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New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-2710-7). 594-603 (2014). </div> <div class="abstract"></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6451589">Cited in <strong>25</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68T05" title="MSC2020">68T05</a> </td> <td class="space"> Learning and adaptive systems in artificial intelligence </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A15A69" title="MSC2020">15A69</a> </td> <td class="space"> Multilinear algebra, tensor calculus </td> </tr><tr> <td class="mono"> 65F30 </td> <td class="space"> Other matrix algorithms (MSC2010) </td> </tr></table> </div> <div class="software"> <h3>Software:</h3><a href="/software/11355">SuLQ</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">&times;</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1315.68203" data-ciurl="/ci/06451589" data-biburl="/bibtex/06451589.bib" data-amsurl="/amsrefs/06451589.bib" data-xmlurl="/xml/06451589.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06451589.pdf" title="Zbl 1315.68203 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1145/2591796.2591881" aria-label="DOI for “Smoothed analysis of tensor decompositions”" title="10.1145/2591796.2591881">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1311.3651"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">E. Allman, C. Matias and J. Rhodes. Identifiability of Parameters in Latent Structure Models with many Observed Variables. Annals of Statistics, pages 3099-3132, 2009. &middot; <a href="/1191.62003" class="nowrap">Zbl 1191.62003</a></td> </tr><tr> <td>[2]</td> <td class="space">A. Anandkumar, D. Hsu and S. Kakade. A method of moments for mixture models and hidden Markov models. In COLT 2012.</td> </tr><tr> <td>[3]</td> <td class="space">A. Anandkumar, R. Ge, D. Hsu and S. Kakade. A Tensor Spectral Approach to Learning Mixed Membership Community Models. In COLT 2013.</td> </tr><tr> <td>[4]</td> <td class="space">A. Anandkumar, R. Ge, D. Hsu, S. Kakade and M. Telgarsky. Tensor Decompositions for Learning Latent Variable Models. arxiv:1210.7559, 2012.</td> </tr><tr> <td>[5]</td> <td class="space">A. Anandkumar, D. Foster, D. Hsu, S. Kakade, Y. Liu. A Spectral Algorithm for Latent Dirichlet Allocation. In NIPS, pages 926-934, 2012.</td> </tr><tr> <td>[6]</td> <td class="space">S. Arora, R. Ge, A. Moitra and S. Sachdeva. Provable ICA with Unknown Gaussian Noise, and Implications for Gaussian Mixtures and Autoencoders. In NIPS, pages 2384-2392, 2012.</td> </tr><tr> <td>[7]</td> <td class="space">M. Belkin, L. Rademacher and J. Voss. Bling Signal Separation in the Presence of Gaussian Noise. In COLT 2013.</td> </tr><tr> <td>[8]</td> <td class="space">M. Belkin and K. Sinha. Polynomial Learning of Distribution Families. In FOCS, pages 103-112, 2010. 10.1109/FOCS.2010.16</td> </tr><tr> <td>[9]</td> <td class="space">A. Bhaskara, M. Charikar and A. Vijayaraghavan. Uniqueness of Tensor Decompositions with Applications to Polynomial Identifiability. arxiv:1304.8087, 2013.</td> </tr><tr> <td>[10]</td> <td class="space">A. Bhaskara, M. Charikar, A. Moitra and A. Vijayaraghavan. Smoothed Analysis of Tensor Decompositions. arxiv:1311.3651, 2013.</td> </tr><tr> <td>[11]</td> <td class="space">J. Chang. Full Reconstruction of Markov Models on Evolutionary Trees: Identifiability and Consistency. Mathematical Biosciences, pages 51-73, 1996. &middot; <a href="/1059.92504" class="nowrap">Zbl 1059.92504</a></td> </tr><tr> <td>[12]</td> <td class="space">P. Comon. Independent Component Analysis: A New Concept? Signal Processing, pages 287-314, 1994. 10.1016/0165-1684(94)90029-9 &middot; <a href="/0791.62004" class="nowrap">Zbl 0791.62004</a></td> </tr><tr> <td>[13]</td> <td class="space">S. Dasgupta. Learning Mixtures of Gaussians. In FOCS, pages 634-644, 1999.</td> </tr><tr> <td>[14]</td> <td class="space">L. De Lathauwer, J Castaing and J. Cardoso. Fourth-order Cumulant-based Blind Identification of Underdetermined Mixtures. IEEE Trans. on Signal Processing, 55(6):2965-2973, 2007. 10.1109/TSP.2007.893943 &middot; <a href="/1391.94505" class="nowrap">Zbl 1391.94505</a></td> </tr><tr> <td>[15]</td> <td class="space">J. Feldman, R. A. Servedio, and R. O&rsquo;Donnell. PAC Learning Axis-aligned Mixtures of Gaussians with No Separation Assumption. In COLT, pages 20-34, 2006. 10.1007/11776420_5 &middot; <a href="/1143.68533" class="nowrap">Zbl 1143.68533</a></td> </tr><tr> <td>[16]</td> <td class="space">A. Frieze, M. Jerrum, R. Kannan. Learning Linear Transformations. In FOCS, pages 359-368, 1996.</td> </tr><tr> <td>[17]</td> <td class="space">N. Goyal, S. Vempala and Y. Xiao. Fourier PCA. In STOC, 2014 (this proceedings).