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info.json
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{
"abstract": "We investigate the power iteration algorithm for the tensor PCA model introduced in Richard and Montanari (2014). Previous work studying the properties of tensor power iteration is either limited to a constant number of iterations, or requires a non-trivial data-independent initialization. In this paper, we move beyond these limitations and analyze the dynamics of randomly initialized tensor power iteration up to polynomially many steps. Our contributions are threefold: First, we establish sharp bounds on the number of iterations required for power method to converge to the planted signal, for a broad range of the signal-to-noise ratios. Second, our analysis reveals that the actual algorithmic threshold for power iteration is smaller than the one conjectured in the literature by a $\\mathrm{polylog}(n)$ factor, where $n$ is the ambient dimension. Finally, we propose a simple and effective stopping criterion for power iteration, which provably outputs a solution that is highly correlated with the true signal. Extensive numerical experiments verify our theoretical results.",
"authors": [
"Yuchen Wu",
"Kangjie Zhou"
],
"emails": [
"wuyc14@wharton.upenn.edu",
"kangjie@stanford.edu"
],
"id": "24-0006",
"issue": 195,
"pages": [
1,
42
],
"title": "Sharp analysis of power iteration for tensor PCA",
"volume": 25,
"year": 2024
}