227 lines
7.2 KiB
Python
227 lines
7.2 KiB
Python
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"""
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Created on Wed Feb 17 15:35:23 2021
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Author: Josef Perktold
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License: BSD-3
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"""
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import numpy as np
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from scipy import stats
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from statsmodels.tools.decorators import cache_readonly
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from statsmodels.distributions.tools import (
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_Grid, cdf2prob_grid, prob2cdf_grid,
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_eval_bernstein_dd, _eval_bernstein_2d, _eval_bernstein_1d)
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class BernsteinDistribution:
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"""Distribution based on Bernstein Polynomials on unit hypercube.
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Parameters
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----------
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cdf_grid : array_like
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cdf values on a equal spaced grid of the unit hypercube [0, 1]^d.
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The dimension of the arrays define how many random variables are
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included in the multivariate distribution.
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Attributes
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----------
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cdf_grid : grid of cdf values
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prob_grid : grid of cell or bin probabilities
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k_dim : (int) number of components, dimension of random variable
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k_grid : (tuple) shape of cdf_grid
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k_grid_product : (int) total number of bins in grid
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_grid : Grid instance with helper methods and attributes
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"""
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def __init__(self, cdf_grid):
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self.cdf_grid = cdf_grid = np.asarray(cdf_grid)
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self.k_dim = cdf_grid.ndim
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self.k_grid = cdf_grid.shape
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self.k_grid_product = np.prod([i-1 for i in self.k_grid])
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self._grid = _Grid(self.k_grid)
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@classmethod
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def from_data(cls, data, k_bins):
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"""Create distribution instance from data using histogram binning.
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Classmethod to construct a distribution instance.
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Parameters
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----------
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data : array_like
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Data with observation in rows and random variables in columns.
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Data can be 1-dimensional in the univariate case.
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k_bins : int or list
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Number or edges of bins to be used in numpy histogramdd.
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If k_bins is a scalar int, then the number of bins of each
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component will be equal to it.
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Returns
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-------
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Instance of a Bernstein distribution
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"""
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data = np.asarray(data)
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if np.any(data < 0) or np.any(data > 1):
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raise ValueError("data needs to be in [0, 1]")
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if data.ndim == 1:
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data = data[:, None]
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k_dim = data.shape[1]
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if np.size(k_bins) == 1:
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k_bins = [k_bins] * k_dim
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bins = [np.linspace(-1 / ni, 1, ni + 2) for ni in k_bins]
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c, e = np.histogramdd(data, bins=bins, density=False)
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# TODO: check when we have zero observations, which bin?
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# check bins start at 0 exept leading bin
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assert all([ei[1] == 0 for ei in e])
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c /= len(data)
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cdf_grid = prob2cdf_grid(c)
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return cls(cdf_grid)
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@cache_readonly
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def prob_grid(self):
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return cdf2prob_grid(self.cdf_grid, prepend=None)
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def cdf(self, x):
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"""cdf values evaluated at x.
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Parameters
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----------
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x : array_like
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Points of multivariate random variable at which cdf is evaluated.
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This can be a single point with length equal to the dimension of
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the random variable, or two dimensional with points (observations)
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in rows and random variables in columns.
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In the univariate case, a 1-dimensional x will be interpreted as
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different points for evaluation.
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Returns
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-------
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pdf values
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Notes
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-----
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Warning: 2-dim x with many points can be memory intensive because
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currently the bernstein polynomials will be evaluated in a fully
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vectorized computation.
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"""
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x = np.asarray(x)
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if x.ndim == 1 and self.k_dim == 1:
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x = x[:, None]
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cdf_ = _eval_bernstein_dd(x, self.cdf_grid)
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return cdf_
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def pdf(self, x):
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"""pdf values evaluated at x.
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Parameters
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----------
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x : array_like
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Points of multivariate random variable at which pdf is evaluated.
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This can be a single point with length equal to the dimension of
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the random variable, or two dimensional with points (observations)
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in rows and random variables in columns.
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In the univariate case, a 1-dimensional x will be interpreted as
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different points for evaluation.
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Returns
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-------
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cdf values
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Notes
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-----
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Warning: 2-dim x with many points can be memory intensive because
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currently the bernstein polynomials will be evaluated in a fully
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vectorized computation.
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"""
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x = np.asarray(x)
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if x.ndim == 1 and self.k_dim == 1:
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x = x[:, None]
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# TODO: check usage of k_grid_product. Should this go into eval?
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pdf_ = self.k_grid_product * _eval_bernstein_dd(x, self.prob_grid)
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return pdf_
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def get_marginal(self, idx):
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"""Get marginal BernsteinDistribution.
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Parameters
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----------
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idx : int or list of int
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Index or indices of the component for which the marginal
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distribution is returned.
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Returns
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-------
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BernsteinDistribution instance for the marginal distribution.
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"""
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# univariate
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if self.k_dim == 1:
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return self
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sl = [-1] * self.k_dim
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if np.shape(idx) == ():
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idx = [idx]
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for ii in idx:
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sl[ii] = slice(None, None, None)
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cdf_m = self.cdf_grid[tuple(sl)]
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bpd_marginal = BernsteinDistribution(cdf_m)
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return bpd_marginal
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def rvs(self, nobs):
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"""Generate random numbers from distribution.
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Parameters
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----------
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nobs : int
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Number of random observations to generate.
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"""
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rvs_mnl = np.random.multinomial(nobs, self.prob_grid.flatten())
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k_comp = self.k_dim
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rvs_m = []
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for i in range(len(rvs_mnl)):
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if rvs_mnl[i] != 0:
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idx = np.unravel_index(i, self.prob_grid.shape)
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rvsi = []
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for j in range(k_comp):
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n = self.k_grid[j]
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xgi = self._grid.x_marginal[j][idx[j]]
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# Note: x_marginal starts at 0
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# x_marginal ends with 1 but that is not used by idx
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rvsi.append(stats.beta.rvs(n * xgi + 1, n * (1-xgi) + 0,
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size=rvs_mnl[i]))
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rvs_m.append(np.column_stack(rvsi))
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rvsm = np.concatenate(rvs_m)
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return rvsm
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class BernsteinDistributionBV(BernsteinDistribution):
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def cdf(self, x):
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cdf_ = _eval_bernstein_2d(x, self.cdf_grid)
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return cdf_
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def pdf(self, x):
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# TODO: check usage of k_grid_product. Should this go into eval?
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pdf_ = self.k_grid_product * _eval_bernstein_2d(x, self.prob_grid)
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return pdf_
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class BernsteinDistributionUV(BernsteinDistribution):
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def cdf(self, x, method="binom"):
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cdf_ = _eval_bernstein_1d(x, self.cdf_grid, method=method)
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return cdf_
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def pdf(self, x, method="binom"):
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# TODO: check usage of k_grid_product. Should this go into eval?
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pdf_ = self.k_grid_product * _eval_bernstein_1d(x, self.prob_grid,
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method=method)
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return pdf_
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