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fitrauto
構文
説明
fitrauto は、指定した予測子と応答データに基づいて、さまざまなハイパーパラメーターの値をもつ回帰モデルのタイプの選択を自動的に試します。既定では、この関数は、ベイズ最適化を使用してモデルとそのハイパーパラメーターの値を選択し、各モデルについて log(1 + valLoss) を計算します。ここで、valLoss は交差検証の平均二乗誤差 (MSE) です。最適化が完了すると、fitrauto は、データ セット全体で学習済みの、新しいデータについての応答が最も優れているとされるモデルを返します。返されたモデルのオブジェクト関数 predict と loss を使用して、新しいデータの予測、および検定セット MSE の計算をそれぞれ行うことができます。
データに最適なモデルのタイプがわからない場合は、fitrauto を使用します。回帰モデルのハイパーパラメーターを調整するための代替方法については、代替機能を参照してください。
データに含まれる観測値が 10,000 を超える場合は、fitrauto を実行するとき、ベイズ最適化の代わりに非同期連続半減アルゴリズム (ASHA) の使用を検討してください。データ セットの観測値が多いと、多くの場合、ベイズ最適化よりも ASHA 最適化の方が優れた解を速く見つけます。
Mdl = fitrauto(Tbl,ResponseVarName)Mdl を返します。テーブル Tbl には予測子変数と応答変数を格納します。ResponseVarName は応答変数の名前です。
Mdl = fitrauto(___,Name,Value)HyperparameterOptimizationOptions を使用して、ベイズ最適化 (既定) または非同期連続半減アルゴリズム (ASHA) を使用するかどうかを指定します。ASHA 最適化を使用するには、"HyperparameterOptimizationOptions",struct("Optimizer","asha") を指定します。この構造体に追加フィールドを含めて、その他の最適化の側面を制御できます。
[ は、Mdl,OptimizationResults] = fitrauto(___)OptimizationResults も返します。これには、モデル選択とハイパーパラメーター調整のプロセスの結果が含まれます。この出力は、ベイズ最適化を使用している場合は BayesianOptimization オブジェクトで、ASHA 最適化を使用している場合は table です。
例
table データを使用した回帰モデルの自動選択
fitrauto を使用し、table に保存されている予測子データと応答データに基づいて、最適化されたハイパーパラメーターをもつ回帰モデルを自動的に選択します。
データの読み込み
carbig データセットを読み込みます。このデータセットには、1970 年代と 1980 年代初期に製造された自動車の測定値が格納されています。
load carbigAcceleration、Displacement などの予測子変数と応答変数 MPG が格納された table を作成します。
cars = table(Acceleration,Displacement,Horsepower, ...
Model_Year,Origin,Weight,MPG);cars から table に欠損値がある行を削除します。
cars = rmmissing(cars);
米国製かどうかに基づいて、自動車を分類します。
cars.Origin = categorical(cellstr(cars.Origin)); cars.Origin = mergecats(cars.Origin,["France","Japan",... "Germany","Sweden","Italy","England"],"NotUSA");
データの分割
データを学習セットと検定セットに分割します。モデル選択とハイパーパラメーター調整のプロセスに観測値の約 80% を使用し、fitrauto によって返された最終モデルのパフォーマンスのテストに観測値の 20% を使用します。cvpartition を使用してデータを分割します。
rng("default") % For reproducibility of the data partition c = cvpartition(height(cars),"Holdout",0.2); trainingIdx = training(c); % Training set indices carsTrain = cars(trainingIdx,:); testIdx = test(c); % Test set indices carsTest = cars(testIdx,:);
fitrauto の実行
学習データを fitrauto に渡します。既定では、fitrauto は、試行する適切なモデルのタイプを決定し、ベイズ最適化を使用して適切なハイパーパラメーター値を求め、パフォーマンスが最大となることが期待される学習済みモデル Mdl を返します。さらに、fitrauto は、最適化のプロット、および最適化の結果の反復表示を提供します。これらの結果を解釈する方法の詳細については、Verbose の表示を参照してください。
このプロセスにいくらか時間がかかることを見込んでください。Parallel Computing Toolbox™ のライセンスがある場合、最適化を並列で実行し、最適化プロセスを高速化することを検討してください。これを行うには、名前と値の引数 "HyperparameterOptimizationOptions",struct("UseParallel",true) を fitrauto に渡します。
Mdl = fitrauto(carsTrain,"MPG");Learner types to explore: ensemble, svm, tree Total iterations (MaxObjectiveEvaluations): 90 Total time (MaxTime): Inf |================================================================================================================================================| | Iter | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| validation loss | validation loss | | | |================================================================================================================================================| | 1 | Best | 3.3416 | 1.2897 | 3.3416 | 3.3416 | tree | MinLeafSize: 118 | | 2 | Accept | 4.1303 | 0.62208 | 3.3416 | 3.3416 | svm | BoxConstraint: 16.579 | | | | | | | | | KernelScale: 0.0045538 | | | | | | | | | Epsilon: 657.79 | | 3 | Best | 2.5197 | 0.18007 | 2.5197 | 2.6121 | tree | MinLeafSize: 2 | | 4 | Best | 2.3335 | 5.719 | 2.3335 | 2.3335 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 291 | | | | | | | | | MinLeafSize: 9 | | 5 | Accept | 2.3398 | 3.7552 | 2.3335 | 2.3366 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 206 | | | | | | | | | MinLeafSize: 13 | | 6 | Best | 2.204 | 5.1042 | 2.204 | 2.2049 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 256 | | | | | | | | | MinLeafSize: 12 | | 7 | Accept | 4.1303 | 0.098853 | 2.204 | 2.2049 | svm | BoxConstraint: 0.0048178 | | | | | | | | | KernelScale: 0.011576 | | | | | | | | | Epsilon: 441.39 | | 8 | Accept | 2.4787 | 0.074041 | 2.204 | 2.2049 | tree | MinLeafSize: 9 | | 9 | Accept | 4.1303 | 0.070297 | 2.204 | 2.2049 | svm | BoxConstraint: 8.581 | | | | | | | | | KernelScale: 61.095 | | | | | | | | | Epsilon: 296.69 | | 10 | Accept | 4.1303 | 0.053978 | 2.204 | 2.2049 | svm | BoxConstraint: 140.96 | | | | | | | | | KernelScale: 0.012197 | | | | | | | | | Epsilon: 69.002 | | 11 | Accept | 2.9157 | 0.045178 | 2.204 | 2.2049 | tree | MinLeafSize: 32 | | 12 | Accept | 3.2199 | 0.050483 | 2.204 | 2.2049 | tree | MinLeafSize: 64 | | 13 | Accept | 2.4157 | 0.048328 | 2.204 | 2.2049 | tree | MinLeafSize: 4 | | 14 | Accept | 4.1303 | 0.076781 | 2.204 | 2.2049 | svm | BoxConstraint: 1.3859 | | | | | | | | | KernelScale: 71.061 | | | | | | | | | Epsilon: 181.44 | | 15 | Accept | 3.4156 | 0.037288 | 2.204 | 2.2049 | tree | MinLeafSize: 102 | | 16 | Accept | 2.5197 | 0.054567 | 2.204 | 2.2049 | tree | MinLeafSize: 2 | | 17 | Accept | 5.4306 | 31.526 | 2.204 | 2.2049 | svm | BoxConstraint: 0.0018102 | | | | | | | | | KernelScale: 0.016815 | | | | | | | | | Epsilon: 8.1687 | | 18 | Accept | 3.1121 | 4.403 | 2.204 | 2.2042 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 288 | | | | | | | | | MinLeafSize: 106 | | 19 | Best | 2.1971 | 4.0613 | 2.1971 | 2.1972 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 227 | | | | | | | | | MinLeafSize: 2 | | 20 | Best | 2.1971 | 3.985 | 2.1971 | 2.1972 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 223 | | | | | | | | | MinLeafSize: 2 | |================================================================================================================================================| | Iter | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| validation loss | validation loss | | | |================================================================================================================================================| | 21 | Accept | 2.2314 | 4.723 | 2.1971 | 2.1972 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 262 | | | | | | | | | MinLeafSize: 5 | | 22 | Accept | 2.5925 | 4.6352 | 2.1971 | 2.1972 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | MinLeafSize: 39 | | 23 | Accept | 2.1971 | 5.0225 | 2.1971 | 2.1972 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 285 | | | | | | | | | MinLeafSize: 2 | | 24 | Accept | 2.3345 | 2.9953 | 2.1971 | 2.1972 | svm | BoxConstraint: 2.2648 | | | | | | | | | KernelScale: 0.92531 | | | | | | | | | Epsilon: 0.51865 | | 25 | Accept | 2.9882 | 3.887 | 2.1971 | 2.1971 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 247 | | | | | | | | | MinLeafSize: 73 | | 26 | Accept | 2.3583 | 4.2468 | 2.1971 | 2.1971 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 255 | | | | | | | | | MinLeafSize: 12 | | 27 | Accept | 2.6476 | 0.042392 | 2.1971 | 2.1971 | tree | MinLeafSize: 28 | | 28 | Accept | 2.4016 | 0.044492 | 2.1971 | 2.1971 | tree | MinLeafSize: 6 | | 29 | Accept | 3.7573 | 0.065073 | 2.1971 | 2.1971 | svm | BoxConstraint: 9.4057 | | | | | | | | | KernelScale: 100.66 | | | | | | | | | Epsilon: 0.24447 | | 30 | Accept | 2.6046 | 0.039155 | 2.1971 | 2.1971 | tree | MinLeafSize: 24 | | 31 | Accept | 2.4157 | 0.045287 | 2.1971 | 2.1971 | tree | MinLeafSize: 4 | | 32 | Accept | 4.1303 | 0.050301 | 2.1971 | 2.1971 | svm | BoxConstraint: 303.85 | | | | | | | | | KernelScale: 0.0083624 | | | | | | | | | Epsilon: 39.54 | | 33 | Accept | 4.146 | 0.056571 | 2.1971 | 2.1971 | svm | BoxConstraint: 0.16546 | | | | | | | | | KernelScale: 248.79 | | | | | | | | | Epsilon: 1.1182 | | 34 | Accept | 3.0466 | 0.038386 | 2.1971 | 2.1971 | tree | MinLeafSize: 46 | | 35 | Accept | 2.3417 | 4.1224 | 2.1971 | 2.1971 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 246 | | | | | | | | | MinLeafSize: 12 | | 36 | Accept | 2.7264 | 4.748 | 2.1971 | 2.1972 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 274 | | | | | | | | | MinLeafSize: 105 | | 37 | Accept | 2.5457 | 4.1701 | 2.1971 | 2.1972 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 257 | | | | | | | | | MinLeafSize: 33 | | 38 | Accept | 2.6603 | 0.055123 | 2.1971 | 2.1972 | tree | MinLeafSize: 1 | | 39 | Accept | 2.36 | 5.3754 | 2.1971 | 2.1972 | svm | BoxConstraint: 56.509 | | | | | | | | | KernelScale: 1.509 | | | | | | | | | Epsilon: 0.5604 | | 40 | Accept | 4.1303 | 0.048283 | 2.1971 | 2.1972 | svm | BoxConstraint: 0.001484 | | | | | | | | | KernelScale: 0.0032176 | | | | | | | | | Epsilon: 22.445 | |================================================================================================================================================| | Iter | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| validation loss | validation loss | | | |================================================================================================================================================| | 41 | Accept | 2.5507 | 0.040831 | 2.1971 | 2.1972 | tree | MinLeafSize: 15 | | 42 | Best | 2.1945 | 5.1078 | 2.1945 | 2.1966 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 289 | | | | | | | | | MinLeafSize: 6 | | 43 | Accept | 3.9873 | 0.056392 | 2.1945 | 2.1966 | svm | BoxConstraint: 31.423 | | | | | | | | | KernelScale: 0.16609 | | | | | | | | | Epsilon: 14.619 | | 44 | Accept | 4.0639 | 0.058227 | 2.1945 | 2.1966 | svm | BoxConstraint: 42.958 | | | | | | | | | KernelScale: 459.03 | | | | | | | | | Epsilon: 0.98679 | | 45 | Accept | 2.5389 | 0.055917 | 2.1945 | 2.1966 | svm | BoxConstraint: 32.844 | | | | | | | | | KernelScale: 24.244 | | | | | | | | | Epsilon: 2.8938 | | 46 | Accept | 4.1222 | 0.055003 | 2.1945 | 2.1966 | svm | BoxConstraint: 0.001348 | | | | | | | | | KernelScale: 5.1158 | | | | | | | | | Epsilon: 2.4534 | | 47 | Best | 2.1533 | 0.074854 | 2.1533 | 2.1534 | svm | BoxConstraint: 161.96 | | | | | | | | | KernelScale: 7.1682 | | | | | | | | | Epsilon: 1.6972 | | 48 | Best | 2.1044 | 0.058537 | 2.1044 | 2.1045 | svm | BoxConstraint: 10.597 | | | | | | | | | KernelScale: 4.8052 | | | | | | | | | Epsilon: 0.68924 | | 49 | Accept | 2.1323 | 0.063815 | 2.1044 | 2.1045 | svm | BoxConstraint: 12.625 | | | | | | | | | KernelScale: 3.7951 | | | | | | | | | Epsilon: 1.9243 | | 50 | Accept | 2.1143 | 0.10138 | 2.1044 | 2.1042 | svm | BoxConstraint: 2.9811 | | | | | | | | | KernelScale: 2.2304 | | | | | | | | | Epsilon: 0.11742 | | 51 | Accept | 2.1121 | 0.097271 | 2.1044 | 2.1044 | svm | BoxConstraint: 4.6122 | | | | | | | | | KernelScale: 2.5002 | | | | | | | | | Epsilon: 0.24122 | | 52 | Accept | 2.3152 | 4.2279 | 2.1044 | 2.1044 | svm | BoxConstraint: 13.002 | | | | | | | | | KernelScale: 1.2194 | | | | | | | | | Epsilon: 0.0097793 | | 53 | Accept | 2.1474 | 0.11001 | 2.1044 | 2.1041 | svm | BoxConstraint: 113.51 | | | | | | | | | KernelScale: 5.567 | | | | | | | | | Epsilon: 0.052251 | | 54 | Accept | 2.1274 | 0.064355 | 2.1044 | 2.1045 | svm | BoxConstraint: 51.97 | | | | | | | | | KernelScale: 7.9449 | | | | | | | | | Epsilon: 0.31232 | | 55 | Accept | 2.1313 | 0.10387 | 2.1044 | 2.1046 | svm | BoxConstraint: 17.469 | | | | | | | | | KernelScale: 3.3438 | | | | | | | | | Epsilon: 0.050142 | | 56 | Accept | 2.2052 | 5.3754 | 2.1044 | 2.1046 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 299 | | | | | | | | | MinLeafSize: 1 | | 57 | Accept | 2.1125 | 0.090322 | 2.1044 | 2.1047 | svm | BoxConstraint: 50.684 | | | | | | | | | KernelScale: 4.764 | | | | | | | | | Epsilon: 0.45053 | | 58 | Accept | 2.3465 | 3.4461 | 2.1044 | 2.1047 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 201 | | | | | | | | | MinLeafSize: 1 | | 59 | Accept | 2.1222 | 0.11319 | 2.1044 | 2.105 | svm | BoxConstraint: 859.14 | | | | | | | | | KernelScale: 12.367 | | | | | | | | | Epsilon: 0.2022 | | 60 | Accept | 2.1461 | 0.19386 | 2.1044 | 2.105 | svm | BoxConstraint: 968.32 | | | | | | | | | KernelScale: 8.9428 | | | | | | | | | Epsilon: 0.01767 | |================================================================================================================================================| | Iter | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| validation loss | validation loss | | | |================================================================================================================================================| | 61 | Accept | 2.1407 | 0.22769 | 2.1044 | 2.1051 | svm | BoxConstraint: 971.76 | | | | | | | | | KernelScale: 8.0121 | | | | | | | | | Epsilon: 0.27594 | | 62 | Accept | 2.132 | 0.063274 | 2.1044 | 2.1051 | svm | BoxConstraint: 7.3349 | | | | | | | | | KernelScale: 4.5654 | | | | | | | | | Epsilon: 0.010146 | | 63 | Accept | 2.1457 | 0.068571 | 2.1044 | 2.1054 | svm | BoxConstraint: 182.05 | | | | | | | | | KernelScale: 13.913 | | | | | | | | | Epsilon: 0.010813 | | 64 | Accept | 2.1195 | 0.068772 | 2.1044 | 2.1069 | svm | BoxConstraint: 7.653 | | | | | | | | | KernelScale: 4.1874 | | | | | | | | | Epsilon: 0.13638 | | 65 | Accept | 2.1127 | 0.09654 | 2.1044 | 2.1075 | svm | BoxConstraint: 1.8061 | | | | | | | | | KernelScale: 2.0447 | | | | | | | | | Epsilon: 0.010408 | | 66 | Accept | 2.1374 | 0.093402 | 2.1044 | 2.1076 | svm | BoxConstraint: 984.16 | | | | | | | | | KernelScale: 17.924 | | | | | | | | | Epsilon: 0.013101 | | 67 | Accept | 2.3467 | 3.4222 | 2.1044 | 2.1076 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 201 | | | | | | | | | MinLeafSize: 3 | | 68 | Accept | 2.1251 | 0.084559 | 2.1044 | 2.1078 | svm | BoxConstraint: 4.8829 | | | | | | | | | KernelScale: 2.7157 | | | | | | | | | Epsilon: 0.011329 | | 69 | Accept | 4.1303 | 0.048665 | 2.1044 | 2.1045 | svm | BoxConstraint: 981.43 | | | | | | | | | KernelScale: 3.7956 | | | | | | | | | Epsilon: 524.32 | | 70 | Best | 2.0946 | 0.078617 | 2.0946 | 2.0958 | svm | BoxConstraint: 9.3796 | | | | | | | | | KernelScale: 3.6153 | | | | | | | | | Epsilon: 0.64581 | | 71 | Accept | 2.1625 | 0.059021 | 2.0946 | 2.0957 | svm | BoxConstraint: 0.14003 | | | | | | | | | KernelScale: 2.3859 | | | | | | | | | Epsilon: 0.0096989 | | 72 | Accept | 2.1254 | 0.062282 | 2.0946 | 2.0957 | svm | BoxConstraint: 1.0541 | | | | | | | | | KernelScale: 2.8873 | | | | | | | | | Epsilon: 0.016892 | | 73 | Accept | 2.2047 | 0.42757 | 2.0946 | 2.0957 | svm | BoxConstraint: 0.20258 | | | | | | | | | KernelScale: 0.89876 | | | | | | | | | Epsilon: 0.0094548 | | 74 | Accept | 4.1303 | 0.056501 | 2.0946 | 2.0957 | svm | BoxConstraint: 705.97 | | | | | | | | | KernelScale: 0.0010614 | | | | | | | | | Epsilon: 0.011029 | | 75 | Accept | 2.1076 | 0.093847 | 2.0946 | 2.0956 | svm | BoxConstraint: 0.57149 | | | | | | | | | KernelScale: 1.6966 | | | | | | | | | Epsilon: 0.028341 | | 76 | Accept | 2.1051 | 0.074496 | 2.0946 | 2.0972 | svm | BoxConstraint: 17.713 | | | | | | | | | KernelScale: 4.1474 | | | | | | | | | Epsilon: 0.46742 | | 77 | Accept | 2.0999 | 0.072478 | 2.0946 | 2.0977 | svm | BoxConstraint: 16.834 | | | | | | | | | KernelScale: 4.194 | | | | | | | | | Epsilon: 0.7058 | | 78 | Accept | 2.117 | 0.073675 | 2.0946 | 2.0976 | svm | BoxConstraint: 0.80221 | | | | | | | | | KernelScale: 2.1521 | | | | | | | | | Epsilon: 0.009312 | | 79 | Accept | 2.1063 | 0.071597 | 2.0946 | 2.0998 | svm | BoxConstraint: 11.766 | | | | | | | | | KernelScale: 4.0434 | | | | | | | | | Epsilon: 0.77028 | | 80 | Accept | 2.131 | 0.11884 | 2.0946 | 2.0997 | svm | BoxConstraint: 639.99 | | | | | | | | | KernelScale: 11.976 | | | | | | | | | Epsilon: 0.045587 | |================================================================================================================================================| | Iter | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| validation loss | validation loss | | | |================================================================================================================================================| | 81 | Accept | 2.1353 | 0.12266 | 2.0946 | 2.0998 | svm | BoxConstraint: 833.03 | | | | | | | | | KernelScale: 12.286 | | | | | | | | | Epsilon: 0.009267 | | 82 | Accept | 2.1002 | 0.075115 | 2.0946 | 2.0995 | svm | BoxConstraint: 28.193 | | | | | | | | | KernelScale: 5.1564 | | | | | | | | | Epsilon: 0.54563 | | 83 | Accept | 2.1087 | 0.083842 | 2.0946 | 2.0993 | svm | BoxConstraint: 22.81 | | | | | | | | | KernelScale: 4.8839 | | | | | | | | | Epsilon: 0.81407 | | 84 | Accept | 2.1047 | 0.08404 | 2.0946 | 2.0998 | svm | BoxConstraint: 11.5 | | | | | | | | | KernelScale: 3.7878 | | | | | | | | | Epsilon: 0.38006 | | 85 | Accept | 2.0999 | 0.076743 | 2.0946 | 2.0996 | svm | BoxConstraint: 7.9463 | | | | | | | | | KernelScale: 3.3494 | | | | | | | | | Epsilon: 0.56823 | | 86 | Accept | 2.121 | 0.12711 | 2.0946 | 2.0996 | svm | BoxConstraint: 1.4247 | | | | | | | | | KernelScale: 1.7405 | | | | | | | | | Epsilon: 0.030609 | | 87 | Accept | 4.1303 | 0.056272 | 2.0946 | 2.0995 | svm | BoxConstraint: 0.0020273 | | | | | | | | | KernelScale: 0.001035 | | | | | | | | | Epsilon: 832.86 | | 88 | Accept | 2.114 | 0.070002 | 2.0946 | 2.1014 | svm | BoxConstraint: 10.323 | | | | | | | | | KernelScale: 3.9111 | | | | | | | | | Epsilon: 0.90254 | | 89 | Accept | 2.1042 | 0.073487 | 2.0946 | 2.1015 | svm | BoxConstraint: 6.5035 | | | | | | | | | KernelScale: 3.1694 | | | | | | | | | Epsilon: 0.63488 | | 90 | Accept | 2.102 | 0.072913 | 2.0946 | 2.1015 | svm | BoxConstraint: 23.367 | | | | | | | | | KernelScale: 4.8485 | | | | | | | | | Epsilon: 0.51211 |
__________________________________________________________ Optimization completed. Total iterations: 90 Total elapsed time: 172.6365 seconds Total time for training and validation: 131.3656 seconds Best observed learner is an svm model with: Learner: svm BoxConstraint: 9.3796 KernelScale: 3.6153 Epsilon: 0.64581 Observed log(1 + valLoss): 2.0946 Time for training and validation: 0.078617 seconds Best estimated learner (returned model) is an svm model with: Learner: svm BoxConstraint: 9.3796 KernelScale: 3.6153 Epsilon: 0.64581 Estimated log(1 + valLoss): 2.1015 Estimated time for training and validation: 0.076063 seconds Documentation for fitrauto display
fitrauto によって返される最終的なモデルが、最適な推定学習器となります。モデルを返す前に、関数は学習データ全体 (carsTrain)、リストされている Learner (またはモデル) のタイプ、および表示されたハイパーパラメーター値を使用して、モデルの再学習を行います。
検定セットのパフォーマンスの評価
検定セットに対するモデルのパフォーマンスを評価します。testError は、検定セットの平均二乗誤差 (MSE) に基づきます。MSE の値が小さいほど、パフォーマンスが優れていることを示します。
testMSE = loss(Mdl,carsTest,"MPG");
testError = log(1 + testMSE)testError = 2.1805
行列データを使用した回帰モデルの自動選択
fitrauto を使用し、個別の変数に保存されている予測子データと応答データに基づいて、最適化されたハイパーパラメーターをもつ回帰モデルを自動的に選択します。
データの読み込み
carbig データセットを読み込みます。このデータセットには、1970 年代と 1980 年代初期に製造された自動車の測定値が格納されています。
load carbig予測子変数 Acceleration、Cylinders などが含まれている行列 X を作成します。応答変数 MPG を変数 Y に保存します。
X = [Acceleration Cylinders Displacement Weight]; Y = MPG;
X および Y からいずれかの配列に欠損値がある行を削除します。
R = rmmissing([X Y]); X = R(:,1:end-1); Y = R(:,end);
カテゴリカルな予測子を示す変数を作成します。Cylinders は X 内で唯一のカテゴリカル変数です。
categoricalVars = [false true false false];
データの分割
データを学習セットと検定セットに分割します。モデル選択とハイパーパラメーター調整のプロセスに観測値の約 80% を使用し、fitrauto によって返された最終モデルのパフォーマンスのテストに観測値の 20% を使用します。cvpartition を使用してデータを分割します。
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);
fitrauto の実行
学習データを fitrauto に渡します。既定では、fitrauto は、試行する適切なモデル (学習器) のタイプを決定し、ベイズ最適化を使用してこれらのモデルの適切なハイパーパラメーター値を求め、パフォーマンスが最大となることが期待される学習済みモデル Mdl を返します。カテゴリカル予測子を指定し、最適化を並列実行します (Parallel Computing Toolbox™ が必要)。ベイズ最適化の詳細が格納された 2 番目の出力 OptimizationResults を返します。
このプロセスにいくらか時間がかかることを見込んでください。既定の設定では、fitrauto は、最適化のプロット、および最適化の結果の反復表示を提供します。これらの結果を解釈する方法の詳細については、Verbose の表示を参照してください。
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: 8). Copying objective function to workers... Done copying objective function to workers. Learner types to explore: ensemble, svm, tree Total iterations (MaxObjectiveEvaluations): 90 Total time (MaxTime): Inf |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 1 | 5 | Best | 3.1329 | 1.9087 | 3.1329 | 3.1399 | tree | MinLeafSize: 5 | | 2 | 5 | Accept | 3.1329 | 1.9094 | 3.1329 | 3.1399 | tree | MinLeafSize: 5 | | 3 | 5 | Accept | 4.1701 | 1.9944 | 3.1329 | 3.1399 | svm | BoxConstraint: 0.033502 | | | | | | | | | | KernelScale: 153.38 | | | | | | | | | | Epsilon: 0.095234 | | 4 | 5 | Accept | 3.1539 | 1.9051 | 3.1329 | 3.1399 | tree | MinLeafSize: 9 | | 5 | 7 | Best | 3.0917 | 0.20244 | 3.0917 | 3.0919 | tree | MinLeafSize: 14 | | 6 | 7 | Accept | 4.1645 | 0.20868 | 3.0917 | 3.0919 | tree | MinLeafSize: 158 | | 7 | 8 | Accept | 3.2871 | 0.14105 | 3.0917 | 3.0919 | tree | MinLeafSize: 2 | | 8 | 8 | Accept | 3.2871 | 0.12338 | 3.0917 | 3.0919 | tree | MinLeafSize: 2 | | 9 | 8 | Accept | 4.1645 | 1.3189 | 3.0917 | 3.0919 | svm | BoxConstraint: 0.003952 | | | | | | | | | | KernelScale: 0.0015586 | | | | | | | | | | Epsilon: 31.184 | | 10 | 8 | Accept | 3.2871 | 0.19579 | 3.0917 | 3.0919 | tree | MinLeafSize: 2 | | 11 | 8 | Accept | 4.1646 | 8.3996 | 3.0917 | 3.0919 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 257 | | | | | | | | | | MinLeafSize: 154 | | 12 | 8 | Best | 2.9469 | 8.7243 | 2.9469 | 2.968 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | | MinLeafSize: 1 | | 13 | 8 | Best | 2.9388 | 9.9614 | 2.9388 | 2.942 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 288 | | | | | | | | | | MinLeafSize: 3 | | 14 | 7 | Accept | 4.1645 | 1.9698 | 2.9388 | 2.9411 | svm | BoxConstraint: 159.44 | | | | | | | | | | KernelScale: 34.732 | | | | | | | | | | Epsilon: 412.2 | | 15 | 7 | Accept | 2.9581 | 8.4974 | 2.9388 | 2.9411 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | | MinLeafSize: 62 | | 16 | 7 | Accept | 3.1637 | 0.98081 | 2.9388 | 2.9411 | tree | MinLeafSize: 6 | | 17 | 7 | Accept | 3.1539 | 0.58494 | 2.9388 | 2.9411 | tree | MinLeafSize: 9 | | 18 | 5 | Accept | 2.9287 | 9.2877 | 2.9287 | 2.9411 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | | MinLeafSize: 16 | | 19 | 5 | Best | 2.9287 | 8.4297 | 2.9287 | 2.9411 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 262 | | | | | | | | | | MinLeafSize: 5 | | 20 | 5 | Accept | 3.9011 | 0.19628 | 2.9287 | 2.9411 | svm | BoxConstraint: 9.4057 | | | | | | | | | | KernelScale: 100.66 | | | | | | | | | | Epsilon: 0.2386 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 21 | 8 | Accept | 4.1862 | 0.23729 | 2.9287 | 2.9411 | svm | BoxConstraint: 7.487 | | | | | | | | | | KernelScale: 81.753 | | | | | | | | | | Epsilon: 12.782 | | 22 | 5 | Accept | 3.1593 | 0.12638 | 2.9287 | 2.9411 | tree | MinLeafSize: 8 | | 23 | 5 | Accept | 3.1163 | 0.2154 | 2.9287 | 2.9411 | tree | MinLeafSize: 42 | | 24 | 5 | Accept | 4.1645 | 0.13652 | 2.9287 | 2.9411 | svm | BoxConstraint: 760.95 | | | | | | | | | | KernelScale: 1.8573 | | | | | | | | | | Epsilon: 83.037 | | 25 | 5 | Accept | 3.0374 | 0.14 | 2.9287 | 2.9411 | tree | MinLeafSize: 16 | | 26 | 8 | Accept | 3.1014 | 0.066518 | 2.9287 | 2.9411 | tree | MinLeafSize: 13 | | 27 | 7 | Accept | 2.9493 | 0.57729 | 2.9287 | 2.9411 | svm | BoxConstraint: 574.43 | | | | | | | | | | KernelScale: 7.3229 | | | | | | | | | | Epsilon: 3.991 | | 28 | 7 | Accept | 3.3681 | 0.19666 | 2.9287 | 2.9411 | tree | MinLeafSize: 69 | | 29 | 5 | Accept | 3.1815 | 7.8877 | 2.9287 | 2.9411 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 247 | | | | | | | | | | MinLeafSize: 74 | | 30 | 5 | Accept | 4.1645 | 1.2207 | 2.9287 | 2.9411 | svm | BoxConstraint: 5.2634 | | | | | | | | | | KernelScale: 0.058706 | | | | | | | | | | Epsilon: 105.48 | | 31 | 5 | Accept | 3.6021 | 0.091822 | 2.9287 | 2.9411 | tree | MinLeafSize: 1 | | 32 | 8 | Accept | 3.1539 | 0.23324 | 2.9287 | 2.9411 | tree | MinLeafSize: 9 | | 33 | 6 | Accept | 2.9351 | 12.312 | 2.9197 | 2.9198 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 282 | | | | | | | | | | MinLeafSize: 2 | | 34 | 6 | Accept | 4.2521 | 0.1172 | 2.9197 | 2.9198 | svm | BoxConstraint: 449.81 | | | | | | | | | | KernelScale: 19.912 | | | | | | | | | | Epsilon: 17.095 | | 35 | 6 | Best | 2.9197 | 0.085188 | 2.9197 | 2.9198 | svm | BoxConstraint: 1.0008 | | | | | | | | | | KernelScale: 2.1267 | | | | | | | | | | Epsilon: 0.034964 | | 36 | 7 | Accept | 4.1091 | 0.081418 | 2.9197 | 2.9411 | svm | BoxConstraint: 42.958 | | | | | | | | | | KernelScale: 459.03 | | | | | | | | | | Epsilon: 0.96311 | | 37 | 7 | Accept | 4.1091 | 0.064642 | 2.9197 | 2.9198 | svm | BoxConstraint: 42.958 | | | | | | | | | | KernelScale: 459.03 | | | | | | | | | | Epsilon: 0.96311 | | 38 | 7 | Accept | 2.9423 | 4.1841 | 2.9197 | 2.9198 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 202 | | | | | | | | | | MinLeafSize: 50 | | 39 | 7 | Accept | 3.1132 | 0.066762 | 2.9197 | 2.9198 | tree | MinLeafSize: 38 | | 40 | 7 | Accept | 9.5074 | 20.851 | 2.9197 | 2.9198 | svm | BoxConstraint: 336.91 | | | | | | | | | | KernelScale: 0.0018275 | | | | | | | | | | Epsilon: 0.10919 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 41 | 7 | Accept | 4.1645 | 0.31377 | 2.9197 | 2.9198 | svm | BoxConstraint: 582.79 | | | | | | | | | | KernelScale: 7.6869 | | | | | | | | | | Epsilon: 74.905 | | 42 | 7 | Accept | 4.1645 | 4.6708 | 2.9197 | 2.9198 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 233 | | | | | | | | | | MinLeafSize: 134 | | 43 | 7 | Accept | 2.935 | 5.2719 | 2.9197 | 2.9198 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 280 | | | | | | | | | | MinLeafSize: 45 | | 44 | 7 | Accept | 3.1177 | 0.88837 | 2.9197 | 2.9198 | svm | BoxConstraint: 127.48 | | | | | | | | | | KernelScale: 105 | | | | | | | | | | Epsilon: 0.58941 | | 45 | 8 | Accept | 3.1329 | 0.10668 | 2.9197 | 2.9198 | tree | MinLeafSize: 5 | | 46 | 8 | Best | 2.8874 | 7.2754 | 2.8874 | 2.8877 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 271 | | | | | | | | | | MinLeafSize: 1 | | 47 | 8 | Accept | 3.9204 | 0.2276 | 2.8874 | 2.8877 | svm | BoxConstraint: 0.014973 | | | | | | | | | | KernelScale: 4.398 | | | | | | | | | | Epsilon: 0.055595 | | 48 | 8 | Accept | 2.8964 | 5.3009 | 2.8874 | 2.8877 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 233 | | | | | | | | | | MinLeafSize: 20 | | 49 | 8 | Accept | 2.8941 | 10.022 | 2.8874 | 2.8908 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 300 | | | | | | | | | | MinLeafSize: 1 | | 50 | 8 | Accept | 2.9227 | 8.3714 | 2.8874 | 2.8908 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 360 | | | | | | | | | | MinLeafSize: 9 | | 51 | 8 | Accept | 3.0945 | 0.10022 | 2.8874 | 2.8908 | tree | MinLeafSize: 11 | | 52 | 8 | Accept | 2.9326 | 7.3667 | 2.8874 | 2.8908 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 316 | | | | | | | | | | MinLeafSize: 51 | | 53 | 8 | Accept | 2.9223 | 6.3741 | 2.8874 | 2.8908 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 234 | | | | | | | | | | MinLeafSize: 35 | | 54 | 6 | Best | 2.8833 | 12.385 | 2.8833 | 2.8875 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 300 | | | | | | | | | | MinLeafSize: 1 | | 55 | 6 | Accept | 4.1645 | 6.146 | 2.8833 | 2.8875 | svm | BoxConstraint: 1.246 | | | | | | | | | | KernelScale: 0.048145 | | | | | | | | | | Epsilon: 337.42 | | 56 | 6 | Accept | 3.5019 | 4.3292 | 2.8833 | 2.8875 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 219 | | | | | | | | | | MinLeafSize: 126 | | 57 | 6 | Best | 2.8758 | 4.1728 | 2.8758 | 2.8875 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 201 | | | | | | | | | | MinLeafSize: 4 | | 58 | 6 | Accept | 3.978 | 0.12062 | 2.8758 | 2.8875 | svm | BoxConstraint: 0.015506 | | | | | | | | | | KernelScale: 4.6409 | | | | | | | | | | Epsilon: 2.9763 | | 59 | 7 | Accept | 3.4183 | 0.049204 | 2.8758 | 2.8875 | tree | MinLeafSize: 93 | | 60 | 7 | Accept | 2.9269 | 4.8518 | 2.8758 | 2.8759 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 236 | | | | | | | | | | MinLeafSize: 19 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 61 | 7 | Accept | 3.0652 | 0.088667 | 2.8758 | 2.8759 | svm | BoxConstraint: 862.71 | | | | | | | | | | KernelScale: 216.51 | | | | | | | | | | Epsilon: 1.9551 | | 62 | 7 | Accept | 2.8816 | 4.0609 | 2.8758 | 2.8767 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 205 | | | | | | | | | | MinLeafSize: 4 | | 63 | 7 | Accept | 4.1645 | 0.1847 | 2.8758 | 2.8767 | svm | BoxConstraint: 654.1 | | | | | | | | | | KernelScale: 0.0009277 | | | | | | | | | | Epsilon: 0.67992 | | 64 | 8 | Accept | 4.1645 | 0.04689 | 2.8758 | 2.8767 | svm | BoxConstraint: 0.0022454 | | | | | | | | | | KernelScale: 1.2218 | | | | | | | | | | Epsilon: 1223.3 | | 65 | 8 | Accept | 2.8789 | 5.3 | 2.8758 | 2.8788 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 279 | | | | | | | | | | MinLeafSize: 4 | | 66 | 8 | Accept | 3.1637 | 0.099659 | 2.8758 | 2.8788 | tree | MinLeafSize: 6 | | 67 | 8 | Accept | 2.8772 | 5.6605 | 2.8758 | 2.8784 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 280 | | | | | | | | | | MinLeafSize: 4 | | 68 | 8 | Accept | 3.2871 | 0.074658 | 2.8758 | 2.8784 | tree | MinLeafSize: 2 | | 69 | 8 | Best | 2.8743 | 6.7691 | 2.8743 | 2.8744 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 296 | | | | | | | | | | MinLeafSize: 7 | | 70 | 8 | Accept | 4.8948 | 28.692 | 2.8743 | 2.8744 | svm | BoxConstraint: 0.093799 | | | | | | | | | | KernelScale: 0.0053728 | | | | | | | | | | Epsilon: 17.621 | | 71 | 7 | Accept | 2.8767 | 6.4563 | 2.8743 | 2.8743 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 298 | | | | | | | | | | MinLeafSize: 9 | | 72 | 7 | Accept | 2.88 | 5.7962 | 2.8743 | 2.8743 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 299 | | | | | | | | | | MinLeafSize: 9 | | 73 | 7 | Accept | 2.8843 | 4.9403 | 2.8743 | 2.8743 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 207 | | | | | | | | | | MinLeafSize: 2 | | 74 | 7 | Accept | 4.1645 | 0.087433 | 2.8743 | 2.8743 | svm | BoxConstraint: 10.694 | | | | | | | | | | KernelScale: 42.019 | | | | | | | | | | Epsilon: 58.68 | | 75 | 8 | Accept | 3.1608 | 0.045498 | 2.8743 | 2.8743 | tree | MinLeafSize: 3 | | 76 | 8 | Accept | 2.8845 | 5.7044 | 2.8743 | 2.8743 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 298 | | | | | | | | | | MinLeafSize: 2 | | 77 | 8 | Accept | 2.9155 | 5.6911 | 2.8743 | 2.8743 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 268 | | | | | | | | | | MinLeafSize: 27 | | 78 | 8 | Accept | 4.1132 | 0.10111 | 2.8743 | 2.8743 | svm | BoxConstraint: 0.0012611 | | | | | | | | | | KernelScale: 2.8609 | | | | | | | | | | Epsilon: 0.037899 | | 79 | 8 | Accept | 3.2869 | 0.080313 | 2.8743 | 2.8743 | tree | MinLeafSize: 66 | | 80 | 8 | Accept | 3.4233 | 6.4584 | 2.8743 | 2.8745 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 301 | | | | | | | | | | MinLeafSize: 119 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 81 | 6 | Accept | 3.2102 | 6.5686 | 2.8743 | 2.8744 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 360 | | | | | | | | | | MinLeafSize: 102 | | 82 | 6 | Accept | 2.8842 | 5.6027 | 2.8743 | 2.8744 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 274 | | | | | | | | | | MinLeafSize: 14 | | 83 | 6 | Accept | 2.8763 | 4.6428 | 2.8743 | 2.8744 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 205 | | | | | | | | | | MinLeafSize: 14 | | 84 | 7 | Accept | 2.8807 | 4.3081 | 2.8743 | 2.8744 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 202 | | | | | | | | | | MinLeafSize: 14 | | 85 | 8 | Accept | 3.0046 | 0.078152 | 2.8743 | 2.8744 | tree | MinLeafSize: 27 | | 86 | 8 | Accept | 3.1256 | 6.3616 | 2.8743 | 2.8744 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 314 | | | | | | | | | | MinLeafSize: 70 | | 87 | 8 | Best | 2.8718 | 5.9613 | 2.8718 | 2.8719 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 300 | | | | | | | | | | MinLeafSize: 5 | | 88 | 8 | Accept | 3.0843 | 0.048367 | 2.8718 | 2.8719 | tree | MinLeafSize: 47 | | 89 | 8 | Accept | 2.8808 | 5.6249 | 2.8718 | 2.8743 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 298 | | | | | | | | | | MinLeafSize: 5 | | 90 | 7 | Accept | 2.9088 | 7.3928 | 2.8718 | 2.8743 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 367 | | | | | | | | | | MinLeafSize: 7 | | 91 | 7 | Accept | 3.0105 | 0.039942 | 2.8718 | 2.8743 | tree | MinLeafSize: 26 |
__________________________________________________________ Optimization completed. Total iterations: 91 Total elapsed time: 65.6875 seconds Total time for training and validation: 337.1441 seconds Best observed learner is an ensemble model with: Learner: ensemble Method: Bag NumLearningCycles: 300 MinLeafSize: 5 Observed log(1 + valLoss): 2.8718 Time for training and validation: 5.9613 seconds Best estimated learner (returned model) is an ensemble model with: Learner: ensemble Method: Bag NumLearningCycles: 296 MinLeafSize: 7 Estimated log(1 + valLoss): 2.8743 Estimated time for training and validation: 6.2667 seconds Documentation for fitrauto display
fitrauto によって返される最終的なモデルが、最適な推定学習器となります。モデルを返す前に、関数は学習データ全体 (XTrain と YTrain)、リストされている Learner (またはモデル) のタイプ、および表示されたハイパーパラメーター値を使用して、モデルの再学習を行います。
検定セットのパフォーマンスの評価
検定セットに対するモデルのパフォーマンスを評価します。testError は、検定セットの平均二乗誤差 (MSE) に基づきます。MSE の値が小さいほど、パフォーマンスが優れていることを示します。
testMSE = loss(Mdl,XTest,YTest); testError = log(1 + testMSE)
testError = 2.6519
最適化された回帰モデルと単純な線形回帰モデルの比較
fitrauto を使用し、table に保存されている予測子データと応答データに基づいて、最適化されたハイパーパラメーターをもつ回帰モデルを自動的に選択します。得られた回帰モデルのパフォーマンスと、fitlm で作成された単純な線形回帰モデルのパフォーマンスを比較します。
データの読み込みと分割
carbig データセットを読み込みます。このデータセットには、1970 年代と 1980 年代初期に製造された自動車の測定値が格納されています。変数 Cylinders を categorical 変数に変換します。Acceleration、Cylinders、Displacement などの予測子変数と応答変数 MPG が格納された table を作成します。
load carbig Cylinders = categorical(Cylinders); cars = table(Acceleration,Cylinders,Displacement, ... Horsepower,Model_Year,Origin,Weight,MPG);
cars から table に欠損値がある行を削除します。
cars = rmmissing(cars);
米国製かどうかに基づいて、自動車を分類します。
cars.Origin = categorical(cellstr(cars.Origin)); cars.Origin = mergecats(cars.Origin,["France","Japan",... "Germany","Sweden","Italy","England"],"NotUSA");
データを学習セットと検定セットに分割します。観測値の約 80% を学習に、観測値の約 20% を検定に使用します。cvpartition を使用してデータを分割します。
rng("default") % For reproducibility of the data partition c = cvpartition(height(cars),"Holdout",0.2); trainingIdx = training(c); % Training set indices carsTrain = cars(trainingIdx,:); testIdx = test(c); % Test set indices carsTest = cars(testIdx,:);
fitrauto の実行
学習データを fitrauto に渡します。既定では、fitrauto は、試行する適切なモデルのタイプを決定し、ベイズ最適化を使用して適切なハイパーパラメーター値を求め、パフォーマンスが最大となることが期待される学習済みモデル autoMdl を返します。最適化可能なすべてのハイパーパラメーターを最適化し、最適化を並列実行するよう指定します (Parallel Computing Toolbox™ が必要)。
このプロセスにいくらか時間がかかることを見込んでください。既定の設定では、fitrauto は、最適化のプロット、および最適化の結果の反復表示を提供します。これらの結果を解釈する方法の詳細については、Verbose の表示を参照してください。
options = struct("UseParallel",true); autoMdl = fitrauto(carsTrain,"MPG","OptimizeHyperparameters","all", ... "HyperparameterOptimizationOptions",options);
Copying objective function to workers...
