Fast Information Gain computation

Question

I need to compute Information Gain scores for >100k features in >10k documents for text classification. Code below works fine but for the full dataset is very slow - takes more than an hour on a laptop. Dataset is 20newsgroup and I am using scikit-learn, chi2 function which is provided in scikit works extremely fast.

Any idea how to compute Information Gain faster for such dataset?

def information_gain(x, y):

    def _entropy(values):
        counts = np.bincount(values)
        probs = counts[np.nonzero(counts)] / float(len(values))
        return - np.sum(probs * np.log(probs))

    def _information_gain(feature, y):
        feature_set_indices = np.nonzero(feature)[1]
        feature_not_set_indices = [i for i in feature_range if i not in feature_set_indices]
        entropy_x_set = _entropy(y[feature_set_indices])
        entropy_x_not_set = _entropy(y[feature_not_set_indices])

        return entropy_before - (((len(feature_set_indices) / float(feature_size)) * entropy_x_set)
                                 + ((len(feature_not_set_indices) / float(feature_size)) * entropy_x_not_set))

    feature_size = x.shape[0]
    feature_range = range(0, feature_size)
    entropy_before = _entropy(y)
    information_gain_scores = []

    for feature in x.T:
        information_gain_scores.append(_information_gain(feature, y))
    return information_gain_scores, []

EDIT:

I merged the internal functions and ran cProfiler as below (on a dataset limited to ~15k features and ~1k documents):

cProfile.runctx(
    """for feature in x.T:
    feature_set_indices = np.nonzero(feature)[1]
    feature_not_set_indices = [i for i in feature_range if i not in feature_set_indices]

    values = y[feature_set_indices]
    counts = np.bincount(values)
    probs = counts[np.nonzero(counts)] / float(len(values))
    entropy_x_set = - np.sum(probs * np.log(probs))

    values = y[feature_not_set_indices]
    counts = np.bincount(values)
    probs = counts[np.nonzero(counts)] / float(len(values))
    entropy_x_not_set = - np.sum(probs * np.log(probs))

    result = entropy_before - (((len(feature_set_indices) / float(feature_size)) * entropy_x_set)
                             + ((len(feature_not_set_indices) / float(feature_size)) * entropy_x_not_set))
    information_gain_scores.append(result)""",
    globals(), locals())

Result top 20 by tottime:

ncalls  tottime percall cumtime percall filename:lineno(function)
1       60.27   60.27   65.48   65.48   <string>:1(<module>)
16171   1.362   0   2.801   0   csr.py:313(_get_row_slice)
16171   0.523   0   0.892   0   coo.py:201(_check)
16173   0.394   0   0.89    0   compressed.py:101(check_format)
210235  0.297   0   0.297   0   {numpy.core.multiarray.array}
16173   0.287   0   0.331   0   compressed.py:631(prune)
16171   0.197   0   1.529   0   compressed.py:534(tocoo)
16173   0.165   0   1.263   0   compressed.py:20(__init__)
16171   0.139   0   1.669   0   base.py:415(nonzero)
16171   0.124   0   1.201   0   coo.py:111(__init__)
32342   0.123   0   0.123   0   {method 'max' of 'numpy.ndarray' objects}
48513   0.117   0   0.218   0   sputils.py:93(isintlike)
32342   0.114   0   0.114   0   {method 'sum' of 'numpy.ndarray' objects}
16171   0.106   0   3.081   0   csr.py:186(__getitem__)
32342   0.105   0   0.105   0   {numpy.lib._compiled_base.bincount}
32344   0.09    0   0.094   0   base.py:59(set_shape)
210227  0.088   0   0.088   0   {isinstance}
48513   0.081   0   1.777   0   fromnumeric.py:1129(nonzero)
32342   0.078   0   0.078   0   {method 'min' of 'numpy.ndarray' objects}
97032   0.066   0   0.153   0   numeric.py:167(asarray)

Looks that most of the time is spent in _get_row_slice. I am not entirely sure about the first row, looks it covers the whole block I provided to cProfile.runctx, though I don't know why there is such a big gap between first line totime=60.27 and second one tottime=1.362. Where was the difference spent in? Is it possible to check it in cProfile?

Basically, looks the problem is with sparse matrix operations (slicing, getting elements) -- the solution probably would be to calculate Information Gain using matrix algebra (like chi2 is implemented in scikit). But I have no idea how to express this calculation in terms of matrices operations... Anyone has an idea??

