Live Notebook

You can run this notebook in a live session Binder or view it on Github.

Hyperparameter optimization with Dask

Every machine learning model has some values that are specified before training begins. These values help adapt the model to the data but must be given before any training data is seen. For example, this might be penalty or C in Scikit-learn’s LogisiticRegression. These values that come before any training data and are called “hyperparameters”. Typical usage looks something like:

from sklearn.linear_model import LogisiticRegression
from sklearn.datasets import make_classification

X, y = make_classification()
est = LogisiticRegression(C=10, penalty="l2")
est.fit(X, y)

These hyperparameters influence the quality of the prediction. For example, if C is too small in the example above, the output of the estimator will not fit the data well.

Determining the values of these hyperparameters is difficult. In fact, Scikit-learn has an entire documentation page on finding the best values: https://scikit-learn.org/stable/modules/grid_search.html

Dask enables some new techniques and opportunities for hyperparameter optimization. One of these opportunities involves stopping training early to limit computation. Naturally, this requires some way to stop and restart training (partial_fit or warm_start in Scikit-learn parlance).

This is especially useful when the search is complex and has many search parameters. Good examples are most deep learning models, which has specialized algorithms for handling many data but have difficulty providing basic hyperparameters (e.g., “learning rate”, “momentum” or “weight decay”).

This notebook will walk through

  • setting up a realistic example

  • how to use HyperbandSearchCV, including

    • understanding the input parameters to HyperbandSearchCV

    • running the hyperparameter optimization

    • how to access informantion from HyperbandSearchCV

This notebook will specifically not show a performance comparison motivating HyperbandSearchCV use. HyperbandSearchCV finds high scores with minimal training; however, this is a tutorial on how to use it. All performance comparisons are relegated to section Learn more.

[1]:
%matplotlib inline

Setup Dask

[2]:
from distributed import Client
client = Client(processes=False, threads_per_worker=4,
                n_workers=1, memory_limit='2GB')
client
[2]:

Client

Cluster

  • Workers: 1
  • Cores: 4
  • Memory: 2.00 GB

Create Data

[3]:
from sklearn.datasets import make_circles
import numpy as np
import pandas as pd

X, y = make_circles(n_samples=30_000, random_state=0, noise=0.09)

pd.DataFrame({0: X[:, 0], 1: X[:, 1], "class": y}).sample(4_000).plot.scatter(
    x=0, y=1, alpha=0.2, c="class", cmap="bwr"
);
../_images/machine-learning_hyperparam-opt_8_0.png

Add random dimensions

[4]:
from sklearn.utils import check_random_state

rng = check_random_state(42)
random_feats = rng.uniform(-1, 1, size=(X.shape[0], 4))
X = np.hstack((X, random_feats))
X.shape
[4]:
(30000, 6)

Split and scale data

[5]:
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=5_000, random_state=42)
[6]:
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split
scaler = StandardScaler().fit(X_train)

X_train = scaler.transform(X_train)
X_test = scaler.transform(X_test)
[7]:
from dask.utils import format_bytes

for name, X in [("train", X_train), ("test", X_test)]:
    print("dataset =", name)
    print("shape =", X.shape)
    print("bytes =", format_bytes(X.nbytes))
    print("-" * 20)
dataset = train
shape = (25000, 6)
bytes = 1.20 MB
--------------------
dataset = test
shape = (5000, 6)
bytes = 240.00 kB
--------------------

Now we have our train and test sets.

Create model and search space

Let’s use Scikit-learn’s MLPClassifier as our model (for convenience). Let’s use this model with 24 neurons and tune some of the other basic hyperparameters.

[8]:
import numpy as np
from sklearn.neural_network import MLPClassifier

model = MLPClassifier()

Deep learning libraries can be used as well. In particular, PyTorch’s Scikit-Learn wrapper Skorch works well with HyperbandSearchCV.

[9]:
params = {
    "hidden_layer_sizes": [
        (24, ),
        (12, 12),
        (6, 6, 6, 6),
        (4, 4, 4, 4, 4, 4),
        (12, 6, 3, 3),
    ],
    "activation": ["relu", "logistic", "tanh"],
    "alpha": np.logspace(-6, -3, num=1000),  # cnts
    "batch_size": [16, 32, 64, 128, 256, 512],
}

Hyperparameter optimization

HyperbandSearchCV is Dask-ML’s meta-estimator to find the best hyperparameters. It can be used as an alternative to RandomizedSearchCV to find similar hyper-parameters in less time by not wasting time on hyper-parameters that are not promising. Specifically, it is almost guaranteed that it will find high performing models with minimal training.

