# Evaluating Model Performance

MLJ allows quick evaluation of a supervised model's performance against a battery of selected losses or scores. For more on available performance measures, see Performance Measures.

In addition to hold-out and cross-validation, the user can specify an explicit list of train/test pairs of row indices for resampling, or define new resampling strategies.

For simultaneously evaluating *multiple* models and/or data sets, see Benchmarking.

## Evaluating against a single measure

```
julia> using MLJ
julia> X = (a=rand(12), b=rand(12), c=rand(12));
julia> y = X.a + 2X.b + 0.05*rand(12);
julia> model = (@load RidgeRegressor pkg=MultivariateStats verbosity=0)()
RidgeRegressor(
lambda = 1.0,
bias = true)
julia> cv=CV(nfolds=3)
CV(
nfolds = 3,
shuffle = false,
rng = Random._GLOBAL_RNG())
julia> evaluate(model, X, y, resampling=cv, measure=l2, verbosity=0)
PerformanceEvaluation object with these fields:
measure, operation, measurement, per_fold,
per_observation, fitted_params_per_fold,
report_per_fold, train_test_rows
Extract:
┌──────────┬───────────┬─────────────┬─────────┬───────────────────────┐
│ measure │ operation │ measurement │ 1.96*SE │ per_fold │
├──────────┼───────────┼─────────────┼─────────┼───────────────────────┤
│ LPLoss( │ predict │ 0.226 │ 0.201 │ [0.267, 0.065, 0.346] │
│ p = 2) │ │ │ │ │
└──────────┴───────────┴─────────────┴─────────┴───────────────────────┘
```

Alternatively, instead of applying `evaluate`

to a model + data, one may call `evaluate!`

on an existing machine wrapping the model in data:

```
julia> mach = machine(model, X, y)
untrained Machine; caches model-specific representations of data
model: RidgeRegressor(lambda = 1.0, …)
args:
1: Source @954 ⏎ Table{AbstractVector{Continuous}}
2: Source @899 ⏎ AbstractVector{Continuous}
julia> evaluate!(mach, resampling=cv, measure=l2, verbosity=0)
PerformanceEvaluation object with these fields:
measure, operation, measurement, per_fold,
per_observation, fitted_params_per_fold,
report_per_fold, train_test_rows
Extract:
┌──────────┬───────────┬─────────────┬─────────┬───────────────────────┐
│ measure │ operation │ measurement │ 1.96*SE │ per_fold │
├──────────┼───────────┼─────────────┼─────────┼───────────────────────┤
│ LPLoss( │ predict │ 0.226 │ 0.201 │ [0.267, 0.065, 0.346] │
│ p = 2) │ │ │ │ │
└──────────┴───────────┴─────────────┴─────────┴───────────────────────┘
```

(The latter call is a mutating call as the learned parameters stored in the machine potentially change. )

## Multiple measures

```
julia> evaluate!(mach,
resampling=cv,
measure=[l1, rms, rmslp1], verbosity=0)
PerformanceEvaluation object with these fields:
measure, operation, measurement, per_fold,
per_observation, fitted_params_per_fold,
report_per_fold, train_test_rows
Extract:
┌──────────────────────────────────────┬───────────┬─────────────┬─────────┬────
│ measure │ operation │ measurement │ 1.96*SE │ p ⋯
├──────────────────────────────────────┼───────────┼─────────────┼─────────┼────
│ LPLoss( │ predict │ 0.428 │ 0.297 │ [ ⋯
│ p = 1) │ │ │ │ ⋯
│ RootMeanSquaredError() │ predict │ 0.475 │ 0.243 │ [ ⋯
│ RootMeanSquaredLogProportionalError( │ predict │ 0.194 │ 0.127 │ [ ⋯
│ offset = 1.0) │ │ │ │ ⋯
└──────────────────────────────────────┴───────────┴─────────────┴─────────┴────
1 column omitted
```

