isodistrreg: Python bindings

Python bindings for Isotonic Distributional Regression (IDR) and Survival-IDR (S-IDR), built with PyO3 and maturin. See the main README for background.

Installation

pip install isodistrreg

Pre-built wheels are provided for Linux, macOS, and Windows on CPython 3.13+. On other platforms pip builds from the source distribution, which requires a Rust toolchain.

The scikit-learn–compatible estimator is available through an optional extra:

pip install "isodistrreg[scikit-learn]"

Examples

We use numpy to set up a toy problem, but plain python lists can also be used.

Precision

CDF outputs (cdf, cdf_at, cdf_grid) are always np.float32. Covariates and thresholds are stored at the dtype of the input arrays passed to IDR(...): float32 inputs stay float32, float64 inputs stay float64, and .X / .thresholds return zero-copy views at the storage dtype. See the docstring on IDR.cdf and IDR.from_cdfs in _core.pyi for the full rules.

Example 1: Covariate 1-dimensional, outcome censored

import numpy as np
# we visualize with matplotlib
from matplotlib import pyplot as plt
from isodistrreg import IDR

# Generate an instance of increasing conditional CDFs with censoring, and a one-dimensional covariate
n = 500
rng = np.random.default_rng(seed=123)
x = rng.uniform(size=n)
y = x + rng.uniform(size=n)
c = x + rng.uniform(size=n)

t = np.minimum(y, c)
d = y <= c

# Fit the IDR / S-IDR model, censoring is indicated by "False"
fit = IDR(t, x, d)

# Sorted and deduplicated covariates and thresholds are available
sorted_x = fit.X
sorted_y = fit.thresholds

# Estimate and plot the complete distributional estimate
cdf_for_each_x = fit.cdf(sorted_x)
def plot_cdfs_nicely(cdfs, centers, times):
    """Plot a picture with the right scale; plt.imshow is simpler, but spacing along the axis is not to scale"""
    plt.pcolormesh(
        [centers[0] - (centers[1] - centers[0]) / 2]
            + list((centers[1:] + centers[:-1]) / 2)
            + [centers[-1] + (centers[-1] - centers[-2]) / 2],
        list(times) + [times[-1] + (times[-1] - times[0]) / len(times)],
        cdfs.T,
        vmin=0.0,
        vmax=1.0,
    )
plot_cdfs_nicely(cdf_for_each_x, sorted_x, sorted_y)
plt.colorbar()

# Estimate and plot the mean
mean_for_each_x = fit.predict(sorted_x)
# Due to censoring, the estimated sub-CDF may not always have a mean
plt.plot(sorted_x, sorted_x + 0.5, color="lightblue", label="true mean")
plt.plot(sorted_x, mean_for_each_x, color="red", label="mean")

# Estimate and plot quantiles
probabilities = np.array([0.2, 0.8])
quantiles = fit.quantile(sorted_x[:, np.newaxis], probabilities)
plt.plot(sorted_x, quantiles, label=[f"{p} quantile" for p in probabilities])

plt.legend(loc="lower right")
plt.show()

Example 2: Covariate 3-dimensional

import numpy as np
from isodistrreg import IDR

## toy data (3-dimensional covariate)
X = np.column_stack([np.arange(1, 5)] * 3)
y = np.array([1, 0, 2, 2])

## fit
idr_fit = IDR(X = X, y = y)

## get CDF for new x at all relevant thresholds
new_x = np.array([[1, 1, 1], [1.5, 1.5, 1.5]])
idr_fit.cdf(new_x) # (one CDF per row = per x)

## broadcasting
idr_fit.cdf_at(new_x, 0) # (evaluate CDF at 0 for all covariates)
idr_fit.cdf_at(new_x, [0,1]) # (evaluate CDF for x1 at 0, x2 at 1)
idr_fit.cdf_at(new_x, np.column_stack([[1, 2, 3], [0, 1, 2]])) # (CDF at 1,2,3 for x1, and 0,1,2 for x2)

## same for quantiles
idr_fit.quantile(new_x, 0.5)
idr_fit.quantile(new_x, [0.25, 0.5])
idr_fit.quantile(new_x, np.column_stack([[0.25, 0.5, 0.75], [0.1, 0.2, 0.3]]))

# Fast grid evaluation for 1-dimensional covariate
X = np.arange(5)
y = np.arange(5)
idr_fit = IDR(X = X, y = y)
idr_fit.cdf_grid(X, y) # (CDF at all covariate-threshold-combinations)

References

Henzi, A., Ziegel, J. and Gneiting, T. (2021). Isotonic distributional regression. J R Stat Soc Series B, 83: 963–993. https://doi.org/10.1111/rssb.12450

Henzi, A., Moesching, A. and Duembgen, L. (2022). Accelerating the Pool-Adjacent-Violators Algorithm for Isotonic Distributional Regression. Methodol Comput Appl Probab. https://doi.org/10.1007/s11009-022-09937-2

Bladt, M., Henzi, A., van den Heuvel, B. and Ziegel, J. (2026). Survival Isotonic Distributional Regression. arXiv preprint arXiv:2608.02914. https://arxiv.org/abs/2608.02914