Matches in SemOpenAlex for { <https://semopenalex.org/work/W4226532961> ?p ?o ?g. }
Showing items 1 to 89 of
89
with 100 items per page.
- W4226532961 abstract "We propose Selective Multiple Power Iterations (SMPI), a new algorithm to address the important Tensor PCA problem that consists in recovering a spike $${varvec{v}}_0^{otimes k}$$ corrupted by a Gaussian noise tensor $${varvec{textsf{Z}}}in (mathbb {R}^n)^{otimes k}$$ such that $${varvec{textsf{T}}}=sqrt{n} beta {varvec{v}}_0^{otimes k} + {varvec{textsf{Z}}}$$ where $$beta$$ is the signal-to-noise ratio. SMPI consists in generating a polynomial number of random initializations, performing a polynomial number of symmetrized tensor power iterations on each initialization, then selecting the one that maximizes $$langle {varvec{textsf{T}}}, {varvec{v}}^k rangle$$ . Various numerical simulations for $$k=3$$ in the conventionally considered range $$n le 1000$$ , where existent algorithms exhibit negligible finite size effects, show that the experimental performances of SMPI improve drastically upon existent algorithms and becomes comparable to the theoretical optimal recovery. We show that these unexpected performances are due to a powerful mechanism in which the noise plays a key role for the signal recovery and that takes place at low $$beta$$ . Furthermore, this mechanism results from five essential features of SMPI that distinguish it from previous algorithms based on power iteration. These remarkable results may have strong impact on both practical and theoretical applications of Tensor PCA. (i) We provide in the supplementary material multiple variants of this algorithm to tackle low-rank CP tensor decomposition. These proposed algorithms also outperforms existent methods even on real data which shows a huge potential impact for practical applications. (ii) We present new theoretical insights on the behavior of SMPI and gradient descent methods for the optimization in high-dimensional non-convex landscapes that are present in various machine learning problems. (iii) We expect that these results may help the discussion concerning the existence of the conjectured statistical-algorithmic gap." @default.
- W4226532961 created "2022-05-05" @default.
- W4226532961 creator A5001854609 @default.
- W4226532961 creator A5011658099 @default.
- W4226532961 creator A5034962986 @default.
- W4226532961 date "2023-06-01" @default.
- W4226532961 modified "2023-10-18" @default.
- W4226532961 title "Selective multiple power iteration: from tensor PCA to gradient-based exploration of landscapes" @default.
- W4226532961 cites W1625271478 @default.
- W4226532961 cites W1985242206 @default.
- W4226532961 cites W2017014096 @default.
- W4226532961 cites W2290522125 @default.
- W4226532961 cites W2580834719 @default.
- W4226532961 cites W2726993892 @default.
- W4226532961 cites W2947984106 @default.
- W4226532961 cites W2950741027 @default.
- W4226532961 cites W2968353065 @default.
- W4226532961 cites W2972186810 @default.
- W4226532961 cites W3004687303 @default.
- W4226532961 cites W3046968338 @default.
- W4226532961 cites W3088227389 @default.
- W4226532961 cites W3098833323 @default.
- W4226532961 cites W3101714678 @default.
- W4226532961 cites W3105661242 @default.
- W4226532961 cites W3168912018 @default.
- W4226532961 cites W3173235944 @default.
- W4226532961 cites W4283791819 @default.
- W4226532961 doi "https://doi.org/10.1140/epjs/s11734-023-00844-2" @default.
- W4226532961 hasPublicationYear "2023" @default.
- W4226532961 type Work @default.
- W4226532961 citedByCount "0" @default.
- W4226532961 crossrefType "journal-article" @default.
- W4226532961 hasAuthorship W4226532961A5001854609 @default.
- W4226532961 hasAuthorship W4226532961A5011658099 @default.
- W4226532961 hasAuthorship W4226532961A5034962986 @default.
- W4226532961 hasBestOaLocation W42265329614 @default.
- W4226532961 hasConcept C11413529 @default.
- W4226532961 hasConcept C114466953 @default.
- W4226532961 hasConcept C114614502 @default.
- W4226532961 hasConcept C115961682 @default.
- W4226532961 hasConcept C118615104 @default.
- W4226532961 hasConcept C134306372 @default.
- W4226532961 hasConcept C154945302 @default.
- W4226532961 hasConcept C155281189 @default.
- W4226532961 hasConcept C159694833 @default.
- W4226532961 hasConcept C162443888 @default.
- W4226532961 hasConcept C164226766 @default.
- W4226532961 hasConcept C199360897 @default.
- W4226532961 hasConcept C202444582 @default.
- W4226532961 hasConcept C33923547 @default.
- W4226532961 hasConcept C41008148 @default.
- W4226532961 hasConcept C90119067 @default.
- W4226532961 hasConcept C99498987 @default.
- W4226532961 hasConceptScore W4226532961C11413529 @default.
- W4226532961 hasConceptScore W4226532961C114466953 @default.
- W4226532961 hasConceptScore W4226532961C114614502 @default.
- W4226532961 hasConceptScore W4226532961C115961682 @default.
- W4226532961 hasConceptScore W4226532961C118615104 @default.
- W4226532961 hasConceptScore W4226532961C134306372 @default.
- W4226532961 hasConceptScore W4226532961C154945302 @default.
- W4226532961 hasConceptScore W4226532961C155281189 @default.
- W4226532961 hasConceptScore W4226532961C159694833 @default.
- W4226532961 hasConceptScore W4226532961C162443888 @default.
- W4226532961 hasConceptScore W4226532961C164226766 @default.
- W4226532961 hasConceptScore W4226532961C199360897 @default.
- W4226532961 hasConceptScore W4226532961C202444582 @default.
- W4226532961 hasConceptScore W4226532961C33923547 @default.
- W4226532961 hasConceptScore W4226532961C41008148 @default.
- W4226532961 hasConceptScore W4226532961C90119067 @default.
- W4226532961 hasConceptScore W4226532961C99498987 @default.
- W4226532961 hasLocation W42265329611 @default.
- W4226532961 hasLocation W42265329612 @default.
- W4226532961 hasLocation W42265329613 @default.
- W4226532961 hasLocation W42265329614 @default.
- W4226532961 hasOpenAccess W4226532961 @default.
- W4226532961 hasPrimaryLocation W42265329611 @default.
- W4226532961 hasRelatedWork W1955967056 @default.
- W4226532961 hasRelatedWork W2067736657 @default.
- W4226532961 hasRelatedWork W2153806284 @default.
- W4226532961 hasRelatedWork W2971195897 @default.
- W4226532961 hasRelatedWork W2984181226 @default.
- W4226532961 hasRelatedWork W3000379329 @default.
- W4226532961 hasRelatedWork W3168377052 @default.
- W4226532961 hasRelatedWork W3210997717 @default.
- W4226532961 hasRelatedWork W4286890099 @default.
- W4226532961 hasRelatedWork W4308669012 @default.
- W4226532961 isParatext "false" @default.
- W4226532961 isRetracted "false" @default.
- W4226532961 workType "article" @default.