Articles

Primer to Probability Theory and Its Philosophy
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Category:Post
June 19, 2020
Probability is a measure defined on events, which are sets of primitive outcomes. Probability theory mostly comes down to constructing events and measuring them. A measure is a generalization of size which corresponds to length, area, and volume (rather than the bijective mapping definition of cardinality).

Notes: Probability & AI Curriculum
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Category:Notes
June 17, 2020
This is a snapshot of my curriculum for exploring the following questions:
 Is probability theory all you need to develop AI?
 If not, what is missing?
 Should a theory of AI be expressed in the framework of probability theory at all?
 Do Brains use probability?
 Is probability theory all you need to develop AI?

Primer to Shannon's Information Theory
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Category:Post
June 9, 2020
Shannonâ€™s theory of information is usually just called information theory, but is it deserving of that title? Does Shannonâ€™s theory completely capture every possible meaning of the word information? In the grand quests to creating AI and understanding the rules of the universe (i.e. grand unified theory) information may be key. Intelligent agents search for information and manipulate it. Particle interactions in physics may be viewed as information transfer. The physics of information may be key to interpreting quantum mechanics and resolving the measurement problem.
If you endeavor to answer these hard questions, it is prudent to understand existing socalled theories of information so you can evaluate whether they are powerful enough and to take inspiration from them.
Shannonâ€™s information theory is a hard nut to crack. Hopefully this primer gets you far enough along to be able to read a textbook like Elements of Information Theory. At the end I start to explore the question of whether Shannonâ€™s theory is a complete theory of information, and where it might be lacking.
This post is long. That is because Shannonâ€™s information theory is a framework of thought. That framework has a vocabulary which is needed to appreciate the whole. I attempt to gradually build up this vocabulary, stopping along the way to build intuition. With this vocabulary in hand, you will be ready to explore the big questions at the end of this post.

Quantum State
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Category:Post
December 22, 2019
The two views of quantum state:
 Quantum states are $L^2$normalized complexvalued functions over classical configuration space.
 Quantum states are unit vectors residing in a complex Hilbert space, $\mathcal{H}$.

BiasVariance Decomposition For Machine Learning
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Category:Post
July 14, 2019
All about the biasvariance decomposition as it pertains to machine learning. All you need to know: