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What branch/branches of math are most relevant in enhancing machine learning (mostly in terms of practical use as opposed to theoretical/possible use)? Specifically, I want to know about math research ...

Let $y\in \mathbb{R}$ and $\mathbf{x},\mathbf{z}\in\mathbb{R}^p$ be random variable and random vectors. Assume $y=f(\mathbf{x}+\mathbf{z},\mathbf{z})$ for some function $f$. Is the following statement ...