## Custom measures and weighted measures

```
julia> my_loss(yhat, y) = maximum((yhat - y).^2);
julia> my_per_observation_loss(yhat, y) = abs.(yhat - y);
julia> MLJ.reports_each_observation(::typeof(my_per_observation_loss)) = true;
julia> my_weighted_score(yhat, y) = 1/mean(abs.(yhat - y));
julia> my_weighted_score(yhat, y, w) = 1/mean(abs.((yhat - y).^w));
julia> MLJ.supports_weights(::typeof(my_weighted_score)) = true;
julia> MLJ.orientation(::typeof(my_weighted_score)) = :score;
julia> holdout = Holdout(fraction_train=0.8)
Holdout(
fraction_train = 0.8,
shuffle = false,
rng = Random._GLOBAL_RNG())
julia> weights = [1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 3, 1];
julia> evaluate!(mach,
resampling=CV(nfolds=3),
measure=[my_loss, my_per_observation_loss, my_weighted_score, l1],
weights=weights, verbosity=0)
┌ Warning: Sample weights ignored in evaluations of the following measures, as unsupported:
│ my_loss, my_per_observation_loss
└ @ MLJBase ~/.julia/packages/MLJBase/LxNAs/src/resampling.jl:775
PerformanceEvaluation object with these fields:
measure, operation, measurement, per_fold,
per_observation, fitted_params_per_fold,
report_per_fold, train_test_rows
Extract:
┌──────────────────────────────────────────────────────────┬───────────┬────────
│ measure │ operation │ measu ⋯
├──────────────────────────────────────────────────────────┼───────────┼────────
│ my_loss (generic function with 1 method) │ predict │ 0.323 ⋯
│ my_per_observation_loss (generic function with 1 method) │ predict │ 0.428 ⋯
│ my_weighted_score (generic function with 2 methods) │ predict │ 3.67 ⋯
│ LPLoss( │ predict │ 0.637 ⋯
│ p = 1) │ │ ⋯
└──────────────────────────────────────────────────────────┴───────────┴────────
3 columns omitted
```

## User-specified train/test sets

Users can either provide an explicit list of train/test pairs of row indices for resampling, as in this example:

```
julia> fold1 = 1:6; fold2 = 7:12;
julia> evaluate!(mach,
resampling = [(fold1, fold2), (fold2, fold1)],
measure=[l1, l2], verbosity=0)
PerformanceEvaluation object with these fields:
measure, operation, measurement, per_fold,
per_observation, fitted_params_per_fold,
report_per_fold, train_test_rows
Extract:
┌──────────┬───────────┬─────────────┬─────────┬────────────────┐
│ measure │ operation │ measurement │ 1.96*SE │ per_fold │
├──────────┼───────────┼─────────────┼─────────┼────────────────┤
│ LPLoss( │ predict │ 0.497 │ 0.0999 │ [0.461, 0.533] │
│ p = 1) │ │ │ │ │
│ LPLoss( │ predict │ 0.319 │ 0.131 │ [0.272, 0.366] │
│ p = 2) │ │ │ │ │
└──────────┴───────────┴─────────────┴─────────┴────────────────┘
```

Or define their own re-usable `ResamplingStrategy`

objects, - see Custom resampling strategies below.

## Built-in resampling strategies

`MLJBase.Holdout`

— Type```
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.

`MLJBase.CV`

— Type`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.

`MLJBase.StratifiedCV`

— Type```
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`

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.

`MLJBase.TimeSeriesCV`

— Type`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 = [ … ]
```

## Custom resampling strategies

To define a new resampling strategy, make relevant parameters of your strategy the fields of a new type `MyResamplingStrategy <: MLJ.ResamplingStrategy`

, and implement one of the following methods:

```
MLJ.train_test_pairs(my_strategy::MyResamplingStrategy, rows)
MLJ.train_test_pairs(my_strategy::MyResamplingStrategy, rows, y)
MLJ.train_test_pairs(my_strategy::MyResamplingStrategy, rows, X, y)
```

Each method takes a vector of indices `rows`

and returns a vector `[(t1, e1), (t2, e2), ... (tk, ek)]`

of train/test pairs of row indices selected from `rows`

. Here `X`

, `y`

are the input and target data (ignored in simple strategies, such as `Holdout`

and `CV`

).

Here is the code for the `Holdout`

strategy as an example:

