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Weak detection in the spiked Wigner model [article]

Hye Won Chung, Ji Oon Lee
2019 arXiv   pre-print
We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible.  ...  We establish a central limit theorem for the linear spectral statistics of general rank-one spiked Wigner matrices as an intermediate step.  ...  Conclusion and Future Works In this paper, we proposed a hypothesis test for a signal detection problem in a rank-one spiked Wigner model.  ... 
arXiv:1809.10827v3 fatcat:qkzujrdx2zhdhpt3ipiip4wbvq

Weak Detection in the Spiked Wigner Model with General Rank [article]

Ji Hyung Jung, Hye Won Chung, Ji Oon Lee
2021 arXiv   pre-print
We study the statistical decision process of detecting the signal from a 'signal+noise' type matrix model with an additive Wigner noise.  ...  We propose a hypothesis test based on the linear spectral statistics of the data matrix, which does not depend on the distribution of the signal or the noise.  ...  Introduction The spiked Wigner model is one of the most natural low-rank models of 'signal-plus-noise' type.  ... 
arXiv:2001.05676v3 fatcat:453fvsnfxjheldv35sa2rfar6e

Temporal and spatial multiplexed infrared single-photon counter based on high-speed avalanche photodiode

Xiuliang Chen, Chengjie Ding, Haifeng Pan, Kun Huang, Julien Laurat, Guang Wu, E Wu
2017 Scientific Reports  
One is based on a sub-saturation operation of APDs, which enables to output a detectable signal proportional to the incident photon number with the help of spike noise cancellation method 16,21 .  ...  In this context, increasing the detection rate is an important challenge.  ...  By subtracting the identical signal in the APD response of the two successive gating cycles, the weak avalanche signal can be extracted from the spike noise.  ... 
doi:10.1038/srep44600 pmid:28294155 pmcid:PMC5353712 fatcat:6qnmtm2zi5dbfjmhwojvvqupda

Optimality and sub-optimality of PCA I: Spiked random matrix models

Amelia Perry, Alexander S. Wein, Afonso S. Bandeira, Ankur Moitra
2018 Annals of Statistics  
Such results form the basis of our understanding of when PCA can detect a low-rank signal in the presence of noise.  ...  A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random  ...  The authors are indebted to Philippe Rigollet for helpful discussions and for many comments on a draft. We thank the anonymous reviewers for many helpful, detailed comments.  ... 
doi:10.1214/17-aos1625 fatcat:7yrxzyhfszeudhjh4jinvnl6wq

Subexponential-Time Algorithms for Sparse PCA [article]

Yunzi Ding, Dmitriy Kunisky, Alexander S. Wein, Afonso S. Bandeira
2020 arXiv   pre-print
We study the computational cost of recovering a unit-norm sparse principal component x ∈R^n planted in a random matrix, in either the Wigner or Wishart spiked model (observing either W + λ xx^ with W drawn  ...  Prior work has shown that when the signal-to-noise ratio (λ or β√(N/n), respectively) is a small constant and the fraction of nonzero entries in the planted vector is x_0 / n = ρ, it is possible to recover  ...  We will study two classical variants of the spiked matrix model: the Wigner and Wishart models. The models differ in how noise is applied to the signal vector.  ... 
arXiv:1907.11635v2 fatcat:ftd7pmyxe5ehdkdo2vhtuxneqm

Statistical limits of spiked tensor models [article]

Amelia Perry and Alexander S. Wein and Afonso S. Bandeira
2017 arXiv   pre-print
For sparse signals (iii), our bounds are also asymptotically tight in the sparse limit ρ→ 0 for any fixed d (including the d=2 case of sparse PCA).  ...  We study the statistical limits of both detecting and estimating a rank-one deformation of a symmetric random Gaussian tensor.  ...  We thank Yash Deshpande and Thibault Lesieur for resolving an issue in the replica predictions section of the first version of this paper.  ... 
arXiv:1612.07728v2 fatcat:i5ana3ou3nbpjlf2cgqoxyk5le

Information-Theoretic Bounds and Phase Transitions in Clustering, Sparse PCA, and Submatrix Localization

Jess Banks, Cristopher Moore, Roman Vershynin, Nicolas Verzelen, Jiaming Xu
2018 IEEE Transactions on Information Theory  
Each of these problems is conjectured to exhibit a sharp information-theoretic threshold, below which the signal is too weak for any algorithm to detect.  ...  We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise.  ...  This corresponds to the sparse, spiked Wigner model of [16] , [29] .  ... 
doi:10.1109/tit.2018.2810020 fatcat:djasi4gkhrb2rk6ochxgec3gwa

Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization

Jess Banks, Cristopher Moore, Roman Vershynin, Nicolas Verzelen, Jiaming Xu
2017 2017 IEEE International Symposium on Information Theory (ISIT)  
Each of these problems is conjectured to exhibit a sharp information-theoretic threshold, below which the signal is too weak for any algorithm to detect.  ...  We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise.  ...  This corresponds to the sparse, spiked Wigner model of [16] , [29] .  ... 
doi:10.1109/isit.2017.8006706 dblp:conf/isit/BanksMVVX17 fatcat:6n7hc2hjbrehviy52ddwsvx2ou

