Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization. Streaming Bayesian inference: Theoretical limits and mini-batch approximate message-passing. Spectral Clustering of graphs with the Bethe Hessian. A Landscape Analysis of Constraint Satisfaction Problems. Fast Randomized Semi-Supervised Clustering. Mutual information in rank-one matrix estimation. Nadler, B. (2008). Finite sample approximation results for principal component analysis: A matrix perturbation approach. Capitaine, M., Donati-Martin, C. and Féral, D. (2009). Perry, A., Wein, A. S., Bandeira, A. S. and Moitra, A. Approximate Survey Propagation for Statistical Inference. How does dblp detect coauthor communities. Intensity-only optical compressive imaging using a multiply scattering material : a double phase retrieval system. Benaych-Georges, F. and Nadakuditi, R. R. (2011). You need to opt-in for them to become active. Sharp detection in PCA under correlations: All eigenvalues matter. Phase retrieval in high dimensions: Statistical and computational phase transitions. Deshpande, Y., Abbé, E. and Montanari, A. CoRR abs/2006.01475 (2020) Modelling the influence of data structure on learning in neural networks. Lelarge, M. and Miolane, L. (2019). Quiet Planting in the Locked Constraint Satisfaction Problems. Robust error correction for real-valued signals via message-passing decoding and spatial coupling. DatesReceived: October 2017Revised: February 2019First available in Project Euclid: 26 May 2020, Permanent link to this documenthttps://projecteuclid.org/euclid.aos/1590480037, Digital Object Identifierdoi:10.1214/19-AOS1826, Mathematical Reviews number (MathSciNet) MR4102679, Subjects Primary: 62H25: Factor analysis and principal components; correspondence analysis Secondary: 62H15: Hypothesis testing 60G15: Gaussian processes 60F05: Central limit and other weak theorems, KeywordsHypothesis testing random matrix models contiguity spin–glasses Sherrington–Kirkpatrick model replica–symmetry, El Alaoui, Ahmed; Krzakala, Florent; Jordan, Michael. The hard-core model on random graphs revisited. Mutual Information in Rank-One Matrix Estimation. Statist. Privacy notice: By enabling the option above, your browser will contact twitter.com and twimg.com to load tweets curated by our Twitter account. In. Paul, D. (2007). Statist., Volume 48, Number 2 (2020), 863-885. Streaming Bayesian inference: theoretical limits and mini-batch approximate message-passing. The Gaussian equivalence of generative models for learning with two-layer neural networks. Kernel computations from large-scale random features obtained by Optical Processing Units. Principled Training of Neural Networks with Direct Feedback Alignment. Fast Phase Retrieval for High Dimensions: A Block-Based Approach. In, El Alaoui, A., Krzakala, F. and Jordan, M. (2020). Dobriban, E. (2017). Read more about accessing full-text. For more information, check out our privacy policy. Deformed ensembles of random matrices. 48 (2020), no. Non-subscribers gain access to supplemental files with the purchase of the article. In. Approximate message-passing for convex optimization with non-separable penalties. Estimation in the Spiked Wigner Model: A Short Proof of the Replica Formula. Ahmed El Alaoui, Florent Krzakala, and Michael Jordan, Full-text: Access denied (no subscription detected), We're sorry, but we are unable to provide you with the Contiguity and non-reconstruction results for planted partition models: The dense case. Replica Analysis and Approximate Message Passing Decoder for Superposition Codes. Clustering from sparse pairwise measurements. Guerra, F. (2003). Spectral Method for Multiplexed Phase Retrieval and Application in Optical Imaging in Complex Media. Inferring Sparsity: Compressed Sensing using Generalized Restricted Boltzmann Machines. Optical Reservoir Computing using multiple light scattering for chaotic systems prediction. Florent Krzakala Ecole Normale Superieure ... Google H-index: 46: Number of Google Citations: 7,834: Number of Articles on DBLP: 151: External Links. On consistency and sparsity for principal components analysis in high dimensions. Non-adaptive pooling strategies for detection of rare faulty items. All settings here will be stored as cookies with your web browser. Project Euclid. Kernel Computations from Large-Scale Random Features Obtained by Optical Processing Units. Inferring sparsity: Compressed sensing using generalized restricted Boltzmann machines. Sum rules for the free energy in the mean field spin glass model. Péché, S. (2006). Performance Limits for Noisy Multi-Measurement Vector Problems. arXiv preprint, Krzakala, F., Xu, J. and Zdeborová, L. (2016). Random Projections through multiple optical scattering: Approximating kernels at the speed of light. Entropy and mutual information in models of deep neural networks. Péché, S. (2014). Onatski, A., Moreira, M. J. and Hallin, M. (2013). Information-theoretic thresholds from the cavity method. On sample eigenvalues in a generalized spiked population model. Asymptotic normality and analysis of variance of