```
struct Holdout <: ResamplingStrategy
fraction_train::Float64
shuffle::Bool
rng::Union{Int,AbstractRNG}
function Holdout(fraction_train, shuffle, rng)
0 < fraction_train < 1 ||
error("`fraction_train` must be between 0 and 1.")
return new(fraction_train, shuffle, rng)
end
end
# Keyword Constructor
function Holdout(; fraction_train::Float64=0.7, shuffle=nothing, rng=nothing)
if rng isa Integer
rng = MersenneTwister(rng)
end
if shuffle === nothing
shuffle = ifelse(rng===nothing, false, true)
end
if rng === nothing
rng = Random.GLOBAL_RNG
end
return Holdout(fraction_train, shuffle, rng)
end
function train_test_pairs(holdout::Holdout, rows)
train, test = partition(rows, holdout.fraction_train,
shuffle=holdout.shuffle, rng=holdout.rng)
return [(train, test),]
end
```

## API

`MLJBase.evaluate!`

— Function```
evaluate!(mach,
resampling=CV(),
measure=nothing,
rows=nothing,
weights=nothing,
class_weights=nothing,
operation=nothing,
repeats=1,
acceleration=default_resource(),
force=false,
verbosity=1,
check_measure=true)
```

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.

Do `subtypes(MLJ.ResamplingStrategy)`

to obtain a list of available resampling strategies. If `resampling`

is not an object of type `MLJ.ResamplingStrategy`

, 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.

The type of operation (`predict`

, `predict_mode`

, etc) to be associated with `measure`

is automatically inferred from measure traits where possible. For example, `predict_mode`

will be used for a `Multiclass`

target, if `model`

is probabilistic but `measure`

is deterministic. The operations applied can be inspected from the `operation`

field of the object returned. Alternatively, operations can be explicitly specified using `operation=...`

. If `measure`

is a vector, then `operation`

must be a single operation, which will be associated with all measures, or a vector of the same length as `measure`

.

The resampling strategy is applied repeatedly (Monte Carlo resampling) if `repeats > 1`

. 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.

If `resampling isa MLJ.ResamplingStrategy`

then one may optionally restrict the data used in evaluation by specifying `rows`

.

An optional `weights`

vector may be passed for measures that support sample weights (`MLJ.supports_weights(measure) == true`

), which is ignored by those that don't. These weights are not to be confused with any weights `w`

bound to `mach`

(as in `mach = machine(model, X, y, w)`

). To pass these to the performance evaluation measures you must explictly specify `weights=w`

in the `evaluate!`

call.

Additionally, optional `class_weights`

dictionary may be passed for measures that support class weights (`MLJ.supports_class_weights(measure) == true`

), which is ignored by those that don't. These weights are not to be confused with any weights `class_w`

bound to `mach`

(as in `mach = machine(model, X, y, class_w)`

). To pass these to the performance evaluation measures you must explictly specify `class_weights=w`

in the `evaluate!`

call.

User-defined measures are supported; see the manual for details.

If no measure is specified, then `default_measure(mach.model)`

is used, unless this default is `nothing`

and an error is thrown.

The `acceleration`

keyword argument is used to specify the compute resource (a subtype of `ComputationalResources.AbstractResource`

) that will be used to accelerate/parallelize the resampling operation.

Although `evaluate!`

is mutating, `mach.model`

and `mach.args`

are untouched.

**Summary of key-word arguments**

`resampling`

- resampling strategy (default is`CV(nfolds=6)`

)`measure`

/`measures`

- measure or vector of measures (losses, scores, etc)`rows`

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

- per-sample weights for measures that support them (not to be confused with weights used in training)`class_weights`

- dictionary of per-class weights for use with measures that support these, in classification problems (not to be confused with per-sample`weights`

or with class weights used in training)`operation`

/`operations`

- 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.`repeats`

- default is 1; set to a higher value for repeated (Monte Carlo) resampling`acceleration`

- parallelization option; currently supported options are instances of`CPU1`

(single-threaded computation)`CPUThreads`

(multi-threaded computation) and`CPUProcesses`

(multi-process computation); default is`default_resource()`

.`force`

- default is`false`

; set to`true`

for force cold-restart of each training event`verbosity`

level, an integer defaulting to 1.`check_measure`

- default is`true`

**Return value**

A `PerformanceEvaluation`

object. See `PerformanceEvaluation`

for details.

`MLJModelInterface.evaluate`

— Functionsome meta-models may choose to implement the `evaluate`

operations

`MLJBase.PerformanceEvaluation`

— Type`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.

`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`aggregation(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 individual observation evaluations of those measures for which`reports_each_observation(measure)`

is true, which is otherwise reported`missing`

. Useful for some forms of hyper-parameter optimization.`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.