Endogenous circannual rhythm in luteinizing hormone secretion: insight from signal analysis coupled with mathematical modelling

A. Vidal, C. Medigue, B. Malpaux, F. Clement
2009 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
To further investigate the LF (low frequency) and HF (high frequency) components of the signals, we have designed a mathematical model of LH plasmatic level accounting for the effect of experimental sampling  ...  The model enables us to confirm the existence of an endogenous circannual rhythm, to investigate the action mechanism of photoperiod on the pulsatile pattern of LH secretion (control of the interpulse  ...  Acknowledgements: The authors would like to thank Xochitl Hernandez for her technical assistance. Grants: This work is part of the Large-Scale Project REGATE (REgulation of the Go-nAdoTropE axis) 2 .  ... 
doi:10.1098/rsta.2009.0136 pmid:19884179 fatcat:6ydrzcepsrc5jndaoo56d5jaim

Notes on computational-to-statistical gaps: predictions using statistical physics [article]

Afonso S. Bandeira, Amelia Perry, Alexander S. Wein
2018 arXiv   pre-print
These notes are based on a lecture series given by the authors at the Courant Institute of Mathematical Sciences in New York City, on May 16th, 2017.  ...  These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient algorithm exists, rendering the problem essentially unsolvable for large instances  ...  The authors would also like to thank Soledad Villar and Lenka Zdeborová for feedback on earlier versions of this manuscript.  ... 
arXiv:1803.11132v2 fatcat:hebxyfuik5hj7gj3p6fi4vci44

1/fNoise Outperforms White Noise in Sensitizing Baroreflex Function in the Human Brain

Rika Soma, Daichi Nozaki, Shin Kwak, Yoshiharu Yamamoto
2003 Physical Review Letters  
In both cases, this noisy galvanic vestibular stimulation optimized covariance between the weak input signals and the heart rate responses.  ...  We examined the compensatory heart rate response to a weak periodic signal introduced via venous blood pressure receptors while adding 1=f or white noise with the same variance to the brain stem through  ...  The ubiquitousness of 1=f noise in the brain, together with a growing recognition that noise can assist neural systems in detecting weak subthreshold signals [6] -a phenomenon known as stochastic resonance  ... 
doi:10.1103/physrevlett.91.078101 pmid:12935054 fatcat:g5yqtodjnnfspg6jgocoqcbrje

Optimality and Sub-optimality of PCA for Spiked Random Matrices and Synchronization [article]

Amelia Perry and Alexander S. Wein and Afonso S. Bandeira and Ankur Moitra
2016 arXiv   pre-print
Such results form the basis of our understanding of when PCA can detect a low-rank signal in the presence of noise.  ...  A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix.  ...  Acknowledgements The authors are indebted to Philippe Rigollet for helpful discussions and for many comments on a draft, and to Amit Singer and his group for discussions about synchronization.  ... 
arXiv:1609.05573v2 fatcat:buxtnl7y2zbkfipyjgl5wgj5rm

Nonlinear Probabilistic Predictive Neural Computations

Robert Skopec
2012 NeuroQuantology  
The self originates from these biochemical processes: the interaction of self with the non-self is represented by second-order representation which occurs mainly in the thalamus.  ...  They also represent the continuity of the given organism.  ...  Acknowledgments The author gratefully acknowledge the assistance of Dr. Marta Ballova, Ing. Konrad Balla, Livuska Ballova, and Ing. Jozef Balla.  ... 
doi:10.14704/nq.2012.10.2.554 fatcat:t7jbhj2cfbbm5ndlwy6pouvqvu

Epileptic transient detection: wavelets and time-frequency approaches

Lotfi Senhadji, Fabrice Wendling
2002 Neurophysiologie clinique  
Chauvel for real data interpretation, performed in the Epilepsy Unit of La Timone Hospital, Marseille, France. HAL author manuscript inserm-00130050, version 1  ...  Acknowledgement : The authors wish to thank the three anonymous reviewers for their many constructive comments and Pr P.  ...  Wavelet transform based interictal transient detection The objective of this section is to illustrate the usefulness of WT through the problem of detection of interictal events, like spikes or spikes-waves  ... 
doi:10.1016/s0987-7053(02)00304-0 pmid:12162183 fatcat:ktblqwhefjedxlkbci777yovie

Detection of Signal in the Spiked Rectangular Models [article]

Ji Hyung Jung, Hye Won Chung, Ji Oon Lee
2021 arXiv   pre-print
We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices.  ...  We also propose a hypothesis test to detect the presence of signal with low computational complexity, based on the linear spectral statistics, which minimizes the sum of the Type-I and Type-II errors when  ...  In these models, the signal is in the form of rank-1 mean matrix (spiked Wigner matrix) or rank-1 perturbation of the identity in the covariance matrix (spiked Wishart matrix).  ... 
arXiv:2104.13517v1 fatcat:cedaichtf5fy3c6wq62eecjaeq
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