תהליכי גאוסי תלויים בתקציב שני-מישורי

תקציר מקורי באנגליתarXiv:2610.10428v1 Announce Type: cross Abstract: Gradient observations promise more accurate Gaussian process (GP) surrogates, but the cost of incorporating them has long stood in the way of realizing that promise. We propose a derivative GP with a budget of just two directions per observed gradient. One direction focuses on each gradient's direct contribution to target prediction, while the other aggregates its indirect contributions through correlations with the conditioning function values. Within a Vecchia approximation, where each prediction conditions on $m$ nearby inputs in $d$ dimensions, this construction represents their $md$ gradient coordinates using at most $2m$ directional derivatives, giving $\mathcal{O}(m^3)$ dense factorization cost per prediction target. For general cond