Speaker: 李章颂（北京大学）
Title: Recent Progress on Tensor PCA: From Kikuchi Spectral Algorithm to Tensor Networks
Language: Chinese
Time & Venue: 2026 年6月19日16:00–17:00 南楼613
Abstract: Tensor PCA is a central model for high-dimensional statistical inference with higher-order interactions. For this model, an intriguing phenomenon is that local algorithms predicted by statistical physics such as gradient descent or AMP are known to be suboptimal. This gap has motivated a search for algorithms that go beyond local marginals and exploit higher-order correlations.
In this talk, I will discuss recent progress on this question, focusing on the smooth computational transition in tensor PCA. These developments include the Kikuchi spectral algorithm, which can be viewed as a higher-order extension of belief propagation and achieves a tradeoff between signal-to-noise ratio and computational cost, as well as new algorithmic perspective based on tensor networks, or equivalently on counting carefully chosen families of weighted hypergraphs. These approaches together highlight how ideas in random matrix theory and combinatorics can be used in modern statistical inference problems.
This talk is based on several recent work by different groups, including my work arXiv:2509.09904.
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