AIM-PIbd-32-Kurbanova-A-A/aimenv/Lib/site-packages/seaborn/_statistics.py
2024-10-02 22:15:59 +04:00

699 lines
24 KiB
Python

"""Statistical transformations for visualization.
This module is currently private, but is being written to eventually form part
of the public API.
The classes should behave roughly in the style of scikit-learn.
- All data-independent parameters should be passed to the class constructor.
- Each class should implement a default transformation that is exposed through
__call__. These are currently written for vector arguments, but I think
consuming a whole `plot_data` DataFrame and return it with transformed
variables would make more sense.
- Some class have data-dependent preprocessing that should be cached and used
multiple times (think defining histogram bins off all data and then counting
observations within each bin multiple times per data subsets). These currently
have unique names, but it would be good to have a common name. Not quite
`fit`, but something similar.
- Alternatively, the transform interface could take some information about grouping
variables and do a groupby internally.
- Some classes should define alternate transforms that might make the most sense
with a different function. For example, KDE usually evaluates the distribution
on a regular grid, but it would be useful for it to transform at the actual
datapoints. Then again, this could be controlled by a parameter at the time of
class instantiation.
"""
from numbers import Number
from statistics import NormalDist
import numpy as np
import pandas as pd
try:
from scipy.stats import gaussian_kde
_no_scipy = False
except ImportError:
from .external.kde import gaussian_kde
_no_scipy = True
from .algorithms import bootstrap
from .utils import _check_argument
class KDE:
"""Univariate and bivariate kernel density estimator."""
def __init__(
self, *,
bw_method=None,
bw_adjust=1,
gridsize=200,
cut=3,
clip=None,
cumulative=False,
):
"""Initialize the estimator with its parameters.
Parameters
----------
bw_method : string, scalar, or callable, optional
Method for determining the smoothing bandwidth to use; passed to
:class:`scipy.stats.gaussian_kde`.
bw_adjust : number, optional
Factor that multiplicatively scales the value chosen using
``bw_method``. Increasing will make the curve smoother. See Notes.
gridsize : int, optional
Number of points on each dimension of the evaluation grid.
cut : number, optional
Factor, multiplied by the smoothing bandwidth, that determines how
far the evaluation grid extends past the extreme datapoints. When
set to 0, truncate the curve at the data limits.
clip : pair of numbers or None, or a pair of such pairs
Do not evaluate the density outside of these limits.
cumulative : bool, optional
If True, estimate a cumulative distribution function. Requires scipy.
"""
if clip is None:
clip = None, None
self.bw_method = bw_method
self.bw_adjust = bw_adjust
self.gridsize = gridsize
self.cut = cut
self.clip = clip
self.cumulative = cumulative
if cumulative and _no_scipy:
raise RuntimeError("Cumulative KDE evaluation requires scipy")
self.support = None
def _define_support_grid(self, x, bw, cut, clip, gridsize):
"""Create the grid of evaluation points depending for vector x."""
clip_lo = -np.inf if clip[0] is None else clip[0]
clip_hi = +np.inf if clip[1] is None else clip[1]
gridmin = max(x.min() - bw * cut, clip_lo)
gridmax = min(x.max() + bw * cut, clip_hi)
return np.linspace(gridmin, gridmax, gridsize)
def _define_support_univariate(self, x, weights):
"""Create a 1D grid of evaluation points."""
kde = self._fit(x, weights)
bw = np.sqrt(kde.covariance.squeeze())
grid = self._define_support_grid(
x, bw, self.cut, self.clip, self.gridsize
)
return grid
def _define_support_bivariate(self, x1, x2, weights):
"""Create a 2D grid of evaluation points."""
clip = self.clip
if clip[0] is None or np.isscalar(clip[0]):
clip = (clip, clip)
kde = self._fit([x1, x2], weights)
bw = np.sqrt(np.diag(kde.covariance).squeeze())
grid1 = self._define_support_grid(
x1, bw[0], self.cut, clip[0], self.gridsize
)
grid2 = self._define_support_grid(
x2, bw[1], self.cut, clip[1], self.gridsize
)
return grid1, grid2
def define_support(self, x1, x2=None, weights=None, cache=True):
"""Create the evaluation grid for a given data set."""
