MWU Calibration

Streaming probability calibration via multiplicative weights.

Installation

pip install streamcal

For development:

pip install -e ".[dev]"

The Problem

ML models output probabilities that are often miscalibrated—a predicted 70% doesn't mean 70% of those cases are positive. Batch calibrators (Platt scaling, isotonic regression) require periodic refits, creating a compute-drift tradeoff.

MWU maintains per-bucket bias factors with O(#buckets) cost per batch, adapting continuously without offline retraining.

Method

Maintain bias factors $c_b$ per bucket. After each batch:

$$c_b \leftarrow c_b \cdot \exp(-\eta \cdot (\bar{p}_b - \bar{y}_b))$$

where $\bar{p}_b$ is the mean calibrated probability and $\bar{y}_b$ is the observed outcome rate in bucket $b$.

Results

Semi-synthetic experiments (LightGBM base model, linear drift, B=50 buckets):

Method	Brier	ECE	CPU ms/batch
MWU	0.133	0.070	0.08
Platt	0.129	0.043	4.92
Isotonic	0.128	0.043	4.36

MWU is 61× faster than Platt while achieving comparable Brier scores.

Usage

from streamcal import MWUCalibrator

cal = MWUCalibrator(n_buckets=50, eta=0.1)

for p_raw, y in data_stream:
    p_calibrated = cal.update(p_raw, y)

Available Calibrators

Streaming (online):

• MWUCalibrator - Multiplicative Weights Update
• OnlineSGD - Online SGD with additive updates
• PerBucketEMA - Per-bucket exponential moving average

Batch (refit on accumulated data):

• PlattScaling - Logistic regression on logits
• IsotonicCalibrator - Isotonic regression
• TemperatureScaling - Temperature scaling

Metrics

from streamcal import brier_score, expected_calibration_error

brier = brier_score(y_true, y_pred)
ece = expected_calibration_error(y_true, y_pred, n_bins=20)

Reproduce Experiments

pip install -e ".[experiments]"
python experiments/run_experiments.py
python experiments/generate_figures.py

Paper

See ms/mwu_calibration.pdf for theory and full results.

Related Work

This uses the same MWU/mirror descent algorithm as onlinerake (survey weighting), applied to probability calibration instead of sample reweighting.

License

MIT