tall 配列を使用したベイズ最適化
この例では、名前と値の引数 'OptimizeHyperparameters' を使用してカーネル分類器の学習に最適なパラメーターをベイズ最適化によって選択する方法を示します。標本データ セット airlinesmall.csv は、飛行機のフライト データについての表形式ファイルが含まれている大規模なデータ セットです。この例では、データが含まれている tall table を作成し、tall table からクラス ラベルと予測子データを抽出して最適化手順を実行します。
tall 配列に対する計算を実行する場合、MATLAB® は並列プール (Parallel Computing Toolbox™ がある場合は既定) またはローカルの MATLAB セッションを使用します。Parallel Computing Toolbox がある場合でもローカルの MATLAB セッションを使用して例を実行するには、関数mapreducerを使用してグローバルな実行環境を変更できます。
MATLAB® へのデータの取得
データがあるフォルダーの場所を参照するデータストアを作成します。データは、単一のファイル、ファイルの集まり、またはフォルダー全体のどれに含まれていてもかまいません。一連のファイルが格納されているフォルダーについて、フォルダー全体の場所を指定するか、'*.csv' のようにワイルドカード文字を使用して、同じファイル拡張子をもつ複数のファイルをデータストアに含めることができます。処理する変数のサブセットを選択します。datastore で NaN 値に置き換えるため、'NA' 値を欠損データとして扱います。データストア内のデータを含む tall table を作成します。
ds = datastore('airlinesmall.csv'); ds.SelectedVariableNames = {'Month','DayofMonth','DayOfWeek',... 'DepTime','ArrDelay','Distance','DepDelay'}; ds.TreatAsMissing = 'NA'; tt = tall(ds) % Tall table
Starting parallel pool (parpool) using the 'Processes' profile ...
Connected to parallel pool with 6 workers.
tt =
M×7 tall table
Month DayofMonth DayOfWeek DepTime ArrDelay Distance DepDelay
_____ __________ _________ _______ ________ ________ ________
10 21 3 642 8 308 12
10 26 1 1021 8 296 1
10 23 5 2055 21 480 20
10 23 5 1332 13 296 12
10 22 4 629 4 373 -1
10 28 3 1446 59 308 63
10 8 4 928 3 447 -2
10 10 6 859 11 954 -1
: : : : : : :
: : : : : : :
クラス ラベルと予測子データの準備
フライトが遅れた場合に真になる論理変数を定義することにより、10 分以上遅れたフライトを判別します。この変数にクラス ラベルを含めます。この変数のプレビューには、はじめの数行が含まれています。
Y = tt.DepDelay > 10 % Class labelsY = M×1 tall logical array 1 0 1 1 0 1 0 0 : :
予測子データの tall 配列を作成します。
X = tt{:,1:end-1} % Predictor dataX =
M×6 tall double matrix
10 21 3 642 8 308
10 26 1 1021 8 296
10 23 5 2055 21 480
10 23 5 1332 13 296
10 22 4 629 4 373
10 28 3 1446 59 308
10 8 4 928 3 447
10 10 6 859 11 954
: : : : : :
: : : : : :
欠損データが含まれている X および Y の行を削除します。
R = rmmissing([X Y]); % Data with missing entries removed
X = R(:,1:end-1);
Y = R(:,end); OptimizeHyperparameters を使用したベイズ最適化の実行
名前と値の引数 'OptimizeHyperparameters' を使用して、ハイパーパラメーターを最適化します。
予測子変数を標準化します。
Z = zscore(X);
ホールドアウト検証セットの損失を最小化する、名前と値の引数 'KernelScale' および 'Lambda' に最適な値を求めます。既定では、データの 20% が検証データとして選択されて確保され、残りのデータがモデルの学習に使用されます。ホールドアウトの比率は、名前と値の引数 'HyperparameterOptimizationOptions' を使用して変更できます。再現性を得るため、'expected-improvement-plus' の獲得関数を使用し、rng と tallrng により乱数発生器のシードを設定します。tall 配列の場合、ワーカーの個数と実行環境によって結果が異なる可能性があります。詳細については、コードの実行場所の制御を参照してください。
rng('default') tallrng('default') Mdl = fitckernel(Z,Y,'Verbose',0,'OptimizeHyperparameters', ... {'KernelScale','Lambda'},'HyperparameterOptimizationOptions', ... struct('AcquisitionFunctionName','expected-improvement-plus'))
Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 2: Completed in 6.4 sec - Pass 2 of 2: Completed in 1.9 sec Evaluation completed in 9.8 sec Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 1.8 sec Evaluation completed in 1.9 sec |=====================================================================================================| | Iter | Eval | Objective | Objective | BestSoFar | BestSoFar | KernelScale | Lambda | | | result | | runtime | (observed) | (estim.) | | | |=====================================================================================================| | 1 | Best | 0.19672 | 83.403 | 0.19672 | 0.19672 | 1.2297 | 0.0080902 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.94 sec Evaluation completed in 1.1 sec | 2 | Accept | 0.19672 | 35.532 | 0.19672 | 0.19672 | 0.039643 | 2.5756e-05 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.97 sec Evaluation completed in 1.1 sec | 3 | Accept | 0.19672 | 35.184 | 0.19672 | 0.19672 | 0.02562 | 1.2555e-08 