Warning: Files that have already been attached are being ignored. To see which files are attached see the 'AttachedFiles' property of the parallel pool.
Done copying objective function to workers. Learner types to explore: ensemble, svm, tree Total iterations (MaxObjectiveEvaluations): 90 Total time (MaxTime): Inf |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 1 | 6 | Best | 3.1155 | 0.593 | 3.1155 | 3.1155 | tree | MinLeafSize: 5 | | | | | | | | | | MaxNumSplits: 2 | | | | | | | | | | NumVariablesToSample: 3 | | 2 | 6 | Accept | 4.1303 | 0.57793 | 3.1155 | 3.1155 | svm | BoxConstraint: 0.73976 | | | | | | | | | | KernelScale: 2.7037 | | | | | | | | | | Epsilon: 38.421 | | 3 | 6 | Accept | 4.1303 | 0.65317 | 3.1155 | 3.1155 | svm | BoxConstraint: 0.0010671 | | | | | | | | | | KernelScale: 19.242 | | | | | | | | | | Epsilon: 44.847 | | 4 | 6 | Accept | 4.1338 | 0.68024 | 3.1155 | 3.1155 | svm | BoxConstraint: 0.095204 | | | | | | | | | | KernelScale: 63.457 | | | | | | | | | | Epsilon: 0.055423 | | 5 | 6 | Accept | 4.1303 | 0.23392 | 3.1155 | 3.1155 | svm | BoxConstraint: 0.01028 | | | | | | | | | | KernelScale: 0.0032203 | | | | | | | | | | Epsilon: 36.299 | | 6 | 6 | Best | 2.5852 | 0.17018 | 2.5852 | 2.7155 | tree | MinLeafSize: 2 | | | | | | | | | | MaxNumSplits: 120 | | | | | | | | | | NumVariablesToSample: 7 | | 7 | 8 | Accept | 4.5891 | 4.8163 | 2.5852 | 2.7155 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0051188 | | | | | | | | | | MinLeafSize: 83 | | | | | | | | | | NumVariablesToSample: NaN | | 8 | 8 | Accept | 4.7998 | 6.0958 | 2.5852 | 2.7155 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0042702 | | | | | | | | | | MinLeafSize: 31 | | | | | | | | | | NumVariablesToSample: NaN | | 9 | 8 | Accept | 2.6407 | 5.1761 | 2.5852 | 2.6533 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 45 | | | | | | | | | | NumVariablesToSample: 6 | | 10 | 8 | Accept | 5.749 | 5.7541 | 2.5852 | 2.6407 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0017397 | | | | | | | | | | MinLeafSize: 22 | | | | | | | | | | NumVariablesToSample: NaN | | 11 | 8 | Accept | 5.749 | 5.8128 | 2.5852 | 2.6408 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0017397 | | | | | | | | | | MinLeafSize: 22 | | | | | | | | | | NumVariablesToSample: NaN | | 12 | 8 | Accept | 5.749 | 6.3666 | 2.5852 | 2.6408 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0017397 | | | | | | | | | | MinLeafSize: 22 | | | | | | | | | | NumVariablesToSample: NaN | | 13 | 7 | Accept | 2.8653 | 3.1249 | 2.5852 | 2.6408 | tree | MinLeafSize: 5 | | | | | | | | | | MaxNumSplits: 61 | | | | | | | | | | NumVariablesToSample: 2 | | 14 | 7 | Accept | 4.1303 | 0.21536 | 2.5852 | 2.6408 | svm | BoxConstraint: 27.717 | | | | | | | | | | KernelScale: 21.172 | | | | | | | | | | Epsilon: 390.93 | | 15 | 5 | Accept | 4.6825 | 10.638 | 2.3273 | 2.6408 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0045559 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 16 | 5 | Best | 2.3273 | 4.6997 | 2.3273 | 2.6408 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: 3 | | 17 | 5 | Accept | 2.8316 | 0.35817 | 2.3273 | 2.6408 | svm | BoxConstraint: 0.038615 | | | | | | | | | | KernelScale: 0.26266 | | | | | | | | | | Epsilon: 5.8807 | | 18 | 8 | Accept | 3.1542 | 0.091401 | 2.3273 | 2.6408 | tree | MinLeafSize: 2 | | | | | | | | | | MaxNumSplits: 2 | | | | | | | | | | NumVariablesToSample: 5 | | 19 | 8 | Accept | 2.6177 | 0.097231 | 2.3273 | 2.6179 | svm | BoxConstraint: 38.6 | | | | | | | | | | KernelScale: 50.168 | | | | | | | | | | Epsilon: 2.0294 | | 20 | 7 | Accept | 4.1551 | 4.3963 | 2.3273 | 2.5864 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.014547 | | | | | | | | | | MinLeafSize: 145 | | | | | | | | | | NumVariablesToSample: NaN | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 21 | 7 | Accept | 2.6846 | 0.20978 | 2.3273 | 2.5864 | tree | MinLeafSize: 1 | | | | | | | | | | MaxNumSplits: 248 | | | | | | | | | | NumVariablesToSample: 7 | | 22 | 7 | Accept | 4.1303 | 0.086412 | 2.3273 | 2.5864 | svm | BoxConstraint: 117.04 | | | | | | | | | | KernelScale: 629.41 | | | | | | | | | | Epsilon: 729.47 | | 23 | 7 | Accept | 2.8059 | 0.051613 | 2.3273 | 2.586 | tree | MinLeafSize: 2 | | | | | | | | | | MaxNumSplits: 4 | | | | | | | | | | NumVariablesToSample: 4 | | 24 | 8 | Accept | 2.496 | 4.9911 | 2.3273 | 2.3286 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 29 | | | | | | | | | | NumVariablesToSample: 3 | | 25 | 8 | Best | 2.3255 | 5.025 | 2.3255 | 2.3426 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 11 | | | | | | | | | | NumVariablesToSample: 3 | | 26 | 8 | Accept | 2.504 | 0.1041 | 2.3255 | 2.3426 | tree | MinLeafSize: 9 | | | | | | | | | | MaxNumSplits: 157 | | | | | | | | | | NumVariablesToSample: 6 | | 27 | 6 | Accept | 2.3265 | 5.0488 | 2.3255 | 2.3426 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.11482 | | | | | | | | | | MinLeafSize: 54 | | | | | | | | | | NumVariablesToSample: NaN | | 28 | 6 | Accept | 2.6931 | 0.12749 | 2.3255 | 2.3426 | svm | BoxConstraint: 8.3226 | | | | | | | | | | KernelScale: 22.717 | | | | | | | | | | Epsilon: 3.2417 | | 29 | 6 | Accept | 4.1303 | 0.05622 | 2.3255 | 2.3426 | svm | BoxConstraint: 0.0011506 | | | | | | | | | | KernelScale: 352.85 | | | | | | | | | | Epsilon: 163.49 | | 30 | 7 | Accept | 2.5184 | 5.2768 | 2.3255 | 2.3299 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 11 | | | | | | | | | | NumVariablesToSample: 1 | | 31 | 6 | Accept | 2.5058 | 5.8769 | 2.2734 | 2.2739 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 11 | | | | | | | | | | NumVariablesToSample: 1 | | 32 | 6 | Best | 2.2734 | 0.74899 | 2.2734 | 2.2739 | svm | BoxConstraint: 344.75 | | | | | | | | | | KernelScale: 3.7441 | | | | | | | | | | Epsilon: 0.20094 | | 33 | 5 | Accept | 2.2734 | 1.1325 | 2.2734 | 2.2739 | svm | BoxConstraint: 344.75 | | | | | | | | | | KernelScale: 3.7441 | | | | | | | | | | Epsilon: 0.20094 | | 34 | 5 | Accept | 2.6958 | 0.05227 | 2.2734 | 2.2739 | tree | MinLeafSize: 4 | | | | | | | | | | MaxNumSplits: 5 | | | | | | | | | | NumVariablesToSample: 6 | | 35 | 8 | Accept | 4.1448 | 0.085799 | 2.2734 | 2.2735 | svm | BoxConstraint: 1.8227 | | | | | | | | | | KernelScale: 977.3 | | | | | | | | | | Epsilon: 2.0809 | | 36 | 6 | Accept | 2.9801 | 0.064816 | 2.2734 | 2.2735 | tree | MinLeafSize: 3 | | | | | | | | | | MaxNumSplits: 72 | | | | | | | | | | NumVariablesToSample: 1 | | 37 | 6 | Accept | 2.6751 | 0.27642 | 2.2734 | 2.2735 | tree | MinLeafSize: 7 | | | | | | | | | | MaxNumSplits: 