Related papers: The Phase Transition Phenomenon of Shuffled Regres…
This paper is concerned with the problem of recovering a structured signal from a relatively small number of corrupted random measurements. Sharp phase transitions have been numerically observed in practice when different convex programming…
In this paper, we study the problem of multivariate shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we investigate the model…
The shuffled linear regression problem aims to recover linear relationships in datasets where the correspondence between input and output is unknown. This problem arises in a wide range of applications including survey data, in which one…
This paper studies the problem of shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we consider the model $y = \Pi_* X \beta_* + w$,…
Shuffled regression concerns settings in which covariates and responses are observed without their correct pairing. In dependent-data problems, a second form of missing correspondence can arise when responses are also detached from the…
The goal of phase-only compressed sensing is to recover a structured signal $\mathbf{x}$ from the phases $\mathbf{z} = {\rm sign}(\mathbf{\Phi}\mathbf{x})$ under some complex-valued sensing matrix $\mathbf{\Phi}$. Exact reconstruction of…
We study here the so-called spiked Wigner and Wishart models, where one observes a low-rank matrix perturbed by some Gaussian noise. These models encompass many classical statistical tasks such as sparse PCA, submatrix localization,…
A sharp phase transition emerges in convex programs when solving the linear inverse problem, which aims to recover a structured signal from its linear measurements. This paper studies this phenomenon in theory under Gaussian random…
Quantum phase transition in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudo-spin transformation method and the trace map method. The exact solutions are presented, the fidelity, the…
Compressed sensing deals with efficient recovery of analog signals from linear encodings. This paper presents a statistical study of compressed sensing by modeling the input signal as an i.i.d. process with known distribution. Three classes…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
The Hartree-Fock approximation to the many-fermion problem can break exact symmetries, and in some cases by changing a parameter in the interaction one can drive the Hartree-Fock minimum from a symmetry-breaking state to a…
In Bayesian statistics, horseshoe prior has attracted increasing attention as an approach to the sparse estimation. The estimation accuracy of compressed sensing with the horseshoe prior is evaluated by statistical mechanical method. It is…
In the field of signal processing, phase transition phenomena have recently attracted great attention. Donoho's work established the signal recovery threshold using indicators such as restricted isotropy (RIP) and incoherence and proved…
We consider a sparse linear regression model Y=X\beta^{*}+W where X has a Gaussian entries, W is the noise vector with mean zero Gaussian entries, and \beta^{*} is a binary vector with support size (sparsity) k. Using a novel conditional…
Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
The pattern maximum likelihood (PML) estimate, introduced by Orlitsky et al., is an estimate of the multiset of probabilities in an unknown probability distribution $\mathbf{p}$, the estimate being obtained from $n$ i.i.d. samples drawn…
We consider the problem of decoding a discrete signal of categorical variables from the observation of several histograms of pooled subsets of it. We present an Approximate Message Passing (AMP) algorithm for recovering the signal in the…
Consider a scenario in which an unknown signal is transformed by a known linear operator, and then the pointwise absolute value of the unknown output function is reported. This scenario appears in several applications, and the goal is to…