2025/05/22 by Masanari Kimura, Kimura, Masanari, Howard D. Bondell +1
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Mechanics and Entropy #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.2505.16244
openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The power prior is a class of informative priors designed to incorporate historical data alongside current data in a Bayesian framework. It includes a power parameter that controls the influence of historical data, providing flexibility and adaptability. A key property of the power prior is that the resulting posterior minimizes a linear combination of KL divergences between two pseudo-posterior distributions: one ignoring historical data and the other fully incorporating it. We extend this framework by identifying the posterior distribution as the minimizer of a linear combination of Amari's α-divergence, a generalization of KL divergence. We show that this generalization can lead to improved performance by allowing for the data to adapt to appropriate choices of the α parameter. Theoretical properties of this generalized power posterior are established, including behavior as a generalized geodesic on the Riemannian manifold of probability distributions, offering novel insights into its geometric interpretation.