BGM - A Bayesian Generative Modeling Approach for Arbitrary Conditional Inference

BGM is the foundational model family in bayesgm for arbitrary conditional inference in high-dimensional settings.

With a trained BGM model, users can perform inference under any observed/missing patterns without retraining from scratch.

BGM applicability

  • Train once, infer under multiple conditioning patterns.

  • Obtain posterior samples for missing or unobserved components.

  • Produce posterior interval estimates in addition to point predictions.

  • Support conditional prediction with prediction intervals (e.g., conformal prediction).

Method highlights

  1. BGM combines Bayesian principles with modern AI techniques for arbitrary conditional inference.

  2. BGM provides significant flexibility and scalability to efficiently handle large, high-dimensional datasets.

  3. BGM outperforms leading conformal prediction methods inpredictive accuracy and calibrated uncertainty quantification.

Quickstart

import yaml
import numpy as np
from sklearn.model_selection import train_test_split
from bayesgm.models import BGM
from bayesgm.datasets import simulate_z_hetero

params = yaml.safe_load(open("src/configs/Sim_heteroskedastic.yaml", "r"))
X, Y = simulate_z_hetero(n=20000, k=10, d=params["x_dim"] - 1)
X_train, X_test, Y_train, _ = train_test_split(X, Y, test_size=0.1, random_state=123)
data_train = np.c_[X_train, Y_train].astype("float32")

# Instantiate a BGM model
model = BGM(params=params, random_seed=None)

# Train the BGM model with EGM initialization and iterative updating algorithm
model.fit(data=data_train, epochs=200, epochs_per_eval=10, use_egm_init=True, egm_n_iter=50000, egm_batches_per_eval=500, verbose=1)

# Prepare test data with missing values
data_test = np.hstack([X_test, np.full((X_test.shape[0], 1), np.nan)])

# Make predictions using the trained BGM model
data_x_pred, pred_interval = model.predict(
    data=data_test, alpha=0.05, n_mcmc=5000, step_size=0.01, seed=42
)

Main reference

  • Qiao Liu and Wing Hung Wong (2026), A Bayesian Generative Modeling Approach for Arbitrary Conditional Inference. arXiv.

Tutorials