AI算法Python实现：Transfer entropy_pyinform

一、原理

Transfer entropy（转移熵/传递熵）是一种非参数统计量，用于测量两个随机过程之间定向（时间不对称）的信息转移量。给定两个随机过程和，在时刻，的值为，随着时间的推移，由于不确定性，到达时刻后，的值只能在一定的范围内被确定。在变化过程中，如果过程对过程（定向）施加一定的影响（信息转移量），那么到达时刻后，的值的范围会发生变化，这个变化的量，就是Transfer entropy所代表的过程到过程，导致变化的非确定性的减少量。用公式可以表示为：

 其中，代表的熵（香农熵）。

二、代码实现

• transferEntropy.py
• main.py

transferEntropy.py

import numpy as np
 
from ctypes import byref, c_int, c_ulong, c_double, POINTER
from pyinform import _inform
from pyinform.error import ErrorCode, error_guard
 
 
def transfer_entropy(source, target, k, condition=None, local=False):
    """
    Compute the local or average transfer entropy from one time series to
    another with target history length *k*. Optionally, time series can be
    provided against which to *condition*.
    :param source: the source time series
    :type source: sequence or ``numpy.ndarray``
    :param target: the target time series
    :type target: sequence or ``numpy.ndarray``
    :param int k: the history length
    :param condition: time series of any conditions
    :type condition: sequence or ``numpy.ndarray``
    :param bool local: compute the local transfer entropy
    :returns: the average or local transfer entropy
    :rtype: float or ``numpy.ndarray``
    :raises ValueError: if the time series have different shapes
    :raises ValueError: if either time series has no initial conditions
    :raises ValueError: if either time series is greater than 2-D
    :raises InformError: if an error occurs within the ``inform`` C call
    """
    ys = np.ascontiguousarray(source, np.int32)
    xs = np.ascontiguousarray(target, np.int32)
    cs = np.ascontiguousarray(condition, np.int32) if condition is not None else None
 
    if xs.shape != ys.shape:
        raise ValueError("source and target timeseries are different shapes")
    elif xs.ndim > 2:
        raise ValueError("source and target have too great a dimension; must be 2 or less")
 
    if cs is None:
        pass
    elif cs.ndim == 1 and cs.shape != xs.shape:
        raise ValueError("condition has a shape that's inconsistent with the source and target")
    elif cs.ndim == 2 and xs.ndim == 1 and cs.shape[1:] != xs.shape:
        raise ValueError("condition has a shape that's inconsistent with the source and target")
    elif cs.ndim == 2 and xs.ndim == 2 and cs.shape != xs.shape:
        raise ValueError("condition has a shape that's inconsistent with the source and target")
    elif cs.ndim == 3 and cs.shape[1:] != xs.shape:
        raise ValueError("condition has a shape that's inconsistent with the source and target")
    elif cs.ndim > 3:
        raise ValueError("condition has too great a dimension; must be 3 or less")
 
    ydata = ys.ctypes.data_as(POINTER(c_int))
    xdata = xs.ctypes.data_as(POINTER(c_int))
    cdata = cs.ctypes.data_as(POINTER(c_int)) if cs is not None else None
 
    if cs is None:
        b = max(2, max(np.amax(xs), np.amax(ys)) + 1)
    else:
        b = max(2, max(np.amax(xs), np.amax(ys), np.amax(cs)) + 1)
 
    if cs is None:
        z = 0
    elif cs.ndim == 1 or (cs.ndim == 2 and xs.ndim == 2):
        z = 1
    elif cs.ndim == 3 or (cs.ndim == 2 and xs.ndim == 1):
        z = cs.shape[0]
    else:
        raise RuntimeError("unexpected state: condition and source are inconsistent shapes")
 
    if xs.ndim == 1:
        n, m = 1, xs.shape[0]
    else:
        n, m = xs.shape
 
    e = ErrorCode(0)
 
    if local is True:
        q = max(0, m - k)
        te = np.empty((n, q), dtype=np.float64)
        out = te.ctypes.data_as(POINTER(c_double))
        _local_transfer_entropy(ydata, xdata, cdata, c_ulong(z), c_ulong(n), c_ulong(m), c_int(b), c_ulong(k), out, byref(e))
    else:
        te = _transfer_entropy(ydata, xdata, cdata, c_ulong(z), c_ulong(n), c_ulong(m), c_int(b), c_ulong(k), byref(e))
 
    error_guard(e)
 
    return te
 
 
_transfer_entropy = _inform.inform_transfer_entropy
_transfer_entropy.argtypes = [POINTER(c_int), POINTER(c_int), POINTER(c_int), c_ulong, c_ulong, c_ulong, c_int, c_ulong, POINTER(c_int)]
_transfer_entropy.restype = c_double
 
_local_transfer_entropy = _inform.inform_local_transfer_entropy
_local_transfer_entropy.argtypes = [POINTER(c_int), POINTER(c_int), POINTER(c_int), c_ulong, c_ulong, c_ulong, c_int, c_ulong, POINTER(c_double), POINTER(c_int)]
_local_transfer_entropy.restype = POINTER(c_double)

main.py

from transferEntropy import *
 
 
xs = [0, 1, 1, 1, 1, 0, 0, 0, 0]
ys = [0, 0, 1, 1, 1, 1, 0, 0, 0]
 
a = transfer_entropy(xs, ys, k=2)
print(a)

测试结果： 

三、参考资料

1. Transfer entropy - Wikipedia

2. Transfer Entropy - PyInform

3. 机器学习——建立因果连系（传递熵）