Adaptive joint distribution learning
This work addresses the challenge of scalable and flexible joint distribution estimation for machine learning applications, though it appears incremental as it builds on existing RKHS methods.
The authors tackled the problem of estimating joint probability distributions by developing a new framework using tensor product reproducing kernel Hilbert spaces (RKHS), which accommodates low-dimensional, normalized, and positive models and handles sample sizes up to millions. Their approach yields well-defined conditional distributions, is computationally fast, and shows favorable numerical results across prediction and classification tasks.
We develop a new framework for estimating joint probability distributions using tensor product reproducing kernel Hilbert spaces (RKHS). Our framework accommodates a low-dimensional, normalized and positive model of a Radon--Nikodym derivative, which we estimate from sample sizes of up to several millions, alleviating the inherent limitations of RKHS modeling. Well-defined normalized and positive conditional distributions are natural by-products to our approach. Our proposal is fast to compute and accommodates learning problems ranging from prediction to classification. Our theoretical findings are supplemented by favorable numerical results.