Байесова оптимизация с длинными массивами

Этот пример показывает, как использовать Байесовую оптимизацию, чтобы выбрать оптимальные параметры для обучения классификатор ядра при помощи аргумента пары "имя-значение" 'OptimizeHyperparameters'. airlinesmall.csv набора выборочных данных является большим набором данных, который содержит табличный файл данных о полете. Этот пример составляет длинную таблицу, содержащую данные, и использует длинную таблицу, чтобы запустить процедуру оптимизации.

Получите данные в MATLAB®

Создайте datastore, который ссылается на местоположение папки с данными. Данные могут содержаться в одном файле, наборе файлов или целой папке. Для папок, которые содержат набор файлов, можно задать целое местоположение папки или использовать подстановочный символ, '*.csv', чтобы включать несколько файлов с тем же расширением файла в datastore. Выберите подмножество переменных, чтобы работать с и обработать значения 'NA' как недостающие данные так, чтобы datastore заменил их на значения NaN. Составьте длинную таблицу, которая содержит данные в datastore.

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 'local' profile ...
Connected to the parallel pool (number of workers: 6).

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   
      :          :             :           :          :           :           :
      :          :             :           :          :           :           :

Когда вы выполняете вычисления на длинных массивах, среда выполнения по умолчанию использует или локальный сеанс работы с MATLAB или локальный параллельный пул (если у вас есть Parallel Computing Toolbox™). Можно использовать функцию mapreducer, чтобы изменить среду выполнения.

Подготовьте метки класса и данные о предикторе

Определите рейсы, которые являются поздними на 10 минут или больше путем определения логической переменной, которая верна для позднего рейса. Эта переменная содержит метки класса. Предварительный просмотр этой переменной включает первые несколько строк.

Y = tt.DepDelay > 10 % Class labels

Y =

  M×1 tall logical array

   1
   0
   1
   1
   0
   1
   0
   0
   :
   :

Создайте длинный массив для данных о предикторе.

X = tt{:,1:end-1} % Predictor data

X =

  M×6 tall double matrix

  Columns 1 through 5

          10          21           3         642           8
          10          26           1        1021           8
          10          23           5        2055          21
          10          23           5        1332          13
          10          22           4         629           4
          10          28           3        1446          59
          10           8           4         928           3
          10          10           6         859          11
          :           :            :          :           :
          :           :            :          :           :

  Column 6

         308
         296
         480
         296
         373
         308
         447
         954
          :
          :

Удалите строки в X и Y, которые содержат недостающие данные.

R = rmmissing([X Y]); % Data with missing entries removed
X = R(:,1:end-1); 
Y = R(:,end);

Выполните байесовую оптимизацию Используя `OptimizeHyperparameters`

Оптимизируйте гиперпараметры автоматически с помощью аргумента пары "имя-значение" 'OptimizeHyperparameters'.

Стандартизируйте переменные прогноза.

Z = zscore(X);

Найдите оптимальные значения для аргументов пары "имя-значение" 'KernelScale' и 'Lambda', которые минимизируют пятикратную потерю перекрестной проверки. Для воспроизводимости используйте функцию приобретения 'expected-improvement-plus' и установите seed генераторов случайных чисел с помощью rng и tallrng. Результаты могут отличаться в зависимости от количества рабочих и среды выполнения для длинных массивов. Для получения дополнительной информации смотрите Управление Где Ваши Выполнения Кода (MATLAB).

rng('default') 
tallrng('default')
Mdl = fitckernel(Z,Y,'Verbose',0,'OptimizeHyperparameters','auto',...
    'HyperparameterOptimizationOptions',struct('AcquisitionFunctionName','expected-improvement-plus'))

Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 2: Completed in 9 sec
- Pass 2 of 2: Completed in 8.9 sec
Evaluation completed in 18 sec

Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.7 sec
Evaluation completed in 2.7 sec
|=====================================================================================================|
| Iter | Eval   | Objective   | Objective   | BestSoFar   | BestSoFar   |  KernelScale |       Lambda |
|      | result |             | runtime     | (observed)  | (estim.)    |              |              |
|=====================================================================================================|
|    1 | Best   |     0.19672 |       153.5 |     0.19672 |     0.19672 |       1.2297 |    0.0080902 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.5 sec
Evaluation completed in 1.5 sec
|    2 | Accept |     0.19672 |      69.775 |     0.19672 |     0.19672 |     0.039643 |   2.5756e-05 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.1 sec
|    3 | Accept |     0.19672 |      72.586 |     0.19672 |     0.19672 |      0.02562 |   1.2555e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.5 sec
Evaluation completed in 1.5 sec
|    4 | Accept |     0.19672 |      81.345 |     0.19672 |     0.19672 |       92.644 |   1.2056e-07 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2 sec
|    5 | Best   |     0.11469 |      116.54 |     0.11469 |     0.12698 |       11.173 |   0.00024836 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2 sec
|    6 | Best   |     0.11365 |      108.21 |     0.11365 |     0.11373 |       10.609 |   0.00025761 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.5 sec
Evaluation completed in 1.5 sec
|    7 | Accept |     0.19672 |      66.926 |     0.11365 |     0.11373 |    0.0059498 |   0.00043861 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2 sec
|    8 | Accept |     0.12122 |      121.38 |     0.11365 |     0.11371 |        11.44 |   0.00045722 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.5 sec
Evaluation completed in 1.5 sec
|    9 | Best   |     0.10417 |      55.569 |     0.10417 |     0.10417 |       8.0424 |   6.7998e-05 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.9 sec
Evaluation completed in 2 sec
|   10 | Accept |     0.10433 |      56.204 |     0.10417 |     0.10417 |       9.6694 |   1.4948e-05 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2 sec
|   11 | Best   |     0.10409 |       56.93 |     0.10409 |     0.10411 |       6.2099 |   6.1093e-06 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.4 sec
Evaluation completed in 1.5 sec
|   12 | Best   |     0.10383 |      61.958 |     0.10383 |     0.10404 |       5.6767 |   7.6134e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.5 sec
Evaluation completed in 1.5 sec
|   13 | Accept |     0.10408 |      60.655 |     0.10383 |     0.10365 |       8.1769 |   8.5993e-09 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2.1 sec
|   14 | Accept |     0.10404 |      57.069 |     0.10383 |     0.10361 |       7.6191 |   6.4079e-07 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.9 sec
Evaluation completed in 1.9 sec
|   15 | Best   |     0.10351 |      56.101 |     0.10351 |     0.10362 |       4.2987 |   9.2645e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2 sec
|   16 | Accept |     0.10404 |      60.269 |     0.10351 |     0.10362 |       4.8747 |   1.7838e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2 sec
|   17 | Accept |     0.10657 |      119.73 |     0.10351 |     0.10357 |       4.8239 |   0.00016344 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.4 sec
Evaluation completed in 1.5 sec
|   18 | Best   |     0.10299 |      55.899 |     0.10299 |     0.10358 |       3.5555 |   2.7165e-06 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2 sec
|   19 | Accept |     0.10366 |      56.413 |     0.10299 |     0.10324 |       3.8035 |   1.3542e-06 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2 sec
|   20 | Accept |     0.10337 |       55.97 |     0.10299 |     0.10323 |        3.806 |   1.8101e-06 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.9 sec
Evaluation completed in 2 sec
|=====================================================================================================|
| Iter | Eval   | Objective   | Objective   | BestSoFar   | BestSoFar   |  KernelScale |       Lambda |
|      | result |             | runtime     | (observed)  | (estim.)    |              |              |
|=====================================================================================================|
|   21 | Accept |     0.10345 |      56.155 |     0.10299 |     0.10322 |       3.3655 |    9.082e-09 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.5 sec
Evaluation completed in 1.5 sec
|   22 | Accept |     0.19672 |       82.67 |     0.10299 |     0.10322 |       999.62 |   1.2609e-06 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2.1 sec
|   23 | Accept |     0.10315 |      56.062 |     0.10299 |     0.10306 |       3.6716 |   1.2445e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2 sec
|   24 | Accept |     0.19672 |      68.283 |     0.10299 |     0.10306 |    0.0010004 |   2.6214e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.9 sec
Evaluation completed in 2 sec
|   25 | Accept |     0.19672 |      67.775 |     0.10299 |     0.10306 |      0.21865 |    0.0026529 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2.1 sec
|   26 | Accept |     0.19672 |      84.329 |     0.10299 |     0.10306 |       299.92 |    0.0032109 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.4 sec
Evaluation completed in 1.4 sec
|   27 | Accept |     0.19672 |      67.871 |     0.10299 |     0.10306 |     0.002436 |    0.0040428 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.4 sec
Evaluation completed in 2.4 sec
|   28 | Accept |     0.19672 |      75.278 |     0.10299 |     0.10305 |      0.50559 |   3.3667e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.2 sec
|   29 | Accept |     0.10354 |      60.527 |     0.10299 |     0.10313 |       3.7754 |   9.5626e-09 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2 sec
|   30 | Accept |     0.10405 |      59.206 |     0.10299 |     0.10315 |       8.9864 |   2.3136e-07 |

