Evaluating Model Performance

evaluate!(mach; resampling=CV(), measure=nothing, options...)

Estimate the performance of a machine mach wrapping a supervised model in data, using the specified resampling strategy (defaulting to 6-fold cross-validation) and measure, which can be a single measure or vector. Returns a PerformanceEvaluation object.

Available resampling strategies are CV, Holdout, StratifiedCV and TimeSeriesCV. If resampling is not an instance of one of these, then a vector of tuples of the form (train_rows, test_rows) is expected. For example, setting

resampling = [((1:100), (101:200)),
               ((101:200), (1:100))]

gives two-fold cross-validation using the first 200 rows of data.

Any measure conforming to the StatisticalMeasuresBase.jl API can be provided, assuming it can consume multiple observations.

Although evaluate! is mutating, mach.model and mach.args are not mutated.

Additional keyword options

• rows - vector of observation indices from which both train and test folds are constructed (default is all observations)

• operation/operations=nothing - One of predict, predict_mean, predict_mode, predict_median, or predict_joint, or a vector of these of the same length as measure/measures. Automatically inferred if left unspecified. For example, predict_mode will be used for a Multiclass target, if model is a probabilistic predictor, but measure is expects literal (point) target predictions. Operations actually applied can be inspected from the operation field of the object returned.

• weights - per-sample Real weights for measures that support them (not to be confused with weights used in training, such as the w in mach = machine(model, X, y, w)).

• class_weights - dictionary of Real per-class weights for use with measures that support these, in classification problems (not to be confused with weights used in training, such as the w in mach = machine(model, X, y, w)).

• repeats::Int=1: set to a higher value for repeated (Monte Carlo) resampling. For example, if repeats = 10, then resampling = CV(nfolds=5, shuffle=true), generates a total of 50 (train, test) pairs for evaluation and subsequent aggregation.

• acceleration=CPU1(): acceleration/parallelization option; can be any instance of CPU1, (single-threaded computation), CPUThreads (multi-threaded computation) or CPUProcesses (multi-process computation); default is default_resource(). These types are owned by ComputationalResources.jl.

• force=false: set to true to force cold-restart of each training event

• verbosity::Int=1 logging level; can be negative

• check_measure=true: whether to screen measures for possible incompatibility with the model. Will not catch all incompatibilities.

• per_observation=true: whether to calculate estimates for individual observations; if false the per_observation field of the returned object is populated with missings. Setting to false may reduce compute time and allocations.

• logger - a logger object (see MLJBase.log_evaluation)

See also evaluate, PerformanceEvaluation

some meta-models may choose to implement the evaluate operations

PerformanceEvaluation

Type of object returned by evaluate (for models plus data) or evaluate! (for machines). Such objects encode estimates of the performance (generalization error) of a supervised model or outlier detection model.

When evaluate/evaluate! is called, a number of train/test pairs ("folds") of row indices are generated, according to the options provided, which are discussed in the evaluate! doc-string. Rows correspond to observations. The generated train/test pairs are recorded in the train_test_rows field of the PerformanceEvaluation struct, and the corresponding estimates, aggregated over all train/test pairs, are recorded in measurement, a vector with one entry for each measure (metric) recorded in measure.

When displayed, a PerformanceEvalution object includes a value under the heading 1.96*SE, derived from the standard error of the per_fold entries. This value is suitable for constructing a formal 95% confidence interval for the given measurement. Such intervals should be interpreted with caution. See, for example, Bates et al. (2021).

Fields

These fields are part of the public API of the PerformanceEvaluation struct.

• model: model used to create the performance evaluation. In the case a tuning model, this is the best model found.

• measure: vector of measures (metrics) used to evaluate performance

• measurement: vector of measurements - one for each element of measure - aggregating the performance measurements over all train/test pairs (folds). The aggregation method applied for a given measure m is StatisticalMeasuresBase.external_aggregation_mode(m) (commonly Mean() or Sum())

• operation (e.g., predict_mode): the operations applied for each measure to generate predictions to be evaluated. Possibilities are: predict, predict_mean, predict_mode, predict_median, or predict_joint.

• per_fold: a vector of vectors of individual test fold evaluations (one vector per measure). Useful for obtaining a rough estimate of the variance of the performance estimate.

• per_observation: a vector of vectors of vectors containing individual per-observation measurements: for an evaluation e, e.per_observation[m][f][i] is the measurement for the ith observation in the fth test fold, evaluated using the mth measure. Useful for some forms of hyper-parameter optimization. Note that an aggregregated measurement for some measure measure is repeated across all observations in a fold if StatisticalMeasures.can_report_unaggregated(measure) == true. If e has been computed with the per_observation=false option, then e_per_observation is a vector of missings.

• fitted_params_per_fold: a vector containing fitted params(mach) for each machine mach trained during resampling - one machine per train/test pair. Use this to extract the learned parameters for each individual training event.

• report_per_fold: a vector containing report(mach) for each machine mach training in resampling - one machine per train/test pair.

• train_test_rows: a vector of tuples, each of the form (train, test), where train and test are vectors of row (observation) indices for training and evaluation respectively.

