Density estimation with Gaussian Kernel with the scikit-learn API (draft)

from scipy import stats

class GaussianKernelDensityEstimation(object):
    """docstring for GaussianKernelDensityEstimation"""
    def __init__(self):
        self.gkde = None

    def fit(self, X):
        """docstring for fit"""
        self.gkde = stats.gaussian_kde(X.T)
        return self

    def predict(self, X):
        return self.gkde.evaluate(X.T)

if __name__ == '__main__':
    import numpy as np

    # Create some dummy data
    X = np.random.randn(400,2)
    X[200:,:] += 3.5

    # Regular grid to evaluate kde upon
    n_grid_points = 128
    xmin, ymin = X.min(axis=0)
    xmax, ymax = X.max(axis=0)
    xx = np.linspace(xmin - 0.5, xmax + 0.5, n_grid_points)
    yy = np.linspace(ymin - 0.5, ymax + 0.5, n_grid_points)

    xg, yg = np.meshgrid(xx, yy)
    grid_coords = np.c_[xg.ravel(), yg.ravel()]

    # Compute density estimation
    kde = GaussianKernelDensityEstimation()
    kde.fit(X) # Fit
    zz = kde.predict(grid_coords) # Evaluate density on grid points

    zz = zz.reshape(*xg.shape)

    import matplotlib.pylab as pl
    pl.close('all')
    pl.set_cmap(pl.cm.Paired)
    pl.figure()
    pl.contourf(xx, yy, zz, label='density')
    pl.scatter(X[:,0], X[:,1], color='k', label='samples')
    pl.axis('tight')
    pl.legend()
    pl.title('Kernel Density Estimation')
    pl.show()

The gaussian_kde of scipy is terribly slow on real problems. Quite often Emmanuelle and I haven't been able to use it. If we are going to expose it in the scikit, I'd like us to make an effort to expose something that actually works on real data.

argh ! I didn't know. Any chance we can do better?

Yes we can (TM). We can use our ball tree to select only the data points from the training set that contribute significantly to a given test point. The problem is that with this strategy, it is harder to vectorize the 'predict' on the test data. Whether scipy's default behavior or the one I am suggesting is the best depends the 'shape' of you data: number of training point, number of testing points, and number of dimensions.

That means that we need a heuristic to decide which strategy to apply.

Also, grouping the test points that are close together to select a common 'active set' for them, and thus vectorizing on that bunch the predict would help.

There is some work to do to get a decent KDE :)

ok so we'll say that this is work in progress... At least the discussion was constructive :)