tree | MinLeafSize: 19 | | 35 | Accept | 2.4438 | 0.068662 | 2.173 | 2.175 | tree | MinLeafSize: 13 | | 36 | Accept | 2.7182 | 0.076403 | 2.173 | 2.175 | tree | MinLeafSize: 1 | | 37 | Accept | 2.4749 | 0.047877 | 2.173 | 2.175 | tree | MinLeafSize: 9 | | 38 | Accept | 13.083 | 30.935 | 2.173 | 2.175 | svm | BoxConstraint: 5.2568 | | | | | | | | | KernelScale: 10.811 | | | | | | | | | Epsilon: 0.073361 | | 39 | Accept | 2.2349 | 5.6292 | 2.173 | 2.1758 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 214 | | | | | | | | | MinLeafSize: 4 | | 40 | Accept | 3.0919 | 0.044015 | 2.173 | 2.1758 | 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 | 6.4037 | 2.173 | 2.1735 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 280 | | | | | | | | | MinLeafSize: 45 | | 42 | Accept | 4.1439 | 0.077174 | 2.173 | 2.1735 | svm | BoxConstraint: 0.093799 | | | | | | | | | KernelScale: 0.0053728 | | | | | | | | | Epsilon: 17.332 | | 43 | Accept | 2.8766 | 0.097864 | 2.173 | 2.1735 | svm | BoxConstraint: 0.20553 | | | | | | | | | KernelScale: 880.29 | | | | | | | | | Epsilon: 4.5637 | | 44 | Accept | 2.1763 | 5.7872 | 2.173 | 2.1731 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 233 | | | | | | | | | MinLeafSize: 2 | | 45 | Accept | 2.4576 | 5.4877 | 2.173 | 2.1732 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 232 | | | | | | | | | MinLeafSize: 27 | | 46 | Accept | 4.1439 | 0.052135 | 2.173 | 2.1732 | svm | BoxConstraint: 0.0010276 | | | | | | | | | KernelScale: 5.6652 | | | | | | | | | Epsilon: 804.02 | | 47 | Accept | 3.1594 | 0.08652 | 2.173 | 2.1732 | svm | BoxConstraint: 0.002278 | | | | | | | | | KernelScale: 906.35 | | | | | | | | | Epsilon: 0.015573 | | 48 | Accept | 14.659 | 21.351 | 2.173 | 2.1732 | svm | BoxConstraint: 0.0010072 | | | | | | | | | KernelScale: 39.716 | | | | | | | | | Epsilon: 0.039845 | | 49 | Accept | 4.1439 | 0.06733 | 2.173 | 2.1732 | svm | BoxConstraint: 0.0010085 | | | | | | | | | KernelScale: 0.24517 | | | | | | | | | Epsilon: 447.36 | | 50 | Accept | 4.1439 | 0.067864 | 2.173 | 2.1732 | svm | BoxConstraint: 893.9 | | | | | | | | | KernelScale: 290.03 | | | | | | | | | Epsilon: 624.64 | |=========================================================================================================================================| | 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 | 2.6859 | 2.8671 | 2.173 | 2.1732 | svm | BoxConstraint: 0.0019596 | | | | | | | | | KernelScale: 264.51 | | | | | | | | | Epsilon: 0.0090654 | | 52 | Accept | 4.1439 | 0.066538 | 2.173 | 2.1732 | svm | BoxConstraint: 904.73 | | | | | | | | | KernelScale: 0.099617 | | | | | | | | | Epsilon: 0.014351 | | 53 | Accept | 4.1439 | 0.050841 | 2.173 | 2.1732 | svm | BoxConstraint: 975.67 | | | | | | | | | KernelScale: 0.50151 | | | | | | | | | Epsilon: 88.566 | | 54 | Accept | 4.1439 | 0.065868 | 2.173 | 2.1732 | svm | BoxConstraint: 0.0011848 | | | | | | | | | KernelScale: 201.25 | | | | | | | | | Epsilon: 441.13 | | 55 | Accept | 4.8245 | 19.19 | 2.173 | 2.1732 | svm | BoxConstraint: 548.22 | | | | | | | | | KernelScale: 548.99 | | | | | | | | | Epsilon: 0.010854 | | 56 | Accept | 4.1439 | 0.08348 | 2.173 | 2.1732 | svm | BoxConstraint: 0.001489 | | | | | | | | | KernelScale: 895.16 | | | | | | | | | Epsilon: 855.15 | | 57 | Accept | 4.1439 | 0.076295 | 2.173 | 2.1732 | svm | BoxConstraint: 0.0074202 | | | | | | | | | KernelScale: 0.3217 | | | | | | | | | Epsilon: 0.0096831 | | 58 | Accept | 4.1439 | 0.085455 | 2.173 | 2.1732 | svm | BoxConstraint: 757.82 | | | | | | | | | KernelScale: 0.065896 | | | | | | | | | Epsilon: 870.69 | | 59 | Accept | 2.6999 | 5.8429 | 2.173 | 2.1732 | svm | BoxConstraint: 0.00131 | | | | | | | | | KernelScale: 249.09 | | | | | | | | | Epsilon: 0.27904 | | 60 | Accept | 4.1439 | 0.076182 | 2.173 | 2.1732 | svm | BoxConstraint: 0.001578 | | | | | | | | | KernelScale: 0.010906 | | | | | | | | | Epsilon: 0.0091265 | |=========================================================================================================================================| | 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 | 4.1439 | 0.057696 | 2.173 | 2.1732 | svm | BoxConstraint: 0.0011475 | | | | | | | | | KernelScale: 1.2958 | | | | | | | | | Epsilon: 354.6 | | 62 | Accept | 4.1439 | 0.077794 | 2.173 | 2.1732 | svm | BoxConstraint: 0.0027272 | | | | | | | | | KernelScale: 0.0010042 | | | | | | | | | Epsilon: 0.014664 | | 63 | Accept | 2.3368 | 5.1396 | 2.173 | 2.1732 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 205 | | | | | | | | | MinLeafSize: 1 | | 64 | Accept | 2.7175 | 12.745 | 2.173 | 2.1732 | svm | BoxConstraint: 0.0011027 | | | | | | | | | KernelScale: 188.56 | | | | | | | | | Epsilon: 0.0089013 | | 65 | Accept | 2.173 | 4.8092 | 2.173 | 2.1731 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 200 | | | | | | | | | MinLeafSize: 1 | | 66 | Accept | 4.1439 | 0.060669 | 2.173 | 2.1731 | svm | BoxConstraint: 0.011536 | | | | | | | | | KernelScale: 0.0039517 | | | | | | | | | Epsilon: 0.0090597 | | 67 | Best | 2.173 | 8.695 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 300 | | | | | | | | | MinLeafSize: 1 | | 68 | Accept | 2.173 | 5.0512 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 202 | | | | | | | | | MinLeafSize: 1 | | 69 | Accept | 2.173 | 7.5798 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 299 | | | | | | | | | MinLeafSize: 1 | | 70 | Accept | 2.173 | 4.8479 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 200 | | | | | | | | | 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) | | | |=========================================================================================================================================| | 71 | Accept | 2.173 | 7.5734 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 300 | | | | | | | | | MinLeafSize: 1 | | 72 | Accept | 2.173 | 7.4612 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 299 | | | | | | | | | MinLeafSize: 1 | | 73 | Accept | 2.173 | 4.7911 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 200 | | | | | | | | | MinLeafSize: 1 | | 74 | Accept | 2.173 | 7.333 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 299 | | | | | | | | | MinLeafSize: 1 | | 75 | Accept | 2.173 | 7.0648 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 277 | | | | | | | | | MinLeafSize: 1 | | 76 | Accept | 2.173 | 4.9778 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 200 | | | | | | | | | MinLeafSize: 1 | | 77 | Accept | 2.173 | 4.6684 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 200 | | | | | | | | | MinLeafSize: 1 | | 78 | Accept | 2.173 | 7.1746 