python-statsmodels 0.4.2-1.2 / usr / share / pyshared / statsmodels / nonparametric / kde.py

"""
Univariate Kernel Density Estimators

References
----------
Racine, Jeff. (2008) "Nonparametric Econometrics: A Primer," Foundation and
    Trends in Econometrics: Vol 3: No 1, pp1-88.
    http://dx.doi.org/10.1561/0800000009

http://en.wikipedia.org/wiki/Kernel_%28statistics%29

Silverman, B.W.  Density Estimation for Statistics and Data Anaylsis.
"""
import numpy as np
from scipy import integrate, stats
from statsmodels.sandbox.nonparametric import kernels
from statsmodels.tools.decorators import (cache_readonly,
                                                    resettable_cache)
import bandwidths
from kdetools import (forrt, revrt, silverman_transform, counts)
try:
    from fast_linbin import linbin
except ImportError:
    from kdetools import linbin

#### Kernels Switch for estimators ####

kernel_switch = dict(gau=kernels.Gaussian, epa=kernels.Epanechnikov,
                    uni=kernels.Uniform, tri=kernels.Triangular,
                    biw=kernels.Biweight, triw=kernels.Triweight,
                    cos=kernels.Cosine)

def _checkisfit(self):
    try:
        self.density
    except:
        raise ValueError("Call fit to fit the density first")


#### Kernel Density Estimator Class ###

class KDE(object):
    """
    Kernel Density Estimator

    Parameters
    ----------
    endog : array-like
        The variable for which the density estimate is desired.

    Notes
    -----
    If cdf, sf, cumhazard, or entropy are computed, they are computed based on
    the definition of the kernel rather than the FFT approximation, even if
    the density is fit with FFT = True.
    """
    _cache = resettable_cache()

    def __init__(self, endog):
        self.endog = np.asarray(endog)

    def fit(self, kernel="gau", bw="scott", fft=True, weights=None,
            gridsize=None, adjust=1, cut=3, clip=(-np.inf, np.inf)):
        """
        Attach the density estimate to the KDE class.

        Parameters
        ----------
        kernel : str
            The Kernel to be used. Choices are:

            - "biw" for biweight
            - "cos" for cosine
            - "epa" for Epanechnikov
            - "gau" for Gaussian.
            - "tri" for triangular
            - "triw" for triweight
            - "uni" for uniform

        bw : str, float
            The bandwidth to use. Choices are:

            - "scott" - 1.059 * A * nobs ** (-1/5.), where A is
              `min(std(X),IQR/1.34)`
            - "silverman" - .9 * A * nobs ** (-1/5.), where A is
              `min(std(X),IQR/1.34)`
            - If a float is given, it is the bandwidth.

        fft : bool
            Whether or not to use FFT. FFT implementation is more
            computationally efficient. However, only the Gaussian kernel
            is implemented. If FFT is False, then a 'nobs' x 'gridsize'
            intermediate array is created.
        gridsize : int
            If gridsize is None, max(len(X), 50) is used.
        cut : float
            Defines the length of the grid past the lowest and highest values
            of X so that the kernel goes to zero. The end points are
            -/+ cut*bw*{min(X) or max(X)}
        adjust : float
            An adjustment factor for the bw. Bandwidth becomes bw * adjust.
        """
        try:
            bw = float(bw)
            self.bw_method = "user-given"
        except:
            self.bw_method = bw
        endog = self.endog

        if fft:
            if kernel != "gau":
                msg = "Only gaussian kernel is available for fft"
                raise NotImplementedError(msg)
            if weights is not None:
                msg = "Weights are not implemented for fft"
                raise NotImplementedError(msg)
            density, grid, bw = kdensityfft(endog, kernel=kernel, bw=bw,
                    adjust=adjust, weights=weights, gridsize=gridsize,
                    clip=clip, cut=cut)
        else:
            density, grid, bw = kdensity(endog, kernel=kernel, bw=bw,
                    adjust=adjust, weights=weights, gridsize=gridsize,
                    clip=clip, cut=cut)
        self.density = density
        self.support = grid
        self.bw = bw
        self.kernel = kernel_switch[kernel](h=bw) # we instantiate twice,
                                                # should this passed to funcs?

    @cache_readonly
    def cdf(self):
        """
        Returns the cumulative distribution function evaluated at the support.

