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Automated Classifier Selection with Bayesian Optimization

This example shows how to use fitcauto to automatically try a selection of classification model types with different hyperparameter values, given training predictor and response data. The function uses Bayesian optimization to select models and their hyperparameter values, and computes the cross-validation classification error for each model. After the optimization is complete, fitcauto returns the model, trained on the entire data set, that is expected to best classify new data. Check the model performance on test data.

Load Sample Data

This example uses the 1994 census data stored in census1994.mat. The data set consists of demographic information from the US Census Bureau that can be used to predict whether an individual makes over $50,000 per year.

Load the sample data census1994, which contains the training data adultdata and the test data adulttest. Preview the first few rows of the training data set.

load census1994
head(adultdata)
ans=8×15 table
    age       workClass          fnlwgt      education    education_num       marital_status           occupation        relationship     race      sex      capital_gain    capital_loss    hours_per_week    native_country    salary
    ___    ________________    __________    _________    _____________    _____________________    _________________    _____________    _____    ______    ____________    ____________    ______________    ______________    ______

    39     State-gov                77516    Bachelors         13          Never-married            Adm-clerical         Not-in-family    White    Male          2174             0                40          United-States     <=50K 
    50     Self-emp-not-inc         83311    Bachelors         13          Married-civ-spouse       Exec-managerial      Husband          White    Male             0             0                13          United-States     <=50K 
    38     Private             2.1565e+05    HS-grad            9          Divorced                 Handlers-cleaners    Not-in-family    White    Male             0             0                40          United-States     <=50K 
    53     Private             2.3472e+05    11th               7          Married-civ-spouse       Handlers-cleaners    Husband          Black    Male             0             0                40          United-States     <=50K 
    28     Private             3.3841e+05    Bachelors         13          Married-civ-spouse       Prof-specialty       Wife             Black    Female           0             0                40          Cuba              <=50K 
    37     Private             2.8458e+05    Masters           14          Married-civ-spouse       Exec-managerial      Wife             White    Female           0             0                40          United-States     <=50K 
    49     Private             1.6019e+05    9th                5          Married-spouse-absent    Other-service        Not-in-family    Black    Female           0             0                16          Jamaica           <=50K 
    52     Self-emp-not-inc    2.0964e+05    HS-grad            9          Married-civ-spouse       Exec-managerial      Husband          White    Male             0             0                45          United-States     >50K  

Each row contains the demographic information for one adult. The last column salary shows whether a person has a salary less than or equal to $50,000 per year or greater than $50,000 per year.

Use Automated Model Selection

Use fitcauto to automatically find an appropriate classifier for the data in adultdata. Set the observation weights, and specify to run the Bayesian optimization in parallel, which requires Parallel Computing Toolbox™. Due to the nonreproducibility of parallel timing, parallel Bayesian optimization does not necessarily yield reproducible results.

Because of the complexity of the optimization, this process can take some time, especially for larger data sets. By default, fitcauto provides a plot of the optimization and an iterative display of the optimization results. For more information on how to interpret these results, see Verbose Display.

