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Variational inference and density estimation with non-negative tensor of hierarchical tucker format
Xun Tang, Haoxuan Chen, Lexing Ying
In this work, we present an efficient method to compress a high-dimensional discrete probability function, i.e., a probability tensor, into a non-negative hierarchical Tucker forma…
Variational inference and density estimation with non-negative tensor train
Xun Tang, Rajat Dwaraknath, Lexing Ying
This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings…
Initialization and training of matrix product state probabilistic models
Xun Tang, Yuehaw Khoo, Lexing Ying
Modeling probability distributions via the wave function of a quantum state is central to quantum-inspired generative modeling and quantum state tomography (QST). We investigate a…
Solving the Fokker-Planck equation of discretized Dean-Kawasaki models with functional hierarchical tensor
Xun Tang, Lexing Ying
We introduce a novel numerical scheme for solving the Fokker-Planck equation of discretized Dean-Kawasaki models with a functional tensor network ansatz. The Dean-Kawasaki model de…
Wavelet-based density sketching with functional hierarchical tensor
Xun Tang, Lexing Ying
We introduce the functional hierarchical tensor under a wavelet basis (FHT-W) ansatz for high-dimensional density estimation in lattice models. Recently, the functional tensor netw…
Approximation of High-Dimensional Gibbs Distributions with Functional Hierarchical Tensors
Nan Sheng, Xun Tang, Haoxuan Chen +1
The numerical representation of high-dimensional Gibbs distributions is challenging due to the curse of dimensionality manifesting through the intractable normalization constant ca…