Abstract: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 format. The methodology is a two-stage procedure. In the first stage, we take an existing interpolation method to compress the target tensor into a hierarchical Tucker (HT) in a manner similar to the CUR decomposition for low-rank matrix reconstruction. In the second stage, we fit the first-stage output against a non-negative hierarchical Tucker ansatz using a second-order method tailored specifically for this setting. When the tensor is of order \(d\), both stages admit an \(\mathcal{O}(d)\) computational complexity, and therefore the proposed methodology readily extends into high-dimensional settings. Numerical experiments show success in compressing various high-dimensional probability tensors.
From: Xun Tang [view email]
[v1]
Mon, 22 Jun 2026 21:20:04 UTC (672 KB)
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