This section will focus on

  1. Understanding the input parameters to HyperbandSearchCV

  2. Using HyperbandSearchCV to find the best hyperparameters

  3. Seeing other use cases of HyperbandSearchCV

[10]:
from dask_ml.model_selection import HyperbandSearchCV

Determining input parameters

A rule-of-thumb to determine HyperbandSearchCV’s input parameters requires knowing:

  1. the number of examples the longest trained model will see

  2. the number of hyperparameters to evaluate

Let’s write down what these should be for this example:

[11]:
# For quick response
n_examples = 4 * len(X_train)
n_params = 8

# In practice, HyperbandSearchCV is most useful for longer searches
# n_examples = 15 * len(X_train)
# n_params = 15

In this, models that are trained the longest will see n_examples examples. This is how much data is required, normally set be the problem difficulty. Simple problems may only need 10 passes through the dataset; more complex problems may need 100 passes through the dataset.

There will be n_params parameters sampled so n_params models will be evaluated. Models with low scores will be terminated before they see n_examples examples. This helps perserve computation.

How can we use these values to determine the inputs for HyperbandSearchCV?

[12]:
max_iter = n_params  # number of times partial_fit will be called
chunks = n_examples // n_params  # number of examples each call sees

max_iter, chunks
[12]:
(8, 12500)

This means that the longest trained estimator will see about n_examples examples (specifically n_params * (n_examples // n_params).

Applying input parameters

Let’s create a Dask array with this chunk size:

[13]:
import dask.array as da
X_train2 = da.from_array(X_train, chunks=chunks)
y_train2 = da.from_array(y_train, chunks=chunks)
X_train2
[13]:
Array Chunk
Bytes 1.20 MB 600.00 kB
Shape (25000, 6) (12500, 6)
Count 3 Tasks 2 Chunks
Type float64 numpy.ndarray
6 25000

Each partial_fit call will receive one chunk.

That means the number of exmaples in each chunk should be (about) the same, and n_examples and n_params should be chosen to make that happen. (e.g., with 100 examples, shoot for chunks with (33, 33, 34) examples not (48, 48, 4) examples).

Now let’s use max_iter to create our HyperbandSearchCV object:

[14]:
search = HyperbandSearchCV(
    model,
    params,
    max_iter=max_iter,
    patience=True,
)

How much computation will be performed?

It isn’t clear how to determine how much computation is done from max_iter and chunks. Luckily, HyperbandSearchCV has a metadata attribute to determine this beforehand:

[15]:
search.metadata["partial_fit_calls"]
[15]:
26

This shows how many partial_fit calls will be performed in the computation. metadata also includes information on the number of models created.

So far, all that’s been done is getting the search ready for computation (and seeing how much computation will be performed). So far, all the computation has been quick and easy.

Performing the computation

Now, let’s do the model selection search and find the best hyperparameters. This is the real core of this notebook. This computation will be take place on all the hardware Dask has available.

[16]:
%%time
search.fit(X_train2, y_train2, classes=[0, 1, 2, 3])
CPU times: user 5.42 s, sys: 1.06 s, total: 6.48 s
Wall time: 4.9 s
[16]:
HyperbandSearchCV(aggressiveness=3,
                  estimator=MLPClassifier(activation='relu', alpha=0.0001,
                                          batch_size='auto', beta_1=0.9,
                                          beta_2=0.999, early_stopping=False,
                                          epsilon=1e-08,
                                          hidden_layer_sizes=(100,),
                                          learning_rate='constant',
                                          learning_rate_init=0.001,
                                          max_iter=200, momentum=0.9,
                                          n_iter_no_change=10,
                                          nesterovs_momentum=True, power_t=0.5,
                                          random_state=None, shuffle...
       9.26759330e-04, 9.33189772e-04, 9.39664831e-04, 9.46184819e-04,
       9.52750047e-04, 9.59360829e-04, 9.66017480e-04, 9.72720319e-04,
       9.79469667e-04, 9.86265846e-04, 9.93109181e-04, 1.00000000e-03]),
                              'batch_size': [16, 32, 64, 128, 256, 512],
                              'hidden_layer_sizes': [(24,), (12, 12),
                                                     (6, 6, 6, 6),
                                                     (4, 4, 4, 4, 4, 4),
                                                     (12, 6, 3, 3)]},
                  patience=True, random_state=None, scoring=None,
                  test_size=None, tol=0.001)

The dashboard will be active while this is running. It will show which workers are running partial_fit and score calls. This takes about 10 seconds.

