glassy

glassy explores predictive multiplicity in linear regression: how much model coefficients and predictions can vary while training error stays close to a reference model's error. For squared-error loss, it computes exact ranges over this set of models.

Install

Install from PyPI:

python -m pip install glassy

Quick start

Prism and Spec are separate objects. Prism analyzes the model set; Spec builds concrete models. Initialize both with a fitted linear regressor and the training data:

import numpy as np
from sklearn.linear_model import LinearRegression
from glassy import Prism, Spec

rng = np.random.default_rng(7)
X = rng.normal(size=(100, 3))
y = 2 * X[:, 0] - X[:, 1] + rng.normal(scale=0.5, size=100)

model = LinearRegression().fit(X, y)

# Include models with training MSE up to 5% above the reference model's MSE.
prism = Prism(model, X, y, r=5.0, units="percent")
spec = Spec(model, X, y)

print(prism.coef_bounds())
predictions = prism.disagreement(X)
print(predictions["min"], predictions["optimal"], predictions["max"])
print(prism.query_droppable("feature_2"))

candidate = spec.sans_features("feature_2")
print(candidate.predict(X)[:5])

Prism.from_data(X, y, r=..., units=...) is a convenience constructor that fits an ordinary least squares reference model for you. Radius units are "percent" (relative to the reference model's training MSE) or "raw" (an additive MSE increase).

API overview

• prism.coef_bounds(...) returns coefficient intervals. Set magnitude=True for ranges of absolute coefficient values. mode can be "both", "min", or "max"; features limits the result to selected names.
• prism.disagreement(X=None) returns min, optimal, and max prediction arrays; it uses the training data when X is omitted.
• prism.query_droppable(features) checks whether features can be removed within the loss limit. prism.droppable(max_terms=1) lists removable subsets up to that size; use max_terms=None to search all subset sizes.
• prism.update_r(r, units=None) changes the radius.
• spec = Spec(model, X, y, feature_names=None) creates a model-building object independently of Prism. spec.sans_features(features) returns a fitted sklearn model with the named coefficients fixed at zero and the others refit.
• spec.from_coefs({"feature_0": value}) returns a fitted model with the specified coefficients fixed and the others refit to minimize training MSE.
• spec.mse(model=None, X=None, y=None) computes training or supplied-data MSE; omitted arguments default to the model and data held by spec.
• prism.spec() is an optional convenience method that creates a Spec from the reference model and data already held by that Prism.

For NumPy arrays, feature names default to feature_0, feature_1, and so on. DataFrame column names are preserved.

Scope and requirements

glassy currently supports numeric linear-regression features, an intercept, and squared-error loss. The feature matrix must have full column rank; redundant or constant columns make the model set unbounded and are rejected. Runtime dependencies are NumPy and scikit-learn.

Development

python -m pip install -r requirements.txt
python -m pytest -q

Example notebooks are in demos/.