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Poster
Statistical Performance of Convex Tensor Decomposition
Ryota Tomioka · Taiji Suzuki · Kohei Hayashi · Hisashi Kashima

Mon Dec 12 10:00 AM -- 02:59 PM (PST) @ None #None

We analyze the statistical performance of a recently proposed convex tensor decomposition algorithm. Conventionally tensor decomposition has been formulated as non-convex optimization problems, which hindered the analysis of their performance. We show under some conditions that the mean squared error of the convex method scales linearly with the quantity we call the normalized rank of the true tensor. The current analysis naturally extends the analysis of convex low-rank matrix estimation to tensors. Furthermore, we show through numerical experiments that our theory can precisely predict the scaling behaviour in practice.

Author Information

Ryota Tomioka (Microsoft Research Cambridge)
Taiji Suzuki (The University of Tokyo/JST-PRESTO/RIKEN)
Kohei Hayashi (Preferred Networks)
Hisashi Kashima

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