The ABC of Model Selection: AIC, BIC and the New CIC
نویسنده
چکیده
The geometric theory of ignorance [1] suggests new criteria for model selection. One example is to choose model M minimizing, CIC = − N ∑ i=1 log p̂(xi)+ d 2 log N 2π + logV + πR N log(d + 1) where (x1, . . . ,xN) is a sample of N iid observations, p̂ ∈ M is the mle, d = dim(M) is the dimension of the model M, V = Vol(M) is its information volume and R = Ricci(M) is the Ricci scalar evaluated at the mle. I study the performance of CIC for the problem of segmentation of bit streams defined as follows: Find n from N iid samples of a complete dag of n bits. The CIC criterion outperforms AIC and BIC by orders of magnitude when n > 3 and it is just better for the cases n = 2,3.
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