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.83 sec Evaluation completed in 0.93 sec | 4 | Accept | 0.19672 | 34.375 | 0.19672 | 0.19672 | 92.644 | 1.2056e-07 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.86 sec Evaluation completed in 0.96 sec | 5 | Best | 0.11469 | 55.874 | 0.11469 | 0.12698 | 11.173 | 0.00024836 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.86 sec Evaluation completed in 0.97 sec | 6 | Best | 0.11365 | 50.865 | 0.11365 | 0.11373 | 10.609 | 0.00025761 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.92 sec Evaluation completed in 1 sec | 7 | Accept | 0.19672 | 34.5 | 0.11365 | 0.11373 | 0.0059498 | 0.00043861 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.86 sec Evaluation completed in 0.95 sec | 8 | Accept | 0.12122 | 56.119 | 0.11365 | 0.11371 | 11.44 | 0.00045722 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.96 sec Evaluation completed in 1.1 sec | 9 | Best | 0.10417 | 28.379 | 0.10417 | 0.10417 | 8.0424 | 6.7998e-05 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.82 sec Evaluation completed in 0.92 sec | 10 | Accept | 0.10433 | 27.657 | 0.10417 | 0.10417 | 9.6694 | 1.4948e-05 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.9 sec Evaluation completed in 0.99 sec | 11 | Best | 0.10409 | 27.999 | 0.10409 | 0.10411 | 6.2099 | 6.1093e-06 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.84 sec Evaluation completed in 0.93 sec | 12 | Best | 0.10383 | 29.942 | 0.10383 | 0.10404 | 5.6767 | 7.6134e-08 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.84 sec Evaluation completed in 0.93 sec | 13 | Accept | 0.10408 | 30.076 | 0.10383 | 0.10365 | 8.1769 | 8.5993e-09 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.87 sec Evaluation completed in 0.96 sec | 14 | Accept | 0.10404 | 28.263 | 0.10383 | 0.10361 | 7.6191 | 6.4079e-07 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.88 sec Evaluation completed in 0.98 sec | 15 | Best | 0.10351 | 28.352 | 0.10351 | 0.10362 | 4.2987 | 9.2645e-08 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.86 sec Evaluation completed in 0.95 sec | 16 | Accept | 0.10404 | 29.934 | 0.10351 | 0.10362 | 4.8747 | 1.7838e-08 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.92 sec Evaluation completed in 1 sec | 17 | Accept | 0.10657 | 57.566 | 0.10351 | 0.10357 | 4.8239 | 0.00016344 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.85 sec Evaluation completed in 0.94 sec | 18 | Best | 0.10299 | 28.692 | 0.10299 | 0.10358 | 3.5555 | 2.7165e-06 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.89 sec Evaluation completed in 0.99 sec | 19 | Accept | 0.10366 | 28.388 | 0.10299 | 0.10324 | 3.8035 | 1.3542e-06 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.86 sec Evaluation completed in 0.95 sec | 20 | Accept | 0.10337 | 28.643 | 0.10299 | 0.10323 | 3.806 | 1.8101e-06 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.88 sec Evaluation completed in 0.97 sec |=====================================================================================================| | Iter | Eval | Objective | Objective | BestSoFar | BestSoFar | KernelScale | Lambda | | | result | | runtime | (observed) | (estim.) | | | |=====================================================================================================| | 21 | Accept | 0.10345 | 28.972 | 0.10299 | 0.10322 | 3.3655 | 9.082e-09 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.86 sec Evaluation completed in 0.95 sec | 22 | Accept | 0.19672 | 36.972 | 0.10299 | 0.10322 | 999.62 | 1.2609e-06 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.86 sec Evaluation completed in 0.96 sec | 23 | Accept | 0.10315 | 28.377 | 0.10299 | 0.10306 | 3.6716 | 1.2445e-08 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.92 sec Evaluation completed in 1 sec | 24 | Accept | 0.19672 | 34.383 | 0.10299 | 0.10306 | 0.0010004 | 2.6214e-08 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.92 sec Evaluation completed in 1 sec | 25 | Accept | 0.19672 | 33.973 | 0.10299 | 0.10306 | 0.21865 | 0.0026529 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.84 sec Evaluation completed in 0.95 sec | 26 | Accept | 0.19672 | 36.951 | 0.10299 | 0.10306 | 299.92 | 0.0032109 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.93 sec Evaluation completed in 1 sec | 27 | Accept | 0.19672 | 34.099 | 0.10299 | 0.10306 | 0.002436 | 0.0040428 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 1.2 sec Evaluation completed in 1.4 sec | 28 | Accept | 0.19672 | 36.694 | 0.10299 | 0.10305 | 0.50559 | 3.3667e-08 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.88 sec Evaluation completed in 0.97 sec | 29 | Accept | 0.10354 | 30.402 | 0.10299 | 0.10313 | 3.7754 | 9.5626e-09 | Evaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.84 sec Evaluation completed in 0.92 sec | 30 | Accept | 0.10405 | 27.686 | 0.10299 | 0.10315 | 8.9864 | 2.3136e-07 | __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 1102.4884 seconds
Total objective function evaluation time: 1088.2513
Best observed feasible point:
KernelScale Lambda
___________ __________
3.5555 2.7165e-06
Observed objective function value = 0.10299
Estimated objective function value = 0.10332
Function evaluation time = 28.6921
Best estimated feasible point (according to models):
KernelScale Lambda
___________ __________
3.6716 1.2445e-08
Estimated objective function value = 0.10315
Estimated function evaluation time = 29.1903
Mdl =
ClassificationKernel
PredictorNames: {'x1' 'x2' 'x3' 'x4' 'x5' 'x6'}
ResponseName: 'Y'
ClassNames: [0 1]
Learner: 'svm'
NumExpansionDimensions: 256
KernelScale: 3.6716
Lambda: 1.2445e-08
BoxConstraint: 665.9442
Properties, Methods
bayesopt の使用によるベイズ最適化の実行
あるいは、関数 bayesopt を使用して、ハイパーパラメーターに最適な値を求めることもできます。
データ セットを学習セットとテスト セットに分割します。テスト セット用に 1/3 のホールドアウト標本を指定します。
rng('default') % For reproducibility tallrng('default') % For reproducibility Partition = cvpartition(Y,'Holdout',1/3); trainingInds = training(Partition); % Indices for the training set testInds = test(Partition); % Indices for the test set
学習データとテスト データを抽出し、予測子データを標準化します。
Ytrain = Y(trainingInds); % Training class labels Xtrain = X(trainingInds,:); [Ztrain,mu,stddev] = zscore(Xtrain); % Standardized training data Ytest = Y(testInds); % Testing class labels Xtest = X(testInds,:); Ztest = (Xtest-mu)./stddev; % Standardized test data
名前と値の引数 'KernelScale' および 'Lambda' に最適な値を求めるため、変数 sigma および lambda を定義します。optimizableVariable を使用し、最適な値は不明なので、変数について広い範囲を指定します。最適な値を対数スケールで求めるため、対数変換を変数に適用します。
N = gather(numel(Ytrain)); % Evaluate the length of the tall training array in memoryEvaluating tall expression using the Parallel Pool 'Processes': - Pass 1 of 1: Completed in 0.85 sec Evaluation completed in 0.99 sec
sigma = optimizableVariable('sigma',[1e-3,1e3],'Transform','log'); lambda = optimizableVariable('lambda',[(1e-3)/N, (1e3)/N],'Transform','log');
ベイズ最適化の目的関数を作成します。目的関数は、変数 sigma および lambda が格納されている table を受け入れ、関数 fitckernel で学習をさせたバイナリ ガウス カーネル分類モデルの分類損失値を計算します。診断情報を反復表示しないようにするため、fitckernel で 'Verbose',0 を設定します。
minfn = @(z)gather(loss(fitckernel(Ztrain,Ytrain, ... 'KernelScale',z.sigma,'Lambda',z.lambda,'Verbose',0), ... Ztest,Ytest));
bayesoptを使用して、カーネル分類モデルのパラメーター [sigma,lambda] を分類損失に関して最適化します。既定では、bayesopt は最適化に関する情報をコマンドラインに繰り返し表示します。再現性を得るために、AcquisitionFunctionName オプションを 'expected-improvement-plus' に設定します。既定の獲得関数は実行時に決定されるので、結果が異なる場合があります。
