A Note on Non-Negative $L_1$-Approximating Polynomials
Researchers have published a note on non-negative $L_1$-approximating polynomials with respect to Gaussian distributions. This work establishes that sets with a bounded Gaussian surface area admit degree-$k$ non-negative polynomials that $\epsilon$-approximate their indicator functions in $L_1$-norm. The findings match existing degree bounds for Gaussian $L_1$-approximation but add the constraint of non-negativity. AI
IMPACT This research contributes to the theoretical underpinnings of computational learning theory, potentially influencing future developments in smoothed learning from positive-only examples.