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In this post I’m going to try and introduce Langevin Monte Carlo, an MCMC method that models the process with Langevin dynamics. This means the process is interpreted like one dictated by the Langevin stochastic differential equation which models a specific combination of random and deterministic forces on a system. UNDER CONSTRUCTION
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In this post I’m going to attempt to give an intuitive introduction to Fisher Information, (very briefly) Jeffrey priors, and the lower bounds on the variance of unbiased estimators i.e. the Cramer-Rao bound. Hopefully this post will be shorter than my last couple…
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In this post, I’ll go through Constant Curvature VAEs (traditional, hyperspherical, and hyperbolic) for image data classification and molecular structure reconstruction.
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In this post I’m going to go through the kernel trick and how it helps or enables various tools in statistics and machine learning including support vector machines, gaussian processes, kernel regression and kernel PCA. This is going to be a bit of a long one, I’ll probably split it up later but for now … sorry? {}
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In this post, I’m going to investigate the underlying relationships between various physical and mental health indicators and student stress levels. In the process I will give an introduction to the Uniform Manifold Approximation and Projection or UMAP dimensional reduction technique.
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In this post, I’ll give an practical introduction to flow matching for the sake of estimating complicated sample distributions and image generation.
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In this post, I’ll give an introduction to variational autoencoders, with some machine learning examples.
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In this post, I’ll attempt to give an introduction to simulation-based inference specifically delving into the method of NRE including rudimentary implementations.
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In this post, I’ll attempt to give an introduction to simulation-based inference specifically delving into the methods NPE and NLE including rudimentary implementations.
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In this post I will attempt to give an introduction to conditional normalising flows, not to be confused with continuous normalising flows, that model both \(\vec{\theta}\) and \(\vec{x}\) in the conditional distribution \(p(\vec{\theta}\vert\vec{x})\). I was nicely surprised at how simple it is to implement compared to unconditional normalising flows, so I thought I’d show this in a straightforward way. Assumes you’ve read my post on Building a normalising flow from scratch using PyTorch.
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In this post I will attempt to give an introduction to continuous normalising flows, an evolution of normalising flows that translate the idea of training a discrete set of transformations to approximate a posterior, into training an ODE or vector field to do the same thing.
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In this post I will attempt to show you how to construct a simple normalising flow using base elements from PyTorch heavily inspired by a similar post by Eric Jang doing the same thing with TensorFlow from 2018 and subsequently his tutorial using JAX from 2019.
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In this post I will attempt to give an introduction to binary classifiers and more generally neural networks.
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In this post I will attempt to give an introduction to variational inference with some examples using the NumPyro python package. Partly under construction
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In this post, I’ll attempt to give an introduction to normalising flows from the perspective of variational inference.
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In this post, I will detail popular diagnostic tests to quantify how well or if your MCMC sampling has converged.
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In this post, I’ll go through “What is MCMC?”, “How is it useful for statistical inference?”, and the conditions under which it is stable.
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In this post, I’m going to try to give an intuitive intro into the Metropolis-Hastings algorithm without getting bogged down in much of the math to show the utility of this method.
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In this post, I’m going to introduce rejection sampling as a way to generate samples from an unnormalized PDF as further background to MCMC.
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Introduction to inverse transform sampling for continuous and discrete probability distributions.
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First blog post, outlining what I’m going to try and do in the next few posts and some basics of Bayesian analysis.