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 297 | | | | | | | | | MinLeafSize: 1 | | 79 | Accept | 2.1763 | 5.5721 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 230 | | | | | | | | | MinLeafSize: 2 | | 80 | Accept | 2.173 | 4.9422 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 200 | | | | | | | | | 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) | | | |=========================================================================================================================================| | 81 | Accept | 2.173 | 7.4431 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 298 | | | | | | | | | MinLeafSize: 1 | | 82 | Accept | 2.173 | 7.4708 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 299 | | | | | | | | | MinLeafSize: 1 | | 83 | Accept | 2.173 | 4.8532 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 202 | | | | | | | | | MinLeafSize: 1 | | 84 | Accept | 2.173 | 7.3628 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 300 | | | | | | | | | MinLeafSize: 1 | | 85 | Accept | 2.173 | 5.8364 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 240 | | | | | | | | | MinLeafSize: 1 | | 86 | Accept | 2.173 | 4.821 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 200 | | | | | | | | | MinLeafSize: 1 | | 87 | Accept | 2.173 | 5.4126 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 220 | | | | | | | | | MinLeafSize: 1 | | 88 | Accept | 2.173 | 7.9721 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 300 | | | | | | | | | MinLeafSize: 1 | | 89 | Accept | 2.173 | 6.8672 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 275 | | | | | | | | | MinLeafSize: 1 | | 90 | Accept | 2.173 | 4.9636 | 2.173 | 2.173 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 216 | | | | | | | | | MinLeafSize: 1 |
__________________________________________________________ Optimization completed. Total iterations: 90 Total elapsed time: 643.9812 seconds Total time for training and validation: 401.0444 seconds Best observed learner is an ensemble model with: Method: LSBoost NumLearningCycles: 300 MinLeafSize: 1 Observed log(1 + valLoss): 2.173 Time for training and validation: 8.695 seconds Best estimated learner (returned model) is an ensemble model with: Method: LSBoost NumLearningCycles: 300 MinLeafSize: 1 Estimated log(1 + valLoss): 2.173 Estimated time for training and validation: 7.5797 seconds Documentation for fitrauto display
Итоговая модель возвращена fitrauto соответствует лучшему предполагаемому ученику. Прежде, чем возвратить модель, функция переобучает его с помощью целых обучающих данных (carsTrain), перечисленный Learner (или модель) тип и отображенные гиперзначения параметров.
Оцените эффективность набора тестов
Оцените эффективность модели на наборе тестов. testError основан на среднеквадратической ошибке (MSE) набора тестов. Меньшие значения MSE указывают на лучшую эффективность.
testMSE = loss(Mdl,carsTest,"MPG");
testError = log(1 + testMSE)testError = 2.2971
Используйте fitrauto автоматически выбрать модель регрессии оптимизированными гиперпараметрами, учитывая предиктор и данные об ответе, хранимые в отдельных переменных.
Загрузка данных
Загрузите carbig набор данных, который содержит измерения автомобилей, сделанных в 1970-х и в начале 1980-х.
load carbigСоздайте матричный X содержа переменные предикторы Acceleration, Cylinders, и так далее. Сохраните переменную отклика MPG в переменной Y.
X = [Acceleration Cylinders Displacement Weight]; Y = MPG;
Создайте переменную, указывающую, какие предикторы являются категориальными. Cylinders единственная категориальная переменная в X.
categoricalVars = [false true false false];
Данные о разделе
Разделите данные в наборы обучающих данных и наборы тестов. Используйте приблизительно 80% наблюдений для выбора модели и настраивающего процесса гиперпараметра, и 20% наблюдений, чтобы проверить производительность итоговой модели, возвращенной fitrauto. Используйте cvpartition разделить данные.
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);
Запустите fitrauto
Передайте обучающие данные fitrauto. По умолчанию, fitrauto определяет соответствующую модель (или ученик) типы, чтобы попробовать, использует Байесовую оптимизацию, чтобы найти хорошие гиперзначения параметров для тех моделей и возвращает обученную модель Mdl с лучшей ожидаемой эффективностью. Задайте категориальные предикторы и запуститесь, оптимизация параллельно (требует Parallel Computing Toolbox™). Возвратите второй выход OptimizationResults это содержит детали Байесовой оптимизации.
Ожидайте, что этот процесс займет время. По умолчанию, fitrauto предоставляет график оптимизации и итеративное отображение результатов оптимизации. Для получения дополнительной информации о том, как интерпретировать эти результаты, смотрите Многословное 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 | 1.4452 | 3.0205 | 3.0329 | tree | MinLeafSize: 6 | | 2 | 5 | Accept | 3.0453 | 1.431 | 3.0205 | 3.0329 | tree | MinLeafSize: 5 | | 3 | 5 | Accept | 4.143 | 2.2922 | 3.0205 | 3.0329 | svm | BoxConstraint: 336.91 | | | | | | | | | | KernelScale: 0.0018275 | | | | | | | | | | Epsilon: 0.1074 | | 4 | 5 | Accept | 4.143 | 0.59844 | 3.0205 | 3.0329 | svm | BoxConstraint: 346.92 | | | | | | | | | | KernelScale: 0.032493 | | | | | | | | | | Epsilon: 0.23974 | | 5 | 6 | Best | 2.9275 | 0.30064 | 2.9275 | 2.9275 | svm | BoxConstraint: 0.033068 | | | | | | | | | | KernelScale: 585.38 | | | | | | | | | | Epsilon: 4.6993 | | 6 | 5 | Accept | 4.1439 | 6.9662 | 2.9275 | 2.9275 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 257 | | | | | | | | | | MinLeafSize: 156 | | 7 | 5 | Accept | 2.9275 | 0.83001 | 2.9275 | 2.9275 | svm | BoxConstraint: 0.033068 | | | | | | | | | | KernelScale: 585.38 | | | | | | | | | | Epsilon: 4.6993 | | 8 | 4 | Accept | 2.938 | 9.5987 | 2.9275 | 2.9275 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | | MinLeafSize: 1 | | 9 | 4 | Accept | 4.143 | 0.15524 | 2.9275 | 2.9275 | svm | BoxConstraint: 48.997 | | | | | | | | | | KernelScale: 0.0045904 | | | | | | | | | | Epsilon: 18.085 | | 10 | 6 | Accept | 4.143 | 0.18295 | 2.9275 | 2.9275 | svm | BoxConstraint: 0.0021787 | | | | | | | | | | KernelScale: 0.018209 | | | | | | | | | | Epsilon: 443.71 | |===================================================================================================================================================| | 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 | 4 | Best | 2.8597 | 8.2455 | 2.8597 | 2.9275 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 278 | | | | | | | | | | MinLeafSize: 13 | | 12 | 4 | Accept | 4.143 | 0.64902 | 2.8597 | 2.9275 | svm | BoxConstraint: 0.0021787 | | | | | | | | | | KernelScale: 0.018209 | | | | | | | | | | Epsilon: 443.71 | | 13 | 4 | Accept | 4.143 | 0.52394 | 2.8597 | 2.9275 | svm | BoxConstraint: 0.0021787 | | | | | | | | | | KernelScale: 0.018209 | | | | | | | | | | Epsilon: 443.71 | | 14 | 5 | Accept | 3.2501 | 0.21659 | 2.8597 | 2.9275 | tree | MinLeafSize: 1 | | 15 | 5 | Accept | 3.2501 | 0.15812 | 2.8597 | 2.9275 | tree | MinLeafSize: 1 | | 16 | 4 | Accept | 2.9167 | 7.7641 | 2.8597 | 2.9275 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | | MinLeafSize: 63 | | 17 | 4 | Accept | 3.2501 | 0.1166 | 2.8597 | 2.9275 | tree | MinLeafSize: 1 | | 18 | 4 | Accept | 3.1971 | 0.37955 | 2.8597 | 2.9275 | tree | MinLeafSize: 2 | | 19 | 2 | Accept | 3.6673 | 21.933 | 2.8597 | 2.9276 | svm | BoxConstraint: 0.033502 | | | | | | | | | | KernelScale: 153.38 | | | | | | | | | | Epsilon: 0.093672 | | 20 | 2 | Accept | 2.8734 | 6.5786 | 2.8597 | 2.9276 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | | MinLeafSize: 17 | |===================================================================================================================================================| | 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 | 2 | Accept | 4.143 | 0.089152 | 2.8597 | 2.9276 | svm | BoxConstraint: 37.028 | | | | | | | | | | KernelScale: 0.033731 | | | | | | | | | | Epsilon: 0.2457 | | 22 | 6 | Accept | 3.3225 | 0.186 | 2.8597 | 2.9276 | tree | MinLeafSize: 122 | | 23 | 4 | Accept | 2.9536 | 0.15373 | 2.8597 | 2.9276 | tree | MinLeafSize: 11 | | 24 | 4 | Accept | 4.143 | 0.2424 | 2.8597 | 2.9276 | svm | BoxConstraint: 240.91 | | | | | | | | | | KernelScale: 0.0063646 | | | | | | | | | | Epsilon: 92.342 | | 25 | 4 | Accept | 2.9969 | 0.2371 | 2.8597 | 2.9276 | tree | MinLeafSize: 40 | | 26 | 4 | Accept | 3.1971 | 0.087498 | 2.8597 | 2.9276 | tree | MinLeafSize: 2 | | 27 | 3 | Accept | 3.0259 | 5.4043 | 2.8597 | 2.8589 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 247 | | | | | | | | | | MinLeafSize: 83 | | 28 | 3 | Accept | 2.8673 | 5.2056 | 2.8597 | 2.8589 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 234 | | | | | | | | | | MinLeafSize: 31 | | 29 | 6 | Accept | 2.9403 | 0.060585 | 2.8597 | 2.8589 | tree | MinLeafSize: 13 | | 30 | 4 | Accept | 2.868 | 4.3862 | 2.8597 | 2.8589 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 229 | | | | | | | | | | MinLeafSize: 52 | |===================================================================================================================================================| | 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 | 4 | Accept | 3.3587 | 0.46693 | 2.8597 | 2.8589 | tree | MinLeafSize: 109 | | 32 | 4 | Accept | 3.1971 | 0.32157 | 2.8597 | 2.8589 | tree | MinLeafSize: 2 | | 33 | 4 | Accept | 3.2501 | 0.078839 | 2.8597 | 2.8589 | tree | MinLeafSize: 1 | | 34 | 4 | Accept | 2.8708 | 5.4437 | 2.8597 | 2.8595 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 235 | | | | | | | | | | MinLeafSize: 26 | | 35 | 3 | Best | 2.8244 | 5.9186 | 2.8244 | 2.8595 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 275 | | | | | | | | | | MinLeafSize: 4 | | 36 | 3 | Accept | 3.112 | 0.053088 | 2.8244 | 2.8595 | tree | MinLeafSize: 62 | | 37 | 6 | Accept | 2.8872 | 5.1029 | 2.8244 | 2.8245 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 214 | | | | | | | | | | MinLeafSize: 4 | | 38 | 5 | Accept | 2.9282 | 0.095731 | 2.8244 | 2.8245 | svm | BoxConstraint: 0.20553 | | | | | | | | | | KernelScale: 880.29 | | | | | | | | | | Epsilon: 4.5637 | | 39 | 5 | Accept | 4.143 | 0.087217 | 2.8244 | 2.8245 | svm | BoxConstraint: 26.303 | | | | | | | | | | KernelScale: 0.40313 | | | | | | | | | | Epsilon: 228.3 | | 40 | 2 | Accept | 2.8652 | 5.7512 | 2.8242 | 2.8242 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 280 | | | | | | | | | | 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) | | | |===================================================================================================================================================| | 41 | 2 | Accept | 3.0951 | 5.1977 | 2.8242 | 2.8242 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 250 | | | | | | | | | | MinLeafSize: 70 | | 42 | 2 | Best | 2.8242 | 5.2948 | 2.8242 | 2.8242 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 207 | | | | | | | | | | MinLeafSize: 8 | | 43 | 2 | Accept | 2.9041 | 5.4999 | 2.8242 | 2.8242 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 233 | | | | | | | | | | MinLeafSize: 2 | | 44 | 5 | Accept | 2.9804 | 0.074442 | 2.8242 | 2.8242 | tree | MinLeafSize: 8 | | 45 | 5 | Accept | 3.3765 | 0.047037 | 2.8242 | 2.8242 | tree | MinLeafSize: 117 | | 46 | 4 | Accept | 4.143 | 0.095028 | 2.8242 | 2.8242 | svm | BoxConstraint: 0.032384 | | | | | | | | | | KernelScale: 797.08 | | | | | | | | | | Epsilon: 64.843 | | 47 | 4 | Accept | 4.143 | 0.061103 | 2.8242 | 2.8242 | svm | BoxConstraint: 28.209 | | | | | | | | | | KernelScale: 77.831 | | | | | | | | | | Epsilon: 21.256 | | 48 | 3 | Accept | 2.8452 | 3.6683 | 2.8242 | 2.8243 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 200 | | | | | | | | | | MinLeafSize: 1 | | 49 | 3 | Accept | 2.8655 | 4.0616 | 2.8242 | 2.8243 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 202 | | | | | | | | | | MinLeafSize: 1 | | 50 | 6 | Accept | 4.143 | 0.10804 | 2.8242 | 2.8243 | svm | BoxConstraint: 267.23 | | | | | | | | | | KernelScale: 0.028148 | | | | | | | | | | Epsilon: 0.097477 | |===================================================================================================================================================| | 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 | 4.8036 | 16.322 | 2.8193 | 2.8188 | svm | BoxConstraint: 0.006061 | | | | | | | | | | KernelScale: 127.62 | | | | | | | | | | Epsilon: 0.0090183 | | 52 | 3 | Best | 2.8193 | 4.0637 | 2.8193 | 2.8188 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 200 | | | | | | | | | | MinLeafSize: 23 | | 53 | 3 | Accept | 2.8228 | 6.0192 | 2.8193 | 2.8188 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 298 | | | | | | | | | | MinLeafSize: 5 | | 54 | 3 | Accept | 2.8448 | 5.0715 | 2.8193 | 2.8188 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 249 | | | | | | | | | | MinLeafSize: 2 | | 55 | 6 | Accept | 3.2501 | 0.077577 | 2.8193 | 2.8188 | tree | MinLeafSize: 1 | | 56 | 4 | Accept | 2.9351 | 0.098541 | 2.8193 | 2.8188 | svm | BoxConstraint: 0.015396 | | | | | | | | | | KernelScale: 707.02 | | | | | | | | | | Epsilon: 1.8654 | | 57 | 4 | Accept | 4.143 | 0.062758 | 2.8193 | 2.8188 | svm | BoxConstraint: 0.20213 | | | | | | | | | | KernelScale: 0.56699 | | | | | | | | | | Epsilon: 803.81 | | 58 | 4 | Accept | 4.143 | 0.076261 | 2.8193 | 2.8188 | svm | BoxConstraint: 0.001047 | | | | | | | | | | KernelScale: 0.0019199 | | | | | | | | | | Epsilon: 4.501 | | 59 | 4 | Accept | 2.8469 | 3.5621 | 2.8193 | 2.8223 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 200 | | | | | | | | | | MinLeafSize: 35 | | 60 | 5 | Accept | 2.8288 | 3.9552 | 2.8193 | 2.8223 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 207 | | | | | | | | | | MinLeafSize: 14 | |===================================================================================================================================================| | 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 | 5 | Accept | 4.143 | 0.066618 | 2.8193 | 2.8223 | svm | BoxConstraint: 0.043338 | | | | | | | | | | KernelScale: 0.026299 | | | | | | | | | | Epsilon: 0.057475 | | 62 | 5 | Accept | 4.143 | 31.142 | 2.8193 | 2.8223 | svm | BoxConstraint: 13.655 | | | | | | | | | | KernelScale: 4.3086 | | | | | | | | | | Epsilon: 6.9116 | | 63 | 4 | Accept | 2.8697 | 7.1892 | 2.8193 | 2.8223 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 291 | | | | | | | | | | MinLeafSize: 8 | | 64 | 4 | Accept | 4.143 | 0.051217 | 2.8193 | 2.8223 | svm | BoxConstraint: 164.25 | | | | | | | | | | KernelScale: 422 | | | | | | | | | | Epsilon: 709.16 | | 65 | 4 | Accept | 15.816 | 29.101 | 2.8193 | 2.8223 | svm | BoxConstraint: 280.6 | | | | | | | | | | KernelScale: 20.045 | | | | | | | | | | Epsilon: 2.9565 | | 66 | 4 | Accept | 2.8697 | 6.626 | 2.8193 | 2.8224 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 300 | | | | | | | | | | MinLeafSize: 8 | | 67 | 3 | Accept | 4.143 | 30.413 | 2.8193 | 2.8223 | svm | BoxConstraint: 1.3468 | | | | | | | | | | KernelScale: 9.6762 | | | | | | | | | | Epsilon: 0.023868 | | 68 | 3 | Accept | 2.8398 | 7.0162 | 2.8193 | 2.8223 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 386 | | | | | | | | | | MinLeafSize: 3 | | 69 | 3 | Accept | 2.8358 | 6.4998 | 2.8193 | 2.8223 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 344 | | | | | | | | | | MinLeafSize: 21 | | 70 | 3 | Accept | 4.143 | 0.076191 | 2.8193 | 2.8223 | svm | BoxConstraint: 6.1442 | | | | | | | | | | KernelScale: 0.068257 | | | | | | | | | | Epsilon: 5.7363 | |===================================================================================================================================================| | 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 | 0.066335 | 2.8193 | 2.8223 | svm | BoxConstraint: 0.027503 | | | | | | | | | | KernelScale: 0.0041093 | | | | | | | | | | Epsilon: 0.051041 | | 72 | 3 | Accept | 4.143 | 0.07249 | 2.8193 | 2.8223 | svm | BoxConstraint: 0.52138 | | | | | | | | | | KernelScale: 0.43854 | | | | | | | | | | Epsilon: 0.67088 | | 73 | 5 | Accept | 2.8214 | 3.9165 | 2.8193 | 2.8215 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 207 | | | | | | | | | | MinLeafSize: 6 | | 74 | 5 | Accept | 2.8872 | 6.1359 | 2.8193 | 2.8215 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 252 | | | | | | | | | | MinLeafSize: 4 | | 75 | 3 | Accept | 2.9284 | 0.054998 | 2.8193 | 2.8215 | tree | MinLeafSize: 20 | | 76 | 3 | Accept | 2.8468 | 3.983 | 2.8193 | 2.8215 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 225 | | | | | | | | | | MinLeafSize: 33 | | 77 | 3 | Accept | 2.9969 | 0.10337 | 2.8193 | 2.8215 | tree | MinLeafSize: 40 | | 78 | 6 | Accept | 3.0866 | 0.058426 | 2.8193 | 2.8215 | svm | BoxConstraint: 0.0070395 | | | | | | | | | | KernelScale: 988.24 | | | | | | | | | | Epsilon: 0.0096375 | | 79 | 5 | Accept | 4.143 | 0.094698 | 2.8193 | 2.8215 | svm | BoxConstraint: 954.83 | | | | | | | | | | KernelScale: 0.0016114 | | | | | | | | | | Epsilon: 45.114 | | 80 | 5 | Accept | 3.2501 | 0.083131 | 2.8193 | 2.8215 | tree | MinLeafSize: 1 | |===================================================================================================================================================| | 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 | 6.269 | 2.8193 | 2.8215 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 294 | | | | | | | | | | MinLeafSize: 162 | | 82 | 3 | Accept | 2.8742 | 6.9216 | 2.8193 | 2.8215 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 293 | | | | | | | | | | MinLeafSize: 27 | | 83 | 3 | Accept | 4.143 | 0.051169 | 2.8193 | 2.8215 | svm | BoxConstraint: 0.47136 | | | | | | | | | | KernelScale: 0.11232 | | | | | | | | | | Epsilon: 0.058234 | | 84 | 2 | Accept | 9.656 | 19.111 | 2.8193 | 2.8215 | svm | BoxConstraint: 121.18 | | | | | | | | | | KernelScale: 196.01 | | | | | | | | | | Epsilon: 0.010913 | | 85 | 2 | Accept | 4.143 | 6.6385 | 2.8193 | 2.8215 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 294 | | | | | | | | | | MinLeafSize: 162 | | 86 | 2 | Accept | 3.0281 | 0.055432 | 2.8193 | 2.8215 | tree | MinLeafSize: 57 | | 87 | 2 | Accept | 3.1971 | 0.10328 | 2.8193 | 2.8215 | tree | MinLeafSize: 2 | | 88 | 2 | Accept | 3.1507 | 0.081176 | 2.8193 | 2.8215 | tree | MinLeafSize: 3 | | 89 | 6 | Accept | 2.8507 | 5.7074 | 2.8193 | 2.8214 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 275 | | | | | | | | | | MinLeafSize: 1 | | 90 | 5 | Accept | 4.143 | 0.078128 | 2.8193 | 2.8214 | svm | BoxConstraint: 220.96 | | | | | | | | | | KernelScale: 28.058 | | | | | | | | | | Epsilon: 66.219 | |===================================================================================================================================================| | 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 | 4.143 | 0.0599 | 2.8193 | 2.8214 | svm | BoxConstraint: 8.342 | | | | | | | | | | KernelScale: 70.835 | | | | | | | | | | Epsilon: 38.428 |
__________________________________________________________ Optimization completed. Total iterations: 91 Total elapsed time: 174.9553 seconds Total time for training and validation: 350.9822 seconds Best observed learner is an ensemble model with: Method: Bag NumLearningCycles: 200 MinLeafSize: 23 Observed log(1 + valLoss): 2.8193 Time for training and validation: 4.0637 seconds Best estimated learner (returned model) is an ensemble model with: Method: Bag NumLearningCycles: 207 MinLeafSize: 6 Estimated log(1 + valLoss): 2.8214 Estimated time for training and validation: 4.0733 seconds Documentation for fitrauto display
Итоговая модель возвращена fitrauto соответствует лучшему предполагаемому ученику. Прежде, чем возвратить модель, функция переобучает его с помощью целых обучающих данных (XTrain и YTrain), перечисленный Learner (или модель) тип и отображенные гиперзначения параметров.
