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  • Oliver Sutton (Department of Mathematics, King's College London):

    Learning from few examples - nonlinearity and dimensionality

    12.03.2024 14:00Místnost 318 (zoom) @ Ústav informatiky
    Pod Vodárenskou věží 2
    Praha, 182 00
    Hora Informaticae

    A lot of attention has been given to the curses and blessings of learning with high dimensional data, and in this talk we will examine how these affect a system's ability to learn from few examples. For example, proving tight bounds on the generalisation performance of even simple classifiers in a conventional distribution-agnostic way typically requires that the quantity of training data grows extremely quickly with the data dimension. The 'curse of dimensionality' embodied by this conventional wisdom would seem to suggest that it is not possible to learn such data from just a few examples - yet we frequently observe this happening in practice! Moreover, practical experience shows that using nonlinear feature maps which artificially inflate data up into higher dimensions often make the learning problem an easier one, something which seems to contradict the expected 'curses of dimensionality'. We reveal that there are in fact large families of data distributions with certain geometric properties where high dimensional concentration phenomena actually make learning and generalising from few examples easier in higher dimensions. We also show that it is possible for carefully designed feature maps to embed data into higher dimensions in a way which meaningfully accelerates these 'blessings of dimensionality'.

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