SuccessiveHalvingRegressor¶

Successive halving algorithm for regression.

Successive halving is a method for performing model selection without having to train each model on all the dataset. At certain points in time (called "rungs"), the worst performing will be discarded and the best ones will keep competing between each other. The rung values are designed so that at most budget model updates will be performed in total.

If you have k combinations of hyperparameters and that your dataset contains n observations, then the maximal budget you can allocate is:

\[\frac{2kn}{eta}\]

It is recommended that you check this beforehand. This bound can't be checked by the function because the size of the dataset is not known. In fact it is potentially infinite, in which case the algorithm will terminate once all the budget has been spent.

If you have a budget of B, and that your dataset contains n observations, then the number of hyperparameter combinations that will spend all the budget and go through all the data is:

\[\left\lceil\left\lfloor\frac{B}{2n}\right\rfloor \times eta \right\rceil\]

Parameters¶

models

The models to compare.
metric (river.metrics.base.Metric)

Metric used for comparing models with.
budget (int)

Total number of model updates you wish to allocate.
eta – defaults to 2

Rate of elimination. At every rung, math.ceil(k / eta) models are kept, where k is the number of models that have reached the rung. A higher eta value will focus on less models but will allocate more iterations to the best models.
verbose – defaults to False

Whether to display progress or not.
print_kwargs

Extra keyword arguments are passed to the print function. For instance, this allows providing a file argument, which indicates where to output progress.

Attributes¶

best_model

The current best model.
models

Examples¶

As an example, let's use successive halving to tune the optimizer of a linear regression. We'll first define the model.

>>> from river import linear_model
>>> from river import preprocessing

>>> model = (
...     preprocessing.StandardScaler() |
...     linear_model.LinearRegression(intercept_lr=.1)
... )

Let's now define a grid of parameters which we would like to compare. We'll try different optimizers with various learning rates.

>>> from river import optim
>>> from river import utils

>>> models = utils.expand_param_grid(model, {
...     'LinearRegression': {
...         'optimizer': [
...             (optim.SGD, {'lr': [.1, .01, .005]}),
...             (optim.Adam, {'beta_1': [.01, .001], 'lr': [.1, .01, .001]}),
...             (optim.Adam, {'beta_1': [.1], 'lr': [.001]}),
...         ]
...     }
... })

We can check how many models we've created.

>>> len(models)
10

We can now pass these models to a SuccessiveHalvingRegressor. We also need to pick a metric to compare the models, and a budget which indicates how many iterations to run before picking the best model and discarding the rest.

>>> from river import model_selection

>>> sh = model_selection.SuccessiveHalvingRegressor(
...     models,
...     metric=metrics.MAE(),
...     budget=2000,
...     eta=2,
...     verbose=True
... )

A SuccessiveHalvingRegressor is also a regressor with a learn_one and a predict_one method. We can therefore evaluate it like any other classifier with evaluate.progressive_val_score.

>>> from river import datasets
>>> from river import evaluate
>>> from river import metrics

>>> evaluate.progressive_val_score(
...     dataset=datasets.TrumpApproval(),
...     model=sh,
...     metric=metrics.MAE()
... )
[1] 5 removed       5 left  50 iterations   budget used: 500        budget left: 1500       best MAE: 4.540491
[2] 2 removed       3 left  100 iterations  budget used: 1000       budget left: 1000       best MAE: 2.458765
[3] 1 removed       2 left  166 iterations  budget used: 1498       budget left: 502        best MAE: 1.583751
[4] 1 removed       1 left  250 iterations  budget used: 1998       budget left: 2  best MAE: 1.147296
MAE: 0.488387

We can now view the best model.

>>> sh.best_model
Pipeline (
  StandardScaler (
    with_std=True
  ),
  LinearRegression (
    optimizer=Adam (
      lr=Constant (
        learning_rate=0.1
      )
      beta_1=0.01
      beta_2=0.999
      eps=1e-08
    )
    loss=Squared ()
    l2=0.
    l1=0.
    intercept_init=0.
    intercept_lr=Constant (
      learning_rate=0.1
    )
    clip_gradient=1e+12
    initializer=Zeros ()
  )
)

Methods¶

append

S.append(value) -- append value to the end of the sequence

Parameters

item

clear

S.clear() -> None -- remove all items from S

copy

count

S.count(value) -> integer -- return number of occurrences of value

Parameters

item

extend

S.extend(iterable) -- extend sequence by appending elements from the iterable

Parameters

other

index

S.index(value, [start, [stop]]) -> integer -- return first index of value. Raises ValueError if the value is not present.

Supporting start and stop arguments is optional, but recommended.

Parameters

item
args

insert

S.insert(index, value) -- insert value before index

Parameters

i
item

learn_one

Fits to a set of features x and a real-valued target y.

Parameters

x (dict)
y (numbers.Number)

Returns

Regressor: self

pop

S.pop([index]) -> item -- remove and return item at index (default last). Raise IndexError if list is empty or index is out of range.

Parameters

i – defaults to -1

predict_one

Predict the output of features x.

Parameters

x

Returns

The prediction.

remove

S.remove(value) -- remove first occurrence of value. Raise ValueError if the value is not present.

Parameters

item

reverse

S.reverse() -- reverse IN PLACE

sort

SuccessiveHalvingRegressor¶

Parameters¶

Attributes¶

Examples¶

Methods¶

References¶