if x2 is None:
support = self._define_support_univariate(x1, weights)
else:
support = self._define_support_bivariate(x1, x2, weights)
if cache:
self.support = support
return support
def _fit(self, fit_data, weights=None):
"""Fit the scipy kde while adding bw_adjust logic and version check."""
fit_kws = {"bw_method": self.bw_method}
if weights is not None:
fit_kws["weights"] = weights
kde = gaussian_kde(fit_data, **fit_kws)
kde.set_bandwidth(kde.factor * self.bw_adjust)
return kde
def _eval_univariate(self, x, weights=None):
"""Fit and evaluate a univariate on univariate data."""
support = self.support
if support is None:
support = self.define_support(x, cache=False)
kde = self._fit(x, weights)
if self.cumulative:
s_0 = support[0]
density = np.array([
kde.integrate_box_1d(s_0, s_i) for s_i in support
])
else:
density = kde(support)
return density, support
def _eval_bivariate(self, x1, x2, weights=None):
"""Fit and evaluate a univariate on bivariate data."""
support = self.support
if support is None:
support = self.define_support(x1, x2, cache=False)
kde = self._fit([x1, x2], weights)
if self.cumulative:
grid1, grid2 = support
density = np.zeros((grid1.size, grid2.size))
p0 = grid1.min(), grid2.min()
for i, xi in enumerate(grid1):
for j, xj in enumerate(grid2):
density[i, j] = kde.integrate_box(p0, (xi, xj))
else:
xx1, xx2 = np.meshgrid(*support)
density = kde([xx1.ravel(), xx2.ravel()]).reshape(xx1.shape)
return density, support
def __call__(self, x1, x2=None, weights=None):
"""Fit and evaluate on univariate or bivariate data."""
if x2 is None:
return self._eval_univariate(x1, weights)
else:
return self._eval_bivariate(x1, x2, weights)
# Note: we no longer use this for univariate histograms in histplot,
# preferring _stats.Hist. We'll deprecate this once we have a bivariate Stat class.
class Histogram:
"""Univariate and bivariate histogram estimator."""
def __init__(
self,
stat="count",
bins="auto",
binwidth=None,
binrange=None,
discrete=False,
cumulative=False,
):
"""Initialize the estimator with its parameters.
Parameters
----------
stat : str
Aggregate statistic to compute in each bin.
- `count`: show the number of observations in each bin
- `frequency`: show the number of observations divided by the bin width
- `probability` or `proportion`: normalize such that bar heights sum to 1
- `percent`: normalize such that bar heights sum to 100
- `density`: normalize such that the total area of the histogram equals 1
bins : str, number, vector, or a pair of such values
Generic bin parameter that can be the name of a reference rule,
the number of bins, or the breaks of the bins.
Passed to :func:`numpy.histogram_bin_edges`.
binwidth : number or pair of numbers
Width of each bin, overrides ``bins`` but can be used with
``binrange``.
binrange : pair of numbers or a pair of pairs
Lowest and highest value for bin edges; can be used either
with ``bins`` or ``binwidth``. Defaults to data extremes.
discrete : bool or pair of bools
If True, set ``binwidth`` and ``binrange`` such that bin
edges cover integer values in the dataset.
cumulative : bool
If True, return the cumulative statistic.
"""
stat_choices = [
"count", "frequency", "density", "probability", "proportion", "percent",
]
_check_argument("stat", stat_choices, stat)
self.stat = stat
self.bins = bins
self.binwidth = binwidth
self.binrange = binrange
self.discrete = discrete
self.cumulative = cumulative
self.bin_kws = None
def _define_bin_edges(self, x, weights, bins, binwidth, binrange, discrete):
"""Inner function that takes bin parameters as arguments."""
if binrange is None:
start, stop = x.min(), x.max()
else:
start, stop = binrange
if discrete:
bin_edges = np.arange(start - .5, stop + 1.5)
elif binwidth is not None:
step = binwidth
bin_edges = np.arange(start, stop + step, step)
# Handle roundoff error (maybe there is a less clumsy way?)
if bin_edges.max() < stop or len(bin_edges) < 2:
bin_edges = np.append(bin_edges, bin_edges.max() + step)
else:
bin_edges = np.histogram_bin_edges(
x, bins, binrange, weights,
)
return bin_edges
def define_bin_params(self, x1, x2=None, weights=None, cache=True):
"""Given data, return numpy.histogram parameters to define bins."""