options = struct('UseParallel',true);
[mdl,results] = fitcauto(adultdata,'salary','Weights','fnlwgt', ...
    'HyperparameterOptimizationOptions',options);
Warning: It is recommended that you first standardize all numeric predictors when optimizing the Naive Bayes 'Width' parameter. Ignore this warning if you have done that.
Starting parallel pool (parpool) using the 'local' profile ...
Connected to the parallel pool (number of workers: 6).
Copying objective function to workers...
Done copying objective function to workers.
Learner types to explore: ensemble, nb, tree
Total iterations (MaxObjectiveEvaluations): 90
Total time (MaxTime): Inf
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|    1 |       5 | Accept |    0.23856 |            2.6087 |          0.1821 |         0.20863 |         tree | MinLeafSize:          10889 |
|    2 |       5 | Best   |     0.1821 |            2.5782 |          0.1821 |         0.20863 |         tree | MinLeafSize:           4990 |
|    3 |       6 | Best   |    0.14971 |             50.17 |         0.14971 |         0.14971 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:              0.41891 |
|    4 |       6 | Accept |    0.17743 |            67.443 |         0.14971 |         0.14971 |     ensemble | Method:                 Bag |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      225 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:           3144 |
|    5 |       6 | Accept |    0.17705 |            68.174 |         0.14971 |         0.14971 |     ensemble | Method:                 Bag |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      225 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:           3144 |
|    6 |       6 | Accept |     0.1623 |             1.029 |         0.14971 |         0.15664 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|    7 |       6 | Accept |     0.1745 |            1.2602 |         0.14971 |         0.15664 |         tree | MinLeafSize:           1292 |
|    8 |       6 | Best   |    0.14014 |            2.7929 |         0.14014 |         0.15664 |         tree | MinLeafSize:             40 |
|    9 |       6 | Accept |    0.15209 |            98.452 |         0.14014 |         0.15664 |     ensemble | Method:                 Bag |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      239 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:            161 |
|   10 |       6 | Accept |    0.16032 |            99.589 |         0.14014 |         0.15807 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:               9.0144 |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   11 |       6 | Accept |    0.17807 |             1.446 |         0.14014 |         0.15807 |         tree | MinLeafSize:           3849 |
|   12 |       6 | Accept |    0.16427 |            116.76 |         0.14014 |         0.15807 |     ensemble | Method:                 Bag |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      294 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:            963 |
|   13 |       6 | Accept |    0.15706 |            53.771 |         0.14014 |         0.15807 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      241 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:              6 |
|   14 |       6 | Accept |    0.14443 |            1.8727 |         0.14014 |         0.15807 |         tree | MinLeafSize:            229 |
|   15 |       6 | Accept |    0.14941 |            49.309 |         0.14014 |         0.15523 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:              0.26346 |
|   16 |       6 | Accept |    0.15139 |            105.88 |         0.14014 |         0.15523 |     ensemble | Method:                 Bag |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      257 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:              2 |
|   17 |       6 | Accept |    0.15434 |            3.5748 |         0.14014 |         0.15262 |         tree | MinLeafSize:              8 |
|   18 |       6 | Accept |    0.14968 |            49.046 |         0.14014 |         0.15262 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:              0.40347 |
|   19 |       6 | Accept |    0.14421 |            2.9271 |         0.14014 |         0.14824 |         tree | MinLeafSize:             23 |
|   20 |       6 | Accept |    0.14923 |            1.6667 |         0.14014 |         0.14673 |         tree | MinLeafSize:            354 |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   21 |       6 | Best   |    0.13996 |            3.0956 |         0.13996 |           0.145 |         tree | MinLeafSize:             39 |
|   22 |       6 | Accept |    0.15111 |            83.972 |         0.13996 |           0.145 |     ensemble | Method:                 Bag |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      208 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:             14 |
|   23 |       6 | Accept |    0.19568 |            98.149 |         0.13996 |           0.145 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:               8643.5 |
|   24 |       6 | Accept |    0.23856 |           0.49289 |         0.13996 |         0.14508 |         tree | MinLeafSize:           8801 |
|   25 |       6 | Accept |     0.1623 |             0.606 |         0.13996 |         0.14508 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|   26 |       6 | Accept |     0.1623 |           0.38862 |         0.13996 |         0.14508 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|   27 |       6 | Accept |     0.1623 |           0.34002 |         0.13996 |         0.14508 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|   28 |       6 | Accept |    0.15847 |            49.535 |         0.13996 |         0.14508 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      212 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:            376 |
|   29 |       6 | Accept |    0.15639 |            63.923 |         0.13996 |         0.14508 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      288 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:           1774 |
|   30 |       6 | Accept |     0.1623 |           0.79402 |         0.13996 |         0.14508 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   31 |       6 | Accept |     0.1453 |            3.0022 |         0.13996 |         0.14429 |         tree | MinLeafSize:             16 |
|   32 |       6 | Accept |     0.1623 |           0.32634 |         0.13996 |         0.14429 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|   33 |       6 | Accept |    0.23856 |            57.127 |         0.13996 |         0.14429 |     ensemble | Method:                 Bag |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      250 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:           6630 |
|   34 |       6 | Accept |    0.23856 |           0.52406 |         0.13996 |         0.14436 |         tree | MinLeafSize:           9982 |
|   35 |       6 | Accept |    0.15781 |            52.097 |         0.13996 |         0.14436 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      224 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:            440 |
|   36 |       6 | Accept |    0.15434 |            3.4554 |         0.13996 |         0.14431 |         tree | MinLeafSize:              8 |
|   37 |       6 | Accept |    0.15669 |            54.961 |         0.13996 |         0.14431 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      252 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:              4 |
|   38 |       6 | Accept |    0.16986 |            1.5157 |         0.13996 |         0.14367 |         tree | MinLeafSize:            791 |
|   39 |       6 | Accept |    0.17708 |              55.2 |         0.13996 |         0.14367 |     ensemble | Method:                 Bag |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      220 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:           4265 |
