We introduce a new GP kernel based on the sinc function for band-limited signals.
problem Designing covariance kernels for band-limited signals.
method Proposes a Gaussian process kernel with a power spectral density modeled by a rectangular function.
result The sinc kernel facilitates efficient signal processing applications like stereo modulation and band-pass filtering.
The paper improves confidence regions for band-limited functions using tighter norm bounds and majority voting.
problem Constructing reliable confidence regions for band-limited functions from noisy data.
method Improved norm bounds using Hoeffding's inequality and empirical Bernstein bound, majority voting to aggregate intervals.
result Confidence intervals retain their simultaneous coverage guarantee even when aggregated from random subsamples.
Wiatowski and Bölcskei, 2015, proved that deformation stability and vertical translation invariance of deep convolutional neural network-based feature extractors are guaranteed by the network structure per se rather than the specific convolution kernels and non-linearities. While the translation invariance result appli…
This paper presents a bias-variance tradeoff of graph Laplacian regularizer, which is widely used in graph signal processing and semi-supervised learning tasks. The scaling law of the optimal regularization parameter is specified in terms of the spectral graph properties and a novel signal-to-noise ratio parameter, whi…
Band-limited training reduces resource usage without sacrificing accuracy.
problem Resource constraints in training Convolutional Neural Networks (CNNs).
method Artificially constraining the frequency spectra of convolutional filters during training.
result CNNs can leverage lower-frequency components effectively, reducing resource usage.
Study on nodal components of random band-limited functions on surfaces, finding a universal law.
problem Distribution of tangencies of nodal components to a vector field on surfaces.
method Analysis of random band-limited functions on smooth compact Riemannian surfaces with vector fields.
result The distribution of tangencies to a vector field on nodal components of random band-limited functions on surfaces follows a universal deterministic law.
Paper presents a unique method to recover signals from their bispectrum.
problem Retrieving signals accurately from their bispectrum.
method Two-step trust region algorithm that minimizes a non-convex objective function.
result Signals with finite spectral or temporal support can be recovered from at least 3B measurements of their bispectrum.
The paper creates nonparametric confidence bands for band-limited functions.
problem Estimating confidence bands for band-limited functions with finite samples and unknown noise.
method Uses Paley-Wiener reproducing kernel Hilbert spaces and gradient-perturbation methods.
result Non-asymptotic guarantees for confidence regions without assuming a parametric model.
We study the volume distribution of nodal domains of random band-limited functions on generic manifolds, and find that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and…
Deep convolutional neural networks (CNNs) used in practice employ potentially hundreds of layers and 10,000s of nodes. Such network sizes entail significant computational complexity due to the large number of convolutions that need to be carried out; in addition, a large number of parameters needs to be learned and…
In this paper, a nonparametric maximum likelihood (ML) estimator for band-limited (BL) probability density functions (pdfs) is proposed. The BLML estimator is consistent and computationally efficient. To compute the BLML estimator, three approximate algorithms are presented: a binary quadratic programming (BQP) algorit…
This work uses sampling theory to analyze smoothness and error bounds of finite neural networks.
problem Analyzing the function space of finite neural networks and providing error bounds.
method Applying sampling theory to finite neural networks with non-expansive activation functions, considering both deterministic and random sampling.
result Novel error bounds for univariate neural networks under band-limited input assumption, highlighting the advantage of deterministic uniform sampling.
The paper improves nonparametric confidence bands for band-limited functions.
problem Constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees.
method Based on Paley-Wiener reproducing kernel Hilbert spaces, the paper relaxes assumptions, improves noise estimation, and tightens constraints.
result Enhanced confidence bands with improved efficiency and tighter constraints.
Band-limited SAC improves learning efficiency and stability in simulated environments.
problem Improving sample efficiency and stability in SAC algorithms.
method Artificially bandlimiting the target critic's spatial resolution using a convolutional filter.
result Bandlimited SAC outperforms classic twin-critic SAC in various Gym environments and is more stable.