if x2 is None:
bin_edges = self._define_bin_edges(
x1, weights, self.bins, self.binwidth, self.binrange, self.discrete,
)
if isinstance(self.bins, (str, Number)):
n_bins = len(bin_edges) - 1
bin_range = bin_edges.min(), bin_edges.max()
bin_kws = dict(bins=n_bins, range=bin_range)
else:
bin_kws = dict(bins=bin_edges)
else:
bin_edges = []
for i, x in enumerate([x1, x2]):
# Resolve out whether bin parameters are shared
# or specific to each variable
bins = self.bins
if not bins or isinstance(bins, (str, Number)):
pass
elif isinstance(bins[i], str):
bins = bins[i]
elif len(bins) == 2:
bins = bins[i]
binwidth = self.binwidth
if binwidth is None:
pass
elif not isinstance(binwidth, Number):
binwidth = binwidth[i]
binrange = self.binrange
if binrange is None:
pass
elif not isinstance(binrange[0], Number):
binrange = binrange[i]
discrete = self.discrete
if not isinstance(discrete, bool):
discrete = discrete[i]
# Define the bins for this variable
bin_edges.append(self._define_bin_edges(
x, weights, bins, binwidth, binrange, discrete,
))
bin_kws = dict(bins=tuple(bin_edges))
if cache:
self.bin_kws = bin_kws
return bin_kws
def _eval_bivariate(self, x1, x2, weights):
"""Inner function for histogram of two variables."""
bin_kws = self.bin_kws
if bin_kws is None:
bin_kws = self.define_bin_params(x1, x2, cache=False)
density = self.stat == "density"
hist, *bin_edges = np.histogram2d(
x1, x2, **bin_kws, weights=weights, density=density
)
area = np.outer(
np.diff(bin_edges[0]),
np.diff(bin_edges[1]),
)
if self.stat == "probability" or self.stat == "proportion":
hist = hist.astype(float) / hist.sum()
elif self.stat == "percent":
hist = hist.astype(float) / hist.sum() * 100
elif self.stat == "frequency":
hist = hist.astype(float) / area
if self.cumulative:
if self.stat in ["density", "frequency"]:
hist = (hist * area).cumsum(axis=0).cumsum(axis=1)
else:
hist = hist.cumsum(axis=0).cumsum(axis=1)
return hist, bin_edges
def _eval_univariate(self, x, weights):
"""Inner function for histogram of one variable."""
bin_kws = self.bin_kws
if bin_kws is None:
bin_kws = self.define_bin_params(x, weights=weights, cache=False)
density = self.stat == "density"
hist, bin_edges = np.histogram(
x, **bin_kws, weights=weights, density=density,
)
if self.stat == "probability" or self.stat == "proportion":
hist = hist.astype(float) / hist.sum()
elif self.stat == "percent":
hist = hist.astype(float) / hist.sum() * 100
elif self.stat == "frequency":
hist = hist.astype(float) / np.diff(bin_edges)
if self.cumulative:
if self.stat in ["density", "frequency"]:
hist = (hist * np.diff(bin_edges)).cumsum()
else:
hist = hist.cumsum()
return hist, bin_edges
def __call__(self, x1, x2=None, weights=None):
"""Count the occurrences in each bin, maybe normalize."""
if x2 is None:
return self._eval_univariate(x1, weights)
else:
return self._eval_bivariate(x1, x2, weights)
class ECDF:
"""Univariate empirical cumulative distribution estimator."""
def __init__(self, stat="proportion", complementary=False):
"""Initialize the class with its parameters
Parameters
----------
stat : {{"proportion", "percent", "count"}}
Distribution statistic to compute.
complementary : bool
If True, use the complementary CDF (1 - CDF)
"""
_check_argument("stat", ["count", "percent", "proportion"], stat)
self.stat = stat
self.complementary = complementary
def _eval_bivariate(self, x1, x2, weights):
"""Inner function for ECDF of two variables."""
raise NotImplementedError("Bivariate ECDF is not implemented")
def _eval_univariate(self, x, weights):
"""Inner function for ECDF of one variable."""
