python中多元核密度估计的条件抽样

Question

可以创建一个多元核密度估计 (KDE) scikitlearn (https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KernelDensity.html#sklearn.neighbors.KernelDensity) 和 scipy (https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gaussian_kde.html)

两者都允许从估计分布中进行随机抽样。有没有办法在两个库（或任何其他库）中的任何一个中进行条件采样？ 在 2 变量 (x,y) 的情况下，这意味着来自 P(x|y)（或 P(y|x)）的样本，因此来自概率函数的横截面（并且该横截面必须重新缩放到其曲线下的单位面积）。

x = np.random.random(100)
y =np.random.random(100)
kde = stats.gaussian_kde([x,y])
# sampling from the whole pdf:
kde.resample()

我正在寻找类似的东西

# sampling y, conditional on x
kde.sample_conditional(x=1.5) #does not exist

Answer 1

此函数根据所有其他列有条件地对一列进行采样。

def conditional_sample(kde, training_data, columns, values, samples = 100):
    if len(values) - len(columns) != 0:
        raise ValueError("length of columns and values should be equal")
    if training_data.shape[1] - len(columns) != 1:
        raise ValueError(f'Expected {training_data.shape[1] - 1} columns/values but {len(columns)} have be given')  
    cols_values_dict = dict(zip(columns, values))
    
    #create array to sample from
    steps = 10000  
    X_test = np.zeros((steps,training_data.shape[1]))
    for i in range(training_data.shape[1]):
        col_data = training_data.iloc[:, i]
        X_test[:, i] = np.linspace(col_data.min(),col_data.max(),steps)
    for col in columns: 
        idx_col_training_data = list(training_data.columns).index(col)
        idx_in_values_list = list(cols_values_dict.keys()).index(col)
        X_test[:, idx_col_training_data] = values[idx_in_values_list] 
        
    #compute probability of each sample
    prob_dist = np.exp(kde.score_samples(X_test))/np.exp(kde.score_samples(X_test)).sum()
    
    #sample using np.random.choice
    return X_test[np.random.choice(range(len(prob_dist)), p=prob_dist, size = (samples))]

Answer 2

此函数适用于只有一维条件的用例。它的构建方式不需要完全满足条件，但有一定的容忍度。

from scipy import stats
import numpy as np

x = np.random.random(1000)
y = np.random.random(1000)
kde = stats.gaussian_kde([x,y])

def conditional_sample(kde, condition, precision = 0.5,  sample_size = 1000):

    block_size = int(sample_size / (2 * precision / 100))
    sample = kde.resample(block_size)

    lower_limit = np.percentile(sample[-1], stats.percentileofscore(sample[-1], condition) - precision)
    upper_limit = np.percentile(sample[-1], stats.percentileofscore(sample[-1], condition) + precision)

    conditional_sample = sample[:, (upper_limit > sample[-1]) * (sample[-1] > lower_limit)]

    return conditional_sample[0:-1]

conditional_sample(kde=kde, condition=0.6)

不是通用解决方案，但对我的用例很有效。