SpaceTimeKhantinuum

Gaussian Process Regression From Scratch In this notebook we will use Julia to code up Gaussian Process Regression (GPR) from scratch i.e., without using any GPR library. I did this to learn both GPR and Julia better. A good reference is the Rasmussen Williams (2006) textbook available for free at http://www.gaussianprocess.org/ In particular Algorithm 2.1 is used. Imports We start by importing the libraries we need. This is a little different to python where we like to do something like [Read More]

introduction In this post I test out JAXNS - nested sampling implemented in JAX. Paper: arxiv.org:2012.15286 Github: github.com/Joshuaalbert/jaxns Thanks to Joshua Albert from JAXNS for helping me understand how to use JAXNS UPDATE: For a more recent version of JAXNS see my google colab notebook code !pip install git+http://github.com/Joshuaalbert/jaxns.git Collecting git+http://github.com/Joshuaalbert/jaxns.git Cloning http://github.com/Joshuaalbert/jaxns.git to /tmp/pip-req-build-60od1v_1 Running command git clone -q http://github.com/Joshuaalbert/jaxns.git /tmp/pip-req-build-60od1v_1 Requirement already satisfied (use --upgrade to upgrade): jaxns==0. [Read More]

demonstrating the ‘f-principle’ Here we try and demonstrate the f-principle, the tendency for ANNs for first fit low frequency data then high frequency. There are quite a few papers on this which you can find by looking at this paper and papers it references and papers that reference this: https://arxiv.org/abs/1901.06523 We also look at the multi-scale artificial neural network (M-scale ANN) from: https://arxiv.org/abs/1910.11710 We show that the M-scale ANN and drastically improve the performance of these ANNs for these regression tasks. [Read More]

You can publish your jupyter notebooks to a personal website like this by following a couple easy steps. write notebook convert notebook to markdown jupyter nbconvert --to markdown [NAME].ipynb fix preamble You need to add the Hugo blog post metadata --- title: Jupyter notebooks to markdown blog posts date: 2020-10-08 tags: ["python"] --- Add images If you have any images the path in the markdown should be in the static directory. [Read More]

I was inspired by Colin Carroll’s blog, specifically his post on using multiple MCMC chains not through multiple processors but through vectorisation. The example I show wouldn’t have been possible without Colin’s code for me to copy so thanks! I’m trying to get my head around basic MCMC still and also TensorFlow/TensorFlow Probability so I have adapted Carroll’s MCMC numpy code above and translated the numpy/scipy code into TF and TFP code to create a very basic MCMC sampler using TF and TFP called tf-minimc, again based on Colin Carroll’s minimc. [Read More]

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The image banners at the top of the page are refered to as “bigimg” in this theme. They are optional, and one more more can be specified. If more than one is specified, the images rotate every 10 seconds. In the front matter, bigimgs are specified using an array of hashes.

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KaTeX can be used to generate complex math formulas. It supports in-line math using the \\( ... \\) delimiters, like this: \( E = mc^2 \). By default, it does not support in-line delimiters $...$ because those occur too commonly in typical webpages. It supports displayed math using the $$ or \\[...\\] delimiters, like this:

Formula 1: $$ \phi = \frac{(1+\sqrt{5})}{2} = 1.6180339887\cdots $$

Formula 2: (same formula, different delimiter) \[ \phi = \frac{(1+\sqrt{5})}{2} = 1.6180339887\cdots \]

Additional details can be found on GitHub or on the Wiki.

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The following are two code samples using syntax highlighting.

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