varvar

Python package to model variance in different ways

Multiplicative variance trees and the varvar algorithm

varvar is a greedy algorithm for multiplicative variance trees.

varvar is to variance as lightgbm/xgboost/... are to expectation.

There are currently two implementations of varvar algorithms:

1. using quantile search at every split (in varvar.qtrees)
2. using histograms, with binning before starting (in varvar.htrees)

Quantile search is much slower, but can be more accurate.

This is similar to the "exact" and "hist" modes in xgboost, except our "exact" algorithm goes over a small (exact) subset of each feature.

Both implementation modules have a multiplicative_variance_trees function.

Use varvar.predict for prediction.

The trees are returned as plain python types and can be serialized with pickle or even as json.

Here is an example:

from varvar.htrees import multiplicative_variance_trees
from varvar import predict
import numpy as np

random = np.random.RandomState(1729)
n = 200000
x = random.uniform(-1000, 1000, n)
correct_threshold = 300
sigma = 1 * (x <= correct_threshold) + 30 * (x > correct_threshold)
e = sigma * random.randn(n)

trees = multiplicative_variance_trees(
    [x], e**2,
    num_trees=1, max_depth=1, mingain=1, learning_rate=1,
    q=np.linspace(0, 1, 100)[1:-1]
)
preds = predict(trees, [x])

found_threshold = trees[1][0][1]
print(correct_threshold, found_threshold)  # 300, 295
print(np.sqrt(min(preds)), np.sqrt(max(preds)))  # 1, 30

conversion to xgboost booster

You can convert multiplicative variance trees to an xgboost booster.

This allows you to use xgboost's predict function (which actually seems to be a bit slower), and more importantly to use the shap package to interpret varvar predictions.

from varvar import mvt_to_xgboost
booster = mvt_to_xgboost(trees)

You need xgboost installed to run this code.