장소: 이학관 526호 권택연 세미나실
일시: 2024년 1월 5일 오후 1시 30분
연사: 서해윤 (University of Maryland)
Title: Unordered data as sets and measures
Abstract: Embedding unordered data on a compact Polish space $X$ with various cardinalities as sets and measures is discussed. This study shed light on how data with different numbers of data points are compared, combined, and processed in machine learning. Three spaces are considered as embedded spaces: the space $\mathcal{K}(X)$ of compact subsets of $X$, $\mathcal{R}(X)$ of Radon probability measures on $X$, and $\mathcal{M}_+(X)$ of positive Radon measures on $X$. It will be shown that a function defined on $\mathcal{K}(X)$ or $\mathcal{R}(X)$ subsumes permutation-invariant functions with various numbers of inputs. A universal approximation theorem will be given for functions defined on $\mathcal{K}(X)$, $\mathcal{R}(X)$, and $\mathcal{M}_+(X)$ as stated in PointNet and Deep Sets. Permutation-equivariant counterparts will be formulated and universal approximation theorems for them will be also presented.