        Notes
        -----
        Will not work if fit has not been called.
        """
        _checkisfit(self)
        density = self.density
        kern = self.kernel
        if kern.domain is None: # TODO: test for grid point at domain bound
            a,b = -np.inf,np.inf
        else:
            a,b = kern.domain
        func = lambda x,s: kern.density(s,x)

        support = self.support
        support = np.r_[a,support]
        gridsize = len(support)
        endog = self.endog
        probs = [integrate.quad(func, support[i-1], support[i],
                    args=endog)[0] for i in xrange(1,gridsize)]
        return np.cumsum(probs)

    @cache_readonly
    def cumhazard(self):
        """
        Returns the hazard function evaluated at the support.

        Notes
        -----
        Will not work if fit has not been called.

        """
        _checkisfit(self)
        return -np.log(self.sf)

    @cache_readonly
    def sf(self):
        """
        Returns the survival function evaluated at the support.

        Notes
        -----
        Will not work if fit has not been called.
        """
        _checkisfit(self)
        return 1 - self.cdf

    @cache_readonly
    def entropy(self):
        """
        Returns the differential entropy evaluated at the support

        Notes
        -----
        Will not work if fit has not been called. 1e-12 is added to each
        probability to ensure that log(0) is not called.
        """
        _checkisfit(self)

        def entr(x,s):
            pdf = kern.density(s,x)
            return pdf*np.log(pdf+1e-12)

        pdf = self.density
        kern = self.kernel

        if kern.domain is not None:
            a,b = self.domain
        else:
            a,b = -np.inf,np.inf
        endog = self.endog
        #TODO: below could run into integr problems, cf. stats.dist._entropy
        return -integrate.quad(entr, a,b, args=(endog,))[0]

    @cache_readonly
    def icdf(self):
        """
        Inverse Cumulative Distribution (Quantile) Function

        Notes
        -----
        Will not work if fit has not been called. Uses
        `scipy.stats.mstats.mquantiles`.
        """
        _checkisfit(self)
        gridsize = len(self.density)
        return stats.mstats.mquantiles(self.endog, np.linspace(0,1,
                    gridsize))

    def evaluate(self, point):
        """
        Evaluate density at a single point.

        Parameters
        ----------
        point : float
            Point at which to evaluate the density.
        """
        _checkisfit(self)
        return self.kernel.density(self.endog, point)

#### Kernel Density Estimator Functions ####

def kdensity(X, kernel="gau", bw="scott", weights=None, gridsize=None,
             adjust=1, clip=(-np.inf,np.inf), cut=3, retgrid=True):
    """
    Rosenblatz-Parzen univariate kernel desnity estimator

    Parameters
    ----------
    X : array-like
        The variable for which the density estimate is desired.
    kernel : str
        The Kernel to be used. Choices are
        - "biw" for biweight
        - "cos" for cosine
        - "epa" for Epanechnikov
        - "gau" for Gaussian.
        - "tri" for triangular
        - "triw" for triweight
        - "uni" for uniform
    bw : str, float
        "scott" - 1.059 * A * nobs ** (-1/5.), where A is min(std(X),IQR/1.34)
        "silverman" - .9 * A * nobs ** (-1/5.), where A is min(std(X),IQR/1.34)
        If a float is given, it is the bandwidth.
    weights : array or None
        Optional  weights. If the X value is clipped, then this weight is
        also dropped.
    gridsize : int
        If gridsize is None, max(len(X), 50) is used.
    adjust : float
        An adjustment factor for the bw. Bandwidth becomes bw * adjust.
    clip : tuple
        Observations in X that are outside of the range given by clip are
        dropped. The number of observations in X is then shortened.
    cut : float
        Defines the length of the grid past the lowest and highest values of X
        so that the kernel goes to zero. The end points are
        -/+ cut*bw*{min(X) or max(X)}
    retgrid : bool
        Whether or not to return the grid over which the density is estimated.

    Returns
    -------
    density : array
        The densities estimated at the grid points.
    grid : array, optional
        The grid points at which the density is estimated.