|   40 |       6 | Accept |    0.16315 |            86.272 |         0.13996 |         0.14367 |     ensemble | Method:                 Bag |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      223 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:            743 |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   41 |       6 | Accept |    0.14449 |            1.9856 |         0.13996 |         0.14391 |         tree | MinLeafSize:            235 |
|   42 |       5 | Accept |      0.167 |            96.272 |         0.13996 |         0.14287 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:               18.272 |
|   43 |       5 | Accept |    0.14377 |            2.0295 |         0.13996 |         0.14287 |         tree | MinLeafSize:            193 |
|   44 |       4 | Accept |    0.15699 |            56.595 |         0.13996 |         0.14152 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      272 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:            997 |
|   45 |       4 | Accept |    0.14013 |            2.4702 |         0.13996 |         0.14152 |         tree | MinLeafSize:             36 |
|   46 |       4 | Accept |    0.14344 |            1.7418 |         0.13996 |         0.14185 |         tree | MinLeafSize:            189 |
|   47 |       4 | Accept |    0.15677 |             1.425 |         0.13996 |         0.14176 |         tree | MinLeafSize:            444 |
|   48 |       3 | Accept |    0.15259 |            83.025 |         0.13996 |         0.14182 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:               4.2748 |
|   49 |       3 | Accept |    0.14368 |            1.6998 |         0.13996 |         0.14182 |         tree | MinLeafSize:            182 |
|   50 |       6 | Accept |     0.1408 |             2.177 |         0.13996 |          0.1411 |         tree | MinLeafSize:             38 |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   51 |       4 | Accept |    0.13996 |            2.5601 |         0.13996 |         0.14072 |         tree | MinLeafSize:             39 |
|   52 |       4 | Accept |    0.17244 |            1.1659 |         0.13996 |         0.14072 |         tree | MinLeafSize:           1038 |
|   53 |       4 | Accept |    0.17797 |           0.98188 |         0.13996 |         0.14072 |         tree | MinLeafSize:           1818 |
|   54 |       3 | Accept |    0.15643 |            57.195 |         0.13996 |         0.14051 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      287 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:             30 |
|   55 |       3 | Accept |    0.14048 |            2.3411 |         0.13996 |         0.14051 |         tree | MinLeafSize:             37 |
|   56 |       6 | Accept |     0.1408 |            2.1605 |         0.13996 |         0.14054 |         tree | MinLeafSize:             38 |
|   57 |       5 | Accept |    0.13996 |            2.5887 |         0.13996 |         0.14054 |         tree | MinLeafSize:             39 |
|   58 |       5 | Accept |     0.1623 |           0.46796 |         0.13996 |         0.14054 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|   59 |       5 | Accept |    0.13996 |            2.4424 |         0.13996 |         0.14017 |         tree | MinLeafSize:             39 |
|   60 |       5 | Accept |    0.14013 |            2.5432 |         0.13996 |         0.14013 |         tree | MinLeafSize:             36 |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   61 |       5 | Accept |    0.16408 |            1.4549 |         0.13996 |         0.14011 |         tree | MinLeafSize:            585 |
|   62 |       5 | Accept |    0.14061 |            2.1993 |         0.13996 |         0.14017 |         tree | MinLeafSize:             85 |
|   63 |       5 | Accept |    0.14314 |            2.6421 |         0.13996 |         0.14013 |         tree | MinLeafSize:             29 |
|   64 |       5 | Accept |    0.14001 |            2.2084 |         0.13996 |         0.14008 |         tree | MinLeafSize:             86 |
|   65 |       5 | Accept |    0.14133 |            2.5565 |         0.13996 |         0.14007 |         tree | MinLeafSize:             35 |
|   66 |       4 | Accept |    0.15943 |            41.891 |         0.13996 |         0.14011 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      201 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:             42 |
|   67 |       4 | Accept |    0.14256 |            2.1949 |         0.13996 |         0.14011 |         tree | MinLeafSize:            125 |
|   68 |       3 | Accept |    0.15631 |            57.502 |         0.13908 |         0.14002 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      291 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:           1162 |
|   69 |       3 | Best   |    0.13908 |            2.0902 |         0.13908 |         0.14002 |         tree | MinLeafSize:             98 |
|   70 |       6 | Accept |    0.14061 |            1.8764 |         0.13908 |         0.14006 |         tree | MinLeafSize:             85 |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   71 |       5 | Accept |    0.14143 |             2.169 |         0.13908 |         0.14002 |         tree | MinLeafSize:            109 |
|   72 |       5 | Accept |    0.14472 |            1.9738 |         0.13908 |         0.14002 |         tree | MinLeafSize:            247 |
|   73 |       5 | Accept |    0.14193 |            2.5079 |         0.13908 |         0.14006 |         tree | MinLeafSize:             34 |
|   74 |       5 | Accept |     0.1507 |            1.5583 |         0.13908 |         0.14007 |         tree | MinLeafSize:            392 |
|   75 |       5 | Accept |    0.13908 |            2.0123 |         0.13908 |         0.13994 |         tree | MinLeafSize:             98 |
|   76 |       5 | Accept |    0.14124 |            2.0292 |         0.13908 |         0.13994 |         tree | MinLeafSize:            111 |
|   77 |       5 | Accept |    0.13917 |            2.0368 |         0.13908 |         0.13969 |         tree | MinLeafSize:             97 |
|   78 |       5 | Accept |    0.14032 |            2.0503 |         0.13908 |         0.13957 |         tree | MinLeafSize:            103 |
|   79 |       4 | Accept |    0.18035 |            87.193 |         0.13908 |         0.13949 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:               483.03 |
|   80 |       4 | Accept |    0.13917 |            2.1151 |         0.13908 |         0.13949 |         tree | MinLeafSize:             97 |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   81 |       4 | Best   |    0.13907 |            1.9149 |         0.13907 |         0.13934 |         tree | MinLeafSize:             96 |
|   82 |       4 | Accept |    0.13917 |            1.9271 |         0.13907 |         0.13927 |         tree | MinLeafSize:             97 |
|   83 |       4 | Accept |    0.13917 |            1.9196 |         0.13907 |         0.13924 |         tree | MinLeafSize:             97 |
|   84 |       4 | Accept |     0.1396 |            1.9448 |         0.13907 |         0.13923 |         tree | MinLeafSize:             91 |
|   85 |       4 | Accept |    0.13908 |            1.9816 |         0.13907 |         0.13921 |         tree | MinLeafSize:             98 |
|   86 |       4 | Accept |    0.14951 |            66.139 |         0.13907 |          0.1392 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:               1.9412 |
|   87 |       4 | Accept |    0.18157 |           0.54864 |         0.13907 |          0.1392 |         tree | MinLeafSize:           4072 |
|   88 |       5 | Accept |    0.13954 |            2.1344 |         0.13907 |         0.13922 |         tree | MinLeafSize:            100 |
|   89 |       5 | Accept |    0.15815 |            1.5244 |         0.13907 |          0.1392 |         tree | MinLeafSize:            492 |
|   90 |       5 | Accept |    0.14765 |            1.7524 |         0.13907 |         0.13922 |         tree | MinLeafSize:            315 |

