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Found 16 papers, 5 papers with code
Average case analysis of Lasso under ultra-sparse conditions
The obtained bound for perfect support recovery is a generalization of that given in previous literature, which only considers the case of Gaussian noise and diverging $d$.
QCM-SGM+: Improved Quantized Compressed Sensing With Score-Based Generative Models
In practical compressed sensing (CS), the obtained measurements typically necessitate quantization to a limited number of bits prior to transmission or storage.
Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems
We consider the ubiquitous linear inverse problems with additive Gaussian noise and propose an unsupervised sampling approach called diffusion model based posterior sampling (DMPS) to reconstruct the unknown signal from noisy linear measurements.
Quantized Compressed Sensing with Score-based Generative Models
We consider the general problem of recovering a high-dimensional signal from noisy quantized measurements.
A Unitary Transform Based Generalized Approximate Message Passing
We consider the problem of recovering an unknown signal ${\mathbf x}\in {\mathbb R}^n$ from general nonlinear measurements obtained through a generalized linear model (GLM), i. e., ${\mathbf y}= f\left({\mathbf A}{\mathbf x}+{\mathbf w}\right)$, where $f(\cdot)$ is a componentwise nonlinear function.
Exact Solutions of a Deep Linear Network
This work finds the analytical expression of the global minima of a deep linear network with weight decay and stochastic neurons, a fundamental model for understanding the landscape of neural networks.
Stochastic Neural Networks with Infinite Width are Deterministic
This work theoretically studies stochastic neural networks, a main type of neural network in use.
On Model Selection Consistency of Lasso for High-Dimensional Ising Models
Moreover, we provide a rigorous proof of the model selection consistency of Lasso with post-thresholding for general tree-like graphs in the paramagnetic phase without further assumptions on the dependency and incoherence conditions.
Ising Model Selection Using $\ell_{1}$-Regularized Linear Regression: A Statistical Mechanics Analysis
We theoretically analyze the typical learning performance of $\ell_{1}$-regularized linear regression ($\ell_1$-LinR) for Ising model selection using the replica method from statistical mechanics.
Unitary Approximate Message Passing for Sparse Bayesian Learning
Sparse Bayesian learning (SBL) can be implemented with low complexity based on the approximate message passing (AMP) algorithm.
Structure Learning in Inverse Ising Problems Using $\ell_2$-Regularized Linear Estimator
Further, to access the underdetermined region $M < N$, we examine the effect of the $\ell_2$ regularization, and find that biases appear in all the coupling estimates, preventing the perfect identification of the network structure.
Training Restricted Boltzmann Machines with Binary Synapses using the Bayesian Learning Rule
However, training RBMs with binary synapses is challenging due to the discrete nature of synapses.
Training Binary Neural Networks using the Bayesian Learning Rule
Our work provides a principled approach for training binary neural networks which justifies and extends existing approaches.
Vector Approximate Message Passing Algorithm for Structured Perturbed Sensing Matrix
In this paper, we consider a general form of noisy compressive sensing (CS) where the sensing matrix is not precisely known.
Signal Processing
A Unified Bayesian Inference Framework for Generalized Linear Models
In this letter, we present a unified Bayesian inference framework for generalized linear models (GLM) which iteratively reduces the GLM problem to a sequence of standard linear model (SLM) problems.
Information Theory Information Theory
Approximate Message Passing with Nearest Neighbor Sparsity Pattern Learning
We consider the problem of recovering clustered sparse signals with no prior knowledge of the sparsity pattern.