log-likelihood ratios in spiked random matrix models. Training Restricted Boltzmann Machine via the Thouless-Anderson-Palmer free energy. Their combined citations are counted only for the first article. Asymptotic Errors for High-Dimensional Convex Penalized Linear Regression beyond Gaussian Matrices. Recipes for metastable states in spin glasses. Clustering from Sparse Pairwise Measurements. Model Selection for Degree-corrected Block Models. Profile was last updated at November 12, 2020, 12:09 am, EPFL : École polytechnique fédérale de Lausanne, Machine Learning & Artificial Intelligence, Computational Linguistics & Speech Processing, Ranking for Top Computer Science Universities 2020, Ranking for Top Scientists in Computer Science and Electronics 2020, 6th Edition, Ranking for Top Scientists in Computer Science and Electronics 2019, 5th Edition, Ranking for Top Scientists in Computer Science and Electronics 2018, Special Issues for Journals With Impact Factor, 2017/2017, Conference Ranking : Top Computer Science Conferences, 2017/2017, Impact Factor for Top Journals of Computer Science and Electronics, 2017, Impact Factor for Top Journals of Computer Science and Electronics, 2016, Impact Factor for Top Journals of Computer Science and Electronics, 2015, How to chart a successful research career by Prof Alan Johnson, Top H-Index for Scholars of Computer Science & Electronics, 2014. https://projecteuclid.org/euclid.aos/1590480037, © Fluctuations of the free energy of the spherical Sherrington–Kirkpatrick model. Gibbs states and the set of solutions of random constraint satisfaction problems. Spectral detection on sparse hypergraphs. At the same time, Twitter will persistently store several cookies with your web browser. While we did signal Twitter to not track our users by setting the "dnt" flag, we do not have any control over how Twitter uses your data. 103rd. Matrices. What is the meaning of the colors in the coauthor index? So please proceed with care and consider checking the OpenCitations privacy policy as well as the AI2 Privacy Policy covering Semantic Scholar. Lesieur, T., Krzakala, F. and Zdeborová, L. (2015). The spiked matrix model with generative priors. Who is Afraid of Big Bad Minima? High-dimensional analysis of semidefinite relaxations for sparse principal components. Onatski, A., Moreira, M. J. and Hallin, M. (2014). Estimation in the spiked Wigner model: A short proof of the replica formula. This establishes the maximal region of contiguity between the planted and null models. On Convergence of Approximate Message Passing. All Conferences. Phase recovery from a Bayesian point of view: The variational approach. High-dimensional generalized linear models are basic building blocks of current data analysis tools including multilayers neural networks. When the spike comes from a prior that is i.i.d. Matrix Completion from Fewer Entries: Spectral Detectability and Rank Estimation. Generalisation error in learning with random features and the hidden manifold model. Some rigorous results on the Sherrington–Kirkpatrick spin glass model. The largest eigenvalue of small rank perturbations of Hermitian random matrices. First-order transitions and the performance of quantum algorithms in random optimization problems. (2018). Eigenvalues of large sample covariance matrices of spiked population models. Florent Krzakala École polytechnique fédérale de Lausanne Email verificata su epfl.ch Pan Zhang Institute of Theoretical Physics, Chinese Academy of Sciences Email verificata su itp.ac.cn Andrea Montanari Professor of Electrical Engineering and Statistics, Stanford University Email … Analysis of gradient-flow in spiked matrix-tensor models. Phase Transitions and Sample Complexity in Bayes-Optimal Matrix Factorization. We study the fundamental limits of detecting the presence of an additive rank-one perturbation, or spike, to a Wigner matrix. Marvels and Pitfalls of the Langevin Algorithm in Noisy High-dimensional Inference. Although we do not have any reason to believe that your call will be tracked, we do not have any control over how the remote server uses your data. Fundamental limits of symmetric low-rank matrix estimation. In, Barbier, J., Dia, M., Macris, N., Krzakala, F., Lesieur, T. and Zdeborová, L. (2016). The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective. The largest eigenvalues of finite rank deformation of large Wigner matrices: Convergence and nonuniversality of the fluctuations. (2018). Privacy notice: By enabling the option above, your browser will contact the API of opencitations.net and semanticscholar.org to load citation information. (2017). (2012). Variational Free Energies for Compressed Sensing. In, El Alaoui, A. and Krzakala, F. (2018). Replica analysis and approximate message passing decoder for superposition codes. 