results = bayesopt(minfn,[sigma,lambda], ... 'AcquisitionFunctionName','expected-improvement-plus')
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
|=====================================================================================================|
| Iter | Eval | Objective | Objective | BestSoFar | BestSoFar | sigma | lambda |
| | result | | runtime | (observed) | (estim.) | | |
|=====================================================================================================|
| 1 | Best | 0.19651 | 55.774 | 0.19651 | 0.19651 | 1.2297 | 0.012135 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 2 | Accept | 0.19651 | 77.257 | 0.19651 | 0.19651 | 0.039643 | 3.8633e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 3 | Accept | 0.19651 | 54.632 | 0.19651 | 0.19651 | 0.02562 | 1.8832e-08 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.99 sec
Evaluation completed in 1.1 sec
| 4 | Accept | 0.19651 | 30.84 | 0.19651 | 0.19651 | 92.644 | 1.8084e-07 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1 sec
Evaluation completed in 1.1 sec
| 5 | Accept | 0.19651 | 31.653 | 0.19651 | 0.19651 | 978.95 | 0.00015066 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 6 | Accept | 0.19651 | 62.207 | 0.19651 | 0.19651 | 0.0089609 | 0.0059189 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 7 | Accept | 0.19651 | 68.693 | 0.19651 | 0.19651 | 0.0010015 | 1.4474e-08 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 8 | Accept | 0.19651 | 53.736 | 0.19651 | 0.19651 | 0.27475 | 0.0044831 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 9 | Accept | 0.19651 | 58.473 | 0.19651 | 0.19651 | 0.81326 | 1.0753e-07 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 10 | Accept | 0.19651 | 68.878 | 0.19651 | 0.19651 | 0.0040507 | 0.00011333 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.99 sec
Evaluation completed in 1.1 sec
| 11 | Accept | 0.19651 | 31.761 | 0.19651 | 0.19651 | 980.38 | 1.362e-08 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.98 sec
Evaluation completed in 1.1 sec
| 12 | Accept | 0.19651 | 31.332 | 0.19651 | 0.19651 | 968.03 | 0.011653 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.2 sec
Evaluation completed in 1.3 sec
| 13 | Accept | 0.19651 | 60.755 | 0.19651 | 0.19651 | 0.41617 | 1.6704e-07 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1 sec
Evaluation completed in 1.1 sec
| 14 | Best | 0.10059 | 25.589 | 0.10059 | 0.1006 | 2.9545 | 2.4479e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.3 sec
| 15 | Accept | 0.10098 | 24.933 | 0.10059 | 0.1006 | 5.3367 | 2.7906e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.3 sec
| 16 | Accept | 0.10101 | 30.013 | 0.10059 | 0.1006 | 4.233 | 1.4951e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 17 | Best | 0.10049 | 28.908 | 0.10049 | 0.10013 | 4.0225 | 2.3847e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.1 sec
| 18 | Accept | 0.10076 | 26.625 | 0.10049 | 0.10032 | 3.7144 | 1.9977e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.2 sec
Evaluation completed in 1.3 sec
| 19 | Accept | 0.10061 | 29.056 | 0.10049 | 0.10025 | 3.5125 | 4.2084e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 20 | Accept | 0.10056 | 26.932 | 0.10049 | 0.10029 | 3.7269 | 2.7754e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1 sec
Evaluation completed in 1.1 sec
|=====================================================================================================|
| Iter | Eval | Objective | Objective | BestSoFar | BestSoFar | sigma | lambda |
| | result | | runtime | (observed) | (estim.) | | |
|=====================================================================================================|
