Optimal Transport: From Theory to Tweaks, Computations and Applications in Machine Learning
Crédits ECTS :
Heures de cours :
Heures de TD :
This course will present recent methodological advances in machine learning that all have in common that they rely on geometric principles, and particularly on the idea that data analysis can be carried out using pairwise comparisons between data points. We will cover in particular the cases where such pairwise comparisons are distances or kernel similarities. The course will answer the following questions:
- Visualization of metric data: how can we represent and visualize data that is available under the form of a matrix of pairwise distances or similarities?
- Learning metrics: Given a task at hand (notably classification), how can we choose a "good" metric or kernel to improve the performance on that task?
- Metrics and kernels for exotic data-types (e.g. text, sequences, time-series, shapes, histograms): how can we choose a metrics or a kernel that performs well in supervised tasks? How can we ensure that they can be seamlessly used in a learning problem (e.g. auto-differentiated with modern frameworks such as tensorflow or pytorch)?
- (3 lectures + 1 programming session) Introduction, motivating examples (k-NN / SVM). Reminders on kernels and distances, Hilbert/Metric spaces, Positive / negative definiteness.
- (2 lectures + 1 programming session). Dimensionality reduction and visualization techniques for geometric data: (kernel)-PCA, (metric) multidimensional scaling, isomap, LLE, t-SNE, embeddings, extensions to (variational) autoencoders
- (2 lectures + 1 programming session). Learning metrics. LMNN, localized FDA and other metric learning algorithms. Learning kernels: multiple kernel learning.
- (3 lectures + 1 programming session). Metrics and kernels for structured data: Fisher kernels, kernels for strings/sequences/texts, DTW/edit-distances for time-series, Distances/kernels on the simplex, Wasserstein and Gromov-Wasserstein metrics, autodifferentiation
Note: Lectures will be taught in english if non-french speakers register to the course, french otherwise.
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