PENDANTSS: PEnalized Norm-ratios Disentangling Additive Noise, Trend and Sparse Spikes

• URL: http://arxiv.org/abs/2301.01514v1
• Date: Wed, 4 Jan 2023 10:11:21 GMT
• Title: PENDANTSS: PEnalized Norm-ratios Disentangling Additive Noise, Trend and Sparse Spikes
• Abstract summary: We propose PENDANTSS for joint trend removal and blind deconvolution of sparse peak-like signals. It blends a parsimonious prior with the hypothesis that smooth trend and noise can somewhat be separated by low-pass filtering.
• Score: 1.9766522384767222
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Denoising, detrending, deconvolution: usual restoration tasks, traditionally decoupled. Coupled formulations entail complex ill-posed inverse problems. We propose PENDANTSS for joint trend removal and blind deconvolution of sparse peak-like signals. It blends a parsimonious prior with the hypothesis that smooth trend and noise can somewhat be separated by low-pass filtering. We combine the generalized quasi-norm ratio SOOT/SPOQ sparse penalties $\ell_p/\ell_q$ with the BEADS ternary assisted source separation algorithm. This results in a both convergent and efficient tool, with a novel Trust-Region block alternating variable metric forward-backward approach. It outperforms comparable methods, when applied to typically peaked analytical chemistry signals. Reproducible code is provided.