__________________________________________________________
Optimization completed.
Total iterations: 90
Total elapsed time: 478.6155 seconds
Total time for training and validation: 2024.0417 seconds

Best observed learner is a tree model with:
	MinLeafSize:             96
Observed validation loss: 0.13907
Time for training and validation: 1.9149 seconds

Best estimated learner (returned model) is a tree model with:
	MinLeafSize:             97
Estimated validation loss: 0.13922
Estimated time for training and validation: 2.0003 seconds

Documentation for fitcauto display

The final model returned by fitcauto corresponds to the best estimated learner. Before returning the model, the function retrains it using the entire training data (adultdata), the listed Learner (or model) type, and the displayed hyperparameter values.

Evaluate Test Set Performance

Evaluate the performance of the returned model mdl on the test set adulttest by using a confusion matrix and a receiver operating characteristic (ROC) curve.

Find the predicted labels and score values for the test set.

[labels,scores] = predict(mdl,adulttest);

Create a confusion matrix from the test set results. The diagonal elements indicate the number of correctly classified instances of a given class. The off-diagonal elements are instances of misclassified observations.

confusionchart(adulttest.salary,labels)

Compute the test set classification accuracy. accuracy is the percentage of correctly classified test set observations.

accuracy = (1-loss(mdl,adulttest,'salary'))*100
accuracy = 85.4486

To plot the ROC curve for the score values corresponding to the label '<=50K', find the column of scores that corresponds to that label. The column order of scores matches the order of the classes in the trained model.

mdl.ClassNames
ans = 2×1 categorical
     <=50K 
     >50K 

Because '<=50K' is listed first, the first column of scores corresponds to that label.

Plot the ROC curve, and compute the area under the curve (AUC). The ROC curve shows the true positive rate versus the false positive rate for different thresholds of the classifier output. For a perfect classifier, whose true positive rate is always 1 regardless of the threshold, AUC = 1. For a binary classifier that randomly assigns observations to classes, AUC = 0.5. A large AUC value (close to 1) indicates good classifier performance.

[X,Y,~,AUC] = perfcurve(adulttest.salary,scores(:,1),'<=50K');
plot(X,Y)
title('ROC Curve')
xlabel('False Positive Rate')
ylabel('True Positive Rate')

AUC
AUC = 0.8848

Based on the accuracy and AUC values, the classifier performs well on the test data.

See Also

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