</td> </tr><tr> <td>[18]</td> <td class="space">R. Harshman. Foundations of the PARFAC procedure: model and conditions for an &rsquo;explanatory&rsquo; multi-mode factor analysis. UCLA Working Papers in Phonetics, pages 1-84, 1970.</td> </tr><tr> <td>[19]</td> <td class="space">J. Håstad. Tensor Rank is NP-Complete. Journal of Algorithms, pages 644-654, 1990. 10.1016/0196-6774(90)90014-6 &middot; <a href="/0716.65043" class="nowrap">Zbl 0716.65043</a></td> </tr><tr> <td>[20]</td> <td class="space">C. Hillar and L-H. Lim. Most Tensor Problems are NP-Hard. arxiv:0911.1393v4, 2013. 10.1145/2512329</td> </tr><tr> <td>[21]</td> <td class="space">R. Horn and C. Johnson. Matrix Analysis. Cambridge University Press, 1990. &middot; <a href="/0704.15002" class="nowrap">Zbl 0704.15002</a></td> </tr><tr> <td>[22]</td> <td class="space">D. Hsu and S. Kakade. Learning Mixtures of Spherical Gaussians: Moment Methods and Spectral Decompositions. In ITCS, pages 11-20, 2013. 10.1145/2422436.2422439 &middot; <a href="/1362.68246" class="nowrap">Zbl 1362.68246</a></td> </tr><tr> <td>[23]</td> <td class="space">A. Hyvärinen, J. Karhunen and E. Oja. Independent Component Analysis. Wiley Interscience, 2001.</td> </tr><tr> <td>[24]</td> <td class="space">A. T. Kalai, A. Moitra, and G. Valiant. Efficiently Learning Mixtures of Two Gaussians. In STOC, pages 553-562, 2010. 10.1145/1806689.1806765 &middot; <a href="/1293.68229" class="nowrap">Zbl 1293.68229</a></td> </tr><tr> <td>[25]</td> <td class="space">A. T. Kalai, A. Samorodnitsky and S-H Teng. Learning and Smoothed Analysis. In FOCS, pages 395-404, 2009. 10.1109/FOCS.2009.60 &middot; <a href="/1292.68132" class="nowrap">Zbl 1292.68132</a></td> </tr><tr> <td>[26]</td> <td class="space">J. Kruskal. Three-way Arrays: Rank and Uniqueness of Trilinear Decompositions. Linear Algebra and Applications, 18:95-138, 1977. &middot; <a href="/0364.15021" class="nowrap">Zbl 0364.15021</a></td> </tr><tr> <td>[27]</td> <td class="space">S. Leurgans, R. Ross and R. Abel. A Decomposition for Three-way Arrays. SIAM Journal on Matrix Analysis and Applications, 14(4):1064-1083, 1993. 10.1137/0614071 &middot; <a href="/0788.65145" class="nowrap">Zbl 0788.65145</a></td> </tr><tr> <td>[28]</td> <td class="space">B. Lindsay. Mixture Models: Theory, Geometry and Applications. Institute for Mathematical Statistics, 1995. &middot; <a href="/1163.62326" class="nowrap">Zbl 1163.62326</a></td> </tr><tr> <td>[29]</td> <td class="space">P. McCullagh. Tensor Methods in Statistics. Chapman and Hall/CRC, 1987. &middot; <a href="/0732.62003" class="nowrap">Zbl 0732.62003</a></td> </tr><tr> <td>[30]</td> <td class="space">A. Moitra and G. Valiant. Setting the Polynomial Learnability of Mixtures of Gaussians. In FOCS, pages 93-102, 2010. 10.1109/FOCS.2010.15</td> </tr><tr> <td>[31]</td> <td class="space">E. Mossel and S. Roch. Learning Nonsingular Phylogenies and Hidden Markov Models. In STOC, pages 366-375, 2005. 10.1145/1060590.1060645 &middot; <a href="/1192.68394" class="nowrap">Zbl 1192.68394</a></td> </tr><tr> <td>[32]</td> <td class="space">Y. Rabani, L. Schulman and C. Swamy. Learning mixtures of arbitrary distributions over large discrete domains. In ITCS 2014. 10.1145/2554797.2554818 &middot; <a href="/1366.68247" class="nowrap">Zbl 1366.68247</a></td> </tr><tr> <td>[33]</td> <td class="space">C. Spearman. General Intelligence. American Journal of Psychology, pages 201-293, 1904.</td> </tr><tr> <td>[34]</td> <td class="space">D. A. Spielman, S. H. Teng. Smoothed Analysis of Algorithms: Why the Simplex Algorithm usually takes Polynomial Time. Journal of the ACM, pages 385-463, 2004. 10.1145/990308.990310 &middot; <a href="/1192.90120" class="nowrap">Zbl 1192.90120</a></td> </tr><tr> <td>[35]</td> <td class="space">D. A. Spielman, S. H. Teng. Smoothed Analysis: An Attempt to Explain the Behavior of Algorithms in Practice. Communications of the ACM, pages 76-84, 2009. 10.1145/1562764.1562785</td> </tr><tr> <td>[36]</td> <td class="space">A. Stegeman and P. Comon. Subtracting a Best Rank-1 Approximation may Increase Tensor Rank. Linear Algebra and Its Applications, pages 1276-1300, 2010. &middot; <a href="/1198.15018" class="nowrap">Zbl 1198.15018</a></td> </tr><tr> <td>[37]</td> <td class="space">H. Teicher. Identifiability of Mixtures. Annals of Mathematical Statistics, pages 244-248, 1961. &middot; <a href="/0146.39302" class="nowrap">Zbl 0146.39302</a></td> </tr><tr> <td>[38]</td> <td class="space">S. Vempala, Y. Xiao. Structure from Local Optima: Learning Subspace Juntas via Higher Order PCA. Arxiv:abs/1108.3329, 2011.</td> </tr><tr> <td>[39]</td> <td class="space">P. Wedin. Perturbation Bounds in Connection with Singular Value Decompositions. BIT, 12:99-111, 1972. &middot; <a href="/0239.15015" class="nowrap">Zbl 0239.15015</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH&nbsp;Open. 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