# 引用 https://www.kaggle.com/code/treename/janestreet-cv-method-combpurgedkfoldcv/notebook
import itertools as itt
import numbers
import numpy as np
import pandas as pd
from abc import abstractmethod
from typing import Iterable, Tuple, List
class BaseTimeSeriesCrossValidator:
"""
Abstract class for time series cross-validation.
Time series cross-validation requires each sample has a prediction time pred_time, at which the features are used to
predict the response, and an evaluation time eval_time, at which the response is known and the error can be
computed. Importantly, it means that unlike in standard sklearn cross-validation, the samples X, response y,
pred_times and eval_times must all be pandas dataframe/series having the same index. It is also assumed that the
samples are time-ordered with respect to the prediction time (i.e. pred_times is non-decreasing).
Parameters
----------
n_splits : int, default=10
Number of folds. Must be at least 2.
"""
def __init__(self, n_splits=10):
if not isinstance(n_splits, numbers.Integral):
raise ValueError(f"The number of folds must be of Integral type. {n_splits} of type {type(n_splits)}"
f" was passed.")
n_splits = int(n_splits)
if n_splits <= 1:
raise ValueError(f"K-fold cross-validation requires at least one train/test split by setting n_splits = 2 "
f"or more, got n_splits = {n_splits}.")
self.n_splits = n_splits
self.pred_times = None
self.eval_times = None
self.indices = None
@abstractmethod
def split(self, X: pd.DataFrame, y: pd.Series = None,
pred_times: pd.Series = None, eval_times: pd.Series = None):
if not isinstance(X, pd.DataFrame) and not isinstance(X, pd.Series):
raise ValueError('X should be a pandas DataFrame/Series.')
if not isinstance(y, pd.Series) and y is not None:
raise ValueError('y should be a pandas Series.')
if not isinstance(pred_times, pd.Series):
raise ValueError('pred_times should be a pandas Series.')
if not isinstance(eval_times, pd.Series):
raise ValueError('eval_times should be a pandas Series.')
if y is not None and (X.index == y.index).sum() != len(y):
raise ValueError('X and y must have the same index')
if (X.index == pred_times.index).sum() != len(pred_times):
raise ValueError('X and pred_times must have the same index')
if (X.index == eval_times.index).sum() != len(eval_times):
raise ValueError('X and eval_times must have the same index')
self.pred_times = pred_times
self.eval_times = eval_times
self.indices = np.arange(X.shape[0])
class CombPurgedKFoldCV(BaseTimeSeriesCrossValidator):
"""
Purged and embargoed combinatorial cross-validation
As described in Advances in financial machine learning, Marcos Lopez de Prado, 2018.
The samples are decomposed into n_splits folds containing equal numbers of samples, without shuffling. In each cross
validation round, n_test_splits folds are used as the test set, while the other folds are used as the train set.
There are as many rounds as n_test_splits folds among the n_splits folds.
Each sample should be tagged with a prediction time pred_time and an evaluation time eval_time. The split is such
that the intervals [pred_times, eval_times] associated to samples in the train and test set do not overlap. (The
overlapping samples are dropped.) In addition, an "embargo" period is defined, giving the minimal time between an
evaluation time in the test set and a prediction time in the training set. This is to avoid, in the presence of
temporal correlation, a contamination of the test set by the train set.
Parameters
----------
n_splits : int, default=10
Number of folds. Must be at least 2.
n_test_splits : int, default=2
Number of folds used in the test set. Must be at least 1.
embargo_td : pd.Timedelta, default=0
Embargo period (see explanations above).
