Probabilistic Machine Learning – notebooks

1D Taylor approximation

Checking that two times jacobian is a hessian

Active Learning

Baseball

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Basic Imports

Basis Functions Regression

Bayes Librarian

BayesOpt Motivation

Bayesian Linear Regression

Bayesian Linear Regression Posterior Figures

Bayesian Logistic Regression

Can we find closed form MLE solution for Bayesian Logistic Regression? It seems, yes. Stay tuned!

Bayesian Optimization

Biased and Unbiased Estimators

Biased and Unbiased Estimators

CIFAR10 and CIFAR100 dataset

https://www.cs.toronto.edu/~kriz/cifar.html

Calculus

If we are to directly call: z.backward() we get the following error.

Capturing uncertainty in neural nets:

The model is the same as in case 1.1.1, but the noise is learned from the data.

Capturing uncertainty in neural nets:

The model is the same as in case 1.1.1, but the noise is learned from the data. Thus, we need to modify the loss function to include the noise parameter \(\sigma\).

Capturing uncertainty in neural nets:

The model is the same as in case 1.1.1, but the noise is learned from the data.

Closed form solution for prior predictive distribution

Closed form solution for prior predictive distribution

\[ I = \int p(\mathcal{D} \mid \theta) p(\theta) \mathrm{d}\theta \]

Computing the evidence term

\[ I = \int p(\mathcal{D} \mid \theta) p(\theta) \mathrm{d}\theta \]

Discrete distributions

The PDF of the Bernoulli distribution is given by

Error Code Dilbert

Gibbs Sampling for Bivariate Normal Distribution

Goals:

Let us first look at G1. Look at the illustration below. We have a normal distribution \(p\) and two other normal distributions \(q_1\) and \(q_2\). Which of \(q_1\) and \…

Goals:

Let us first look at G1. Look at the illustration below. We have a normal distribution \(p\) and two other normal distributions \(q_1\) and \(q_2\). Which of \(q_1\) and \…

Heteroskedastic N

Hypernetwork

Let us now write a function to generate…

Importance Sampling

Imports

Create a dataset with rotated images and corresponding labels. We can now use a much larger dataset

Inverse CDF Sampling

Linear Regression Tutorial

Let us compute the maximum likelihood estimate for a given training set

Monte Carlo Dropout and Deep Ensemble for Bayesian Deep Learning

Monte Carlo Sampling

Overconfident Neural Networks

Reference: https://www.kaggle.com/code/jramkiss/overconfident-neural-networks/notebook

Parameters

The transition matrix is the same for all time steps.

Sampling from an unnormalized distribution

Setting Up & Imports

Setting Up & Imports

Train on all tasks

Vanilla Linear Regression

\(\alpha \sim \text{Normal}(0, 500)\)

Variance in Value of Pi in MC Sampling

Sampling (Sampler.HMC; Integrator.IMPLICIT) Time spent | Time remain.| Progress | Samples | Samples/sec tensor(-1433.3967, grad_fn=) tensor(-1.8629, grad_fn=)…

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