Learning Complexity and Generalization Bounds

In a typical supervised learning setting, we are given access to a dataset of samples \(S = (X_1, y_1), (X_2, y_2), ..., (X_n, y_n)\) which we assume are drawn from a distribution \(\mathcal{D}\) over \(\textbf{X} \times \textbf{y}\). For simplicity, we will assume that \(\mathbf{X}\) is either the space \(\{0,1\}^n\) or... [Read More]
Tags: Learning, Complexity, Generalization, VC Dimension, Vapnik, Chervonenkis, Rademacher

Models of Learning

Machine Learning researchers have a tough time agreeing on the best formulations for the problems they face. Even within the relatively well-defined setting of supervised learning, there are lots of ways to express the nature of the problem. At a very high level, we can express supervised learning as a... [Read More]
Tags: PAC, Computational, Learning, Theory

White Noise is Pretty Weird

I recently went off on a tangent trying to figure out how white noise works, and I found that there is a lot of strangeness to it that may not be apparent at a first glance. The content in this post is primarily from: This stackexchange answer This stackexchange answer... [Read More]
Tags: White Noise, Probability, Random Variables, Stochastic Process

What are you modeling?

In this post, we will explore how Discriminative/Generative and Frequentist/Bayesian algorithms make different decisions about what variables to model probabilistically. There are many ways to characterize Machine Learning algorithms. This is a direct consequence of the rich history, broad applicability and interdisciplinary nature of the field. One of the clearest... [Read More]
Tags: Machine Learning, Probability, Discriminative, Generative, Frequentist, Bayesian

Compositional Structures in Machine Learning

As researchers apply Machine Learning to increasingly complex tasks, there is mounting interest in strategies for combining multiple simple models into more powerful algorithms. In this post we will explore some of these techniques. We will use a little bit of language from Category Theory, but not much. In the... [Read More]
Tags: Machine Learning, Neural Networks, Category Theory, Composition