Medians of (Randomized) Means and U-statistics

Summary

This Python package contains code to compute Medians of (Randomized) Means and U-statistics. The main functions are MoM (for Median of Means), MoRM (for Median of Randomized Means), MoCU (for Median of Complete U-statistics) and MoIU (for Median of Incomplete U-statistics). They take as input a 2-dimensional array X, and hyperparameters such as the number of blocks K, the size of the blocks B, and possibly the sampling scheme or the kernel for U-statistics. They return the corresponding estimator.

Installation

To install the package, simply clone it, and then do:

$ pip install -e .

To check that everything worked, the command

$ python -c 'import morm'

should not return any error.

Use

Here is a toy example (complete version is available at examples/toy_example.py)

import numpy as np
from morm import MoM, MoRM, MoCU, MoIU

mean, var = 0.0, 1.0
n = 1000
X = np.random.normal(loc=mean, scale=var, size=n).reshape(-1, 1)

K = 10
B = 100

# Mean estimation
mom = MoM(X, K)
morm = MoRM(X, K, B)
print("mean : %s" % mean)
print("mom  : %s" % mom)
print("morm : %s" % morm)

print("\n")

# Variance estimation
mocu = MoCU(X, K, kernel='squared_norm')
moiu = MoIU(X, K, B, kernel='squared_norm')
print("var  : %s" % var)
print("mocu : %s" % mocu)
print("moiu : %s" % moiu)