We propose a linear algebraic framework for performing density estimation. It consists of three simple steps: convolving the empirical distribution with certain smoothing kernels to remove the exponentially large variance; compressing the empirical distribution after convolution as a tensor train, with efficient tensor decomposition algorithms; and finally, applying a deconvolution step to recover the estimated density from such tensor-train representation. Numerical results demonstrate the high accuracy and efficiency of the proposed methods.

翻译：本文提出了一种用于执行密度估计的线性代数框架。该框架包含三个简单步骤：首先，将经验分布与特定的平滑核进行卷积，以消除指数级大的方差；其次，利用高效的张量分解算法，将卷积后的经验分布压缩为张量链表示；最后，通过反卷积步骤从该张量链表示中恢复估计的密度。数值实验结果验证了所提方法的高精度与高效性。