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Important note @MateuszKwaśnicki in the comment section has raised a fundamental issue with the current statement of the problem. I'm trying to bugfix it. Setup I wish to show that a Lipschitz ...

Let $P$ be a probability distribution on $\mathbb R^d \times \mathbb R$, and let $(x_1,y_1), \ldots, (x_n,y_n)$ be an iid sample of size $n$ from $P$. Fix $\epsilon,t\gt 0$. For any unit-vector $w \in ...