31 | | | | | | | | | | NumVariablesToSample: 3 | | 38 | 6 | Accept | 4.1303 | 0.11917 | 2.2734 | 2.2735 | svm | BoxConstraint: 0.032336 | | | | | | | | | | KernelScale: 0.34645 | | | | | | | | | | Epsilon: 382.33 | | 39 | 6 | Best | 2.1806 | 0.3992 | 2.1806 | 2.1809 | svm | BoxConstraint: 197.52 | | | | | | | | | | KernelScale: 4.7757 | | | | | | | | | | Epsilon: 0.029282 | | 40 | 7 | Accept | 2.6007 | 0.052877 | 2.1806 | 2.1809 | tree | MinLeafSize: 14 | | | | | | | | | | MaxNumSplits: 311 | | | | | | | | | | NumVariablesToSample: 4 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 41 | 8 | Accept | 2.4301 | 0.064636 | 2.1806 | 2.1809 | tree | MinLeafSize: 7 | | | | | | | | | | MaxNumSplits: 16 | | | | | | | | | | NumVariablesToSample: 7 | | 42 | 8 | Accept | 2.3683 | 4.1134 | 2.1806 | 2.1809 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.52017 | | | | | | | | | | MinLeafSize: 3 | | | | | | | | | | NumVariablesToSample: NaN | | 43 | 8 | Accept | 4.1303 | 0.077599 | 2.1806 | 2.1809 | svm | BoxConstraint: 188.58 | | | | | | | | | | KernelScale: 0.009867 | | | | | | | | | | Epsilon: 27.186 | | 44 | 8 | Accept | 2.2817 | 4.1073 | 2.1806 | 2.1809 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.39343 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 45 | 8 | Accept | 2.2905 | 0.33312 | 2.1806 | 2.181 | svm | BoxConstraint: 3.1495 | | | | | | | | | | KernelScale: 1.5767 | | | | | | | | | | Epsilon: 0.015324 | | 46 | 8 | Accept | 2.1862 | 4.5949 | 2.1806 | 2.181 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.39847 | | | | | | | | | | MinLeafSize: 4 | | | | | | | | | | NumVariablesToSample: NaN | | 47 | 8 | Accept | 4.0238 | 0.1936 | 2.1806 | 2.181 | svm | BoxConstraint: 47.384 | | | | | | | | | | KernelScale: 407.1 | | | | | | | | | | Epsilon: 5.789 | | 48 | 8 | Accept | 2.3271 | 5.613 | 2.1806 | 2.181 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 22 | | | | | | | | | | NumVariablesToSample: 6 | | 49 | 8 | Accept | 4.1303 | 4.2256 | 2.1806 | 2.181 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.21695 | | | | | | | | | | MinLeafSize: 156 | | | | | | | | | | NumVariablesToSample: NaN | | 50 | 8 | Accept | 4.1303 | 3.9433 | 2.1806 | 2.181 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.24031 | | | | | | | | | | MinLeafSize: 156 | | | | | | | | | | NumVariablesToSample: NaN | | 51 | 8 | Accept | 5.9837 | 25.376 | 2.1806 | 2.1808 | svm | BoxConstraint: 3.3336 | | | | | | | | | | KernelScale: 0.20068 | | | | | | | | | | Epsilon: 1.2333 | | 52 | 8 | Best | 2.1775 | 4.8819 | 2.1775 | 2.1775 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.13486 | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: NaN | | 53 | 8 | Accept | 4.1472 | 0.098786 | 2.1775 | 2.1775 | svm | BoxConstraint: 0.024211 | | | | | | | | | | KernelScale: 234.23 | | | | | | | | | | Epsilon: 0.65694 | | 54 | 7 | Accept | 16.058 | 30.775 | 2.1775 | 2.1774 | svm | BoxConstraint: 0.87942 | | | | | | | | | | KernelScale: 0.042698 | | | | | | | | | | Epsilon: 4.1252 | | 55 | 7 | Accept | 4.1295 | 3.4872 | 2.1775 | 2.1774 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 165 | | | | | | | | | | NumVariablesToSample: 5 | | 56 | 7 | Accept | 4.1303 | 0.064431 | 2.1775 | 2.1774 | svm | BoxConstraint: 0.0077264 | | | | | | | | | | KernelScale: 11.935 | | | | | | | | | | Epsilon: 22.619 | | 57 | 6 | Accept | 5.2259 | 40.653 | 2.1775 | 2.1773 | svm | BoxConstraint: 0.95481 | | | | | | | | | | KernelScale: 0.0033698 | | | | | | | | | | Epsilon: 0.060804 | | 58 | 6 | Accept | 4.5815 | 6.4959 | 2.1775 | 2.1773 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0048265 | | | | | | | | | | MinLeafSize: 7 | | | | | | | | | | NumVariablesToSample: NaN | | 59 | 5 | Accept | 5.8709 | 9.4038 | 2.1775 | 2.1773 | svm | BoxConstraint: 0.046968 | | | | | | | | | | KernelScale: 0.0027305 | | | | | | | | | | Epsilon: 1.2478 | | 60 | 5 | Accept | 4.1489 | 0.059253 | 2.1775 | 2.1773 | svm | BoxConstraint: 0.0029753 | | | | | | | | | | KernelScale: 357.77 | | | | | | | | | | Epsilon: 1.3007 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 61 | 8 | Accept | 2.1923 | 4.9912 | 2.1775 | 2.177 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.027552 | | | | | | | | | | MinLeafSize: 15 | | | | | | | | | | NumVariablesToSample: NaN | | 62 | 6 | Accept | 2.3235 | 0.13508 | 2.1775 | 2.177 | svm | BoxConstraint: 0.060693 | | | | | | | | | | KernelScale: 1.9336 | | | | | | | | | | Epsilon: 2.9377 | | 63 | 6 | Accept | 4.1303 | 0.10264 | 2.1775 | 2.177 | svm | BoxConstraint: 283.72 | | | | | | | | | | KernelScale: 0.66147 | | | | | | | | | | Epsilon: 800.44 | | 64 | 6 | Accept | 3.2671 | 0.056364 | 2.1775 | 2.177 | tree | MinLeafSize: 3 | | | | | | | | | | MaxNumSplits: 2 | | | | | | | | | | NumVariablesToSample: 2 | | 65 | 7 | Accept | 4.1303 | 0.072693 | 2.1775 | 2.177 | svm | BoxConstraint: 958.92 | | | | | | | | | | KernelScale: 0.70563 | | | | | | | | | | Epsilon: 537.94 | | 66 | 7 | Accept | 2.1872 | 4.1631 | 2.1775 | 2.1772 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.12361 | | | | | | | | | | MinLeafSize: 15 | | | | | | | | | | NumVariablesToSample: NaN | | 67 | 7 | Accept | 4.1303 | 0.18462 | 2.1775 | 2.1772 | tree | MinLeafSize: 140 | | | | | | | | | | MaxNumSplits: 5 | | | | | | | | | | NumVariablesToSample: 2 | | 68 | 6 | Accept | 6.622 | 24.87 | 2.1775 | 1.4529 | svm | BoxConstraint: 154.74 | | | | | | | | | | KernelScale: 0.43817 | | | | | | | | | | Epsilon: 0.069304 | | 69 | 6 | Accept | 2.2017 | 4.3959 | 2.1775 | 1.4529 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.10067 | | | | | | | | | | MinLeafSize: 13 | | | | | | | | | | NumVariablesToSample: NaN | | 70 | 5 | Accept | 2.2891 | 4.5089 | 2.1775 | 2.1774 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.024227 | | | | | | | | | | MinLeafSize: 35 | | | | | | | | | | NumVariablesToSample: NaN | | 71 | 5 | Accept | 4.1303 | 0.062327 | 2.1775 | 2.1774 | svm | BoxConstraint: 1246.2 | | | | | | | | | | KernelScale: 0.053143 | | | | | | | | | | Epsilon: 53.963 | | 72 | 8 | Accept | 2.2118 | 4.6015 | 2.1775 | 2.1774 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.11646 | | | | | | | | | | MinLeafSize: 14 | | | | | | | | | | NumVariablesToSample: NaN | | 73 | 6 | Accept | 2.1969 | 4.3467 | 2.1775 | 2.1774 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.12319 | | | | | | | | | | MinLeafSize: 14 | | | | | | | | | | NumVariablesToSample: NaN | | 74 | 6 | Accept | 4.1303 | 0.10057 | 2.1775 | 2.1774 | svm | BoxConstraint: 0.50824 | | | | | | | | | | KernelScale: 