7 problems

Let $c$ denote the parameter-to-sample ratio and let $\mu>0$ be the signal parameter in the risk curve described above. Peak-location conjecture. The peak of the generalization err…

Let $\{a_n,b_n,c_n\}$ denote the set of pseudopivot points at iteration $n$ for the initial set under consideration. Unbounded range conjecture. The range of pseudopivot points wil…

Let $\mathcal{X}=[0,1]$ and let $P$ be a probability measure on $\mathcal{X}$ with Lebesgue density bounded away from $0$ and $\infty$. Let $\xi_i$ be i.i.d. mean-zero errors indep…

Covariance spectral-approximation sample-size conjecture. The improvement obtainable from accelerating stochastic gradient descent, relative to averaged stochastic gradient descent…

Let $f(\theta)=\langle a,\theta\rangle$ and let $g_N$ be a quadratic non-strongly convex regularization chosen for a finite horizon $N$, with $\psi_N(\theta)=f(\theta)+g_N(\theta)$…

SGD applicability conjecture. The algorithm and results of the paper also apply to the regular stochastic gradient descent case.

Slope heuristics conjecture. The restriction to piecewise constant-function models is mainly technical, and the slope heuristics should remain valid at least in the general least-s…