AI算法Python实现：Transfer entropy
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 npfrom ctypes import byref, c_int, c_ulong, c_double, POINTER
from pyinform import _inform
from pyinform.error import ErrorCode, error_guarddef transfer_entropy(source, target, k, condition=None, local=False):"""Compute the local or average transfer entropy from one time series toanother with target history length *k*. Optionally, time series can beprovided 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 Noneif 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:passelif 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 Noneif 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 = 0elif cs.ndim == 1 or (cs.ndim == 2 and xs.ndim == 2):z = 1elif 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.shapee = 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）
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