我正在使用真实数据或sklearn生成的数据集测试此代码。在这两种情况下，如果模型中的因子数量小于6，则代码可以正常工作而不会出错。有7个因素，我得到一个错误：
RuntimeWarning: overflow encountered in square return np.mean((y_true - y_pred)**2)
在超过9个因素的情况下，我已经得到了几个错误，预测值变成了Nan:
RuntimeWarning: overflow encountered in reduce
return ufunc.reduce(obj, axis, dtype, out, **passkwargs)
RuntimeWarning: overflow encountered in square
return np.mean((y_true - y_pred)**2)
很明显，问题出在维度上，因为当变量数量增加时会出现错误，但我不知道如何解决。我已经在使用np.float64(类似问题的建议(，但它没有帮助。我附上了整个代码(是的，它远非完美，因为我对编程相对陌生(
import numpy as np
import copy
from itertools import *
def MSE(y_true, y_pred):
return np.mean((y_true - y_pred)**2)
def weight_mult(c, weights):
r = copy.deepcopy(c)
for idx, num in enumerate(weights):
r[idx] = r[idx] * num
return r
def power_factors(X, deg):
X_power = []
for x in X:
x_power = x**deg
X_power.append(x_power)
return np.array(X_power)
def normalise_x(X):
X_norm = []
for x in X.T:
min_idx = np.argmin(x)
x -= x[min_idx]
max_idx = np.argmax(x)
x = x/x[max_idx]
X_norm.append(x)
return np.array(X_norm).T
def normalise_y(X):
min_idx = np.argmin(X)
X -= X[min_idx]
max_idx = np.argmax(X)
X = X/X[max_idx]
return X
class TakagiSugeno:
def __init__(self, cluster_n=2, lr=0.01, n_iters=1500):
self.lr = lr
self.n_iters = n_iters
self.weights = None
self.bias = None
self.weights_best = None
self.bias_best = None
self.combination_best = None
self.cluster_n = cluster_n
def fit(self, X, y, cluster_w):
power_degree = np.arange(self.cluster_n)
power_degree += 1
models_list = [[], [], [], []]
for combination in permutations(power_degree):
X_polynom = []
for c in combination:
X_power = power_factors(X, c)
X_polynom.append(X_power)
self.model_estimation(X_polynom, y, cluster_w)
y_pred = self.y_estimation(X_polynom, cluster_w)
mse = MSE(y, y_pred)
models_list[0].append(copy.deepcopy(self.weights))
models_list[1].append(copy.deepcopy(self.bias))
models_list[2].append(mse)
models_list[3].append(combination)
best_model = np.argmin(models_list[2])
self.weights_best = models_list[0][best_model]
self.bias_best = models_list[1][best_model]
self.combination_best = models_list[3][best_model]
def model_estimation(self, X_polynom, y, cluster_w):
n_samples, n_features = X_polynom[0].shape
self.weights = np.zeros((self.cluster_n, n_features))
self.bias = np.zeros(self.cluster_n)
for _ in range(self.n_iters):
y_predicted = np.zeros(n_samples)
for c in range(self.cluster_n):
# evaluate y
y_pred_cluster = np.dot(X_polynom[c], self.weights[c]) + self.bias[c]
weighted_y_pred = weight_mult(y_pred_cluster, cluster_w[c])
y_predicted += weighted_y_pred
for c in range(self.cluster_n):
# multiple grad count
dw = (2 / n_samples) * np.dot(weight_mult(X_polynom[c], cluster_w[c]).T, (y_predicted - y))
db = (2 / n_samples) * np.sum(weight_mult((y_predicted - y), cluster_w[c]))
# weights update
self.weights[c] -= self.lr * dw
self.bias[c] -= self.lr * db
def y_estimation(self, X_polynom, cluster_w):
y_predicted = np.zeros(len(X_polynom[0]))
for c in range(self.cluster_n):
# evaluate y
y_pred_cluster = np.dot(X_polynom[c], self.weights[c]) + self.bias[c]
weighted_y_pred = weight_mult(y_pred_cluster, cluster_w[c])
y_predicted += weighted_y_pred
return y_predicted
def predict(self, X, cluster_w):
y_predicted = np.zeros(len(X))
X_polynom = []
for c in self.combination_best:
X_power = power_factors(X, c)
X_polynom.append(X_power)
for c in range(self.cluster_n):
# evaluate y
y_pred_cluster = np.dot(X_polynom[c], self.weights_best[c]) + self.bias_best[c]
weighted_y_pred = weight_mult(y_pred_cluster, cluster_w[c])
y_predicted += weighted_y_pred
return y_predicted
if __name__ == '__main__':
import matplotlib.pyplot as plt
from sklearn import datasets
# Prepare data
X_numpy, y_numpy = datasets.make_regression(n_samples=100, n_features=10, noise=20, random_state=1)
# Normalisation
X_norm = np.array(normalise_x(X_numpy), dtype=np.float64)
y_norm = np.array(normalise_y(y_numpy), dtype=np.float64)
# Create y
y_sq = power_factors(y_norm, 2)
y = y_norm * 0.6 + y_sq * 0.4
# Create membership matrix
membership = np.zeros((len(X_norm), 2))
membership[:, 0] = 0.6
membership[:, 1] = 0.4
membership = np.array(membership, dtype=np.float64)
membership = membership.T
# training loop
model = TakagiSugeno(lr=1, n_iters=1000)
model.fit(X_norm, y, membership)
y_pred = model.predict(X_norm, membership)
我自己发现了这个问题。代码本身没有错误，但它使用梯度下降进行优化。我将学习率设置为1和2000次迭代。当然，这太过分了，而且正在进行再培训。梯度继续不受控制地增长，我得到了巨大的价值。最好的解决方案是设置一个停止标准。