The class of non-rigid registration methods proposed in the framework of PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting family of physically meaningful diffeomorphic registration methods. PDE-constrained LDDMM methods are formulated as constrained variational problems, wher…
Compression of Neural Networks (NN) has become a highly studied topic in recent years. The main reason for this is the demand for industrial scale usage of NNs such as deploying them on mobile devices, storing them efficiently, transmitting them via band-limited channels and most importantly doing inference at scale. I…
Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go, and image captioning. Many of these applications first perform feature extraction …
Paper advances sparse regularisation theory for measures with new kernel insights.
problem Estimating sparse measures from noisy observations using continuous sparse regularisation.
method Develops new continuous sparse regularisation theory on measures with Beurling-LASSO, introduces kernel switch analysis.
result Proves the ``sinc-4'' kernel satisfies a technical LPC assumption for error bounds.
Study proper sampling for X-ray transforms on simple surfaces.
problem Proper discretizing and sampling issues related to geodesic X-ray transforms on simple surfaces.
method Provide minimal sampling rates for faithful reconstruction, quantify sampling quality, and predict artifacts.
result Minimal sampling rates and artifact prediction for geodesic X-ray transforms on simple surfaces.
New method constrains CNN filter frequencies to improve robustness.
problem CNN bias towards low frequency components, leading to poor performance in scenario transformations.
method Frequency domain regularization by constraining filter spectra, training valid frequency range end-to-end.
result Demonstrated effectiveness in defending adversarial perturbations, reducing generalization gap, and improving transfer learning.
In this paper, we show synchronization for a group of output passive agents that communicate with each other according to an underlying communication graph to achieve a common goal. We propose a distributed event-triggered control framework that will guarantee synchronization and considerably decrease the required comm…
Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.
problem Diffusion models on spherical data face unique geometric and stochastic issues.
method Extended spectral diffusion to spherical harmonics, introducing modified stochastic differential equations.
result Introduced a geometry-dependent inductive bias in spectral diffusion models.
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these measures satisfy all the Granger's axioms for an "ideal measure". One such ideal…
GNNs outperform NNs in interpolating bandlimited functions on Euclidean cubes.
problem Interpolating bandlimited functions on Euclidean cubes using GNNs vs. NNs.
method Investigates optimal GNN configurations and weights for function interpolation.
result GNNs require fewer weights and samples to interpolate bandlimited functions compared to NNs.
A new geometry for comparing signals, overcoming traditional limitations.
problem Comparing and interpolating discontinuous and signed signals.
method Investigation of Riemannian geometry on signal space, introducing a metric that measures both horizontal and vertical deformations.
result Characterization of metric properties and establishment of geodesic regularity and stability.
New method uses CNN for seismic inversion uncertainty quantification.
problem Uncertainty quantification in seismic inversion for noisy data.
method Plug-and-Play Stein Variational Gradient Descent (PnP-SVGD) with CNN denoiser.
result High-resolution, trustworthy posterior samples for subsurface structures.
Paper proposes efficient methods for clustering and signal recovery in high-dimensional data with block structures.
problem High-dimensional clustering and signal recovery under block signal structures.
method CFA-PCA and MA-PCA methods for sparse and dense block signals.
result Proposed methods achieve computational minimax optimality for clustering and signal recovery.
Proposes a novel graph signal model using narrowband kernels.
problem Graph signals with multiple concentrated frequency regions.
method Jointly learns graph signal model parameters and coefficients.
result Joint learning improves signal interpolation accuracy.
AaSP improves audio self-supervised learning by addressing aliasing issues.
problem Alias issues in audio spectrogram transformers.
method AaSP combines aliasing-aware patch representation, teacher-student masked modeling, cross-attention predictor, and contrastive regularization.
result AaSP learns more stable representations that integrate high-frequency cues.
New framework models graph signals as distribution-valued signals in Wasserstein space.
problem Limitations of classical vector-based GSP, including synchronous observations and uncertainty.
method Introduces graph distribution-valued signals (GDSs) in the Wasserstein space.
result GDSs naturally encode uncertainty and stochasticity, generalizing traditional graph signals.
New algorithms improve signal processing in federated learning.
problem Efficiently process distributed signal samples with privacy and communication constraints.
method Proposes overpredictive signal approximations using convex optimization.
result Quantifies tradeoffs between communication cost, sampling rate, and approximation error.
