[MRG] implements log-uniform random variable

doc/modules/grid_search.rst

@@ -121,6 +121,7 @@ discrete choices (which will be sampled uniformly) can be specified::
 This example uses the ``scipy.stats`` module, which contains many useful
 distributions for sampling parameters, such as ``expon``, ``gamma``,
 ``uniform`` or ``randint``.
+
 In principle, any function can be passed that provides a ``rvs`` (random
 variate sample) method to sample a value. A call to the ``rvs`` function should
 provide independent random samples from possible parameter values on
@@ -139,6 +140,22 @@ For continuous parameters, such as ``C`` above, it is important to specify
 a continuous distribution to take full advantage of the randomization. This way,
 increasing ``n_iter`` will always lead to a finer search.
 
+A continuous log-uniform random variable is available through
+:class:`~sklearn.utils.fixes.loguniform`. This is a continuous version of
+log-spaced parameters. For example to specify ``C`` above, ``loguniform(1,
+100)`` can be used instead of ``[1, 10, 100]`` or ``np.logspace(0, 2,
+num=1000)``. This is an alias to SciPy's `stats.reciprocal
+<https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.reciprocal.html>`_.
+
+Mirroring the example above in grid search, we can specify a continuous random
+variable that is log-uniformly distributed between ``1e0`` and ``1e3``::
+
+  from sklearn.utils.fixes import loguniform
+  {'C': loguniform(1e0, 1e3),
+   'gamma': loguniform(1e-4, 1e-3),
+   'kernel': ['rbf'],
+   'class_weight':['balanced', None]}
+
 .. topic:: Examples:
 
     * :ref:`sphx_glr_auto_examples_model_selection_plot_randomized_search.py` compares the usage and efficiency

doc/whats_new/v0.22.rst

@@ -554,6 +554,13 @@ Changelog
   :func:`~utils.estimator_checks.parametrize_with_checks`, to parametrize
   estimator checks for a list of estimators. :pr:`14381` by `Thomas Fan`_.
 
+- A new random variable, :class:`utils.fixes.loguniform` implements a
+  log-uniform random variable (e.g., for use in RandomizedSearchCV).
+  For example, the outcomes ``1``, ``10`` and ``100`` are all equally likely
+  for ``loguniform(1, 100)``. See :issue:`11232` by
+  :user:`Scott Sievert <stsievert>` and :user:`Nathaniel Saul <sauln>`,
+  and `SciPy PR 10815 <https://github.com/scipy/scipy/pull/10815>`.
+
 - |API| The following utils have been deprecated and are now private:
   - ``choose_check_classifiers_labels``
   - ``enforce_estimator_tags_y``

examples/model_selection/plot_randomized_search.py

@@ -12,8 +12,8 @@
 parameters. The result in parameter settings is quite similar, while the run
 time for randomized search is drastically lower.
 
-The performance is slightly worse for the randomized search, though this
-is most likely a noise effect and would not carry over to a held-out test set.
+The performance is may slightly worse for the randomized search, and is likely
+due to a noise effect and would not carry over to a held-out test set.
 
 Note that in practice, one would not search over this many different parameters
 simultaneously using grid search, but pick only the ones deemed most important.
@@ -23,18 +23,19 @@
 import numpy as np
 
 from time import time
-from scipy.stats import randint as sp_randint
+import scipy.stats as stats
+from sklearn.utils.fixes import loguniform
 
-from sklearn.model_selection import GridSearchCV
-from sklearn.model_selection import RandomizedSearchCV
+from sklearn.model_selection import GridSearchCV, RandomizedSearchCV
 from sklearn.datasets import load_digits
-from sklearn.ensemble import RandomForestClassifier
+from sklearn.linear_model import SGDClassifier
 
 # get some data
 X, y = load_digits(return_X_y=True)
 
 # build a classifier
-clf = RandomForestClassifier(n_estimators=20)
+clf = SGDClassifier(loss='hinge', penalty='elasticnet',
+                    fit_intercept=True)
 
 
 # Utility function to report best scores
@@ -43,19 +44,17 @@ def report(results, n_top=3):
         candidates = np.flatnonzero(results['rank_test_score'] == i)
         for candidate in candidates:
             print("Model with rank: {0}".format(i))
-            print("Mean validation score: {0:.3f} (std: {1:.3f})".format(
-                  results['mean_test_score'][candidate],
-                  results['std_test_score'][candidate]))
+            print("Mean validation score: {0:.3f} (std: {1:.3f})"
+                  .format(results['mean_test_score'][candidate],
+                          results['std_test_score'][candidate]))
             print("Parameters: {0}".format(results['params'][candidate]))
             print("")
 
