The coefficients in this RF expansion are optimized to fit the given data of input-output pairs.

So far the community has considered`2 as the underlying distance.

We consider the problem of estimating the Fréchet and conditional Fréchet mean from data taking values in separable metric spaces. Unlike Euclidean spaces, where well-established methods are available, there is no practical estimator that works universally for all metric spaces. Therefore, we introduce a computable estimator for the Fréchet mean based on random quantization techniques and establish its universal consistency across any separable metric spaces. Additionally, we propose another estimator for the conditional Fréchet mean, leveraging data-driven partitioning and quantization, and demonstrate its universal consistency when the output space is any Banach space.

We present an effective method for supervised feature construction.

We describe how BWGAN can be efficiently implemented.

In contrast, deep learning research has mostly endeavored to find inductive solutions, relying on stochastic gradient descent to faithfully encode functional relationships described by large datasets into the weights of a neural network.

The coefficients in this RF expansion are optimized to fit the given data of input-output pairs.

SGD analysis which requires a Hilbert space norm.