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Showing posts with the label non-parametric statistics

Constrained MDPs and the reward hypothesis

It's been a looong ago that I posted on this blog. But this should not mean the blog is dead. Slow and steady wins the race, right? Anyhow, I am back and today I want to write about constrained Markovian Decision Process (CMDPs). The post is prompted by a recent visit of Eugene Feinberg , a pioneer of CMDPs, of our department, and also by a growing interest in CMPDs in the RL community (see this , this , or this paper). For impatient readers, a CMDP is like an MDP except that there are multiple reward functions, one of which is used to set the optimization objective, while the others are used to restrict what policies can do. Now, it seems to me that more often than not the problems we want to solve are easiest to specify using multiple objectives (in fact, this is a borderline tautology!). An example, which given our current sad situation is hard to escape, is deciding what interventions a government should apply to limit the spread of a virus while maintaining economic ...

Statistical Modeling: The Two Cultures

Sometimes people ask what is the difference between what statisticians and machine learning researchers do. The best answer that I have found so far can be found in " Statistical Modeling: The Two Cultures " by Leo Breiman (Statistical Science, 16:199-231, 2001). According to this, statisticians like to start by making modeling assumptions about how the data is generated (e.g., the response is a noise added to the linear combination of the predictor variables), while in machine learning people use algorithm models and treat the data mechanism as unknown. He estimates that (back in 2001) less than 2% of statisticians work in the realm when the data mechanism is considered as unknown. It seems that there are two problem with the data model approach. One is that the this approach does not address the ultimate question which is making good predictions: if the data does not fit the model, this approach has nothing to offer (it does not make sense to apply a statistical test if th...