__________________________________________________________
Optimization completed.
MaxObjectiveEvaluations of 30 reached.
Total function evaluations: 30
Total elapsed time: 2243.1781 seconds.
Total objective function evaluation time: 2221.1816

Best observed feasible point:
    KernelScale      Lambda  
    ___________    __________

      3.5555       2.7165e-06

Observed objective function value = 0.10299
Estimated objective function value = 0.10315
Function evaluation time = 55.8993

Best estimated feasible point (according to models):
    KernelScale      Lambda  
    ___________    __________

      3.6716       1.2445e-08

Estimated objective function value = 0.10315
Estimated function evaluation time = 57.638

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

Выполните байесовую оптимизацию при помощи `bayesopt`

Также можно использовать функцию bayesopt, чтобы найти оптимальные значения гиперпараметров.

Разделите набор данных в наборы обучающих данных и наборы тестов. Задайте 1/3 выборку затяжки для набора тестов.

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

Извлеките данные об обучении и тестировании и стандартизируйте данные о предикторе.

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

Задайте переменные sigma и lambda, чтобы найти оптимальные значения для аргументов пары "имя-значение" 'KernelScale' и 'Lambda'. Используйте optimizableVariable и задайте широкий спектр для переменных, потому что оптимальные значения неизвестны. Примените логарифмическое преобразование к переменным, чтобы искать оптимальные значения на логарифмической шкале.

N = gather(numel(Ytrain)); % Evaluate the length of the tall training array in memory

Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.2 sec
Evaluation completed in 1.2 sec

sigma = optimizableVariable('sigma',[1e-3,1e3],'Transform','log');
lambda = optimizableVariable('lambda',[(1e-3)/N, (1e3)/N],'Transform','log');

Создайте целевую функцию для Байесовой оптимизации. Целевая функция берет в таблице, которая содержит переменные sigma и lambda, и затем вычисляет значение классификации потерь для бинарной Гауссовой модели классификации ядер, обученной с помощью функции fitckernel. Установите 'Verbose',0 в fitckernel подавлять итеративное отображение диагностической информации.

minfn = @(z)gather(loss(fitckernel(Ztrain,Ytrain, ...
    'KernelScale',z.sigma,'Lambda',z.lambda,'Verbose',0), ...
    Ztest,Ytest));

Оптимизируйте параметры [sigma,lambda] модели классификации ядер относительно потери классификации при помощи bayesopt. По умолчанию bayesopt отображает итеративную информацию об оптимизации в командной строке. Для воспроизводимости, набор опция AcquisitionFunctionName к 'expected-improvement-plus'. Функция приобретения по умолчанию зависит от времени выполнения и, поэтому, может дать переменные результаты.

