Search Results for « Causal Bayesian Optimization »

Abstract Safe intervention optimization becomes difficult when several objectives must be improved while costly constraint violations are avoided under an uncertain causal graph. Existing causal Bayesian optimization methods often condition on a known graph or on a single estimated graph, which can make both the causal prior and the safety boundary overconfident. This study introduces conformal risk-calibrated low-tail structural multi-objective causal Bayesian optimization (CRC-LS-MOCBO), a sequential optimizer that carries candidate-graph uncertainty through the causal prior, residual surrogate, risk aggregation and acquisition step. Candidate graphs are learned from bootstrap samples and weighted by stability and relative fit. For each graph, a causal prior is combined with a residual Gaussian-process surrogate; objective gains are aggregated by graph weights, whereas constraint risk is screened by a low-tail structural rule and an online conformal buffer. In 600 runs on four synthetic or semi-synthetic benchmarks, CRC-LS-MOCBO achieved an average safe hypervolume of 4.326 and a violation rate of 0.0070. It outperformed the noncausal and random-search baselines and reduced violations relative to a single MAP causal prior. The method is therefore best viewed as a conservative and reproducible template for limited-budget safe intervention search under structural uncertainty, rather than as a substitute for accurate causal knowledge.

Abstract Bayesian causal inference in randomized experiments usually imposes model-based structure on potential outcomes. Yet causal inferences from randomized experiments are especially credible because they depend on a known assignment process, not a probability model of potential outcomes. In this article, I derive a randomization-based procedure for Bayesian inference of causal effects in a finite population setting. I formally show that this procedure satisfies Bayesian analogues of unbiasedness and consistency under weak conditions on a prior distribution. Unlike existing model-based methods of Bayesian causal inference, my procedure supposes neither probability models that generate potential outcomes nor independent and identically distributed random sampling. Unlike existing randomization-based methods of Bayesian causal inference, my procedure does not suppose that potential outcomes are discrete and bounded. Consequently, researchers can reap the benefits of Bayesian inference without sacrificing the properties that make inferences from randomized experiments especially credible in the first place.

Objective: Differentiable causal discovery methods produce point estimates of directed acyclic graphs (DAGs) but lack uncertainty quantification. Existing uncertainty-aware methods are limited to d ≤ 50 due to O(d 3) complexity, while genomic studies routinely profile d ≥ 500 genes. We develop a Bayesian bootstrap ensemble of low-rank models to produce posterior edge probabilities under a Dirichlet process prior (Rubin 1981). Results: Low-rank factorization (W = U V ⊤ , r ≪ d) reduces the DAG constraint from O(d 3) to O(dr 2). Dirichlet-weighted Bayesian bootstrap across 20-50 training runs yields ensemble distributions over the adjacency matrix, outperforming standard resampling-based bootstrap on difficult configurations: at d = 50, standard bootstrap detects zero edges (F1 = 0.000) while the Bayesian bootstrap recovers edges (F1 = 0.025); at d = 200, the Bayesian bootstrap more than doubles F1 (0.080 vs. 0.034; Supplementary Table S4). On synthetic Erdős-Rényi DAGs (d = 30-500), expected calibration error (ECE) decreases from 0.036 at d = 30 (comparable to DiBS at 0.038) to 0.003 at d = 500, where DiBS is inapplicable. On TCGA BRCA expression data (d = 500, n = 1,218), the 21 edges with posterior probability exceeding baseline (P > 0.1, out of 250,000 candidates) achieve 71.4% combined STRING protein-protein interaction validation precision (vs. 10.6% baseline)-a 6.7-fold enrichment.