Data Compression With and Without Deep Probabilistic Models
(Summer Term 2022)

Course by Prof. Robert Bamler at University of Tuebingen.

At a Glance

Links

Additional Resources

Tentative Schedule & Course Materials

Details of the following schedule are still subject to change.

Overview and Symbol Codes

What is the connection between data compression, probabilistic models, and error correction? We answer these questions with some concrete examples of so-called symbol codes.
1
Lecture
21 April
Tutorial
22. & 29.

Theoretical Bounds of Lossless Compression (feat. Entropy)

We prove the Source Coding The­o­rem. This cornerstone of information theory quantifies information content, and it states a fundamental lower bound for the bit rate of lossless compression.
2
Lecture
28 April
Tutorial
6 May

Proof of Optimality of Huffman Coding

We prove that the famous Huffman Coding algorithm constructs an opti­mal symbol code. Then we introduce an information theoretical measure for model mismatch, the “KL-divergence”.
3
Lecture
5 May
Tutorial
13 May

Mutual Information and Tax­on­o­my of Probabilistic Models

How can we build powerful prob­a­bi­lis­tic models without sacrificing ef­fi­cien­cy? We'll discuss various designs after introducing important concepts from probability and information theory.
4
Lecture
12 May
Tutorial
20 May

Stream Codes I: Arithmetic Coding And Range Coding

We've proved that Huffman Codes are optimal symbol codes. But it turns out that we can do better than symbol codes—by thinking in fractional bits.
5
Lecture
19 May
Tutorial
27 May

Stream Codes II: Asym­met­ric Numeral Systems (ANS)

This recently invented stream code is as performant as range coding while being much easier to implement. But it has a caveat—or is it a feature?
(Yes, that's a clickbait teaser; sue me.)
6
Lecture
2 June
Tutorial
17 June

Bits-Back Coding

We generalize the so-called “bits-back trick” from the ANS algorithm to arbi­trary latent variable models. This allows us to use latent variables for data compression without paying for them. Think of it as “short selling” bits.
7
Lecture
3 June (!)
Tutorial
24 June

Variational Inference

This method for approximate Bayesian inference is a mainstay of modern probabilistic machine learning. And—curiously—its most natural derivation actually builds on the bits-back coding algorithm.
8
Lecture
23 June
Tutorial
1 July

Variational Autoencoders and Lossy Neural Compression

We extend variational inference and learn both the generative model and how to do inference in it from training data. This results in a popular class of models for lossy data compression.
9
Lecture
30 June
Tutorial
8 July

Channel Coding Theorem and Source-Channel Separation

We take a step back from com­pres­sion and consider the wider problem of efficient communication. This will come in handy for lossy compression too.
10
Lecture
7 July
Tutorial
15 July

Theoretical Bounds of
Lossy Compression
(Rate/Distortion Theory)

Lossy compression methods can achieve lower bit rates than lossless methods. But they have a limit too— which turns out to be an old friend.
11
Lecture
14 July
Tutorial
22 July

Recent Advances in Machine-Learning Based Data Compression

Flows, quantization methods, prob­a­bi­lis­tic models for videos, ... — modern compression research is a vibrant field.
12
Lecture
21 July
Tutorial
29 July

Cancelled

As discussed in the lecture, we'll skip this week's Thursday time slot due to a conflict with an exam.
13
Lecture
28 July