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Short Notes: The Multivariate Gaussian Distribution With a Diagonal Covariance Matrix
This post explores how a multivariate Gaussian distribution simplifies when the covariance matrix is diagonal. By breaking down the math, we show how the density function factorizes into a product of independent univariate Gaussians—making both interpretation and computation more tractable.
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Building Intelligent Agents for Connect-4: First Steps
A deep dive into the construction of intelligent agents for Connect-4. This introductory post covers the historical context, motivation, complexity of the game, and foundational concepts behind AI-based approaches—particularly tree search and reinforcement learning methods. Includes a preview of the full 7-part series and links to an open-source Python3/C++ framework.
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Understanding Bootstrap Sampling: Where Euler’s Number Meets Random Forests
A common problem involves drawing a sample of size n from a set of n elements, with replacement. For example, in Random Forests, each decision tree is trained on a bootstrap sample drawn n times with replacement from the training data. A natural question is: how many unique examples can we expect in such a sample? Since sampling is done with replacement, some examples are likely selected multiple times, while others may not be selected at all.
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Beyond 3D: Generalizing the Vector Cross Product
Imagine you are working in three-dimensional space and have two directions. You want to find a third direction that is perpendicular to both of them. In this setting, there's a well-known solution: the cross product. When applied to the two original directions, it produces a new one that is exactly orthogonal to both.
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Math Challenge: The Sequence of Fibonacho
The Fibonacho Sequence is a playful and intriguing twist on the classical Fibonacci numbers. Unlike its better-known cousin, the Fibonacho Sequence does not follow the same simple recurrence relation. Instead, it introduces a slightly different structure, making it a entertaining puzzle for math enthusiasts and programmers alike. Are you ready to dive into the challenge?