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Found 14 papers, 3 papers with code
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.
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.
Reconstructing Sparse Signals via Greedy Monte-Carlo Search
We propose a Monte-Carlo-based method for reconstructing sparse signals in the formulation of sparse linear regression in a high-dimensional setting.
Learning performance in inverse Ising problems with sparse teacher couplings
These results are considered to be exact in the thermodynamic limit on locally tree-like networks, such as the regular random or Erd\H{o}s--R\'enyi graphs.
Empirical Bayes Method for Boltzmann Machines
In this study, we consider an empirical Bayes method for Boltzmann machines and propose an algorithm for it.
Cross validation in sparse linear regression with piecewise continuous nonconvex penalties and its acceleration
Second, we develop an approximate formula efficiently computing the cross-validation error without actually conducting the cross-validation, which is also applicable to the non-i. i. d.
Perfect reconstruction of sparse signals with piecewise continuous nonconvex penalties and nonconvexity control
A part of the discrepancy is resolved by introducing the control of the nonconvexity parameters to guide the AMP trajectory to the basin of the attraction.
Mean-field theory of graph neural networks in graph partitioning
A theoretical performance analysis of the graph neural network (GNN) is presented.
Statistical mechanical analysis of sparse linear regression as a variable selection problem
The analysis is conducted through evaluation of the entropy, an exponential rate of the number of combinations of variables giving a specific value of fit error to given data which is assumed to be generated from a linear process using the design matrix.
Semi-Analytic Resampling in Lasso
An approximate method for conducting resampling in Lasso, the $\ell_1$ penalized linear regression, in a semi-analytic manner is developed, whereby the average over the resampled datasets is directly computed without repeated numerical sampling, thus enabling an inference free of the statistical fluctuations due to sampling finiteness, as well as a significant reduction of computational time.
Accelerating Cross-Validation in Multinomial Logistic Regression with $\ell_1$-Regularization
We develop an approximate formula for evaluating a cross-validation estimator of predictive likelihood for multinomial logistic regression regularized by an $\ell_1$-norm.
Approximate cross-validation formula for Bayesian linear regression
Cross-validation (CV) is a technique for evaluating the ability of statistical models/learning systems based on a given data set.
Boltzmann-Machine Learning of Prior Distributions of Binarized Natural Images
Prior distributions of binarized natural images are learned by using a Boltzmann machine.