    Notes
    -----
    Creates an intermediate (`gridsize` x `nobs`) array. Use FFT for a more
    computationally efficient version.
    """
    X = np.asarray(X)
    if X.ndim == 1:
        X = X[:,None]
    clip_x = np.logical_and(X>clip[0], X<clip[1])
    X = X[clip_x]

    nobs = float(len(X)) # after trim

    if gridsize == None:
        gridsize = max(nobs,50) # don't need to resize if no FFT

        # handle weights
    if weights is None:
        weights = np.ones(nobs)
        q = nobs
    else:
        if len(weights) != len(clip_x):
            msg = "The length of the weights must be the same as the given X."
            raise ValueError(msg)
        weights = weights[clip_x.squeeze()]
        q = weights.sum()

    # if bw is None, select optimal bandwidth for kernel
    try:
        bw = float(bw)
    except:
        bw = bandwidths.select_bandwidth(X, bw, kernel)
    bw *= adjust

    a = np.min(X,axis=0) - cut*bw
    b = np.max(X,axis=0) + cut*bw
    grid = np.linspace(a, b, gridsize)

    k = (X.T - grid[:,None])/bw  # uses broadcasting to make a gridsize x nobs

    # instantiate kernel class
    kern = kernel_switch[kernel](h=bw)
    # truncate to domain
    if kern.domain is not None: # won't work for piecewise kernels like parzen
        z_lo, z_high = kern.domain
        domain_mask = (k < z_lo) | (k > z_high)
        k = kern(k) # estimate density
        k[domain_mask] = 0
    else:
        k = kern(k) # estimate density

    k[k<0] = 0 # get rid of any negative values, do we need this?

    dens = np.dot(k,weights)/(q*bw)

    if retgrid:
        return dens, grid, bw
    else:
        return dens, bw

def kdensityfft(X, kernel="gau", bw="scott", weights=None, gridsize=None,
                adjust=1, clip=(-np.inf,np.inf), cut=3, retgrid=True):
    """
    Rosenblatz-Parzen univariate kernel desnity estimator

    Parameters
    ----------
    X : array-like
        The variable for which the density estimate is desired.
    kernel : str
        ONLY GAUSSIAN IS CURRENTLY IMPLEMENTED.
        "bi" for biweight
        "cos" for cosine
        "epa" for Epanechnikov, default
        "epa2" for alternative Epanechnikov
        "gau" for Gaussian.
        "par" for Parzen
        "rect" for rectangular
        "tri" for triangular
    bw : str, float
        "scott" - 1.059 * A * nobs ** (-1/5.), where A is min(std(X),IQR/1.34)
        "silverman" - .9 * A * nobs ** (-1/5.), where A is min(std(X),IQR/1.34)
        If a float is given, it is the bandwidth.
    weights : array or None
        WEIGHTS ARE NOT CURRENTLY IMPLEMENTED.
        Optional  weights. If the X value is clipped, then this weight is
        also dropped.
    gridsize : int
        If gridsize is None, min(len(X), 512) is used. Note that the provided
        number is rounded up to the next highest power of 2.
    adjust : float
        An adjustment factor for the bw. Bandwidth becomes bw * adjust.
        clip : tuple
        Observations in X that are outside of the range given by clip are
        dropped. The number of observations in X is then shortened.
    cut : float
        Defines the length of the grid past the lowest and highest values of X
        so that the kernel goes to zero. The end points are
        -/+ cut*bw*{X.min() or X.max()}
    retgrid : bool
        Whether or not to return the grid over which the density is estimated.

    Returns
    -------
    density : array
        The densities estimated at the grid points.
    grid : array, optional
        The grid points at which the density is estimated.

    Notes
    -----
    Only the default kernel is implemented. Weights aren't implemented yet.
    This follows Silverman (1982) with changes suggested by Jones and Lotwick
    (1984). However, the discretization step is replaced by linear binning
    of Fan and Marron (1994). This should be extended to accept the parts
    that are dependent only on the data to speed things up for
    cross-validation.

    References
    ---------- ::

    Fan, J. and J.S. Marron. (1994) `Fast implementations of nonparametric
        curve estimators`. Journal of Computational and Graphical Statistics.
        3.1, 35-56.
    Jones, M.C. and H.W. Lotwick. (1984) `Remark AS R50: A Remark on Algorithm
        AS 176. Kernal Density Estimation Using the Fast Fourier Transform`.
        Journal of the Royal Statistical Society. Series C. 33.1, 120-2.
    Silverman, B.W. (1982) `Algorithm AS 176. Kernel density estimation using
        the Fast Fourier Transform. Journal of the Royal Statistical Society.
        Series C. 31.2, 93-9.
    """
    X = np.asarray(X)
    X = X[np.logical_and(X>clip[0], X<clip[1])] # won't work for two columns.
                                                # will affect underlying data?
    try:
        bw = float(bw)
    except:
        bw = bandwidths.select_bandwidth(X, bw, kernel) # will cross-val fit this pattern?
    bw *= adjust