results = bayesopt(minfn,[sigma,lambda],'AcquisitionFunctionName','expected-improvement-plus')

Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 2: Completed in 1 sec
- Pass 2 of 2: Completed in 1.9 sec
Evaluation completed in 3 sec
|=====================================================================================================|
| Iter | Eval   | Objective   | Objective   | BestSoFar   | BestSoFar   |        sigma |       lambda |
|      | result |             | runtime     | (observed)  | (estim.)    |              |              |
|=====================================================================================================|
|    1 | Best   |     0.19651 |      167.42 |     0.19651 |     0.19651 |       1.2297 |     0.012135 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.2 sec
|    2 | Accept |     0.19651 |      230.16 |     0.19651 |     0.19651 |     0.039643 |   3.8633e-05 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.2 sec
Evaluation completed in 2.2 sec
|    3 | Accept |     0.19651 |      161.51 |     0.19651 |     0.19651 |      0.02562 |   1.8832e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.7 sec
Evaluation completed in 1.7 sec
|    4 | Accept |     0.19651 |      106.77 |     0.19651 |     0.19651 |       92.644 |   1.8084e-07 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.1 sec
|    5 | Accept |     0.19651 |       106.9 |     0.19651 |     0.19651 |       978.95 |   0.00015066 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.2 sec
|    6 | Accept |     0.19651 |      185.97 |     0.19651 |     0.19651 |    0.0089609 |    0.0059189 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.3 sec
Evaluation completed in 2.3 sec
|    7 | Accept |     0.19651 |      107.88 |     0.19651 |     0.19651 |       97.709 |   0.00010771 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.2 sec
|    8 | Accept |     0.19651 |      97.478 |     0.19651 |     0.19651 |       422.03 |    4.841e-06 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.2 sec
Evaluation completed in 2.2 sec
|    9 | Accept |     0.19651 |      167.96 |     0.19651 |     0.19651 |    0.0012826 |   5.5116e-07 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.6 sec
Evaluation completed in 1.7 sec
|   10 | Accept |     0.19651 |      212.44 |     0.19651 |     0.19651 |     0.031682 |   3.1742e-05 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.2 sec
|   11 | Best   |     0.10029 |      65.889 |     0.10029 |      0.1003 |       3.9327 |   3.5022e-06 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.6 sec
Evaluation completed in 1.6 sec
|   12 | Accept |     0.10059 |      65.692 |     0.10029 |      0.1003 |       3.1844 |    7.385e-07 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.2 sec
Evaluation completed in 2.2 sec
|   13 | Accept |     0.10098 |      69.683 |     0.10029 |     0.10031 |       5.2372 |   4.9773e-07 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.5 sec
Evaluation completed in 1.6 sec
|   14 | Accept |     0.10133 |      72.595 |     0.10029 |    0.099825 |       4.2748 |    1.262e-06 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.6 sec
Evaluation completed in 1.7 sec
|   15 | Accept |     0.10141 |       76.94 |     0.10029 |     0.10059 |       3.3388 |   2.1269e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.6 sec
Evaluation completed in 1.6 sec
|   16 | Accept |     0.12235 |      143.29 |     0.10029 |     0.10058 |       9.0019 |    0.0010713 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.2 sec
Evaluation completed in 2.2 sec
|   17 | Accept |     0.10668 |      141.51 |     0.10029 |     0.10042 |       3.6288 |   0.00063589 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.1 sec
|   18 | Best   |     0.10016 |      70.404 |     0.10016 |     0.10058 |        4.311 |   1.2975e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.1 sec
|   19 | Accept |     0.10034 |      68.692 |     0.10016 |     0.10001 |       3.8228 |   8.1818e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.2 sec
|   20 | Accept |     0.10123 |      71.019 |     0.10016 |     0.10004 |       6.3387 |   1.2575e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.6 sec
Evaluation completed in 1.6 sec
|=====================================================================================================|
| Iter | Eval   | Objective   | Objective   | BestSoFar   | BestSoFar   |        sigma |       lambda |
|      | result |             | runtime     | (observed)  | (estim.)    |              |              |
|=====================================================================================================|
|   21 | Accept |     0.10113 |      70.865 |     0.10016 |    0.099988 |       5.1223 |   1.2705e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.1 sec
Evaluation completed in 2.2 sec
|   22 | Accept |     0.10041 |      70.621 |     0.10016 |     0.10006 |       3.6363 |   4.4732e-07 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.6 sec
Evaluation completed in 1.6 sec
|   23 | Accept |     0.10061 |      64.482 |     0.10016 |     0.10019 |       3.7705 |   2.8022e-07 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.6 sec
Evaluation completed in 1.6 sec
|   24 | Accept |     0.10044 |      69.779 |     0.10016 |     0.10025 |       3.6538 |   3.4072e-07 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2 sec
Evaluation completed in 2.1 sec
|   25 | Accept |     0.19651 |      220.15 |     0.10016 |     0.10026 |      0.24021 |   1.3156e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.6 sec
Evaluation completed in 1.6 sec
|   26 | Best   |     0.10016 |      69.161 |     0.10016 |     0.10024 |       3.5161 |   4.6627e-07 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.6 sec
Evaluation completed in 1.7 sec
|   27 | Accept |     0.16207 |      59.461 |     0.10016 |     0.10024 |       28.573 |    1.356e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.5 sec
Evaluation completed in 1.6 sec
|   28 | Accept |     0.10036 |      70.388 |     0.10016 |     0.10025 |       3.5285 |   7.3662e-07 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 1.6 sec
Evaluation completed in 1.6 sec
|   29 | Accept |     0.19651 |      166.35 |     0.10016 |     0.10025 |    0.0038154 |   1.3372e-08 |
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: Completed in 2.2 sec
Evaluation completed in 2.2 sec
|   30 | Accept |     0.19651 |       180.6 |     0.10016 |     0.10024 |      0.12353 |     0.012337 |

