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Extra info for A relativist's toolkit : the mathematics of black-hole mechanics / [...] XD-US
As the environment became more familiar, neurons tended to be active across smaller proportions of the environment, and there appeared to be segregation into a higher and a lower rate group where the higher firing rate neurons were also more spatially selective. It is as though these explicit memory circuits were actually developing sparse explanatory predictive memory models in the course of learning. But unlike stepwise regression’s unstable and arbitrary feature selection, the brain’s sparse explicit memory features are stable and meaningful.
As in this example, it does not matter whether the entropy of the estimated probability distribution is maximized subject to constraints or the log likelihood is instead maximized. The very same estimated probability distribution simultaneously maximizes both objectives. With the exception of certain pathological cases, both maximum entropy and maximum likelihood logistic regression are also well-behaved optimization objectives where any local optimum is also a global optimum. One pathological condition is where perfect discrimination accuracy with zero error can be observed known as complete or quasi-complete separation, depending upon whether ties exist.
Thus, there will be considerable risk when we need to rely upon an assumption that the predictive environment is stable. 40 To avoid the risk associated with black box models and environmental instability, there is a strong desire for models with accurate causal explanatory insights. The problem is that the popular standard methods used to generate parsimonious “explanatory” models like standard stepwise regression methods do not really work to model putative causes because what they generate are often completely arbitrary unstable solutions.