Nonparametric Density Estimation in High Dimensions via Tensor Trains

Abstract: We propose a tensor-based linear algebraic framework for density estimation and sampling. The method consists of two simple steps: first, smoothing the empirical density tensor with cluster-basis kernels to reduce estimator variance; second, compressing the smoothed empirical density tensor into tensor-train format. Numerical results show that the proposed method achieves accurate density estimation and sampling in dimensions up to 100.