"""
def __init__(self, n_splits=10, n_test_splits=2, embargo_td=0):
super().__init__(n_splits)
if not isinstance(n_test_splits, numbers.Integral):
raise ValueError(f"The number of test folds must be of Integral type. {n_test_splits} of type "
f"{type(n_test_splits)} was passed.")
n_test_splits = int(n_test_splits)
if n_test_splits <= 0 or n_test_splits > self.n_splits - 1:
raise ValueError(f"K-fold cross-validation requires at least one train/test split by setting "
f"n_test_splits between 1 and n_splits - 1, got n_test_splits = {n_test_splits}.")
self.n_test_splits = n_test_splits
if embargo_td < 0:
raise ValueError(f"The embargo time should be positive, got embargo = {embargo_td}.")
self.embargo_td = embargo_td
def split(self, X: pd.DataFrame, y: pd.Series = None,
pred_times: pd.Series = None, eval_times: pd.Series = None) -> Iterable[Tuple[np.ndarray, np.ndarray]]:
"""
Yield the indices of the train and test sets.
Although the samples are passed in the form of a pandas dataframe, the indices returned are position indices,
not labels.
Parameters
----------
X : pd.DataFrame, shape (n_samples, n_features), required
Samples. Only used to extract n_samples.
y : pd.Series, not used, inherited from _BaseKFold
pred_times : pd.Series, shape (n_samples,), required
Times at which predictions are made. pred_times.index has to coincide with X.index.
eval_times : pd.Series, shape (n_samples,), required
Times at which the response becomes available and the error can be computed. eval_times.index has to
coincide with X.index.
Returns
-------
train_indices: np.ndarray
A numpy array containing all the indices in the train set.
test_indices : np.ndarray
A numpy array containing all the indices in the test set.
"""
super().split(X, y, pred_times, eval_times)
# Fold boundaries
fold_bounds = [(fold[0], fold[-1] + 1) for fold in np.array_split(self.indices, self.n_splits)]
# List of all combinations of n_test_splits folds selected to become test sets
selected_fold_bounds = list(itt.combinations(fold_bounds, self.n_test_splits))
# In order for the first round to have its whole test set at the end of the dataset
selected_fold_bounds.reverse()
for fold_bound_list in selected_fold_bounds:
# Computes the bounds of the test set, and the corresponding indices
test_fold_bounds, test_indices = self.compute_test_set(fold_bound_list)
# Computes the train set indices
train_indices = self.compute_train_set(test_fold_bounds, test_indices)
yield train_indices, test_indices
def compute_train_set(self, test_fold_bounds: List[Tuple[int, int]], test_indices: np.ndarray) -> np.ndarray:
"""
Compute the position indices of samples in the train set.
Parameters
----------
test_fold_bounds : List of tuples of position indices
Each tuple records the bounds of a block of indices in the test set.
test_indices : np.ndarray
A numpy array containing all the indices in the test set.
Returns
-------
train_indices: np.ndarray
A numpy array containing all the indices in the train set.
"""
# As a first approximation, the train set is the complement of the test set
train_indices = np.setdiff1d(self.indices, test_indices)
# But we now have to purge and embargo
for test_fold_start, test_fold_end in test_fold_bounds:
# Purge
train_indices = purge(self, train_indices, test_fold_start, test_fold_end)
# Embargo
train_indices = embargo(self, train_indices, test_indices, test_fold_end)
return train_indices
def compute_test_set(self, fold_bound_list: List[Tuple[int, int]]) -> Tuple[List[Tuple[int, int]], np.ndarray]:
"""
Compute the indices of the samples in the test set.
Parameters
----------
fold_bound_list: List of tuples of position indices
Each tuple records the bounds of the folds belonging to the test set.
Returns
-------
test_fold_bounds: List of tuples of position indices
Like fold_bound_list, but with the neighboring folds in the test set merged.
test_indices: np.ndarray
A numpy array containing the test indices.
"""
test_indices = np.empty(0)
test_fold_bounds = []
for fold_start, fold_end in fold_bound_list:
# Records the boundaries of the current test split
if not test_fold_bounds or fold_start != test_fold_bounds[-1][-1]:
test_fold_bounds.append((fold_start, fold_end))
# If the current test split is contiguous to the previous one, simply updates the endpoint
elif fold_start == test_fold_bounds[-1][-1]:
test_fold_bounds[-1] = (test_fold_bounds[-1][0], fold_end)
test_indices = np.union1d(test_indices, self.indices[fold_start:fold_end]).astype(int)
return test_fold_bounds, test_indices
def compute_fold_bounds(cv: BaseTimeSeriesCrossValidator, split_by_time: bool) -> List[int]:
"""
Compute a list containing the fold (left) boundaries.