0.015015 | | | | | | | | | | Epsilon: 96.096 | | 75 | 6 | Accept | 2.932 | 0.057265 | 2.1775 | 2.1774 | tree | MinLeafSize: 7 | | | | | | | | | | MaxNumSplits: 22 | | | | | | | | | | NumVariablesToSample: 1 | | 76 | 7 | Accept | 2.7649 | 0.12548 | 2.1775 | 2.1774 | tree | MinLeafSize: 16 | | | | | | | | | | MaxNumSplits: 43 | | | | | | | | | | NumVariablesToSample: 3 | | 77 | 7 | Accept | 2.1913 | 4.8165 | 2.1775 | 2.1761 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.057539 | | | | | | | | | | MinLeafSize: 3 | | | | | | | | | | NumVariablesToSample: NaN | | 78 | 7 | Accept | 2.4788 | 4.6057 | 2.1775 | 2.1774 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.99513 | | | | | | | | | | MinLeafSize: 19 | | | | | | | | | | NumVariablesToSample: NaN | | 79 | 8 | Accept | 6.1274 | 5.0102 | 2.1775 | 2.1759 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.000767 | | | | | | | | | | MinLeafSize: 37 | | | | | | | | | | NumVariablesToSample: NaN | | 80 | 8 | Accept | 4.13 | 3.7349 | 2.1775 | 2.176 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 171 | | | | | | | | | | NumVariablesToSample: 5 | |==========================================================================================================================================================| | Iter | Active | Eval | log(1+valLoss)| Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| validation loss | validation loss | | | |==========================================================================================================================================================| | 81 | 8 | Accept | 2.2406 | 6.658 | 2.1775 | 2.176 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 3 | | | | | | | | | | NumVariablesToSample: 7 | | 82 | 8 | Accept | 2.6476 | 0.054688 | 2.1775 | 2.176 | tree | MinLeafSize: 28 | | | | | | | | | | MaxNumSplits: 129 | | | | | | | | | | NumVariablesToSample: 7 | | 83 | 8 | Accept | 2.255 | 6.6774 | 2.1775 | 2.176 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 3 | | | | | | | | | | NumVariablesToSample: 7 | | 84 | 7 | Accept | 2.6645 | 10.337 | 2.1775 | 2.176 | svm | BoxConstraint: 334.64 | | | | | | | | | | KernelScale: 2.0733 | | | | | | | | | | Epsilon: 0.039959 | | 85 | 7 | Accept | 4.1303 | 0.062936 | 2.1775 | 2.176 | svm | BoxConstraint: 88.122 | | | | | | | | | | KernelScale: 0.00080559 | | | | | | | | | | Epsilon: 80.763 | | 86 | 7 | Accept | 2.2384 | 5.8157 | 2.1775 | 2.1761 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: 6 | | 87 | 7 | Accept | 6.0666 | 6.0896 | 2.1775 | 2.1759 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.00091284 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 88 | 7 | Accept | 3.2269 | 0.045413 | 2.1775 | 2.1759 | tree | MinLeafSize: 14 | | | | | | | | | | MaxNumSplits: 6 | | | | | | | | | | NumVariablesToSample: 1 | | 89 | 8 | Accept | 2.2427 | 6.3348 | 2.1775 | 2.176 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 3 | | | | | | | | | | NumVariablesToSample: 7 | | 90 | 6 | Accept | 4.5354 | 8.5876 | 2.1775 | 2.1768 | svm | BoxConstraint: 0.022073 | | | | | | | | | | KernelScale: 0.0034124 | | | | | | | | | | Epsilon: 2.9088 | | 91 | 6 | Accept | 2.2072 | 4.8166 | 2.1775 | 2.1768 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.067559 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 92 | 6 | Accept | 3.0936 | 4.1763 | 2.1775 | 2.1768 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.011017 | | | | | | | | | | MinLeafSize: 76 | | | | | | | | | | NumVariablesToSample: NaN |
__________________________________________________________ Optimization completed. Total iterations: 92 Total elapsed time: 65.349 seconds Total time for training and validation: 369.4973 seconds Best observed learner is an ensemble model with: Learner: ensemble Method: LSBoost LearnRate: 0.13486 MinLeafSize: 2 NumVariablesToSample: NaN Observed log(1 + valLoss): 2.1775 Time for training and validation: 4.8819 seconds Best estimated learner (returned model) is an ensemble model with: Learner: ensemble Method: LSBoost LearnRate: 0.13486 MinLeafSize: 2 NumVariablesToSample: NaN Estimated log(1 + valLoss): 2.1768 Estimated time for training and validation: 4.7705 seconds Documentation for fitrauto display
fitrauto によって返される最終的なモデルが、最適な推定学習器となります。モデルを返す前に、関数は学習データ全体 (carsTrain)、リストされている Learner (またはモデル) のタイプ、および表示されたハイパーパラメーター値を使用して、モデルの再学習を行います。
単純なモデルの作成
関数 fitlm を使用して、単純な線形回帰モデル linearMdl を作成します。
linearMdl = fitlm(carsTrain);
linearMdl オブジェクトは autoMdl オブジェクトと厳密に同一のプロパティとメソッドをもつわけではありませんが、オブジェクト関数 predict を使った新しいデータの応答値の予測に、両方のモデルを使用できます。
モデルの検定セットのパフォーマンスの比較
検定データ セットに対する linearMdl モデルと autoMdl モデルのパフォーマンスを比較します。各モデルについて、検定セットの平均二乗誤差 (MSE) を計算します。MSE の値が小さいほど、パフォーマンスが優れていることを示します。
ypred = predict(linearMdl,carsTest);
linearMSE = mean((carsTest.MPG-ypred).^2,"omitnan")linearMSE = 10.0558
autoMSE = loss(autoMdl,carsTest,"MPG")autoMSE = 7.2140
autoMdl モデルは linearMdl モデルよりも性能が高いと考えられます。
入力引数
出力引数
詳細
ヒント
データ セットのサイズ、指定した学習器の数、および選択した最適化手法によっては、
fitrautoの処理に時間がかかる場合があります。Parallel Computing Toolbox のライセンスがある場合、最適化を並列実行して計算を高速化することができます。これを行うには、
"HyperparameterOptimizationOptions",struct("UseParallel",true)を指定します。この構造体に追加フィールドを含めて、その他の最適化の側面を制御できます。HyperparameterOptimizationOptionsを参照してください。学習セットの観測値の数が原因 (たとえば 10,000 を超える場合) でベイズ最適化による
fitrautoの実行に長い時間がかかる場合は、代わりに ASHA 最適化によるfitrautoを使用することを検討してください。データ セットの観測値が多いと、多くの場合、ベイズ最適化よりも ASHA 最適化の方が優れた解を速く見つけます。ASHA 最適化を使用するには、"HyperparameterOptimizationOptions",struct("Optimizer","asha")を指定します。この構造体に追加フィールドを含めて、追加の最適化の側面を制御できます。特に、時間の制約がある場合は、HyperparameterOptimizationOptions構造体のMaxTimeフィールドを指定して、fitrautoを実行する秒数を制限します。
アルゴリズム
代替機能
使用するデータ セットに最適なモデルがわからない場合は、回帰学習器アプリを代わりに使用することができます。このアプリを使用すると、さまざまなモデルについてハイパーパラメーターを調整して、パフォーマンスが最も高い最適化済みモデルを選択できます。回帰学習器では、モデルのハイパーパラメーターを調整する前に特定のモデルを選択しなければなりませんが、最適化可能なハイパーパラメーターの選択とハイパーパラメーター値の設定をより柔軟に行うことができます。このアプリにより、さまざまな線形回帰モデルの学習を行うことも可能になります (線形回帰モデルを参照)。ただし、このアプリでは、最適化を並列実行することや、学習器として
"linear"または"kernel"を最適化すること、観測値の重みを指定すること、ASHA 最適化を使用することはできません。詳細は、回帰学習器アプリのハイパーパラメーターの最適化を参照してください。使用するデータに適合するモデルがわかっている場合は、対応するモデル近似関数を使用し、名前と値の引数
OptimizeHyperparametersを指定して、ハイパーパラメーターを調整することもできます。複数のモデルの結果を比較して最適な回帰モデルを選択できます。分類モデルに適用する、このプロセスの例については、ベイズ最適化を使用したモデル選択の自動化への移行を参照してください。
参照
[1] Li, Liam, Kevin Jamieson, Afshin Rostamizadeh, Ekaterina Gonina, Moritz Hardt, Benjamin Recht, and Ameet Talwalkar. “A System for Massively Parallel Hyperparameter Tuning.” ArXiv:1810.05934v5 [Cs], March 16, 2020. https://arxiv.org/abs/1810.05934v5.
拡張機能
バージョン履歴
R2020b で導入
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