Integration

HyperbandSearchCV follows the Scikit-learn API and mirrors Scikit-learn’s RandomizedSearchCV. This means that it “just works”. All the Scikit-learn attributes and methods are available:

[17]:
search.best_score_
[17]:
0.6188
[18]:
search.best_estimator_
[18]:
MLPClassifier(activation='tanh', alpha=9.077326525210224e-06, batch_size=16,
              beta_1=0.9, beta_2=0.999, early_stopping=False, epsilon=1e-08,
              hidden_layer_sizes=(12, 6, 3, 3), learning_rate='constant',
              learning_rate_init=0.001, max_iter=200, momentum=0.9,
              n_iter_no_change=10, nesterovs_momentum=True, power_t=0.5,
              random_state=None, shuffle=True, solver='adam', tol=0.0001,
              validation_fraction=0.1, verbose=False, warm_start=False)
[19]:
cv_results = pd.DataFrame(search.cv_results_)
cv_results.head()
[19]:
model_id params std_score_time rank_test_score bracket std_partial_fit_time mean_partial_fit_time param_alpha mean_score_time param_activation test_score partial_fit_calls param_batch_size param_hidden_layer_sizes
0 bracket=1-0 {'hidden_layer_sizes': (12, 6, 3, 3), 'batch_s... 0.001032 1 1 0.685215 1.382006 0.000009 0.020570 tanh 0.6188 4 16 (12, 6, 3, 3)
1 bracket=1-1 {'hidden_layer_sizes': (6, 6, 6, 6), 'batch_si... 0.007308 2 1 0.144302 0.627134 0.000011 0.049291 tanh 0.4920 2 64 (6, 6, 6, 6)
2 bracket=1-2 {'hidden_layer_sizes': (24,), 'batch_size': 12... 0.010239 3 1 0.305380 0.952417 0.000005 0.022313 relu 0.4844 2 128 (24,)
3 bracket=0-0 {'hidden_layer_sizes': (12, 12), 'batch_size':... 0.011947 1 0 0.266926 0.947174 0.000003 0.026551 logistic 0.5144 3 256 (12, 12)
4 bracket=0-1 {'hidden_layer_sizes': (24,), 'batch_size': 16... 0.003251 2 0 0.082016 0.771284 0.000102 0.018327 logistic 0.5118 3 16 (24,)
[20]:
search.score(X_test, y_test)
[20]:
0.6018
[21]:
search.predict(X_test)
[21]:
Array Chunk
Bytes 40.00 kB 40.00 kB
Shape (5000,) (5000,)
Count 2 Tasks 1 Chunks
Type int64 numpy.ndarray
5000 1
[22]:
search.predict(X_test).compute()
[22]:
array([1, 1, 1, ..., 1, 0, 1])

It also has some other attributes.

[23]:
hist = pd.DataFrame(search.history_)
hist.head()
[23]:
model_id params partial_fit_calls partial_fit_time score score_time elapsed_wall_time bracket
0 bracket=0-0 {'hidden_layer_sizes': (12, 12), 'batch_size':... 1 1.214100 0.5144 0.014604 1.397113 0
1 bracket=0-1 {'hidden_layer_sizes': (24,), 'batch_size': 16... 1 0.689268 0.5048 0.021578 1.397115 0
2 bracket=1-0 {'hidden_layer_sizes': (12, 6, 3, 3), 'batch_s... 1 1.790225 0.5052 0.019829 1.978584 1
3 bracket=1-1 {'hidden_layer_sizes': (6, 6, 6, 6), 'batch_si... 1 0.482831 0.4908 0.056599 1.978597 1
4 bracket=1-2 {'hidden_layer_sizes': (24,), 'batch_size': 12... 1 1.257797 0.4738 0.012073 1.978598 1

This illustrates the history after every partial_fit call. There’s also an attributed model_history_ that records the history for each model (it’s a reorganization of history_).

Learn more

This notebook covered basic usage HyperbandSearchCV. The following documentation and resources might be useful to learn more about HyperbandSearchCV, including some of the finer use cases:

Performance comparisons can be found in the SciPy 2019 talk/paper.