sorter = x.argsort()
x = x[sorter]
weights = weights[sorter]
y = weights.cumsum()
if self.stat in ["percent", "proportion"]:
y = y / y.max()
if self.stat == "percent":
y = y * 100
x = np.r_[-np.inf, x]
y = np.r_[0, y]
if self.complementary:
y = y.max() - y
return y, x
def __call__(self, x1, x2=None, weights=None):
"""Return proportion or count of observations below each sorted datapoint."""
x1 = np.asarray(x1)
if weights is None:
weights = np.ones_like(x1)
else:
weights = np.asarray(weights)
if x2 is None:
return self._eval_univariate(x1, weights)
else:
return self._eval_bivariate(x1, x2, weights)
class EstimateAggregator:
def __init__(self, estimator, errorbar=None, **boot_kws):
"""
Data aggregator that produces an estimate and error bar interval.
Parameters
----------
estimator : callable or string
Function (or method name) that maps a vector to a scalar.
errorbar : string, (string, number) tuple, or callable
Name of errorbar method (either "ci", "pi", "se", or "sd"), or a tuple
with a method name and a level parameter, or a function that maps from a
vector to a (min, max) interval, or None to hide errorbar. See the
:doc:`errorbar tutorial </tutorial/error_bars>` for more information.
boot_kws
Additional keywords are passed to bootstrap when error_method is "ci".
"""
self.estimator = estimator
method, level = _validate_errorbar_arg(errorbar)
self.error_method = method
self.error_level = level
self.boot_kws = boot_kws
def __call__(self, data, var):
"""Aggregate over `var` column of `data` with estimate and error interval."""
vals = data[var]
if callable(self.estimator):
# You would think we could pass to vals.agg, and yet:
# https://github.com/mwaskom/seaborn/issues/2943
estimate = self.estimator(vals)
else:
estimate = vals.agg(self.estimator)
# Options that produce no error bars
if self.error_method is None:
err_min = err_max = np.nan
elif len(data) <= 1:
err_min = err_max = np.nan
# Generic errorbars from user-supplied function
elif callable(self.error_method):
err_min, err_max = self.error_method(vals)
# Parametric options
elif self.error_method == "sd":
half_interval = vals.std() * self.error_level
err_min, err_max = estimate - half_interval, estimate + half_interval
elif self.error_method == "se":
half_interval = vals.sem() * self.error_level
err_min, err_max = estimate - half_interval, estimate + half_interval
# Nonparametric options
elif self.error_method == "pi":
err_min, err_max = _percentile_interval(vals, self.error_level)
elif self.error_method == "ci":
units = data.get("units", None)
boots = bootstrap(vals, units=units, func=self.estimator, **self.boot_kws)
err_min, err_max = _percentile_interval(boots, self.error_level)
return pd.Series({var: estimate, f"{var}min": err_min, f"{var}max": err_max})
class WeightedAggregator:
def __init__(self, estimator, errorbar=None, **boot_kws):
"""
Data aggregator that produces a weighted estimate and error bar interval.
Parameters
----------
estimator : string
Function (or method name) that maps a vector to a scalar. Currently
supports only "mean".
errorbar : string or (string, number) tuple
Name of errorbar method or a tuple with a method name and a level parameter.
Currently the only supported method is "ci".
boot_kws
Additional keywords are passed to bootstrap when error_method is "ci".
"""
if estimator != "mean":
# Note that, while other weighted estimators may make sense (e.g. median),
# I'm not aware of an implementation in our dependencies. We can add one
# in seaborn later, if there is sufficient interest. For now, limit to mean.
raise ValueError(f"Weighted estimator must be 'mean', not {estimator!r}.")
self.estimator = estimator
method, level = _validate_errorbar_arg(errorbar)
if method is not None and method != "ci":
# As with the estimator, weighted 'sd' or 'pi' error bars may make sense.
# But we'll keep things simple for now and limit to (bootstrap) CI.
raise ValueError(f"Error bar method must be 'ci', not {method!r}.")
self.error_method = method
self.error_level = level
self.boot_kws = boot_kws
def __call__(self, data, var):
"""Aggregate over `var` column of `data` with estimate and error interval."""
