Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce data
This addresses the challenge of data scarcity in high-dimensional domains like genomics, though it appears incremental as it builds on existing gradient flow and regularization techniques.
The authors tackled the problem of learning arbitrary target distributions from scarce, high-dimensional data by developing a new class of generative particle algorithms based on Lipschitz-regularized gradient flows, achieving stable transport of gene expression data with dimensions over 54K using sample sizes in the hundreds.
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.