Liam C. Pinchbeck

Liam C. Pinchbeck

he/him

PhD student at Monash University studying Bayesian methods for analysing very high energy gamma ray event data in the search for dark matter

Posts by Tags

ADVI

Variational Inference Introduction

36 minute read

Published:

In this post I will attempt to give an introduction to variational inference with some examples using the NumPyro python package. Partly under construction

BBVI

Variational Inference Introduction

36 minute read

Published:

In this post I will attempt to give an introduction to variational inference with some examples using the NumPyro python package. Partly under construction

Bayesian Analysis

First Blog Post/Fitting a line I

14 minute read

Published:

First blog post, outlining what I’m going to try and do in the next few posts and some basics of Bayesian analysis.

Bayesian Inference

I <3 Kernels

91 minute read

Published:

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? {}

CAVI

Variational Inference Introduction

36 minute read

Published:

In this post I will attempt to give an introduction to variational inference with some examples using the NumPyro python package. Partly under construction

Conditional Density Estimation

A RealNVP conditional normalising flow (from scratch?)

15 minute read

Published:

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.

Control Variates

Variational Inference Introduction

36 minute read

Published:

In this post I will attempt to give an introduction to variational inference with some examples using the NumPyro python package. Partly under construction

Deep Learning

Dimensional Reduction

I <3 Kernels

91 minute read

Published:

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? {}

Investigating student stress indicators using UMAP (Kaggle Dataset)

18 minute read

Published:

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.

Flow Matching

FlowJAX

Gaussian Processes

I <3 Kernels

91 minute read

Published:

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? {}

Geometric deep learning

Introductory

I <3 Kernels

91 minute read

Published:

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? {}

Investigating student stress indicators using UMAP (Kaggle Dataset)

18 minute read

Published:

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.

Markov Chain (+) Monte Carlo methods

21 minute read

Published:

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.

Rejection Sampling

10 minute read

Published:

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.

Inverse Transform Sampling

6 minute read

Published:

Introduction to inverse transform sampling for continuous and discrete probability distributions.

First Blog Post/Fitting a line I

14 minute read

Published:

First blog post, outlining what I’m going to try and do in the next few posts and some basics of Bayesian analysis.

JAX

Variational Inference Introduction

36 minute read

Published:

In this post I will attempt to give an introduction to variational inference with some examples using the NumPyro python package. Partly under construction

Langevin Monte Carlo

Speeding up MCMC with Langevin Dynamics - Langevin Monte Carlo

13 minute read

Published:

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

MCMC

Speeding up MCMC with Langevin Dynamics - Langevin Monte Carlo

13 minute read

Published:

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

Markov Chain (+) Monte Carlo methods

21 minute read

Published:

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.

Machine Learning

I <3 Kernels

91 minute read

Published:

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? {}

Investigating student stress indicators using UMAP (Kaggle Dataset)

18 minute read

Published:

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.

Manifold Learning

NLE

NPE

NRE

Neural Networks

Normalising Flows

A RealNVP conditional normalising flow (from scratch?)

15 minute read

Published:

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.

An introduction to continuous normalising flows

25 minute read

Published:

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.

NumPyro

Variational Inference Introduction

36 minute read

Published:

In this post I will attempt to give an introduction to variational inference with some examples using the NumPyro python package. Partly under construction

PyTorch

A RealNVP conditional normalising flow (from scratch?)

15 minute read

Published:

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.

An introduction to continuous normalising flows

25 minute read

Published:

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.

Pyro

A RealNVP conditional normalising flow (from scratch?)

15 minute read

Published:

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.

An introduction to continuous normalising flows

25 minute read

Published:

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.

RealNVP

Regression

I <3 Kernels

91 minute read

Published:

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? {}

Sampling Methods

Rejection Sampling

10 minute read

Published:

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.

Inverse Transform Sampling

6 minute read

Published:

Introduction to inverse transform sampling for continuous and discrete probability distributions.

Simulation Based Inference

Stochastic Processes

Speeding up MCMC with Langevin Dynamics - Langevin Monte Carlo

13 minute read

Published:

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

Support Vector Machines

I <3 Kernels

91 minute read

Published:

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? {}

VAEs

Variational Autoencoders

Variational Inference

A RealNVP conditional normalising flow (from scratch?)

15 minute read

Published:

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.

An introduction to continuous normalising flows

25 minute read

Published:

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.

Variational Inference Introduction

36 minute read

Published:

In this post I will attempt to give an introduction to variational inference with some examples using the NumPyro python package. Partly under construction