Parameters
----------
cv: BaseTimeSeriesCrossValidator
Cross-validation object for which the bounds need to be computed.
split_by_time: bool
If False, the folds contain an (approximately) equal number of samples. If True, the folds span identical
time intervals.
"""
if split_by_time:
full_time_span = cv.pred_times.max() - cv.pred_times.min()
fold_time_span = full_time_span / cv.n_splits
fold_bounds_times = [cv.pred_times.iloc[0] + fold_time_span * n for n in range(cv.n_splits)]
return cv.pred_times.searchsorted(fold_bounds_times)
else:
return [fold[0] for fold in np.array_split(cv.indices, cv.n_splits)]
def embargo(cv: BaseTimeSeriesCrossValidator, train_indices: np.ndarray,
test_indices: np.ndarray, test_fold_end: int) -> np.ndarray:
"""
Apply the embargo procedure to part of the train set.
This amounts to dropping the train set samples whose prediction time occurs within self.embargo_dt of the test
set sample evaluation times. This method applies the embargo only to the part of the training set immediately
following the end of the test set determined by test_fold_end.
Parameters
----------
cv: Cross-validation class
Needs to have the attributes cv.pred_times, cv.eval_times, cv.embargo_dt and cv.indices.
train_indices: np.ndarray
A numpy array containing all the indices of the samples currently included in the train set.
test_indices : np.ndarray
A numpy array containing all the indices of the samples in the test set.
test_fold_end : int
Index corresponding to the end of a test set block.
Returns
-------
train_indices: np.ndarray
The same array, with the indices subject to embargo removed.
"""
if not hasattr(cv, 'embargo_td'):
raise ValueError("The passed cross-validation object should have a member cv.embargo_td defining the embargo"
"time.")
last_test_eval_time = cv.eval_times.iloc[cv.indices[:test_fold_end]].max()
min_train_index = len(cv.pred_times[cv.pred_times <= last_test_eval_time + cv.embargo_td])
if min_train_index < cv.indices.shape[0]:
allowed_indices = np.concatenate((cv.indices[:test_fold_end], cv.indices[min_train_index:]))
train_indices = np.intersect1d(train_indices, allowed_indices)
return train_indices
def purge(cv: BaseTimeSeriesCrossValidator, train_indices: np.ndarray,
test_fold_start: int, test_fold_end: int) -> np.ndarray:
"""
Purge part of the train set.
Given a left boundary index test_fold_start of the test set, this method removes from the train set all the
samples whose evaluation time is posterior to the prediction time of the first test sample after the boundary.
Parameters
----------
cv: Cross-validation class
Needs to have the attributes cv.pred_times, cv.eval_times and cv.indices.
train_indices: np.ndarray
A numpy array containing all the indices of the samples currently included in the train set.
test_fold_start : int
Index corresponding to the start of a test set block.
test_fold_end : int
Index corresponding to the end of the same test set block.
Returns
-------
train_indices: np.ndarray
A numpy array containing the train indices purged at test_fold_start.
"""
time_test_fold_start = cv.pred_times.iloc[test_fold_start]
# The train indices before the start of the test fold, purged.
train_indices_1 = np.intersect1d(train_indices, cv.indices[cv.eval_times < time_test_fold_start])