62H25: Factor analysis and principal components; correspondence analysis, 60F05: Central limit and other weak theorems, Optimality and sub-optimality of PCA I: Spiked random matrix models, Central limit theorems for cavity and local fields of the Sherrington-Kirkpatrick model, Spin glass models from the point of view of spin distributions, The Aizenman-Sims-Starr and Guerras schemes for the SK model with multidimensional spins, Variational representations for the Parisi functional and the two-dimensional Guerra–Talagrand bound, Disorder chaos in the Sherrington–Kirkpatrick model with external field, Computational and statistical boundaries for submatrix localization in a large noisy matrix. In. Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Models. The mutual information in random linear estimation. Detection limits in the high-dimensional spiked rectangular model. Privacy notice: By enabling the option above, your browser will contact the API of unpaywall.org to load hyperlinks to open access articles. Approximate Message Passing with Restricted Boltzmann Machine Priors. Large-Scale Optical Reservoir Computing for Spatiotemporal Chaotic Systems Prediction. 2, 863--885. doi:10.1214/19-AOS1826. In. Privacy notice: By enabling the option above, your browser will contact the APIs of crossref.org, opencitations.net, and semanticscholar.org to load article reference information. Intensity-only optical compressive imaging using a multiply scattering material and a double phase retrieval approach. The role of regularization in classification of high-dimensional noisy Gaussian mixture. A. and Wainwright, M. J. Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications. In Proceedings of the 31st Conference on Learning Theory (COLT) 75 410–438. To protect your privacy, all features that rely on external API calls from your browser are turned off by default. Johnstone, I. M. (2001). across coordinates, we prove that the log-likelihood ratio of the spiked model against the nonspiked one is asymptotically normal below a certain reconstruction threshold which is not necessarily of a “spectral” nature, and that it is degenerate above. (2018). Adaptive Damping and Mean Removal for the Generalized Approximate Message Passing Algorithm. Blind Calibration for Sparse Regression: A State Evolution Analysis. Baik, J. and Silverstein, J. W. (2006). Fluctuations of the free energy of the spherical Sherrington–Kirkpatrick model with ferromagnetic interaction. Supplement to “Fundamental limits of detection in the spiked Wigner model”. Spectral detection in the censored block model. Blind Calibration in Compressed Sensing using Message Passing Algorithms. Their combined citations are counted only for the first article. Compressed sensing and Approximate Message Passing with spatially-coupled Fourier and Hadamard matrices. Although we do not have any reason to believe that your call will be tracked, we do not have any control over how the remote server uses your data. Compressed sensing under matrix uncertainty: Optimum thresholds and robust approximate message passing. Approximate Message-Passing Decoder and Capacity Achieving Sparse Superposition Codes. Reweighted Belief Propagation and Quiet Planting for Random K-SAT. Johnstone, I. M. and Onatski, A. Mutual information in rank-one matrix estimation. (2016). load references from crossref.org and opencitations.net. So please proceed with care and consider checking the Crossref privacy policy and the OpenCitations privacy policy, as well as the AI2 Privacy Policy covering Semantic Scholar. Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices. Scampi: a robust approximate message-passing framework for compressive imaging. Statistical physics-based reconstruction in compressed sensing. 2020 Phase transitions and optimal algorithms in high-dimensional Gaussian mixture clustering. Dynamical mean-field theory for stochastic gradient descent in Gaussian mixture classification. Exact asymptotics for phase retrieval and compressed sensing with random generative priors. Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula. Detection limits in the high-dimensional spiked rectangular model. Light-in-the-loop: using a photonics co-processor for scalable training of neural networks. El Alaoui, A. and Jordan, M. I. Fundamental limits of detection in the spiked Wigner model. (2015). Boucheron, S., Lugosi, G. and Massart, P. (2013). Compressed Sensing of Approximately-Sparse Signals: Phase Transitions and Optimal Reconstruction. Decoding from Pooled Data: Sharp Information-Theoretic Bounds. Robust Phase Retrieval with the Swept Approximate Message Passing (prSAMP) Algorithm. For more information see our F.A.Q. Spectral redemption: clustering sparse networks. Reservoir Computing meets Recurrent Kernels and Structured Transforms. This supplement (El Alaoui, Krzakala and Jordan (2020)) contains the proof of convergence of the moments of the overlap $R_{1,*}$ thereby completing the proof of Theorem 10, and the proof of Lemma 14. the dblp computer science bibliography is funded by: Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation. G2R World Ranking Phase Transitions in the Coloring of Random Graphs. On convergence of approximate message passing. Spectral Detection in the Censored Block Model. It is known that this threshold also marks a phase