Nonconvex Latent Optimally Partitioned Block-Sparse Recovery via Log-Sum and Minimax Concave Penalties

• URL: http://arxiv.org/abs/2603.01304v1
• Date: Sun, 01 Mar 2026 22:17:50 GMT
• Title: Nonconvex Latent Optimally Partitioned Block-Sparse Recovery via Log-Sum and Minimax Concave Penalties
• Abstract summary: Two non regularization methods are proposed for recovering block-sparse signals with unknown block partitions.<n>We develop efficient Alternating Method of Multipliers (ADMM)-based algorithms for these formulations that exhibit stable empirical convergence.
• Score: 25.783674050119515
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose two nonconvex regularization methods, LogLOP-l2/l1 and AdaLOP-l2/l1, for recovering block-sparse signals with unknown block partitions. These methods address the underestimation bias of existing convex approaches by extending log-sum penalty and the Minimax Concave Penalty (MCP) to the block-sparse domain via novel variational formulations. Unlike Generalized Moreau Enhancement (GME) and Bayesian methods dependent on the squared-error data fidelity term, our proposed methods are compatible with a broad range of data fidelity terms. We develop efficient Alternating Direction Method of Multipliers (ADMM)-based algorithms for these formulations that exhibit stable empirical convergence. Numerical experiments on synthetic data, angular power spectrum estimation, and denoising of nanopore currents demonstrate that our methods outperform state-of-the-art baselines in estimation accuracy.

Related papers

• Achieving $\widetilde{\mathcal{O}}(\sqrt{T})$ Regret in Average-Reward POMDPs with Known Observation Models [69.1820058966619]
  We tackle average-reward infinite-horizon POMDPs with an unknown transition model.<n>We present a novel and simple estimator that overcomes this barrier.
  arXiv  Detail & Related papers  (2025-01-30T22:29:41Z)
• Total Uncertainty Quantification in Inverse PDE Solutions Obtained with Reduced-Order Deep Learning Surrogate Models [50.90868087591973]
  We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models. We test the proposed framework by comparing it with the iterative ensemble smoother and deep ensembling methods for a non-linear diffusion equation.
  arXiv  Detail & Related papers  (2024-08-20T19:06:02Z)
• A Unified Theory of Stochastic Proximal Point Methods without Smoothness [52.30944052987393]
  Proximal point methods have attracted considerable interest owing to their numerical stability and robustness against imperfect tuning. This paper presents a comprehensive analysis of a broad range of variations of the proximal point method (SPPM)
  arXiv  Detail & Related papers  (2024-05-24T21:09:19Z)
• Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance [52.093434664236014]
  Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation.
  arXiv  Detail & Related papers  (2024-02-03T13:35:39Z)
• Primal-dual regression approach for Markov decision processes with general state and action space [0.30458514384586394]
  We develop a regression based primal-dual martingale approach for solving finite time MDPs with general state and action space. As a result, our method allows for the construction of tight upper and lower biased approximations of the value functions, and, provides tight approximations to the optimal policy.
  arXiv  Detail & Related papers  (2022-10-01T11:48:22Z)
• Posterior and Computational Uncertainty in Gaussian Processes [52.26904059556759]
  Gaussian processes scale prohibitively with the size of the dataset. Many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited computation, is entirely ignored when using the approximate posterior. We develop a new class of methods that provides consistent estimation of the combined uncertainty arising from both the finite number of data observed and the finite amount of computation expended.
  arXiv  Detail & Related papers  (2022-05-30T22:16:25Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• Rigid and Articulated Point Registration with Expectation Conditional Maximization [20.096170794358315]
  We introduce an innovative EM-like algorithm, namely the Conditional Expectation Maximization for Point Registration (ECMPR) algorithm. We analyse in detail the associated consequences in terms of estimation of the registration parameters. We extend rigid registration to articulated registration.
  arXiv  Detail & Related papers  (2020-12-09T17:36:11Z)
• Non-Convex Exact Community Recovery in Stochastic Block Model [31.221745716673546]
  Community detection in graphs that are generated according to symmetric block models (SBMs) has received much attention lately. We show that in the logarithmic sparsity regime of the problem, with high probability the proposed two-stage method can exactly recover the two communities down to the information-theoretic limit in $mathcalO(nlog2n/loglog n)$ time. We also conduct numerical experiments on both synthetic and real data sets to demonstrate the efficacy of our proposed method and complement our theoretical development.
  arXiv  Detail & Related papers  (2020-06-29T07:03:27Z)
• Bayesian System ID: Optimal management of parameter, model, and measurement uncertainty [0.0]
  We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. We show that the log posterior has improved geometric properties compared with the objective function surfaces of traditional methods.
  arXiv  Detail & Related papers  (2020-03-04T22:48:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.