• March 23, 2018

    How to use R packages such as ggplot in Julia

    Julia is a wonderful programming language. It’s modern with good functional programming support, and unlike R and Python - both slow - Julia is fast. Writing packages is straightforward, and high performance can be obtained without bindings to a lower-level language. Unfortunately, its plotting frameworks are, at least in my view, not as good as the ggplot package in R. Fortunately, Julia’s interoperability with other programming languages is outstanding. In this post, I illustrate how to make ggplot work near-seamlessly with Julia using the RCall package.

  • February 9, 2018

    What does it really mean to be Bayesian?

    In my previous posts, I introduced Bayesian models and argued that they are meaningful. I claimed that studying them is worthwhile because the probabilistic interpretation of learning that they offered can be more intuitive than other interpretations. I showcased an example illustrating what a Bayesian model looks like. I did not, however, say what a Bayesian model actually is – at least not in a sufficiently general setting to encompass models people regularly use. I’m going to discuss that in this post, and then showcase some surprising behavior in infinite-dimensional settings where the general approach is necessary. The subject matter here can be highly technical, but will be discussed at an intuitive level meant to explain what is going on.

  • November 3, 2017

    What does it mean to be Bayesian?

    Bayesian statistics provides powerful theoretical tools, but it is also sometimes viewed as a philosophical framework. This has lead to rich academic debates over what statistical learning is and how it should be done. Academic debates are healthy when their content is precise and independent issues are not conflated. In this post, I argue that it is not always meaningful to consider the merits of Bayesian learning directly, because the fundamental questions surrounding it encompass not one issue, but several, that are best understood independently. These can be viewed informally as follows.

  • August 16, 2017

    Deep Learning with function spaces

    Deep learning is perhaps the single most important breakthrough in statistics, machine learning, and artificial intelligence that has been popularized in recent years. It has allows us to classify images - for decades a challenging problem - with nowadays usually better-than-human accuracy. It has solved Computer Go, which for decades was the classical example of a board game that was exceedingly difficult for computers to play. But what exactly is deep learning?

  • July 5, 2017

    Bayesian Learning - by example

    Welcome to my blog! For my first post, I decided that it would be useful to write a short introduction to Bayesian learning, and its relationship with the more traditional optimization-theoretic perspective often used in artificial intelligence and machine learning, presented in a minimally technical fashion. We begin by introducing an example.