vals = data[var]
weights = data["weight"]
estimate = np.average(vals, weights=weights)
if self.error_method == "ci" and len(data) > 1:
def error_func(x, w):
return np.average(x, weights=w)
boots = bootstrap(vals, weights, func=error_func, **self.boot_kws)
err_min, err_max = _percentile_interval(boots, self.error_level)
else:
err_min = err_max = np.nan
return pd.Series({var: estimate, f"{var}min": err_min, f"{var}max": err_max})
class LetterValues:
def __init__(self, k_depth, outlier_prop, trust_alpha):
"""
Compute percentiles of a distribution using various tail stopping rules.
Parameters
----------
k_depth: "tukey", "proportion", "trustworthy", or "full"
Stopping rule for choosing tail percentiled to show:
- tukey: Show a similar number of outliers as in a conventional boxplot.
- proportion: Show approximately `outlier_prop` outliers.
- trust_alpha: Use `trust_alpha` level for most extreme tail percentile.
outlier_prop: float
Parameter for `k_depth="proportion"` setting the expected outlier rate.
trust_alpha: float
Parameter for `k_depth="trustworthy"` setting the confidence threshold.
Notes
-----
Based on the proposal in this paper:
https://vita.had.co.nz/papers/letter-value-plot.pdf
"""
k_options = ["tukey", "proportion", "trustworthy", "full"]
if isinstance(k_depth, str):
_check_argument("k_depth", k_options, k_depth)
elif not isinstance(k_depth, int):
err = (
"The `k_depth` parameter must be either an integer or string "
f"(one of {k_options}), not {k_depth!r}."
)
raise TypeError(err)
self.k_depth = k_depth
self.outlier_prop = outlier_prop
self.trust_alpha = trust_alpha
def _compute_k(self, n):
# Select the depth, i.e. number of boxes to draw, based on the method
if self.k_depth == "full":
# extend boxes to 100% of the data
k = int(np.log2(n)) + 1
elif self.k_depth == "tukey":
# This results with 5-8 points in each tail
k = int(np.log2(n)) - 3
elif self.k_depth == "proportion":
k = int(np.log2(n)) - int(np.log2(n * self.outlier_prop)) + 1
elif self.k_depth == "trustworthy":
normal_quantile_func = np.vectorize(NormalDist().inv_cdf)
point_conf = 2 * normal_quantile_func(1 - self.trust_alpha / 2) ** 2
k = int(np.log2(n / point_conf)) + 1
else:
# Allow having k directly specified as input
k = int(self.k_depth)
return max(k, 1)
def __call__(self, x):
"""Evaluate the letter values."""
k = self._compute_k(len(x))
exp = np.arange(k + 1, 1, -1), np.arange(2, k + 2)
levels = k + 1 - np.concatenate([exp[0], exp[1][1:]])
percentiles = 100 * np.concatenate([0.5 ** exp[0], 1 - 0.5 ** exp[1]])
if self.k_depth == "full":
percentiles[0] = 0
percentiles[-1] = 100
values = np.percentile(x, percentiles)
fliers = np.asarray(x[(x < values.min()) | (x > values.max())])
median = np.percentile(x, 50)
return {
"k": k,
"levels": levels,
"percs": percentiles,
"values": values,
"fliers": fliers,
"median": median,
}
def _percentile_interval(data, width):
"""Return a percentile interval from data of a given width."""
edge = (100 - width) / 2
percentiles = edge, 100 - edge
return np.nanpercentile(data, percentiles)
def _validate_errorbar_arg(arg):
"""Check type and value of errorbar argument and assign default level."""
DEFAULT_LEVELS = {
"ci": 95,
"pi": 95,
"se": 1,
"sd": 1,
}
usage = "`errorbar` must be a callable, string, or (string, number) tuple"
if arg is None:
return None, None
elif callable(arg):
return arg, None
elif isinstance(arg, str):
method = arg
level = DEFAULT_LEVELS.get(method, None)
else:
try:
method, level = arg
except (ValueError, TypeError) as err:
raise err.__class__(usage) from err
_check_argument("errorbar", list(DEFAULT_LEVELS), method)
if level is not None and not isinstance(level, Number):
raise TypeError(usage)
return method, level