3 problems

Let $g_1$ be a differentiable function, let $U$ be an orthogonal matrix, and define $g_2(\bm{y}):= g_1(U\bm{y})$ under the coordinate transformation $\bm{y}=U^T\bm{x}$. Let…

Optimal polynomial-weight conjecture. It is optimal to choose the family of orthonormal polynomials so that the weight function corresponds to the probability density function of…

Sample-complexity conjecture. The number of samples needed for accurate Monte Carlo estimates of the activity scores $\alpha_i$ may be smaller than the number of samples needed for…