Quantitative Data Analysis

Course goals

By the end of the course, for complex and high-dimensional data, you will be able to:

1. Decide how to estimate the underlying distribution of a dataset, denoise and normalise it, and justify the choices you made.
2. Use dimensionality reduction and representation learning to expose structure in a dataset you have never seen before.
3. Use covariate analysis, regression, and classification on high-dimensional data, interpret the results with explainable AI, and evaluate the full pipeline rather than just the final model.
4. Quantify and report the uncertainty in your conclusions, so that downstream users know how much to trust them.
5. Translate your findings back into the language of the real-world problem they came from.

Assessment
Module (3 times) assessment by written examination  - 75%
Journal Clubs and Guest Lectures - 25%
Participation in UKP 2026 (solving at least one task) - 5% (extra)

Attendance
Lectures, Tutorials, Journal clubs, Guest Lectures - mandatory attendance.

Content

A single experiment can now give you the expression of every gene in 100'000 individual cells. A drone-mounted spectrometer can record the light reflected from every square meter of a wheat field. A vision model exposes its internal activations for every layer, on millions of images. Different problems (genomics, proteomics, hyperspectral imaging, sensor networks, the internal states of large AI models) produce data of the same shape: tens or hundreds of thousands of features per sample, far more features than samples, and most of the signal hidden in the noise.

This course teaches you how to get from raw measurements like these to answers. What distinguishes healthy from diseased tissue? Which crop varieties cope with drought? Which gene or protein is responsible for the difference? Why did a model make one prediction and not another? You will work through real high-throughput datasets and learn the statistical and machine learning techniques that turn them into reliable conclusions, and into honest estimates of how reliable those conclusions are.

Module 1. My data is a mess. Can I trust any of it?
Real measurements are noisy, biased, and recorded on different scales. Before any analysis is meaningful, you need to know what the noise looks like, what is signal and what is artefact, how to normalise across batches, and when a multiple-testing problem is fooling you. Each topic is paired with a hands-on session.

Module 2. There are 20,000 features. What is going on?
Once the data is clean, you need to see it. We cover ways to reduce thousands of dimensions to two or three you can plot, and ways to find structure you did not know to look for: PCA, MDS, t-SNE, UMAP, clustering, and self-supervised representation learning, including variational autoencoders.

Module 3. Which features matter, and how sure am I?
Finding patterns is easy. Finding patterns that hold up is the hard part. This module covers covariate analysis, regression and classification on high-dimensional data, feature importance through explainable AI, evaluation for tabular and time-series problems (HMMs, RNNs), and benchmarking an entire analysis pipeline rather than just a model. We also spend time on the question that quietly decides whether the rest of the analysis was worth doing: how uncertain are the conclusions?

Guest lectures and journal clubs throughout the course connect each module to ongoing research and to current problems in academia and industry.