| 21 | Accept | 0.10089 | 25.84 | 0.10049 | 0.10044 | 3.8681 | 2.9799e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1 sec
Evaluation completed in 1.1 sec
| 22 | Accept | 0.10101 | 25.461 | 0.10049 | 0.10052 | 6.1914 | 8.6976e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 23 | Accept | 0.10161 | 27.882 | 0.10049 | 0.10053 | 5.1566 | 5.2959e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1 sec
Evaluation completed in 1.1 sec
| 24 | Accept | 0.1028 | 61.428 | 0.10049 | 0.10053 | 3.8952 | 0.00012578 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.99 sec
Evaluation completed in 1.1 sec
| 25 | Accept | 0.11158 | 50.54 | 0.10049 | 0.10053 | 12.25 | 0.00018879 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 0.95 sec
Evaluation completed in 1 sec
| 26 | Best | 0.10014 | 25.922 | 0.10014 | 0.10042 | 3.5501 | 2.292e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 27 | Accept | 0.19651 | 70.888 | 0.10014 | 0.10042 | 0.0010185 | 1.3606e-06 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 28 | Accept | 0.10103 | 24.309 | 0.10014 | 0.10053 | 3.4712 | 2.1357e-05 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1 sec
Evaluation completed in 1.1 sec
| 29 | Accept | 0.19651 | 32.212 | 0.10014 | 0.10053 | 980.28 | 1.8241e-06 |
Evaluating tall expression using the Parallel Pool 'Processes':
- Pass 1 of 1: Completed in 1.1 sec
Evaluation completed in 1.2 sec
| 30 | Accept | 0.19651 | 66.958 | 0.10014 | 0.10053 | 0.0010035 | 0.011867 |
__________________________________________________________
Optimization completed.
MaxObjectiveEvaluations of 30 reached.
Total function evaluations: 30
Total elapsed time: 1361.76 seconds
Total objective function evaluation time: 1289.4879
Best observed feasible point:
sigma lambda
______ _________
3.5501 2.292e-05
Observed objective function value = 0.10014
Estimated objective function value = 0.10053
Function evaluation time = 25.9216
Best estimated feasible point (according to models):
sigma lambda
______ _________
3.5501 2.292e-05
Estimated objective function value = 0.10053
Estimated function evaluation time = 26.7715
results =
BayesianOptimization with properties:
ObjectiveFcn: @(z)gather(loss(fitckernel(Ztrain,Ytrain,'KernelScale',z.sigma,'Lambda',z.lambda,'Verbose',0),Ztest,Ytest))
VariableDescriptions: [1×2 optimizableVariable]
Options: [1×1 struct]
MinObjective: 0.1001
XAtMinObjective: [1×2 table]
MinEstimatedObjective: 0.1005
XAtMinEstimatedObjective: [1×2 table]
NumObjectiveEvaluations: 30
TotalElapsedTime: 1.3618e+03
NextPoint: [1×2 table]
XTrace: [30×2 table]
ObjectiveTrace: [30×1 double]
ConstraintsTrace: []
UserDataTrace: {30×1 cell}
ObjectiveEvaluationTimeTrace: [30×1 double]
IterationTimeTrace: [30×1 double]
ErrorTrace: [30×1 double]
FeasibilityTrace: [30×1 logical]
FeasibilityProbabilityTrace: [30×1 double]
IndexOfMinimumTrace: [30×1 double]
ObjectiveMinimumTrace: [30×1 double]
EstimatedObjectiveMinimumTrace: [30×1 double]
関数 bestPoint を使用して、ベイズ モデル results 内の最良の実行可能点を取得します。既定の基準 min-visited-upper-confidence-interval を使用します。この基準では、目的関数の値に対して信頼区間の上限を最小化する探索済みの点が最良の実行可能点になります。
zbest = bestPoint(results)
zbest=1×2 table
sigma lambda
______ _________
3.5501 2.292e-05
table zbest には、名前と値の引数 'KernelScale' および 'Lambda' に最適な推定値が格納されます。これらの値は、次の構文を使用して新しい最適化済みカーネル分類器に学習をさせるときに指定できます。
Mdl = fitckernel(Ztrain,Ytrain,'KernelScale',zbest.sigma,'Lambda',zbest.lambda)
tall 配列の場合、最適化手順に時間がかかる可能性があります。最適化手順を実行するにはデータ セットが大きすぎる場合、データの一部だけを使用してパラメーターの最適化を試すことができます。関数 datasample を使用し、'Replace','false' を指定して、データを非復元抽出します。
参考
bayesopt | bestPoint | cvpartition | datastore | fitckernel | gather | loss | optimizableVariable | tall
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