141 citations · 1.7k across the 117 of their papers we have counts for
30 papers · 1 filter
Storage capacity of perceptron with variable selection
Yingying Xu, Masayuki Ohzeki, Yoshiyuki Kabashima
A central challenge in machine learning is to distinguish genuine structure from chance correlations in high-dimensional data. In this work, we address this issue for the perceptro…
Decision Theoretic Cutoff and ROC Analysis for Bayesian Optimal Group Testing
Ayaka Sakata, Yoshiyuki Kabashima
We study the inference problem in the group testing to identify defective items from the perspective of the decision theory. We introduce Bayesian inference and consider the Bayesi…
Macroscopic Analysis of Vector Approximate Message Passing in a Model Mismatch Setting
Takashi Takahashi, Yoshiyuki Kabashima
Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particul…
Statistical mechanics analysis of thresholding 1-bit compressed sensing
Yingying Xu, Yoshiyuki Kabashima
The one-bit compressed sensing framework aims to reconstruct a sparse signal by only using the sign information of its linear measurements. To compensate for the loss of scale info…
Sampling approach to sparse approximation problem: determining degrees of freedom by simulated annealing
Tomoyuki Obuchi, Yoshiyuki Kabashima
The approximation of a high-dimensional vector by a small combination of column vectors selected from a fixed matrix has been actively debated in several different disciplines. In…
Sparse approximation problem: how rapid simulated annealing succeeds and fails
Tomoyuki Obuchi, Yoshiyuki Kabashima
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given datas…
Cross validation in LASSO and its acceleration
Tomoyuki Obuchi, Yoshiyuki Kabashima
We investigate leave-one-out cross validation (CV) as a determinator of the weight of the penalty term in the least absolute shrinkage and selection operator (LASSO). First, on the…
Sparse approximation based on a random overcomplete basis
Yoshinori Nakanishi-Ohno, Tomoyuki Obuchi, Masato Okada +1
We discuss a strategy of sparse approximation that is based on the use of an overcomplete basis, and evaluate its performance when a random matrix is used as this basis. A small co…
Online compressed sensing
Paulo V. Rossi, Yoshiyuki Kabashima, Jun-ichi Inoue
In this paper, we explore the possibilities and limitations of recovering sparse signals in an online fashion. Employing a mean field approximation to the Bayes recursion formula y…
Replica Symmetric Bound for Restricted Isometry Constant
Ayaka Sakata, Yoshiyuki Kabashima
We develop a method for evaluating restricted isometry constants (RICs). This evaluation is reduced to the identification of the zero-points of entropy, which is defined for submat…
Signal recovery using expectation consistent approximation for linear observations
Yoshiyuki Kabashima, Mikko Vehkapera
A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be…
Reconstruction algorithm in compressed sensing based on maximum a posteriori estimation
Koujin Takeda, Yoshiyuki Kabashima
We propose a systematic method for constructing a sparse data reconstruction algorithm in compressed sensing at a relatively low computational cost for general observation matrix.…
Statistical Mechanics Approach to Sparse Noise Denoising
Mikko Vehkapera, Yoshiyuki Kabashima, Saikat Chatterjee
Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the l1-norm based convex optimizati…
Statistical mechanics approach to 1-bit compressed sensing
Yingying Xu, Yoshiyuki Kabashima
Compressed sensing is a technique for recovering a high-dimensional signal from lower-dimensional data, whose components represent partial information about the signal, utilizing p…
Typical -recovery limit of sparse vectors represented by concatenations of random orthogonal matrices
Yoshiyuki Kabashima, Mikko Vehkapera, Saikat Chatterjee
We consider the problem of recovering an -dimensional sparse vector $\vm{x}$ from its linear transformation $\vm{y}=\vm{D} \vm{x}$ of dimension. Minimizing the -…
Compressed sensing with sparse, structured matrices
Maria Chiara Angelini, Federico Ricci-Tersenghi, Yoshiyuki Kabashima
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a ρ0-sparse signal of length N in…
Analysis of Sparse Representations Using Bi-Orthogonal Dictionaries
Mikko Vehkaperä, Yoshiyuki Kabashima, Saikat Chatterjee +3
The sparse representation problem of recovering an N dimensional sparse vector x from M < N linear observations y = Dx given dictionary D is considered. The standard approach is to…
A study of the universal threshold in the L1 recovery by statistical mechanics
Koujin Takeda, Yoshiyuki Kabashima
We discuss the universality of the L1 recovery threshold in compressed sensing. Previous studies in the fields of statistical mechanics and random matrix integration have shown tha…
A signal recovery algorithm for sparse matrix based compressed sensing
Yoshiyuki Kabashima, Tadashi Wadayama
We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The…
Statistical mechanical assessment of a reconstruction limit of compressed sensing: Toward theoretical analysis of correlated signals
Koujin Takeda, Yoshiyuki Kabashima
We provide a scheme for exploring the reconstruction limit of compressed sensing by minimizing the general cost function under the random measurement constraints for generic correl…
Statistical Mechanical Analysis of Compressed Sensing Utilizing Correlated Compression Matrix
Koujin Takeda, Yoshiyuki Kabashima
We investigate a reconstruction limit of compressed sensing for a reconstruction scheme based on the L1-norm minimization utilizing a correlated compression matrix with a statistic…
Statistical Mechanical Analysis of a Typical Reconstruction Limit of Compressed Sensing
Yoshiyuki Kabashima, Tadashi Wadayama, Toshiyuki Tanaka
We use the replica method of statistical mechanics to examine a typical performance of correctly reconstructing -dimensional sparse vector from its linear transformat…
Statistical mechanical analysis of the Kronecker channel model for MIMO wireless communication
Atsushi Hatabu, Koujin Takeda, Yoshiyuki Kabashima
The Kronecker channel model of wireless communication is analyzed using statistical mechanics methods. In the model, spatial proximities among transmission/reception antennas are t…
A typical reconstruction limit of compressed sensing based on Lp-norm minimization
Y. Kabashima, T. Wadayama, T. Tanaka
We consider the problem of reconstructing an -dimensional continuous vector $\bx$ from constraints which are generated by its linear transformation under the assumption that…