# The train indices after the end of the test fold.
train_indices_2 = np.intersect1d(train_indices, cv.indices[test_fold_end:])
return np.concatenate((train_indices_1, train_indices_2))
n_split=5
n_test_splits=2
n_purge = 10
embargo_td = 0
t1_ = time_bar.reset_index().index
t1 = pd.Series(t1_).shift(n_purge).fillna(0).astype(int)
t2 = pd.Series(t1_).shift(-n_purge).fillna(1e12).astype(int)
cpcv = CombPurgedKFoldCV(n_splits=n_split, n_test_splits=n_test_splits, embargo_td=embargo_td)
cv = list(cpcv.split(time_bar.reset_index(), pred_times=t1, eval_times=t2))
i = 1
print(f'グループ数{n_split}')
print(f'交差検証の組み合わせ数{n_split*(n_split-1)/2}')
for train_idx, val_idx in cv:
plot_cv(time_bar,
train_idx,
val_idx,
i=i,
n=n_split * (n_split - 1) / 2,
figsize=(10, 14))
i += 1
plt.show()
def CPCV(df, n_split=5, n_purge=5):
"""CPCV用のK-Fold
Parameters:
----------
df: pd.DataFrame
特徴量と目的変数を格納したDataFrame
n_split: int
CVの分割数
n_purge: int
パージングする数
Returns:
----------
ret: list
以下の要素を持ったリスト
- train_idx: list
学習期間のインデックス
- val_idx1: list
一つ目の検証期間のインデックス
- val_idx2: list
二つ目の検証期間のインデックス
"""
length = len(df)
idx = list(range(length))
ret = []
split_idx = [int(length * i / n_split) for i in range(n_split + 1)]
for i in range(n_split):
for j in range(i + 1, n_split):
val_from1 = split_idx[i]
val_to1 = split_idx[i + 1]
val_from2 = split_idx[j]
val_to2 = split_idx[j + 1]
val_idx1 = idx[val_from1:val_to1]
val_idx2 = idx[val_from2:val_to2]
train_idx = []
if val_from1 - n_purge > 1:
train_idx += idx[:val_from1 - n_purge]
if val_to1 + n_purge < val_from2 - n_purge:
train_idx += idx[val_to1 + n_purge:val_from2 - n_purge]
if val_to2 + n_purge < len(idx):
train_idx += idx[val_to2 + n_purge:]
ret.append([train_idx, val_idx1, val_idx2])
return ret
# CPCV法
n_split = 5
cv = CPCV(time_bar, n_split=n_split, n_purge=10)
i = 1
print(f'グループ数{n_split}')
print(f'交差検証の組み合わせ数{n_split*(n_split-1)/2}')
for train_idx, val_idx1, val_idx2 in cv:
plot_cv(time_bar,
train_idx,
val_idx1 + val_idx2,
i=i,
n=n_split * (n_split - 1) / 2,
figsize=(10, 14))
i += 1
plt.show()
# バックテスト経路の作成
def get_backtest_path(df, features, y, model, n_path=5, n_purge=5):
"""
1. 経路生成数n_pathに基づき，cpcvを実行
2. modelを受け取り学習
3. 学習済みモデルの推論結果をretに保存する
Parameters:
----------
df: pd.DataFrame
特徴量と目的変数を格納したDataFrame
features: list
予測に使用する列名が入ったリスト
y: str
dfに含まれる目的変数名
model:
fitとpredictメソッドを持つ機械学習モデル
n_path: int
バックテスト経路数
n_purge: int
パージングする数
Returns:
----------
ret: pd.DataFrame
各バックテスト経路分の予測結果を持ったデータフレーム
各列は，バックテストの経路番号を表す
"""
n_split = n_path + 1
cv = CPCV(df, n_split=n_split, n_purge=n_purge)
# 結果格納用のDataFrame
ret = df[[y]].copy()
for i in range(n_path):
ret.loc[:, i] = np.nan
for train_idx, val_idx1, val_idx2 in cv:
train_idx = df.index[train_idx]
val_idx1 = df.index[val_idx1]
val_idx2 = df.index[val_idx2]
model.fit(df.loc[train_idx, features], df.loc[train_idx, y])
for i in range(n_path): # 対象Foldが未格納のカラムに格納する
if np.isnan(ret.loc[val_idx1[0], i]):
ret.loc[val_idx1, i] = model.predict(df.loc[val_idx1,
features])
break
for i in range(n_path):
if np.isnan(ret.loc[val_idx2[0], i]):
ret.loc[val_idx2, i] = model.predict(df.loc[val_idx2,
features])
break
return ret