Answer 1

Here is a version that uses matrix operations. The IG for a feature is a mean over its class-specific scores.

import numpy as np
from scipy.sparse import issparse
from sklearn.preprocessing import LabelBinarizer
from sklearn.utils import check_array
from sklearn.utils.extmath import safe_sparse_dot


def ig(X, y):

    def get_t1(fc, c, f):
        t = np.log2(fc/(c * f))
        t[~np.isfinite(t)] = 0
        return np.multiply(fc, t)

    def get_t2(fc, c, f):
        t = np.log2((1-f-c+fc)/((1-c)*(1-f)))
        t[~np.isfinite(t)] = 0
        return np.multiply((1-f-c+fc), t)

    def get_t3(c, f, class_count, observed, total):
        nfc = (class_count - observed)/total
        t = np.log2(nfc/(c*(1-f)))
        t[~np.isfinite(t)] = 0
        return np.multiply(nfc, t)

    def get_t4(c, f, feature_count, observed, total):
        fnc = (feature_count - observed)/total
        t = np.log2(fnc/((1-c)*f))
        t[~np.isfinite(t)] = 0
        return np.multiply(fnc, t)

    X = check_array(X, accept_sparse='csr')
    if np.any((X.data if issparse(X) else X) < 0):
        raise ValueError("Input X must be non-negative.")

    Y = LabelBinarizer().fit_transform(y)
    if Y.shape[1] == 1:
        Y = np.append(1 - Y, Y, axis=1)

    # counts

    observed = safe_sparse_dot(Y.T, X)          # n_classes * n_features
    total = observed.sum(axis=0).reshape(1, -1).sum()
    feature_count = X.sum(axis=0).reshape(1, -1)
    class_count = (X.sum(axis=1).reshape(1, -1) * Y).T

    # probs

    f = feature_count / feature_count.sum()
    c = class_count / float(class_count.sum())
    fc = observed / total

    # the feature score is averaged over classes
    scores = (get_t1(fc, c, f) +
            get_t2(fc, c, f) +
            get_t3(c, f, class_count, observed, total) +
            get_t4(c, f, feature_count, observed, total)).mean(axis=0)

    scores = np.asarray(scores).reshape(-1)

    return scores, []

On a dataset with 1000 instances and 1000 unique features, this implementation is >100 faster than the one without matrix operations.

Answer 2

Don't know whether it still helps since a year has passed. But now I happen to be faced with the same task for text classification. I've rewritten your code using the nonzero() function provided for sparse matrix. Then I just scan nz, count the corresponding y_value and calculate the entropy.

The following code only needs seconds to run news20 dataset (loaded in using libsvm sparse matrix format).

def information_gain(X, y):

    def _calIg():
        entropy_x_set = 0
        entropy_x_not_set = 0
        for c in classCnt:
            probs = classCnt[c] / float(featureTot)
            entropy_x_set = entropy_x_set - probs * np.log(probs)
            probs = (classTotCnt[c] - classCnt[c]) / float(tot - featureTot)
            entropy_x_not_set = entropy_x_not_set - probs * np.log(probs)
        for c in classTotCnt:
            if c not in classCnt:
                probs = classTotCnt[c] / float(tot - featureTot)
                entropy_x_not_set = entropy_x_not_set - probs * np.log(probs)
        return entropy_before - ((featureTot / float(tot)) * entropy_x_set
                             +  ((tot - featureTot) / float(tot)) * entropy_x_not_set)

    tot = X.shape[0]
    classTotCnt = {}
    entropy_before = 0
    for i in y:
        if i not in classTotCnt:
            classTotCnt[i] = 1
        else:
            classTotCnt[i] = classTotCnt[i] + 1
    for c in classTotCnt:
        probs = classTotCnt[c] / float(tot)
        entropy_before = entropy_before - probs * np.log(probs)

    nz = X.T.nonzero()
    pre = 0
    classCnt = {}
    featureTot = 0
    information_gain = []
    for i in range(0, len(nz[0])):
        if (i != 0 and nz[0][i] != pre):
            for notappear in range(pre+1, nz[0][i]):
                information_gain.append(0)
            ig = _calIg()
            information_gain.append(ig)
            pre = nz[0][i]
            classCnt = {}
            featureTot = 0
        featureTot = featureTot + 1
        yclass = y[nz[1][i]]
        if yclass not in classCnt:
            classCnt[yclass] = 1
        else:
            classCnt[yclass] = classCnt[yclass] + 1
    ig = _calIg()
    information_gain.append(ig)

    return np.asarray(information_gain)