Three Approaches to Probability Model Selection
This work addresses model selection for researchers and practitioners in statistics and AI, offering a computationally efficient method, though it is incremental as it builds on existing penalized likelihood frameworks.
This paper tackles the problem of selecting probability models for data by comparing three approaches based on penalized likelihood, showing that the third approach reduces to the second under specific conditions and is applicable even when models lack physical interpretation. It illustrates these methods using Gaussian mixture models, highlighting the third approach's utility in AI applications due to its computational focus.
This paper compares three approaches to the problem of selecting among probability models to fit data (1) use of statistical criteria such as Akaike's information criterion and Schwarz's "Bayesian information criterion," (2) maximization of the posterior probability of the model, and (3) maximization of an effectiveness ratio? trading off accuracy and computational cost. The unifying characteristic of the approaches is that all can be viewed as maximizing a penalized likelihood function. The second approach with suitable prior distributions has been shown to reduce to the first. This paper shows that the third approach reduces to the second for a particular form of the effectiveness ratio, and illustrates all three approaches with the problem of selecting the number of components in a mixture of Gaussian distributions. Unlike the first two approaches, the third can be used even when the candidate models are chosen for computational efficiency, without regard to physical interpretation, so that the likelihood and the prior distribution over models cannot be interpreted literally. As the most general and computationally oriented of the approaches, it is especially useful for artificial intelligence applications.