# How to resample one dataset to conform to the distribution of another dataset?

I have two datasets with 20 features, but with different feature distributions (DS_A and DS_B). How can I sample the DS_A to make its distribution similar to DS_B, with respect to multiple features??

I check the similarity/difference of two datasets by checking individual features from DS_A against DS_B, in shape, and percentiles. Features are mostly numerical, some binary, some normalized.

Background:

Some time ago I trained a model using dataset DS_B as ground truth. Now, I want to retrain the model with more recent data and see if the performance improves. The new ground truth data I collect is DS_A, but due to practical reasons, new data is collected somewhat differently, and hence the feature distribution in the new data set is different from the old data set.

One simple way is to transform your distribution linearly. That should work fine if the distribution of your data has changed approximately linearly.

Question is how to change the distribution of DS_A to match distribution of DS_B, with respect to multiple features?

That being said you could transform your feature distribution DS_A by

1. Substructing mean(DS_A) and add the mean(DS_B)
2. Divide with the standard deviation of DS_A and multiply with the standard deviation of DS_B

Long story short:You change the mean and the standard Deviation of the DS_A distribution to match the DS_B.

Here is a code in python that apply this transformation to two gaussian distributions

import seaborn as sns
import numpy as np
import matplotlib.pyplot as plt

m1, m2 = 0, 10
s1, s2 = 1, 3

x1 = np.random.normal(m1,s1, 1000)
x2 = np.random.normal(m2,s2, 1000)

sns.distplot(x1, hist_kws=dict(alpha=0.1), color='red', label='Distribution 1')
sns.distplot(x2, hist_kws=dict(alpha=0.1), color='green', label='Distribution 2')

estimated_x1_mean = np.mean(x1)
estimated_x1_sd   = np.std(x1)
estimated_x2_mean = np.mean(x2)
estimated_x2_sd   = np.std(x2)

x2_new = (x2 - estimated_x2_mean + estimated_x1_mean)  * estimated_x1_sd / estimated_x2_sd
sns.distplot(x2_new, color='blue', hist_kws=dict(alpha=0.1, edgecolor='black'), label='Distribution 2 after Transformation')
plt.legend()


And the result

• I cannot change the value of features in DS_A, since I am going to use this dataset to retrain my model. How can I sample data from DS_A, and create a smaller dataset, so that the distribution of the new dataset will be similar to DS_b, i.e. the shape of the features and percentiles of each feature. – cybergeek654 Feb 7 '20 at 16:56
• You mentioned that "new data is collected somewhat differently", what do you mean by that? It's crucial in order to help you furher! – Giannis Krilis Feb 7 '20 at 17:43
• I'm working on a recommendation system. After the main recommendation model creates recommendations, I fine-tune the position of the recommendations by a second model, called reranker. To train reranker model I use a ground truth dataset, consisting of several user/reco features and output if the user interacted with reco or not. First time training the reranker model was easy, output of the main recommendation model was presented to users, user reactions were collected and reranker model was trained. Since the reranker module is now in production, my input data are not same as before. – cybergeek654 Feb 10 '20 at 12:22
• The aim is to retrain the reranker. The flow of re-training the reranker model is same as training it in the first place, except the recos that user sees and interacts with are already influenced by the reranker model in production. That's why I want to resample the new data that I collect to match the distribution of the initial training dataset (when reranker was absent). – cybergeek654 Feb 10 '20 at 12:30