import numpy as np
from pytensor_distributions import categorical as ptd_categorical
from preliz.distributions.distributions import Discrete
from preliz.internal.distribution_helper import all_not_none, eps, pytensor_jit, pytensor_rng_jit
from preliz.internal.optimization import optimize_ml
from preliz.internal.special import expit, logit
[docs]
class Categorical(Discrete):
R"""
Categorical distribution.
The most general discrete distribution. The pmf of this distribution is
.. math:: f(x \mid p) = p_x
.. plot::
:context: close-figs
from preliz import Categorical, style
style.use('preliz-doc')
ps = [[0.1, 0.6, 0.3], [0.3, 0.1, 0.1, 0.5]]
for p in ps:
Categorical(p).plot_pdf()
======== ===================================
Support :math:`x \in \{0, 1, \ldots, |p|-1\}`
======== ===================================
Parameters
----------
p : array of floats
p > 0 and the elements of p must sum to 1.
logit_p : float
Alternative log odds for the probability of success.
"""
def __init__(self, p=None, logit_p=None):
super().__init__()
self._parametrization(p, logit_p)
def _parametrization(self, p=None, logit_p=None):
if all_not_none(p, logit_p):
raise ValueError("Incompatible parametrization. Either use p or logit_p.")
self.param_names = "p"
self.params_support = ((eps, np.inf),)
if logit_p is not None:
p = self._from_logit_p(logit_p)
self.param_names = ("logit_p",)
self.p = p
self.logit_p = logit_p
if self.p is not None:
self.support = (0, len(p) - 1)
self._update(self.p)
def _from_logit_p(self, logit_p):
return expit(logit_p)
def _to_logit_p(self, p):
return logit(p)
def _update(self, p):
self.p = np.array(p)
self._n = len(p)
self.logit_p = self._to_logit_p(self.p)
if self.param_names[0] == "p":
self.params = (self.p,)
elif self.param_names[0] == "logit_p":
self.params = (self.logit_p,)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.p)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.p)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.p)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.p)
[docs]
def entropy(self):
return ptd_entropy(self.p)
[docs]
def mean(self):
return ptd_mean(self.p)
[docs]
def mode(self):
return ptd_mode(self.p)
[docs]
def var(self):
return ptd_var(self.p)
[docs]
def std(self):
return ptd_std(self.p)
[docs]
def skewness(self):
return ptd_skewness(self.p)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.p)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.p, size=size, rng=random_state)
def _fit_mle(self, sample):
optimize_ml(self, sample)
@pytensor_jit
def ptd_pdf(x, p):
return ptd_categorical.pdf(x, p)
@pytensor_jit
def ptd_cdf(x, p):
return ptd_categorical.cdf(x, p)
@pytensor_jit
def ptd_ppf(q, p):
return ptd_categorical.ppf(q, p)
@pytensor_jit
def ptd_logpdf(x, p):
return ptd_categorical.logpdf(x, p)
@pytensor_jit
def ptd_entropy(p):
return ptd_categorical.entropy(p)
@pytensor_jit
def ptd_mean(p):
return ptd_categorical.mean(p)
@pytensor_jit
def ptd_mode(p):
return ptd_categorical.mode(p)
@pytensor_jit
def ptd_median(p):
return ptd_categorical.median(p)
@pytensor_jit
def ptd_var(p):
return ptd_categorical.var(p)
@pytensor_jit
def ptd_std(p):
return ptd_categorical.std(p)
@pytensor_jit
def ptd_skewness(p):
return ptd_categorical.skewness(p)
@pytensor_jit
def ptd_kurtosis(p):
return ptd_categorical.kurtosis(p)
@pytensor_rng_jit
def ptd_rvs(p, size, rng):
return ptd_categorical.rvs(p, size=size, random_state=rng)