Related papers

• Nonparametric Deconvolution and Denoising using Simulation Based Inference [3.6640504352010885]
  We learn a latent generative model by matching the observed data distribution to the noise-convolved model distribution.<n>Our method provides a practical, theoretically grounded approach to deconvolution under generative latent distribution models.
  arXiv  Detail & Related papers  (2026-06-20T07:03:37Z)
• Closed-Form Spectral Regularization for Multi-Task Model Merging [96.82449201305234]
  Model merging combines several independently fine-tuned experts into a single multi-task model without any training data.<n>State-of-the-art merging methods formulate merging as a layer-wise interference problem.<n>We propose SWUDI, a closed-form method that combines a soft exponential filter, which matches the gradient-flow trajectory of iterative descent.
  arXiv  Detail & Related papers  (2026-06-05T14:00:47Z)
• Finite-Iteration Local Dynamics and Warm Starts for Alternating Power Iteration in Spiked Tensor PCA [9.454986540713655]
  We study simultaneous alternating power iteration for rank-one spiked tensor models.<n>Our main contribution is a finite-iteration local theory.<n>We verify the required correlation and same-sample first-sweep noise bound under i.i.d. finite-fourth-moment noise.
  arXiv  Detail & Related papers  (2026-06-02T13:44:12Z)
• Decoupled PFNs: Identifiable Epistemic-Aleatoric Decomposition via Structured Synthetic Priors [25.166488691037078]
  Prior-Fitted Networks (PFNs) amortize Bayesian prediction by meta-learning over a synthetic task prior, but their standard output is a posterior predictive distribution over noisy observations.<n>We show that this epistemic--aleatoric split is not identifiable in general from the posterior predictive distribution alone.<n>We use these labels to train a decoupled PFN with separate latent-signal and aleatoric heads.
  arXiv  Detail & Related papers  (2026-05-07T15:22:35Z)
• Exact Finite-Sample Variance Decomposition of Subagging: A Spectral Filtering Perspective [17.68593329351594]
  We use the Hoeffding-ANOVA decomposition to derive the first exact, finite-sample variance decomposition for subagging.<n>We show that subagging preserves low-order structural signals while atten $c$-th order interaction variance by a geometric factor approaching $c$.<n>This decoupling reveals why default baselines often under-regularize high-capacity interpolators, which instead require smaller $$ to exponentially suppress spurious high-order noise.
  arXiv  Detail & Related papers  (2026-04-12T05:47:41Z)
• Why Self-Training Helps and Hurts: Denoising vs. Signal Forgetting [6.369253528507392]
  Iterative self-training repeatedly refits a model on pseudo-labels generated by its own predictions.<n>We derive deterministic-equivalent recursions for the prediction risk and effective noise across iterations.
  arXiv  Detail & Related papers  (2026-02-15T07:28:12Z)
• Why is Normalization Preferred? A Worst-Case Complexity Theory for Stochastically Preconditioned SGD under Heavy-Tailed Noise [17.899443444882888]
  We develop a worst-case complexity theory for inequalityally preconditioned gradient descent (SPSGD)<n>We demonstrate that normalization guarantees convergence to a first-order stationary point at rate $mathcalO(T-fracp-13p-2)$ when problem parameters are known, and $mathcalO(T-fracp-12p)$ when problem parameters are unknown.<n>In contrast, we prove that clipping may fail to converge in the worst case due to the statistical dependence between the preconditioner and the gradient estimates.
  arXiv  Detail & Related papers  (2026-02-13T19:29:17Z)
• Integrating Reweighted Least Squares with Plug-and-Play Diffusion Priors for Noisy Image Restoration [6.402777145722335]
  We propose a plug-and-play image restoration framework based on generative diffusion priors for robust removal of general noise types, including impulse noise.<n> Experimental results on benchmark datasets demonstrate that the proposed method effectively removes non-Gaussian impulse noise and achieves superior restoration performance.
  arXiv  Detail & Related papers  (2025-11-10T08:11:20Z)
• Nonasymptotic Convergence Rates for Plug-and-Play Methods With MMSE Denoisers [5.736588561666141]
  We show that MMSE denoiser corresponds to regularizer that can be written as an upperdimensional envelope of negative log-marginal density.<n>We derive (toblur best of our knowledge) the first sub- convergence guarantee for MMSE denoiser.
  arXiv  Detail & Related papers  (2025-10-31T06:12:49Z)
• MARS-Sep: Multimodal-Aligned Reinforced Sound Separation [72.85468563236005]
  MARS-Sep is a reinforcement learning framework for sound separation.<n>It learns a factorized Beta mask policy that is optimized by a clipped trust-region surrogate.<n>Experiments on multiple benchmarks demonstrate consistent gains in Text-, Audio-, and Image-Queried separation.
  arXiv  Detail & Related papers  (2025-10-12T09:05:28Z)
• Smoothed Normalization for Efficient Distributed Private Optimization [54.197255548244705]
  Federated learning enables machine learning models with privacy of participants. There is no differentially private distributed method for training, non-feedback problems. We introduce a new distributed algorithm $alpha$-$sf NormEC$ with provable convergence guarantees.
  arXiv  Detail & Related papers  (2025-02-19T07:10:32Z)
• Denoising Diffusions with Optimal Transport: Localization, Curvature, and Multi-Scale Complexity [5.075506385456813]
  Diffusion-based generative models aim to denoise a Langevin diffusion chain. We show that score denoising is the optimal backward map in transportation cost.
  arXiv  Detail & Related papers  (2024-11-03T16:47:05Z)
• Fast Semisupervised Unmixing Using Nonconvex Optimization [80.11512905623417]
  We introduce a novel convex convex model for semi/library-based unmixing. We demonstrate the efficacy of Alternating Methods of sparse unsupervised unmixing.
  arXiv  Detail & Related papers  (2024-01-23T10:07:41Z)
• An adaptive ensemble filter for heavy-tailed distributions: tuning-free inflation and localization [0.3749861135832072]
  Heavy tails is a common feature of filtering distributions that results from the nonlinear dynamical and observation processes. We propose an algorithm to estimate the prior-to-posterior update from samples of joint forecast distribution of the states and observations. We demonstrate the benefits of this new ensemble filter on challenging filtering problems.
  arXiv  Detail & Related papers  (2023-10-12T21:56:14Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• $z$-SignFedAvg: A Unified Stochastic Sign-based Compression for Federated Learning [14.363110221372274]
  Federated Learning (FL) is a promising privacy-preserving distributed learning paradigm. FL suffers from high communication cost when training large-scale machine learning models. We propose a novel noisy perturbation scheme with a general symmetric noise distribution for sign-based compression.
  arXiv  Detail & Related papers  (2023-02-06T06:54:49Z)
• Diffusion Posterior Sampling for General Noisy Inverse Problems [50.873313752797124]
  We extend diffusion solvers to handle noisy (non)linear inverse problems via approximation of the posterior sampling. Our method demonstrates that diffusion models can incorporate various measurement noise statistics.
  arXiv  Detail & Related papers  (2022-09-29T11:12:27Z)
• Heavy-tailed denoising score matching [5.371337604556311]
  We develop an iterative noise scaling algorithm to consistently initialise the multiple levels of noise in Langevin dynamics. On the practical side, our use of heavy-tailed DSM leads to improved score estimation, controllable sampling convergence, and more balanced unconditional generative performance for imbalanced datasets.
  arXiv  Detail & Related papers  (2021-12-17T22:04:55Z)
• Minibatch vs Local SGD with Shuffling: Tight Convergence Bounds and Beyond [63.59034509960994]
  We study shuffling-based variants: minibatch and local Random Reshuffling, which draw gradients without replacement. For smooth functions satisfying the Polyak-Lojasiewicz condition, we obtain convergence bounds which show that these shuffling-based variants converge faster than their with-replacement counterparts. We propose an algorithmic modification called synchronized shuffling that leads to convergence rates faster than our lower bounds in near-homogeneous settings.
  arXiv  Detail & Related papers  (2021-10-20T02:25:25Z)
• Detecting Label Noise via Leave-One-Out Cross Validation [0.0]
  We present a simple algorithm for identifying and correcting real-valued noisy labels from a mixture of clean and corrupted samples. A heteroscedastic noise model is employed, in which additive Gaussian noise terms with independent variances are associated with each and all of the observed labels. We show that the presented method can pinpoint corrupted samples and lead to better regression models when trained on synthetic and real-world scientific data sets.
  arXiv  Detail & Related papers  (2021-03-21T10:02:50Z)
• When Does Preconditioning Help or Hurt Generalization? [74.25170084614098]
  We show how the textitimplicit bias of first and second order methods affects the comparison of generalization properties. We discuss several approaches to manage the bias-variance tradeoff, and the potential benefit of interpolating between GD and NGD.
  arXiv  Detail & Related papers  (2020-06-18T17:57:26Z)
• Preventing Posterior Collapse with Levenshtein Variational Autoencoder [61.30283661804425]
  We propose to replace the evidence lower bound (ELBO) with a new objective which is simple to optimize and prevents posterior collapse. We show that Levenstein VAE produces more informative latent representations than alternative approaches to preventing posterior collapse.
  arXiv  Detail & Related papers  (2020-04-30T13:27:26Z)

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.