    nobs = float(len(X)) # after trim

    # 1 Make grid and discretize the data
    if gridsize == None:
        gridsize = np.max((nobs,512.))
    gridsize = 2**np.ceil(np.log2(gridsize)) # round to next power of 2

    a = np.min(X)-cut*bw
    b = np.max(X)+cut*bw
    grid,delta = np.linspace(a,b,gridsize,retstep=True)
    RANGE = b-a

#TODO: Fix this?
# This is the Silverman binning function, but I believe it's buggy (SS)
# weighting according to Silverman
#    count = counts(X,grid)
#    binned = np.zeros_like(grid)    #xi_{k} in Silverman
#    j = 0
#    for k in range(int(gridsize-1)):
#        if count[k]>0: # there are points of X in the grid here
#            Xingrid = X[j:j+count[k]] # get all these points
#            # get weights at grid[k],grid[k+1]
#            binned[k] += np.sum(grid[k+1]-Xingrid)
#            binned[k+1] += np.sum(Xingrid-grid[k])
#            j += count[k]
#    binned /= (nobs)*delta**2 # normalize binned to sum to 1/delta

#NOTE: THE ABOVE IS WRONG, JUST TRY WITH LINEAR BINNING
    binned = linbin(X,a,b,gridsize)/(delta*nobs)

    # step 2 compute FFT of the weights, using Munro (1976) FFT convention
    y = forrt(binned)

    # step 3 and 4 for optimal bw compute zstar and the density estimate f
    # don't have to redo the above if just changing bw, ie., for cross val

#NOTE: silverman_transform is the closed form solution of the FFT of the
#gaussian kernel. Not yet sure how to generalize it.
    zstar = silverman_transform(bw, gridsize, RANGE)*y # 3.49 in Silverman
                                                   # 3.50 w Gaussian kernel
    f = revrt(zstar)
    if retgrid:
        return f, grid, bw
    else:
        return f, bw

if __name__ == "__main__":
    import numpy as np
    np.random.seed(12345)
    xi = np.random.randn(100)
    f,grid, bw1 = kdensity(xi, kernel="gau", bw=.372735, retgrid=True)
    f2, bw2 = kdensityfft(xi, kernel="gau", bw="silverman",retgrid=False)

# do some checking vs. silverman algo.
# you need denes.f, http://lib.stat.cmu.edu/apstat/176
#NOTE: I (SS) made some changes to the Fortran
# and the FFT stuff from Munro http://lib.stat.cmu.edu/apstat/97o
# then compile everything and link to denest with f2py
#Make pyf file as usual, then compile shared object
#f2py denest.f -m denest2 -h denest.pyf
#edit pyf
#-c flag makes it available to other programs, fPIC builds a shared library
#/usr/bin/gfortran -Wall -c -fPIC fft.f
#f2py -c denest.pyf ./fft.o denest.f

    try:
        from denest2 import denest
        a = -3.4884382032045504
        b = 4.3671504686785605
        RANGE = b - a
        bw = bandwidths.bw_silverman(xi)

        ft,smooth,ifault,weights,smooth1 = denest(xi,a,b,bw,np.zeros(512),np.zeros(512),0,
                np.zeros(512), np.zeros(512))
# We use a different binning algo, so only accurate up to 3 decimal places
        np.testing.assert_almost_equal(f2, smooth, 3)
#NOTE: for debugging
#        y2 = forrt(weights)
#        RJ = np.arange(512/2+1)
#        FAC1 = 2*(np.pi*bw/RANGE)**2
#        RJFAC = RJ**2*FAC1
#        BC = 1 - RJFAC/(6*(bw/((b-a)/M))**2)
#        FAC = np.exp(-RJFAC)/BC
#        SMOOTH = np.r_[FAC,FAC[1:-1]] * y2

#        dens = revrt(SMOOTH)

    except:
#        ft = np.loadtxt('./ft_silver.csv')
#        smooth = np.loadtxt('./smooth_silver.csv')
        print "Didn't get the estimates from the Silverman algorithm"