TY - JOUR
T1 - Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce data
AU - Gu, Hyemin
AU - Birmpa, Panagiota
AU - Pantazis, Yannis
AU - Rey-Bellet, Luc
AU - Katsoulakis, Markos A.
PY - 2024/6/11
Y1 - 2024/6/11
N2 - We build a new class of generative algorithms capable of efficiently learning an arbitrary target distribution from possibly scarce, high-dimensional data and subsequently generate new samples. These generative algorithms are particle-based and are constructed as gradient flows of Lipschitz-regularized Kullback-Leibler or other $f$-divergences, where data from a source distribution can be stably transported as particles, towards the vicinity of the target distribution. As a highlighted result in data integration, we demonstrate that the proposed algorithms correctly transport gene expression data points with dimension exceeding 54K, while the sample size is typically only in the hundreds.
AB - We build a new class of generative algorithms capable of efficiently learning an arbitrary target distribution from possibly scarce, high-dimensional data and subsequently generate new samples. These generative algorithms are particle-based and are constructed as gradient flows of Lipschitz-regularized Kullback-Leibler or other $f$-divergences, where data from a source distribution can be stably transported as particles, towards the vicinity of the target distribution. As a highlighted result in data integration, we demonstrate that the proposed algorithms correctly transport gene expression data points with dimension exceeding 54K, while the sample size is typically only in the hundreds.
KW - stat.ML
KW - cs.LG
KW - 35Q84, 49Q22, 62B10, 65C35, 68T07, 94A17
M3 - Article
SN - 2577-0187
JO - SIAM Journal on Mathematics of Data Science
JF - SIAM Journal on Mathematics of Data Science
ER -