We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We propose a graph signal model and formulate signal recovery as a cor…
Improved language identification accuracy through signal combination methods.
problem Enhancing speech recognition accuracy across multiple languages.
method Combining low-level acoustic signals with language-specific recognizer signals using lattice-based ensemble models and deep neural networks.
result Deep neural network model outperforms lattice-based ensemble model, reducing error rate from 5.5% to 4.3%.
Proposes a new signal model for high-dimensional, small-sample-size data.
problem Signal detection in high-dimensional, small-sample-size datasets.
method Intrinsic signal model based on dynamical system assumption.
result Taguchi method effectively detects signals in the proposed model.
This paper reconstructs complex graph signals using kernel methods on manifolds.
problem Reconstructing complex graph signals from samples on graph vertices.
method Kernel methods on complex manifolds, embedding vertices into higher-dimensional spaces.
result Effective reconstruction of complex graph signals, outperforming conventional methods.
Study on signal-plus-noise decomposition in nonlinear spiked random matrices.
problem Nonlinear spiked random matrix models with rank-one signal and noise.
method Signal-plus-noise decomposition and phase transition analysis.
result Identified precise phase transitions in signal components at critical thresholds.
We find ways to make physical signals misclassified by computer vision models.
problem Vulnerability of signal classifiers to adversarial perturbations in physical signals.
method Solving PDE-constrained optimization problems to construct imperceptible perturbations.
result Effective and physically realizable adversarial perturbations can be computed for machine learning models.
The presence of noise is common in signal processing regardless the signal type. Deep neural networks have shown good performance in noise removal, especially on the image domain. In this work, we consider deep neural networks as a denoising tool where our focus is on one dimensional signals. We introduce an encoder-de…
In this paper, we address the problem of reconstructing a time-domain signal (or a phase spectrogram) solely from a magnitude spectrogram. Since magnitude spectrograms do not contain phase information, we must restore or infer phase information to reconstruct a time-domain signal. One widely used approach for dealing w…
Optimizes signal detection in particle physics by decorrelating classifiers.
problem Systematic errors in background models can mislead signal detection.
method Use optimal transport to decorrelate classifiers from protected variables, then apply semiparametric mixture model.
result Decorrelation and signal enrichment improve the stability, robustness, and power of signal detection tests.
Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm optimization. Recent investigation shows that some signals are sparse in multiple domains.…
Paper improves signal proportion estimation by accounting for variable dependence.
problem Traditional estimators assume independence, limiting applicability in real-world scenarios.
method Integrates arbitrary covariance dependence information using principal factor approximation.
result Method outperforms state-of-the-art estimators in accuracy and detection of weaker signals.
Signal retrieval from a series of indirect measurements is a common task in many imaging, metrology and characterization platforms in science and engineering. Because most of the indirect measurement processes are well-described by physical models, signal retrieval can be solved with an iterative optimization that enfo…
Goal: This paper deals with the problems that some EEG signals have no good sparse representation and single channel processing is not computationally efficient in compressed sensing of multi-channel EEG signals. Methods: An optimization model with L0 norm and Schatten-0 norm is proposed to enforce cosparsity and low r…
A new model classifies lightning signals more accurately across different scales.
problem Classifying VLF lightning transients to reduce interference and improve navigation system reliability.
method Introduces a multi-scale residual transformer (MRTransformer) to classify lightning signals.
result Achieved 90% accuracy in lightning signal classification.
Generalizes PCA and ICA for continuous-time signals using neural networks.
problem Low-rank decomposition of continuous-time vector-valued signals.
method Implicit neural network framework to learn numerical approximations of PCA and ICA.
result Unified approach to PCA and ICA in continuous domain, enforcing decorrelation and independence.
Research compares ML and Time Series methods for generating trading signals.
problem Efficiency of on-line learning Algorithms in generating trading signals.
method Used technical indicators and ensemble of Random Forests, also Kalman Filter.
result Kalman Filter outperformed Random Forests in on-line learning predictions of stock prices.
In this manuscript, we investigate deep invertible networks for EEG-based brain signal decoding and find them to generate realistic EEG signals as well as classify novel signals above chance. Further ideas for their regularization towards better decoding accuracies are discussed.