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9 avril 2024


C. Bénézet (ENSIIE)

 Learning conditional distributions on continuous spaces.

Abstract : We investigate sample-based learning of conditional distributions on multi-dimensional unit boxes, allowing for different dimensions of the input and output spaces. Our approach involves grouping data near varying query points in the input space to create empirical measures in the output space. We employ two distinct grouping methods: one based on a fixed-radius ball and the other on nearest neighbors. We establish upper bounds for the convergence rates of both methods and, from these bounds, deduce optimal configurations for the radius and the number of neighbors. We propose to incorporate the nearest neighbor method into neural network training, as our theoretical and empirical analysis indicates an improvement in accuracy. We provide numerical results showing the performance of the methodology developed. This is a joint work with Z. Cheng (UToronto) and S. Jaimungal (UToronto).

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