Question: I have a Pandas DataFrame containing a dataset D of instances drawn from a distribution x. x may be a uniform distribution for example. Now, I want to draw n samples from D, sampled according to some new target_distribution, such as a gaussian, that is in general different than x. How can I do this efficiently? Right now, I sample a value x, subset D such that it contains all x +- eps and sample from that. But this is quite slow when the datasets get bigger. People must have come up with a better solution. Maybe the solution is already good but could be implemented more efficiently? I could split x into strata, which would be faster, but is there a solution without this? My current code, which works fine but is slow (1 min for 30k/100k, but I have 200k/700k or so.) import numpy as np import pandas as pd import numpy.random as rnd from matplotlib import pyplot as plt from tqdm import tqdm n_target = 30000 n_dataset = 100000 x_target_distribution = rnd.normal(size=n_target) # In reality this would be x_target_distribution = my_dataset["x"].sample(n_target, replace=True) df = pd.DataFrame({ 'instances': np.arange(n_dataset), 'x': rnd.uniform(-5, 5, size=n_dataset) }) plt.hist(df["x"], histtype="step", density=True) plt.hist(x_target_distribution, histtype="step", density=True) def sample_instance_with_x(x, eps=0.2): try: return df.loc[abs(df["x"] - x) < eps].sample(1) except ValueError: # fallback if no instance possible return df.sample(1) df_sampled_ = [sample_instance_with_x(x) for x in tqdm(x_target_distribution)] df_sampled = pd.concat(df_sampled_) plt.hist(df_sampled["x"], histtype="step", density=True) plt.hist(x_target_distribution, histtype="step", density=True) 

Answer: Rather than generating new points and finding a closest neighbor in df.x, define the probability that each point should be sampled according to your target distribution. You can use np.random.choice. A million points are sampled from df.x in a second or so for a gaussian target distribution like this: x = np.sort(df.x) f_x = np.gradient(x)*np.exp(-x**2/2) sample_probs = f_x/np.sum(f_x) samples = np.random.choice(x, p=sample_probs, size=1000000)  sample_probs is the key quantity, as it can be joined back to the dataframe or used as an argument to df.sample, e.g.: # sample df rows without replacement df_samples = df["x"].sort_values().sample( n=1000, weights=sample_probs, replace=False, )  The result of plt.hist(samples, bins=100, density=True):  We can also try gaussian distributed x, uniform target distribution x = np.sort(np.random.normal(size=100000)) f_x = np.gradient(x)*np.ones(len(x)) sample_probs = f_x/np.sum(f_x) samples = np.random.choice(x, p=sample_probs, size=1000000)   The tails would look more uniform if we increased the bin size; this is an artifact that D is sparse at the edges. comments This approach basically computes the probability of sampling any x_i as the span of x associated with x_i and the probability density in the neighborhood: prob(x_i) ~ delta_x*rho(x_i) A more robust treatment would be to integrate rho over the span delta_x associated with each x_i. Also note that there will be error if the delta_x term is ignored, as can be seen below. It would be much worse if the original x_i wasn't approximately uniformly sampled: