Li, Artemiou and Li (2011) presented the novel idea of using Support Vector Machines to perform sufficient dimension reduction. In this work, we investigate the potential improvement in recovering the dimension reduction subspace when one changes the Support Vector Machines algorithm to treat imbalance based on several proposals in the machine learning literature. We find out that in most situa...

The causal states of computational mechanics define the minimal sufficient (prescient) memory for a given stationary stochastic process. They induce the ε-machine which is a hidden Markov model (HMM) generating the process. The ε-machine is, however, not the minimal generative HMM and minimal internal state entropy of a generative HMM is a tighter upper bound for excess entropy than provided by...