transition for estimating the spike: the latter task is possible above the threshold and impossible below. (1987). (2016). Proceedings of the third "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'16). Hiding Quiet Solutions in Random Constraint Satisfaction Problems. Generalisation dynamics of online learning in over-parameterised neural networks. Decoding from pooled data: Phase transitions of message passing. Add a list of citing articles from and to record detail pages. Scaling Up Echo-State Networks With Multiple Light Scattering. Amini, A. Further information on the performance of the optimal test is also provided. The following articles are merged in Scholar. A Deterministic and Generalized Framework for Unsupervised Learning with Restricted Boltzmann Machines. Guide2Research uses the information to contact you about our relevant content. The largest eigenvalue of rank one deformation of large Wigner matrices. Florent Krzakala École polytechnique fédérale de Lausanne Verified email at epfl.ch Luca Leuzzi, PhD Institute of Nanotechnology, CNR, Italy Verified email at cnr.it Guilhem Semerjian LPT … Franz, S. and Parisi, G. (1998). So please proceed with care and consider checking the Internet Archive privacy policy. Variational free energies for compressed sensing. Training Restricted Boltzmann Machines via the Thouless-Anderson-Palmer Free Energy. Supplement to “Fundamental limits of detection in the spiked Wigner model.”. Multi-Layer Generalized Linear Estimation. El Alaoui, A. and Jordan, M. I. Swept Approximate Message Passing for Sparse Estimation. Effective potential in glassy systems: Theory and simulations. TRAMP: Compositional Inference with TRee Approximate Message Passing. Phase transitions and sample complexity in Bayes-optimal matrix factorization. (2008). Robust phase retrieval with the swept approximate message passing (prSAMP) algorithm. Optimality and sub-optimality of PCA I: Spiked random matrix models. Blind calibration for compressed sensing: State evolution and an online algorithm. Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Berthet, Q. and Rigollet, P. (2013). Analysis of Gradient-Flow in a Spiked Matrix-Tensor Model. High-temperature Expansions and Message Passing Algorithms. Asymptotic power of sphericity tests for high-dimensional data. In. Bai, Z. and Yao, J. The following articles are merged in Scholar. Spectral Clustering of Graphs with the Bethe Hessian. Phase Diagram and Approximate Message Passing for Blind Calibration and Dictionary Learning. Complex Dynamics in Simple Neural Networks: Understanding Gradient Flow in Phase Retrieval. Direct Feedback Alignment Scales to Modern Deep Learning Tasks and Architectures. They arise in signal processing, statistical inference, machine learning, communication theory, and other fields. Julien Launay, Iacopo Poli, Kilian Müller, Igor Carron, Laurent Daudet, Florent Krzakala, Sylvain Gigan: Light-in-the-loop: using a photonics co-processor for scalable training of neural networks. Privacy notice: By enabling the option above, your browser will contact the API of web.archive.org to check for archived content of web pages that are no longer available. Statistical physics of inference: Thresholds and algorithms. Although we do not have any reason to believe that your call will be tracked, we do not have any control over how the remote server uses your data. Broken replica symmetry bounds in the mean field spin glass model. Florent Krzakala Ecole Normale Supérieure Paris, Sorbonne Université, LightOn Verified email at ens.fr Alaa Saade Research Engineer at Deepmind Verified email at google.com Angélique Drémeau ENSTA Bretagne Verified email at ensta-bretagne.fr Random projections through multiple optical scattering: Approximating Kernels at the speed of light. Supplemental files are immediately available to subscribers. Dynamics of stochastic gradient descent for two-layer neural networks in the teacher-student setup. Baik, J. and Lee, J. O. Féral, D. and Péché, S. (2007). Phase Transitions, Optimal Errors and Optimality of Message-Passing in Generalized Linear Models. Threshold values, stability analysis and high-q asymptotics for the coloring problem on random graphs. ; El Alaoui, A. and Krzakala, F. (2018). If you have a personal subscription to this journal, Our proofs are based on Gaussian interpolation methods and a rigorous incarnation of the cavity method, as devised by Guerra and Talagrand in their study of the Sherrington–Kirkpatrick spin-glass model. Decoding from Pooled Data: Phase Transitions of Message Passing. Ann. Although we do not have any reason to believe that your call will be tracked, we do not have any control over how the remote server uses your data. Baik, J., Ben Arous, G. and Péché, S. (2005). In. Constrained Low-rank Matrix Estimation: Phase Transitions, Approximate Message Passing and Applications. Google Scholar Profile; List of Publications on DBLP ... 11:28 pm Guide2Research Ranking is based on Google Scholar H-Index. Statistical and computational phase transitions in spiked tensor estimation. Finite Size Corrections and Likelihood Ratio Fluctuations in the Spiked Wigner Model. Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems. Scaling up Echo-State Networks with multiple light scattering. Approximate message-passing decoder and capacity-achieving sparse superposition codes. SourceAnn. Rank-one matrix estimation: analysis of algorithmic and information theoretic limits by the spatial coupling method. Report Missing or Incorrect Information. Fast phase retrieval for high dimensions: A block-based approach. MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel. Banerjee, D. and Ma, Z. If you are already logged in, then you may need Epidemic mitigation by statistical inference from contact tracing data. Passed & Spurious: analysing descent algorithms and local minima in spiked matrix-tensor model. full text of this article because we are not able to identify you as So please proceed with care and consider checking the Twitter privacy policy. Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. last updated on 2020-10-27 22:14 CET by the dblp team, all metadata released as open data under CC0 1.0 license, see also: Terms of Use | Privacy Policy | Imprint. Quantum energy gaps and first-order mean-field-like transitions. Decoding From Pooled Data: Phase Transitions of Message Passing. Optimal detection of sparse principal components in high dimension. Florent Krzakala Ecole Normale Supérieure Paris, Sorbonne Université, LightOn Verified email at ens.fr Paolo Tombesi Università di Camerino Verified email at unicam.it Hugo Defienne Lecturer and Marie Curie-Sklodowska fellow, University of Glasgow Verified email at glasgow.ac.uk The Mutual Information in Random Linear Estimation Beyond i.i.d. On the distribution of the largest eigenvalue in principal components analysis. Asymptotic mutual information for the binary stochastic block model. Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula. What is the meaning of the colors in the publication lists? Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. The committee machine: Computational to statistical gaps in learning a two-layers neural network. Compressed Sensing under Matrix Uncertainty: Optimum Thresholds and Robust Approximate Message Passing. Phase transitions in sparse PCA. to update your profile to register your subscription. Signal detection in high dimension: The multispiked case. Aizenman, M., Lebowitz, J. L. and Ruelle, D. (1987). Testing in high-dimensional spiked models. a subscriber. Phase Transitions and Computational Difficulty in Random Constraint Satisfaction Problems. Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization. The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices. Central limit theorems for eigenvalues in a spiked population model. Phase transition in the detection of modules in sparse networks. Adaptive damping and mean removal for the generalized approximate message passing algorithm. Add open access links from to the list of external document links (if available). (2018). Phase recovery from a Bayesian point of view: the variational approach. Sparse Estimation with the Swept Approximated Message-Passing Algorithm. Multi-layer generalized linear estimation. Phase diagram and approximate message passing for blind calibration and dictionary learning. then please login. Mézard, M., Parisi, G. and Virasoro, M. A. Add a list of references from , , and to record detail pages. Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime. Belief Propagation Reconstruction for Discrete Tomography. (2009). Passed & Spurious: Descent Algorithms and Local Minima in Spiked Matrix-Tensor Models. Who is Afraid of Big Bad Minima? So please proceed with care and consider checking the Unpaywall privacy policy. Guerra, F. (2001). Ledoit, O. and Wolf, M. (2002). Spectral density of the non-backtracking operator. The Mutual Information in Random Linear Estimation. Baik, J. and Lee, J. O. 3729th, G2R Switzerland Ranking Bai, Z. and Yao, J. For web page which are no longer available, try to retrieve content from the of the Internet Archive (if available). Therefore, both estimation and detection undergo the same transition in this random matrix model. (2017). Franz, S. and Parisi, G. (1995). Spectral Detection on Sparse Hypergraphs. On the Universality of Noiseless Linear Estimation with Respect to the Measurement Matrix. Comparative Study for Inference of Hidden Classes in Stochastic Block Models. Banerjee, D. (2018). Johnstone, I. M. and Lu, A. Y. Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (or : How to Prove Kabashima's Replica Formula). ... Florent Krzakala École polytechnique fédérale de Lausanne Verified email at epfl.ch. Compressed sensing of approximately-sparse signals: Phase transitions and optimal reconstruction. Rademacher complexity and spin glasses: A link between the replica and statistical theories of learning. Performance Limits for Noisy Multimeasurement Vector Problems. arXiv preprint, Banks, J., Moore, C., Vershynin, R., Verzelen, N. and Xu, J. (2009).
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