__________________________________________________________
Optimization completed.
MaxObjectiveEvaluations of 30 reached.
Total function evaluations: 30
Total elapsed time: 3629.6678 seconds.
Total objective function evaluation time: 3432.0825

Best observed feasible point:
    sigma       lambda  
    ______    __________

    3.5161    4.6627e-07

Observed objective function value = 0.10016
Estimated objective function value = 0.10024
Function evaluation time = 69.1611

Best estimated feasible point (according to models):
    sigma       lambda  
    ______    __________

    3.6538    3.4072e-07

Estimated objective function value = 0.10024
Estimated function evaluation time = 68.4572

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: 0.1002
                   XAtMinObjective: [1×2 table]
             MinEstimatedObjective: 0.1002
          XAtMinEstimatedObjective: [1×2 table]
           NumObjectiveEvaluations: 30
                  TotalElapsedTime: 3.6297e+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]

Возвратите лучшую допустимую точку в модели Bayesian results при помощи функции bestPoint. Используйте критерий по умолчанию min-visited-upper-confidence-interval, который определяет лучшую допустимую точку как посещаемую точку, которая минимизирует верхний доверительный интервал на значении целевой функции.

zbest = bestPoint(results)

zbest=1×2 table
    sigma       lambda  
    ______    __________

    3.6538    3.4072e-07

Таблица zbest содержит оптимальные ориентировочные стоимости для аргументов пары "имя-значение" 'KernelScale' и 'Lambda'. Можно задать эти значения когда обучение новый оптимизированный классификатор ядра при помощи

Mdl = fitckernel(Ztrain,Ytrain,'KernelScale',zbest.sigma,'Lambda',zbest.lambda)

Для длинных массивов может занять много времени процедура оптимизации. Если набор данных является слишком большим, чтобы запустить процедуру оптимизации, можно попытаться оптимизировать параметры только при помощи частичных данных. Используйте datasample, функционируют и задают 'Replace','false' к выборочным данным без замены.

Документация