TL;DR
This paper discusses formalizing the scientific process mathematically, introduces new theoretical tools like a data processing inequality and bias-variance decomposition, and simplifies proofs of key theorems in the field.
Contribution
It presents novel theoretical contributions including a general data processing inequality, a bias-variance decomposition, and streamlined proofs of foundational theorems.
Findings
A new general data processing inequality
A bias-variance decomposition for canonical losses
Streamlined proofs of Blackwell-Sherman-Stein and Randomization theorems
Abstract
The scientific process is a means to turn the results of experiments into knowledge about the world in which we live. Much research effort has been directed toward automating this process. To do this, one needs to formulate the scientific process in a precise mathematical language. This paper outlines one such language. What is presented here is hardly new. The material is based on great thinkers from times past well as more modern contributions. The novel contributions of this paper are: A new general data processing inequality, a bias variance decomposition for canonical losses, streamlined proofs of the Blackwell-Sherman-Stein and Randomization theorems. means of calculating deficiency through linear programming.
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Taxonomy
TopicsRisk and Portfolio Optimization · Stochastic Gradient Optimization Techniques · Complexity and Algorithms in Graphs