Оцените эффективность набора тестов
Оцените эффективность модели на наборе тестов. testError основан на среднеквадратической ошибке (MSE) набора тестов. Меньшие значения MSE указывают на лучшую эффективность.
testMSE = loss(Mdl,XTest,YTest); testError = log(1 + testMSE)
testError = 2.8921
Используйте fitrauto автоматически выбрать модель регрессии оптимизированными гиперпараметрами, учитывая предиктор и данные об ответе, хранимые в таблице. Сравните эффективность получившейся модели регрессии к эффективности простой модели линейной регрессии, созданной с fitlm.
Загрузка и данные о разделе
Загрузите carbig набор данных, который содержит измерения автомобилей, сделанных в 1970-х и в начале 1980-х. Преобразуйте Cylinders переменная к categorical переменная. Составьте таблицу, содержащую переменные предикторы 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 в наборы обучающих данных и наборы тестов. Используйте приблизительно 80% наблюдений для обучения и 20% наблюдений для тестирования. Используйте cvpartition разделить данные.
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,:);
Запустите fitrauto
Передайте обучающие данные fitrauto. По умолчанию, fitrauto определяет соответствующие типы модели, чтобы попробовать, использует Байесовую оптимизацию, чтобы найти хорошие гиперзначения параметров и возвращает обученную модель autoMdl с лучшей ожидаемой эффективностью. Задайте, чтобы оптимизировать по всем optimizable гиперпараметрам и запуститься, оптимизация параллельно (требует Parallel Computing Toolbox™).
Ожидайте, что этот процесс займет время. По умолчанию, fitrauto предоставляет график оптимизации и итеративное отображение результатов оптимизации. Для получения дополнительной информации о том, как интерпретировать эти результаты, смотрите Многословное 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 | 3.1825 | 1.8704 | 2.6934 | 2.6935 | tree | MinLeafSize: 38 | | | | | | | | | | MaxNumSplits: 2 | | | | | | | | | | NumVariablesToSample: 1 | | 2 | 4 | Accept | 2.8075 | 1.8645 | 2.6934 | 2.6935 | tree | MinLeafSize: 1 | | | | | | | | | | MaxNumSplits: 44 | | | | | | | | | | NumVariablesToSample: 4 | | 3 | 4 | Best | 2.6934 | 1.854 | 2.6934 | 2.6935 | tree | MinLeafSize: 29 | | | | | | | | | | MaxNumSplits: 52 | | | | | | | | | | NumVariablesToSample: 6 | | 4 | 4 | Accept | 4.1439 | 2.6026 | 2.6934 | 2.6935 | svm | BoxConstraint: 0.010718 | | | | | | | | | | KernelScale: 1.7547 | | | | | | | | | | Epsilon: 182.6 | | 5 | 2 | Accept | 2.4136 | 7.0256 | 2.2154 | 2.6935 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.64294 | | | | | | | | | | MinLeafSize: 39 | | | | | | | | | | NumVariablesToSample: NaN | | 6 | 2 | Best | 2.2154 | 7.7597 | 2.2154 | 2.6935 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.033855 | | | | | | | | | | MinLeafSize: 6 | | | | | | | | | | NumVariablesToSample: NaN | | 7 | 2 | Accept | 4.1439 | 0.27852 | 2.2154 | 2.6935 | svm | BoxConstraint: 0.012677 | | | | | | | | | | KernelScale: 351.81 | | | | | | | | | | Epsilon: 140.99 | | 8 | 6 | Accept | 4.1439 | 0.85944 | 2.2154 | 2.6935 | svm | BoxConstraint: 37.191 | | | | | | | | | | KernelScale: 21.113 | | | | | | | | | | Epsilon: 33.874 | | 9 | 6 | Accept | 2.7394 | 1.4707 | 2.2154 | 2.6935 | svm | BoxConstraint: 0.057859 | | | | | | | | | | KernelScale: 448.87 | | | | | | | | | | Epsilon: 4.2169 | | 10 | 4 | Accept | 2.5848 | 5.8685 | 2.2154 | 2.4611 | 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 | 4 | Accept | 2.6816 | 5.073 | 2.2154 | 2.4611 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 51 | | | | | | | | | | NumVariablesToSample: 2 | | 12 | 4 | Accept | 2.4608 | 0.25674 | 2.2154 | 2.4611 | tree | MinLeafSize: 6 | | | | | | | | | | MaxNumSplits: 32 | | | | | | | | | | NumVariablesToSample: 5 | | 13 | 4 | Accept | 3.2336 | 6.4662 | 2.2154 | 2.4611 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.56281 | | | | | | | | | | MinLeafSize: 123 | | | | | | | | | | NumVariablesToSample: NaN | | 14 | 6 | Accept | 2.845 | 0.35832 | 2.2154 | 2.4611 | svm | BoxConstraint: 0.0027083 | | | | | | | | | | KernelScale: 413.17 | | | | | | | | | | Epsilon: 0.13572 | | 15 | 4 | Accept | 2.7122 | 5.2558 | 2.2154 | 2.4611 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.74839 | | | | | | | | | | MinLeafSize: 88 | | | | | | | | | | NumVariablesToSample: NaN | | 16 | 4 | Accept | 2.845 | 0.9025 | 2.2154 | 2.4611 | svm | BoxConstraint: 0.0027083 | | | | | | | | | | KernelScale: 413.17 | | | | | | | | | | Epsilon: 0.13572 | | 17 | 4 | Accept | 2.845 | 0.81343 | 2.2154 | 2.4611 | svm | BoxConstraint: 0.0027083 | | | | | | | | | | KernelScale: 413.17 | | | | | | | | | | Epsilon: 0.13572 | | 18 | 3 | Accept | 2.6527 | 4.4298 | 2.2154 | 2.4723 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 46 | | | | | | | | | | NumVariablesToSample: 2 | | 19 | 3 | Accept | 2.5035 | 0.29266 | 2.2154 | 2.4723 | tree | MinLeafSize: 5 | | | | | | | | | | MaxNumSplits: 18 | | | | | | | | | | NumVariablesToSample: 5 | | 20 | 6 | Accept | 2.8243 | 0.15229 | 2.2154 | 2.4616 | tree | MinLeafSize: 12 | | | | | | | | | | MaxNumSplits: 5 | | | | | | | | | | 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) | | | |===================================================================================================================================================| | 21 | 4 | Accept | 4.143 | 0.064514 | 2.2154 | 2.4607 | tree | MinLeafSize: 132 | | | | | | | | | | MaxNumSplits: 8 | | | | | | | | | | NumVariablesToSample: 5 | | 22 | 4 | Accept | 4.143 | 0.18836 | 2.2154 | 2.4607 | tree | MinLeafSize: 138 | | | | | | | | | | MaxNumSplits: 3 | | | | | | | | | | NumVariablesToSample: 7 | | 23 | 4 | Accept | 3.3663 | 0.13449 | 2.2154 | 2.4607 | tree | MinLeafSize: 83 | | | | | | | | | | MaxNumSplits: 41 | | | | | | | | | | NumVariablesToSample: 2 | | 24 | 3 | Accept | 2.3614 | 4.546 | 2.2154 | 2.4607 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: 2 | | 25 | 3 | Accept | 4.1439 | 0.58435 | 2.2154 | 2.4607 | svm | BoxConstraint: 0.0050384 | | | | | | | | | | KernelScale: 0.18651 | | | | | | | | | | Epsilon: 11.818 | | 26 | 6 | Accept | 4.1439 | 0.07419 | 2.2154 | 2.4607 | svm | BoxConstraint: 0.19519 | | | | | | | | | | KernelScale: 0.48473 | | | | | | | | | | Epsilon: 0.02267 | | 27 | 6 | Accept | 2.5796 | 0.081162 | 2.2154 | 2.4613 | tree | MinLeafSize: 8 | | | | | | | | | | MaxNumSplits: 85 | | | | | | | | | | NumVariablesToSample: 5 | | 28 | 5 | Accept | 5.9862 | 5.516 | 2.2154 | 2.4622 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.001143 | | | | | | | | | | MinLeafSize: 104 | | | | | | | | | | NumVariablesToSample: NaN | | 29 | 5 | Accept | 2.6716 | 0.071817 | 2.2154 | 2.4622 | tree | MinLeafSize: 6 | | | | | | | | | | MaxNumSplits: 43 | | | | | | | | | | NumVariablesToSample: 2 | | 30 | 2 | Accept | 4.1439 | 33.722 | 2.2154 | 2.4815 | svm | BoxConstraint: 0.15265 | | | | | | | | | | KernelScale: 1.4893 | | | | | | | | | | Epsilon: 0.44287 | |===================================================================================================================================================| | 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 | 2.2534 | 6.2607 | 2.2154 | 2.4815 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 12 | | | | | | | | | | NumVariablesToSample: 7 | | 32 | 2 | Accept | 2.9788 | 6.8285 | 2.2154 | 2.4815 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.010155 | | | | | | | | | | MinLeafSize: 13 | | | | | | | | | | NumVariablesToSample: NaN | | 33 | 2 | Accept | 2.7529 | 0.055823 | 2.2154 | 2.4815 | tree | MinLeafSize: 1 | | | | | | | | | | MaxNumSplits: 123 | | | | | | | | | | NumVariablesToSample: 2 | | 34 | 6 | Accept | 3.0557 | 0.4318 | 2.2154 | 2.494 | tree | MinLeafSize: 42 | | | | | | | | | | MaxNumSplits: 4 | | | | | | | | | | NumVariablesToSample: 4 | | 35 | 3 | Accept | 4.1439 | 0.27218 | 2.2154 | 2.494 | svm | BoxConstraint: 2.1967 | | | | | | | | | | KernelScale: 0.02117 | | | | | | | | | | Epsilon: 0.20631 | | 36 | 3 | Accept | 3.2946 | 0.066155 | 2.2154 | 2.494 | tree | MinLeafSize: 88 | | | | | | | | | | MaxNumSplits: 2 | | | | | | | | | | NumVariablesToSample: 2 | | 37 | 3 | Accept | 4.1439 | 0.13289 | 2.2154 | 2.494 | svm | BoxConstraint: 127.62 | | | | | | | | | | KernelScale: 0.0010166 | | | | | | | | | | Epsilon: 16.049 | | 38 | 3 | Accept | 4.1439 | 0.12273 | 2.2154 | 2.494 | svm | BoxConstraint: 77.831 | | | | | | | | | | KernelScale: 11.323 | | | | | | | | | | Epsilon: 24.046 | | 39 | 6 | Accept | 4.1439 | 0.090716 | 2.2154 | 2.494 | svm | BoxConstraint: 1.5262 | | | | | | | | | | KernelScale: 0.16982 | | | | | | | | | | Epsilon: 0.09432 | | 40 | 5 | Accept | 4.1439 | 0.060884 | 2.2154 | 2.494 | svm | BoxConstraint: 347.06 | | | | | | | | | | KernelScale: 0.024995 | | | | | | | | | | Epsilon: 0.012891 | |===================================================================================================================================================| | 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 | 4.1439 | 0.078944 | 2.2154 | 2.494 | svm | BoxConstraint: 0.017688 | | | | | | | | | | KernelScale: 968.17 | | | | | | | | | | Epsilon: 350.72 | | 42 | 4 | Accept | 2.5097 | 14.423 | 2.1926 | 2.1939 | svm | BoxConstraint: 5.9191 | | | | | | | | | | KernelScale: 699.18 | | | | | | | | | | Epsilon: 0.010916 | | 43 | 4 | Best | 2.1926 | 6.6572 | 2.1926 | 2.1939 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.03225 | | | | | | | | | | MinLeafSize: 6 | | | | | | | | | | NumVariablesToSample: NaN | | 44 | 4 | Accept | 4.1439 | 0.055712 | 2.1926 | 2.1939 | svm | BoxConstraint: 0.00076626 | | | | | | | | | | KernelScale: 0.27348 | | | | | | | | | | Epsilon: 0.18351 | | 45 | 2 | Accept | 13.985 | 32.958 | 2.1926 | 2.1967 | svm | BoxConstraint: 797.08 | | | | | | | | | | KernelScale: 43.175 | | | | | | | | | | Epsilon: 4.1489 | | 46 | 2 | Accept | 4.1439 | 30.972 | 2.1926 | 2.1967 | svm | BoxConstraint: 0.067167 | | | | | | | | | | KernelScale: 6.6015 | | | | | | | | | | Epsilon: 0.010914 | | 47 | 2 | Accept | 2.2235 | 6.0717 | 2.1926 | 2.1967 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.022919 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 48 | 6 | Accept | 4.1439 | 0.054027 | 2.1926 | 2.1967 | svm | BoxConstraint: 1.4081 | | | | | | | | | | KernelScale: 1068.3 | | | | | | | | | | Epsilon: 47.856 | | 49 | 2 | Accept | 2.5906 | 4.7498 | 2.1926 | 2.0428 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.96713 | | | | | | | | | | MinLeafSize: 14 | | | | | | | | | | NumVariablesToSample: NaN | | 50 | 2 | Accept | 4.1439 | 0.080148 | 2.1926 | 2.0428 | svm | BoxConstraint: 19.339 | | | | | | | | | | KernelScale: 336.27 | | | | | | | | | | Epsilon: 745.75 | |===================================================================================================================================================| | 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 | 2 | Accept | 2.4027 | 0.12426 | 2.1926 | 2.0428 | tree | MinLeafSize: 8 | | | | | | | | | | MaxNumSplits: 80 | | | | | | | | | | NumVariablesToSample: 5 | | 52 | 2 | Accept | 3.3875 | 0.1023 | 2.1926 | 2.0428 | tree | MinLeafSize: 84 | | | | | | | | | | MaxNumSplits: 4 | | | | | | | | | | NumVariablesToSample: 7 | | 53 | 2 | Accept | 4.1439 | 0.050927 | 2.1926 | 2.0428 | svm | BoxConstraint: 94.294 | | | | | | | | | | KernelScale: 0.0014232 | | | | | | | | | | Epsilon: 0.0090047 | | 54 | 6 | Accept | 4.859 | 6.2453 | 2.1926 | 2.2036 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0040831 | | | | | | | | | | MinLeafSize: 10 | | | | | | | | | | NumVariablesToSample: NaN | | 55 | 1 | Accept | 2.624 | 4.7525 | 2.1926 | 2.2036 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 51 | | | | | | | | | | NumVariablesToSample: 6 | | 56 | 1 | Accept | 2.7473 | 0.060583 | 2.1926 | 2.2036 | tree | MinLeafSize: 9 | | | | | | | | | | MaxNumSplits: 204 | | | | | | | | | | NumVariablesToSample: 2 | | 57 | 1 | Accept | 4.1439 | 0.066677 | 2.1926 | 2.2036 | svm | BoxConstraint: 0.0012156 | | | | | | | | | | KernelScale: 0.015427 | | | | | | | | | | Epsilon: 0.060481 | | 58 | 1 | Accept | 4.1439 | 0.094823 | 2.1926 | 2.2036 | svm | BoxConstraint: 0.44269 | | | | | | | | | | KernelScale: 0.004171 | | | | | | | | | | Epsilon: 0.12586 | | 59 | 1 | Accept | 3.0883 | 0.0586 | 2.1926 | 2.2036 | tree | MinLeafSize: 23 | | | | | | | | | | MaxNumSplits: 4 | | | | | | | | | | NumVariablesToSample: 2 | | 60 | 1 | Accept | 4.1439 | 0.056798 | 2.1926 | 2.2036 | svm | BoxConstraint: 0.038648 | | | | | | | | | | KernelScale: 1.6731 | | | | | | | | | | Epsilon: 181.22 | |===================================================================================================================================================| | 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 | 6 | Accept | 4.1439 | 0.067435 | 2.1926 | 2.2036 | svm | BoxConstraint: 0.0073804 | | | | | | | | | | KernelScale: 0.26555 | | | | | | | | | | Epsilon: 0.0091652 | | 62 | 2 | Accept | 2.4796 | 4.6971 | 2.1926 | 2.2036 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 5 | | | | | | | | | | NumVariablesToSample: 1 | | 63 | 2 | Accept | 2.5862 | 0.087002 | 2.1926 | 2.2036 | tree | MinLeafSize: 2 | | | | | | | | | | MaxNumSplits: 36 | | | | | | | | | | NumVariablesToSample: 4 | | 64 | 2 | Accept | 2.5227 | 4.8002 | 2.1926 | 2.2036 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 35 | | | | | | | | | | NumVariablesToSample: 5 | | 65 | 2 | Accept | 2.2692 | 5.7741 | 2.1926 | 2.2036 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.025248 | | | | | | | | | | MinLeafSize: 29 | | | | | | | | | | NumVariablesToSample: NaN | | 66 | 2 | Accept | 4.1439 | 0.061232 | 2.1926 | 2.2036 | svm | BoxConstraint: 0.015213 | | | | | | | | | | KernelScale: 121.18 | | | | | | | | | | Epsilon: 228.77 | | 67 | 6 | Accept | 3.0619 | 0.20501 | 2.1926 | 2.2036 | tree | MinLeafSize: 8 | | | | | | | | | | MaxNumSplits: 37 | | | | | | | | | | NumVariablesToSample: 1 | | 68 | 2 | Accept | 4.1439 | 32.145 | 2.1926 | 2.1946 | svm | BoxConstraint: 0.023727 | | | | | | | | | | KernelScale: 2.1083 | | | | | | | | | | Epsilon: 0.026879 | | 69 | 2 | Accept | 2.2059 | 6.3033 | 2.1926 | 2.1946 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.030274 | | | | | | | | | | MinLeafSize: 9 | | | | | | | | | | NumVariablesToSample: NaN | | 70 | 2 | Accept | 2.5736 | 5.4884 | 2.1926 | 2.1946 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.015531 | | | | | | | | | | MinLeafSize: 76 | | | | | | | | | | 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 | 2 | Accept | 2.2438 | 6.4062 | 2.1926 | 2.1946 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 6 | | | | | | | | | | NumVariablesToSample: 7 | | 72 | 2 | Accept | 4.1429 | 4.1039 | 2.1926 | 2.1946 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 134 | | | | | | | | | | NumVariablesToSample: 2 | | 73 | 5 | Accept | 4.143 | 4.4894 | 2.1926 | 2.1946 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.17357 | | | | | | | | | | MinLeafSize: 177 | | | | | | | | | | NumVariablesToSample: NaN | | 74 | 5 | Accept | 4.1439 | 0.054069 | 2.1926 | 2.1946 | svm | BoxConstraint: 2.4711 | | | | | | | | | | KernelScale: 0.00086032 | | | | | | | | | | Epsilon: 0.65606 | | 75 | 3 | Accept | 4.1439 | 0.09691 | 2.1926 | 2.1949 | svm | BoxConstraint: 131.74 | | | | | | | | | | KernelScale: 0.0031145 | | | | | | | | | | Epsilon: 0.028465 | | 76 | 3 | Accept | 4.143 | 0.092964 | 2.1926 | 2.1949 | tree | MinLeafSize: 156 | | | | | | | | | | MaxNumSplits: 1 | | | | | | | | | | NumVariablesToSample: 5 | | 77 | 3 | Accept | 2.3039 | 4.4363 | 2.1926 | 2.1949 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 9 | | | | | | | | | | NumVariablesToSample: 3 | | 78 | 5 | Accept | 2.6824 | 0.088024 | 2.1926 | 2.1949 | tree | MinLeafSize: 11 | | | | | | | | | | MaxNumSplits: 6 | | | | | | | | | | NumVariablesToSample: 3 | | 79 | 5 | Accept | 4.1439 | 0.065162 | 2.1926 | 2.1949 | svm | BoxConstraint: 0.0010003 | | | | | | | | | | KernelScale: 0.85686 | | | | | | | | | | Epsilon: 699.42 | | 80 | 2 | Accept | 10.894 | 31.235 | 2.1926 | 2.1952 | svm | BoxConstraint: 0.05924 | | | | | | | | | | KernelScale: 16.477 | | | | | | | | | | Epsilon: 1.204 | |===================================================================================================================================================| | 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 | 2.3629 | 4.051 | 2.1926 | 2.1952 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: 2 | | 82 | 2 | Accept | 3.3755 | 0.057721 | 2.1926 | 2.1952 | tree | MinLeafSize: 79 | | | | | | | | | | MaxNumSplits: 65 | | | | | | | | | | NumVariablesToSample: 3 | | 83 | 2 | Accept | 2.3673 | 4.0629 | 2.1926 | 2.1952 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: 2 | | 84 | 6 | Accept | 2.6199 | 4.7274 | 2.1926 | 2.1952 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 53 | | | | | | | | | | NumVariablesToSample: 6 | | 85 | 2 | Accept | 3.1414 | 4.2529 | 2.1926 | 2.1985 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 75 | | | | | | | | | | NumVariablesToSample: 7 | | 86 | 2 | Accept | 2.2514 | 5.0768 | 2.1926 | 2.1985 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 4 | | | | | | | | | | NumVariablesToSample: 5 | | 87 | 2 | Accept | 4.1439 | 0.077312 | 2.1926 | 2.1985 | svm | BoxConstraint: 230.13 | | | | | | | | | | KernelScale: 15.715 | | | | | | | | | | Epsilon: 425.18 | | 88 | 2 | Accept | 4.1439 | 0.06662 | 2.1926 | 2.1985 | svm | BoxConstraint: 10.758 | | | | | | | | | | KernelScale: 0.020507 | | | | | | | | | | Epsilon: 4.9755 | | 89 | 2 | Accept | 2.2525 | 6.0028 | 2.1926 | 2.1985 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: 7 | | 90 | 5 | Accept | 2.5768 | 4.4924 | 2.1926 | 2.1985 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 40 | | | | | | | | | | NumVariablesToSample: 5 | |===================================================================================================================================================| | 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 | 4.1439 | 0.062303 | 2.1926 | 2.1985 | svm | BoxConstraint: 2.5681 | | | | | | | | | | KernelScale: 0.19989 | | | | | | | | | | Epsilon: 0.59994 |
__________________________________________________________ Optimization completed. Total iterations: 91 Total elapsed time: 279.9304 seconds Total time for training and validation: 366.0998 seconds Best observed learner is an ensemble model with: Method: LSBoost LearnRate: 0.03225 MinLeafSize: 6 NumVariablesToSample: NaN Observed log(1 + valLoss): 2.1926 Time for training and validation: 6.6572 seconds Best estimated learner (returned model) is an ensemble model with: Method: LSBoost LearnRate: 0.03225 MinLeafSize: 6 NumVariablesToSample: NaN Estimated log(1 + valLoss): 2.1985 Estimated time for training and validation: 6.572 seconds Documentation for fitrauto display
Итоговая модель возвращена fitrauto соответствует лучшему предполагаемому ученику. Прежде, чем возвратить модель, функция переобучает его с помощью целых обучающих данных (carsTrain), перечисленный Learner (или модель) тип и отображенные гиперзначения параметров.
Создайте простую модель
Создайте простую модель linearMdl линейной регрессии при помощи fitlm функция.
linearMdl = fitlm(carsTrain);
Несмотря на то, что linearMdl объект не имеет тех же самых свойств и методов как autoMdl объект, можно использовать обе модели, чтобы предсказать значения отклика для новых данных при помощи predict объектная функция.
Сравните эффективность набора тестов моделей
Сравните эффективность linearMdl и autoMdl модели на тестовых данных установлены. Для каждой модели вычислите среднеквадратическую ошибку (MSE) набора тестов. 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 = 8.8322
autoMdl модель, кажется, превосходит по характеристикам linearMdl модель.
В зависимости от размера вашего набора данных, количества учеников, которых вы задаете, и метод оптимизации, который вы выбираете, fitrauto может занять время, чтобы запуститься.
Если у вас есть лицензия Parallel Computing Toolbox, можно ускорить расчеты путем выполнения оптимизации параллельно. Для этого задайте "HyperparameterOptimizationOptions",struct("UseParallel",true). Можно включать дополнительные поля в структуру, чтобы управлять другими аспектами оптимизации. Смотрите HyperparameterOptimizationOptions.
Если fitrauto с Байесовой оптимизацией занимает много времени, чтобы запуститься из-за количества наблюдений в вашем наборе обучающих данных (например, более чем 10 000), рассмотреть использование fitrauto с оптимизацией ASHA вместо этого. Оптимизация ASHA часто находит хорошие решения быстрее, чем Байесова оптимизация для наборов данных со многими наблюдениями. Чтобы использовать оптимизацию ASHA, задайте "HyperparameterOptimizationOptions",struct("Optimizer","asha"). Можно включать дополнительные поля в структуру, чтобы управлять дополнительными аспектами оптимизации. В частности, если вы имеете ограничение времени, задаете MaxTime поле HyperparameterOptimizationOptions структура, чтобы ограничить номер секунд fitrauto запуски.
Если вы не уверены, какие модели работают лучше всего на ваш набор данных, можно альтернативно использовать приложение Regression Learner. Используя приложение, можно выполнить гиперпараметр, настраивающийся для различных моделей, и выбрать оптимизированную модель, которая выполняет лучше всего. Несмотря на то, что необходимо выбрать определенную модель, прежде чем можно будет настроить гиперпараметры модели, Regression Learner обеспечивает большую гибкость для выбора optimizable гиперпараметров и установки гиперзначений параметров. Приложение также позволяет вам обучать множество моделей линейной регрессии (см. Модели Линейной регрессии). Однако вы не можете оптимизировать параллельно, оптимизировать "linear" или "kernel" ученики, задайте веса наблюдения или используйте оптимизацию ASHA в приложении. Для получения дополнительной информации смотрите Гипероптимизацию параметров управления в Приложении Regression Learner.
Если вы знаете, какие модели могут удовлетворить вашим данным, можно альтернативно использовать соответствующие подходящие функции модели и задать OptimizeHyperparameters аргумент значения имени, чтобы настроить гиперпараметры. Можно сравнить результаты через модели, чтобы выбрать лучшую модель регрессии. Поскольку пример этого процесса применился к моделям классификации, смотрите, что Двигающий Выбор Модели Автоматизации Использует Байесовую Оптимизацию.
[1] Литий, Лиам, Кевин Джемисон, Afshin Rostamizadeh, Екатерина Гонина, Мориц Хардт, Бенджамин Речт и Амит Тэлволкэр. “Система для Настройки Гиперпараметра С массовым параллелизмом”. ArXiv:1810.05934v5 [Cs], 16 марта 2020. https://arxiv.org/abs/1810.05934v5.
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