2016/07/15 by Joe Suzuki, Suzuki, Joe · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1607.04427
openalex publication_date 2016/07/15 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28
In Bayesian network structure learning (BNSL), we need the prior probability over structures and parameters. If the former is the uniform distribution, the latter determines the correctness of BNSL. In this paper, we compare BDeu (Bayesian Dirichlet equivalent uniform) and Jeffreys' prior w.r.t. their consistency. When we seek a parent set U of a variable X, we require regularity that if H(X|U)≤ H(X|U') and U\subsetneq U', then U should be chosen rather than U'. We prove that the BDeu scores violate the property and cause fatal situations in BNSL. This is because for the BDeu scores, for any sample size n,there exists a probability in the form P(X,Y,Z)=P(XZ)P(YZ)/P(Z) such that the probability of deciding that X and Y are not conditionally independent given Z is more than a half. For Jeffreys' prior, the false-positive probability uniformly converges to zero without depending on any parameter values, and no such an inconvenience occurs.