• resampling: the resampling strategy used to generate the train/test pairs.

• repeats: the number of times the resampling strategy was repeated.

holdout = Holdout(; fraction_train=0.7,
                     shuffle=nothing,
                     rng=nothing)

Holdout resampling strategy, for use in evaluate!, evaluate and in tuning.

train_test_pairs(holdout, rows)

Returns the pair [(train, test)], where train and test are vectors such that rows=vcat(train, test) and length(train)/length(rows) is approximatey equal to fraction_train`.

Pre-shuffling of rows is controlled by rng and shuffle. If rng is an integer, then the Holdout keyword constructor resets it to MersenneTwister(rng). Otherwise some AbstractRNG object is expected.

If rng is left unspecified, rng is reset to Random.GLOBAL_RNG, in which case rows are only pre-shuffled if shuffle=true is specified.

cv = CV(; nfolds=6,  shuffle=nothing, rng=nothing)

Cross-validation resampling strategy, for use in evaluate!, evaluate and tuning.

train_test_pairs(cv, rows)

Returns an nfolds-length iterator of (train, test) pairs of vectors (row indices), where each train and test is a sub-vector of rows. The test vectors are mutually exclusive and exhaust rows. Each train vector is the complement of the corresponding test vector. With no row pre-shuffling, the order of rows is preserved, in the sense that rows coincides precisely with the concatenation of the test vectors, in the order they are generated. The first r test vectors have length n + 1, where n, r = divrem(length(rows), nfolds), and the remaining test vectors have length n.

Pre-shuffling of rows is controlled by rng and shuffle. If rng is an integer, then the CV keyword constructor resets it to MersenneTwister(rng). Otherwise some AbstractRNG object is expected.

If rng is left unspecified, rng is reset to Random.GLOBAL_RNG, in which case rows are only pre-shuffled if shuffle=true is explicitly specified.

stratified_cv = StratifiedCV(; nfolds=6,
                               shuffle=false,
                               rng=Random.GLOBAL_RNG)

Stratified cross-validation resampling strategy, for use in evaluate!, evaluate and in tuning. Applies only to classification problems (OrderedFactor or Multiclass targets).

train_test_pairs(stratified_cv, rows, y)

Returns an nfolds-length iterator of (train, test) pairs of vectors (row indices) where each train and test is a sub-vector of rows. The test vectors are mutually exclusive and exhaust rows. Each train vector is the complement of the corresponding test vector.

Unlike regular cross-validation, the distribution of the levels of the target y corresponding to each train and test is constrained, as far as possible, to replicate that of y[rows] as a whole.

The stratified train_test_pairs algorithm is invariant to label renaming. For example, if you run replace!(y, 'a' => 'b', 'b' => 'a') and then re-run train_test_pairs, the returned (train, test) pairs will be the same.

Pre-shuffling of rows is controlled by rng and shuffle. If rng is an integer, then the StratifedCV keywod constructor resets it to MersenneTwister(rng). Otherwise some AbstractRNG object is expected.

If rng is left unspecified, rng is reset to Random.GLOBAL_RNG, in which case rows are only pre-shuffled if shuffle=true is explicitly specified.

tscv = TimeSeriesCV(; nfolds=4)

Cross-validation resampling strategy, for use in evaluate!, evaluate and tuning, when observations are chronological and not expected to be independent.

train_test_pairs(tscv, rows)

Returns an nfolds-length iterator of (train, test) pairs of vectors (row indices), where each train and test is a sub-vector of rows. The rows are partitioned sequentially into nfolds + 1 approximately equal length partitions, where the first partition is the first train set, and the second partition is the first test set. The second train set consists of the first two partitions, and the second test set consists of the third partition, and so on for each fold.

The first partition (which is the first train set) has length n + r, where n, r = divrem(length(rows), nfolds + 1), and the remaining partitions (all of the test folds) have length n.

Examples

julia> MLJBase.train_test_pairs(TimeSeriesCV(nfolds=3), 1:10)
3-element Vector{Tuple{UnitRange{Int64}, UnitRange{Int64}}}:
 (1:4, 5:6)
 (1:6, 7:8)
 (1:8, 9:10)

julia> model = (@load RidgeRegressor pkg=MultivariateStats verbosity=0)();

julia> data = @load_sunspots;

julia> X = (lag1 = data.sunspot_number[2:end-1],
            lag2 = data.sunspot_number[1:end-2]);

julia> y = data.sunspot_number[3:end];

julia> tscv = TimeSeriesCV(nfolds=3);

julia> evaluate(model, X, y, resampling=tscv, measure=rmse, verbosity=0)
┌───────────────────────────┬───────────────┬────────────────────┐
│ _.measure                 │ _.measurement │ _.per_fold         │
├───────────────────────────┼───────────────┼────────────────────┤
│ RootMeanSquaredError @753 │ 21.7          │ [25.4, 16.3, 22.4] │
└───────────────────────────┴───────────────┴────────────────────┘
_.per_observation = [missing]
_.fitted_params_per_fold = [ … ]
_.report_per_fold = [ … ]
_.train_test_rows = [ … ]