Vous êtes un professionnel et vous avez besoin d'une formation ? RAG (Retrieval-Augmented Generation)
et Fine Tuning d'un LLM Voir le programme détaillé

Module « scipy.stats »

Fonction differential_entropy - module scipy.stats

Signature de la fonction differential_entropy

def differential_entropy(values: Union[collections.abc.Buffer, numpy._typing._array_like._SupportsArray[numpy.dtype[Any]], numpy._typing._nested_sequence._NestedSequence[numpy._typing._array_like._SupportsArray[numpy.dtype[Any]]], bool, int, float, complex, str, bytes, numpy._typing._nested_sequence._NestedSequence[bool | int | float | complex | str | bytes]], *, window_length: int | None = None, base: float | None = None, axis: int = 0, method: str = 'auto', nan_policy='propagate', keepdims=False) -> numpy.number | numpy.ndarray 

Description

help(scipy.stats.differential_entropy)

    


Given a sample of a distribution, estimate the differential entropy.

Several estimation methods are available using the `method` parameter. By
default, a method is selected based the size of the sample.

Parameters
----------
values : sequence
    Sample from a continuous distribution.
window_length : int, optional
    Window length for computing Vasicek estimate. Must be an integer
    between 1 and half of the sample size. If ``None`` (the default), it
    uses the heuristic value
    
    .. math::
        \left \lfloor \sqrt{n} + 0.5 \right \rfloor
    
    where :math:`n` is the sample size. This heuristic was originally
    proposed in [2]_ and has become common in the literature.
base : float, optional
    The logarithmic base to use, defaults to ``e`` (natural logarithm).
axis : int or None, default: 0
    If an int, the axis of the input along which to compute the statistic.
    The statistic of each axis-slice (e.g. row) of the input will appear in a
    corresponding element of the output.
    If ``None``, the input will be raveled before computing the statistic.
method : {'vasicek', 'van es', 'ebrahimi', 'correa', 'auto'}, optional
    The method used to estimate the differential entropy from the sample.
    Default is ``'auto'``.  See Notes for more information.
nan_policy : {'propagate', 'omit', 'raise'}
    Defines how to handle input NaNs.
    
    - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
      which the  statistic is computed, the corresponding entry of the output
      will be NaN.
    - ``omit``: NaNs will be omitted when performing the calculation.
      If insufficient data remains in the axis slice along which the
      statistic is computed, the corresponding entry of the output will be
      NaN.
    - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
keepdims : bool, default: False
    If this is set to True, the axes which are reduced are left
    in the result as dimensions with size one. With this option,
    the result will broadcast correctly against the input array.

Returns
-------
entropy : float
    The calculated differential entropy.

Notes
-----
This function will converge to the true differential entropy in the limit

.. math::
    n \to \infty, \quad m \to \infty, \quad \frac{m}{n} \to 0

The optimal choice of ``window_length`` for a given sample size depends on
the (unknown) distribution. Typically, the smoother the density of the
distribution, the larger the optimal value of ``window_length`` [1]_.

The following options are available for the `method` parameter.

* ``'vasicek'`` uses the estimator presented in [1]_. This is
  one of the first and most influential estimators of differential entropy.
* ``'van es'`` uses the bias-corrected estimator presented in [3]_, which
  is not only consistent but, under some conditions, asymptotically normal.
* ``'ebrahimi'`` uses an estimator presented in [4]_, which was shown
  in simulation to have smaller bias and mean squared error than
  the Vasicek estimator.
* ``'correa'`` uses the estimator presented in [5]_ based on local linear
  regression. In a simulation study, it had consistently smaller mean
  square error than the Vasiceck estimator, but it is more expensive to
  compute.
* ``'auto'`` selects the method automatically (default). Currently,
  this selects ``'van es'`` for very small samples (<10), ``'ebrahimi'``
  for moderate sample sizes (11-1000), and ``'vasicek'`` for larger
  samples, but this behavior is subject to change in future versions.

All estimators are implemented as described in [6]_.

Beginning in SciPy 1.9, ``np.matrix`` inputs (not recommended for new
code) are converted to ``np.ndarray`` before the calculation is performed. In
this case, the output will be a scalar or ``np.ndarray`` of appropriate shape
rather than a 2D ``np.matrix``. Similarly, while masked elements of masked
arrays are ignored, the output will be a scalar or ``np.ndarray`` rather than a
masked array with ``mask=False``.

References
----------
.. [1] Vasicek, O. (1976). A test for normality based on sample entropy.
       Journal of the Royal Statistical Society:
       Series B (Methodological), 38(1), 54-59.
.. [2] Crzcgorzewski, P., & Wirczorkowski, R. (1999). Entropy-based
       goodness-of-fit test for exponentiality. Communications in
       Statistics-Theory and Methods, 28(5), 1183-1202.
.. [3] Van Es, B. (1992). Estimating functionals related to a density by a
       class of statistics based on spacings. Scandinavian Journal of
       Statistics, 61-72.
.. [4] Ebrahimi, N., Pflughoeft, K., & Soofi, E. S. (1994). Two measures
       of sample entropy. Statistics & Probability Letters, 20(3), 225-234.
.. [5] Correa, J. C. (1995). A new estimator of entropy. Communications
       in Statistics-Theory and Methods, 24(10), 2439-2449.
.. [6] Noughabi, H. A. (2015). Entropy Estimation Using Numerical Methods.
       Annals of Data Science, 2(2), 231-241.
       https://link.springer.com/article/10.1007/s40745-015-0045-9

Examples
--------
>>> import numpy as np
>>> from scipy.stats import differential_entropy, norm

Entropy of a standard normal distribution:

>>> rng = np.random.default_rng()
>>> values = rng.standard_normal(100)
>>> differential_entropy(values)
1.3407817436640392

Compare with the true entropy:

>>> float(norm.entropy())
1.4189385332046727

For several sample sizes between 5 and 1000, compare the accuracy of
the ``'vasicek'``, ``'van es'``, and ``'ebrahimi'`` methods. Specifically,
compare the root mean squared error (over 1000 trials) between the estimate
and the true differential entropy of the distribution.

>>> from scipy import stats
>>> import matplotlib.pyplot as plt
>>>
>>>
>>> def rmse(res, expected):
...     '''Root mean squared error'''
...     return np.sqrt(np.mean((res - expected)**2))
>>>
>>>
>>> a, b = np.log10(5), np.log10(1000)
>>> ns = np.round(np.logspace(a, b, 10)).astype(int)
>>> reps = 1000  # number of repetitions for each sample size
>>> expected = stats.expon.entropy()
>>>
>>> method_errors = {'vasicek': [], 'van es': [], 'ebrahimi': []}
>>> for method in method_errors:
...     for n in ns:
...        rvs = stats.expon.rvs(size=(reps, n), random_state=rng)
...        res = stats.differential_entropy(rvs, method=method, axis=-1)
...        error = rmse(res, expected)
...        method_errors[method].append(error)
>>>
>>> for method, errors in method_errors.items():
...     plt.loglog(ns, errors, label=method)
>>>
>>> plt.legend()
>>> plt.xlabel('sample size')
>>> plt.ylabel('RMSE (1000 trials)')
>>> plt.title('Entropy Estimator Error (Exponential Distribution)')

Vous êtes un professionnel et vous avez besoin d'une formation ? RAG (Retrieval-Augmented Generation)
et Fine Tuning d'un LLM Voir le programme détaillé