Mathematics of machine learning: mathematical learning methods for adaptive and robust data analysis

Berkeley Image Database

Since the dawn of computing (or even earlier, if you include fiction) humankind has been concerned with `smart machines’: machines like robots or other automated machines that are equipped with artificial intelligence. `Smart’ is all about endowing information with meaning in an organised manner. Machines need to acquire information – they should not just `read’ an image as an aggregate of pixels but `understand’ it as, for example, a collection of moving objects – and comprehend it: they should understand the unfolding scene and decide how to react to it subject to predetermined goals. Autonomous cars, for instance, need to be able to decide on the go whether something on the road is a child or just a paperbag which can be run over. As another example, automated tools in medical diagnosis should be able to make the same decision that doctors make. Based on different imaging modalities, they should, for example, be able to decide whether a patient is diagnosed with cancer or not. Imaging, image analysis and processing belong to the main areas within this context, and much progress has been made in the past years to automise them with machine learning algorithms in order to progress towards smart machines.
As impressive as many recent developments in machine learning are in terms of their performance for certain tasks when trained correctly, their theoretical analysis — in particular in terms of their robustness to outliers and their error control and prediction — is mostly missing. One of the cornerstones of the Institute will be the development of rigorous learning methodologies that are accessible by mathematical and statistical analysis techniques, resulting in controllable guarantees on the decision-making of smart machines. Recent developments in this context include so-called bi- (or multi-) level optimisation approaches http://arxiv.org/abs/1505.02120 whose mathematical analysis and computational solution are key for proposing both adaptive and reliable analysis techniques. Applications of interest include adaptive image analysis such as image classification, segmentation and enhancement, all the way to inverse problems in industrial and medical imaging, seismics and inference for high-dimensional data.

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Jose Henry Leon-Janampa
Published 21/01/2017
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