 
 # specify parameters and distributions to sample from
-param_dist = {"max_depth": [3, None],
-              "max_features": sp_randint(1, 11),
-              "min_samples_split": sp_randint(2, 11),
-              "bootstrap": [True, False],
-              "criterion": ["gini", "entropy"]}
+param_dist = {'average': [True, False],
+              'l1_ratio': stats.uniform(0, 1),
+              'alpha': loguniform(1e-4, 1e0)}
 
 # run randomized search
 n_iter_search = 20
@@ -69,11 +68,9 @@ def report(results, n_top=3):
 report(random_search.cv_results_)
 
 # use a full grid over all parameters
-param_grid = {"max_depth": [3, None],
-              "max_features": [1, 3, 10],
-              "min_samples_split": [2, 3, 10],
-              "bootstrap": [True, False],
-              "criterion": ["gini", "entropy"]}
+param_grid = {'average': [True, False],
+              'l1_ratio': np.linspace(0, 1, num=10),
+              'alpha': np.power(10, np.arange(-4, 1, dtype=float))}
 
 # run grid search
 grid_search = GridSearchCV(clf, param_grid=param_grid)

sklearn/utils/fixes.py

@@ -15,6 +15,7 @@
 import numpy as np
 import scipy.sparse as sp
 import scipy
+import scipy.stats
 from scipy.sparse.linalg import lsqr as sparse_lsqr  # noqa
 
 
@@ -256,3 +257,52 @@ def _joblib_parallel_args(**kwargs):
         if require == 'sharedmem':
             args['backend'] = 'threading'
     return args
+
+
+class loguniform(scipy.stats.reciprocal):
+    """A class supporting log-uniform random variables.
+
+    Parameters
+    ----------
+    low : float
+        The minimum value
+    high : float
+        The maximum value
+
+    Methods
+    -------
+    rvs(self, size=None, random_state=None)
+        Generate log-uniform random variables
+
+    The most useful method for Scikit-learn usage is highlighted here.
+    For a full list, see
+    `scipy.stats.reciprocal
+    <https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.reciprocal.html>`_.
+    This list includes all functions of ``scipy.stats`` continuous
+    distributions such as ``pdf``.
+
+    Notes
+    -----
+    This class generates values between ``low`` and ``high`` or
+
+        low <= loguniform(low, high).rvs() <= high
+
+    The logarithmic probability density function (PDF) is uniform. When
+    ``x`` is a uniformly distributed random variable between 0 and 1, ``10**x``
+    are random variales that are equally likely to be returned.
+
+    This class is an alias to ``scipy.stats.reciprocal``, which uses the
+    reciprocal distribution:
+    https://en.wikipedia.org/wiki/Reciprocal_distribution
+
+    Examples
+    --------
+
+    >>> from sklearn.utils.fixes import loguniform
+    >>> rv = loguniform(1e-3, 1e1)
+    >>> rvs = rv.rvs(random_state=42, size=1000)
+    >>> rvs.min()  # doctest: +SKIP
+    0.0010435856341129003
+    >>> rvs.max()  # doctest: +SKIP
+    9.97403052786026
+    """

sklearn/utils/tests/test_fixes.py

@@ -3,16 +3,19 @@
 #          Lars Buitinck
 # License: BSD 3 clause
 
+import math
 import pickle
 
 import numpy as np
 import pytest
+import scipy.stats
 
 from sklearn.utils.testing import assert_array_equal
 
 from sklearn.utils.fixes import MaskedArray
 from sklearn.utils.fixes import _joblib_parallel_args
 from sklearn.utils.fixes import _object_dtype_isnan
+from sklearn.utils.fixes import loguniform
 
 
 def test_masked_array_obj_dtype_pickleable():
@@ -68,3 +71,27 @@ def test_object_dtype_isnan(dtype, val):
     mask = _object_dtype_isnan(X)
 
     assert_array_equal(mask, expected_mask)
+
+
+@pytest.mark.parametrize("low,high,base",
+                         [(-1, 0, 10), (0, 2, np.exp(1)), (-1, 1, 2)])
+def test_loguniform(low, high, base):
+    rv = loguniform(base ** low, base ** high)
+    assert isinstance(rv, scipy.stats._distn_infrastructure.rv_frozen)
+    rvs = rv.rvs(size=2000, random_state=0)
+
+    # Test the basics; right bounds, right size
+    assert (base ** low <= rvs).all() and (rvs <= base ** high).all()
+    assert len(rvs) == 2000
+
+    # Test that it's actually (fairly) uniform
+    log_rvs = np.array([math.log(x, base) for x in rvs])
+    counts, _ = np.histogram(log_rvs)
+    assert counts.mean() == 200
+    assert np.abs(counts - counts.mean()).max() <= 40
+
+    # Test that random_state works
+    assert (
+        loguniform(base ** low, base ** high).rvs(random_state=0)
+        == loguniform(base ** low, base ** high).rvs(random_state=0)
+    )