(1) Unsupervised component analysis for neuroimaging data and (2) scheduling with predictions
Séminaire Données et Aléatoire Théorie & Applications
6/10/2022 - 14:00 Hugo Richard Salle 106
There will be two talks: (1) In brain mapping, a rising trend is to experiment with naturalistic stimuli such as movie watching or audio track listening rather than tightly controlled but outrageously simple stimuli. However, the analysis of these "naturalistic" stimuli is more difficult to carry. Independent component analysis (ICA) is a popular method to analyze the data of a single subject but it is challenging to generalize ICA to datasets with multiple subjects. We present several methods to perform ICA in such a context. (2) A popular approach to go beyond the worst-case analysis of online algorithms is to assume the existence of predictions that can be leveraged to improve performances. Those predictions are usually given by some external sources that cannot be fully trusted. Instead, we argue that trustful predictions can be built by algorithms, while they run. We investigate this idea in the illustrative context of static scheduling with exponential job sizes. Indeed, we prove that algorithms agnostic to this structure do not perform better than in the worst case. In contrast, when the expected job sizes are known, we show that the best algorithm using this information, called Follow-The-Perfect-Prediction (FTPP), exhibits much better performances. Then, we introduce two adaptive explore-then-commit types of algorithms: they both first (partially) learn expected job sizes and then follow FTPP once their self-predictions are confident enough. On the one hand, ETCU explores in "series", by completing jobs sequentially to acquire information. On the other hand, ETCRR, inspired by the optimal worst-case algorithm Round-Robin (RR), explores efficiently in "parallel". We prove that both of them asymptotically reach the performances of FTPP, with a faster rate for ETCRR. Those findings are empirically evaluated on synthetic data.