Improves signal detection in non-Gaussian noise using transformed data.
problem Signal detection in rank-one signal-plus-noise data matrices.
method Pre-transforming matrix entries and using linear spectral statistics for hypothesis testing.
result Sharp phase transition of largest eigenvalues in spiked rectangular matrices.
LNGCA extends ICA to non-Gaussian signals and noise, improving estimation and testing.
problem Modeling multivariate data with non-Gaussian components and Gaussian noise.
method Linear latent factor model, simultaneous estimation of non-Gaussian and Gaussian components, discrepancy maximization, resampling-based test.
result Improved estimation and testing of non-Gaussian components over competing methods.
Improves detection of low-rank signals from noisy data matrices.
problem Statistical detection of low-rank signals in noisy data matrices.
method Entrywise pre-transforming data matrix for non-Gaussian noise, sharp phase transition thresholds, central limit theorem for linear spectral statistics, hypothesis test.
result Improves detection of low-rank signals from noisy data matrices, generalizing known results.
Enhances EEG signal classification using non-Gaussian neutral vectors.
problem Challenges in classifying EEG signals for brain-computer interfaces.
method Transformed mDWT coefficients into neutral vectors, applied feature selection.
result Feature selection improves classification accuracy.
Smooths GPS data with splines for noisy, irregularly sampled data.
problem Noisy, irregularly sampled GPS data with non-Gaussian noise.
method Smoothing splines with chosen spline order and tension parameter, allowing for non-Gaussian noise and outliers.
result Effective smoothing and interpolation of GPS data.
A new method removes whitening for better non-Gaussian component analysis.
problem Data covariance matrix ill-conditioning hinders LSNGCA performance.
method Developed a whitening-free least-squares NGCA method.
result Demonstrated superior performance compared to whitened LSNGCA.
Study detects signals in spiked Wigner models using log likelihood ratio.
problem Detecting signals in rank-one spiked Wigner models with non-Gaussian noise.
method Proved asymptotic normality of log likelihood ratio and computed error thresholds.
result Optimal signal-to-noise ratio threshold for reliable detection.
A variational Bayesian method improves image restoration in Poisson-Gaussian noise.
problem Signal recovery in the presence of non-Gaussian noise, especially Poisson-Gaussian.
method Variational Bayesian framework for estimating posterior distribution, majorization technique for non-Gaussian likelihood.
result The proposed method achieves performance comparable to manually tuned regularization parameters.
The paper finds non-Gaussian directions in high-dimensional data using Wasserstein distance.
problem Locating interesting non-Gaussian features in high-dimensional data.
method Projection pursuit using 2-Wasserstein distance to maximize the difference from Gaussian.
result Statistical guarantees for accurately approximating an unknown low-dimensional non-Gaussian subspace.
Improved Kalman filter for non-linear, non-Gaussian data.
problem Estimating hidden variables with non-linear, non-Gaussian observations.
method Reproduces and extends Burkhart et al.'s discriminative Kalman filter.
result Enhanced filter performance for complex observation models.
Develops algorithm to infer correlated signals from unknown structures.
problem Inference of correlated signal fields with unknown correlation structures.
method Free energy exploration (FrEE) strategy within information field theory (IFT).
result Algorithm efficiently identifies optimal field estimates and their uncertainties.
Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.
problem Modeling non-Gaussian time-series with stationary increments.
method Complex wavelet transform for scale variations, joint correlation matrix for scale dependencies, second wavelet transform for diagonalization, maximum entropy models conditioned by scattering spectra coefficients.
result Scattering spectra of self-similar processes are scale invariant, allowing statistical testing and generation of new time-series.
Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construc…
CVAE detects weak complex signals in maritime radar, improving detection over classical methods.
problem Detecting weak complex-valued signals in non-Gaussian, range-varying interference.
method Complex-valued Variational AutoEncoder (CVAE) trained on clutter-plus-noise, whitening, ANMF fusion.
result CVAE yields higher detection probability Pd at matched false-alarm rate Pfa, especially with whitening.
Optimal test for detecting signal in noisy matrix model.
problem Signal detection in noisy matrix models with unknown rank.
method Hypothesis test based on linear spectral statistics, optimal under Gaussian noise.
result Optimal test under Gaussian noise, improved with non-Gaussian noise.
A new kernel risk-sensitive loss improves adaptive filtering robustness and speed.
problem Improving adaptive filtering performance in non-Gaussian environments.
method Introducing kernel risk-sensitive loss (KRSL) and developing MKRSL algorithm.
result MKRSL achieves faster convergence and higher accuracy with robustness to outliers.
Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as a natural nonlinear extension to optimal Wiener filtering. After establishing th…
NGCA identifies non-Gaussian components in multidimensional data.
problem Identifying non-Gaussian components in multidimensional data.
method Uses relative entropy to approximate the non-Gaussian subspace.
result Algorithm approximates non-Gaussian subspace with polynomial time complexity.
Picard-O improves ICA for faster, robust separation of signals.
problem Efficiently separating signals in multi-channel data.
method Preconditioned L-BFGS over orthogonal matrices.
result Picard-O outperforms FastICA in speed and robustness.
OT-ICA uses optimal transport to find independent components, outperforming traditional methods.
problem Finding independent components from linear mixtures of signals.
method OT-ICA uses the squared Wasserstein distance to maximize non-Gaussianity, optimizing projections via gradient descent.
result OT-ICA outperforms traditional proxy-based methods in various applications.
A test for weak signal detection in noisy data matrices.
problem Detecting a weak signal in a noisy Wigner matrix when the signal-to-noise ratio is small.
method Utilizes linear spectral statistics and hypothesis testing on the data matrix.
result The proposed test is optimal when the noise is Gaussian and can be improved with known noise density.
Transformers can solve complex filtering problems for non-Gaussian signals.
problem Non-linear and non-Markovian filtering problems for conditionally Gaussian signals.
method Continuous-time transformer models called filterformers.
result Filterformers can approximate the conditional law of non-Markovian and conditionally Gaussian signal processes.
Estimates complex models without assuming Gaussian symmetry, achieving near-optimal performance.
problem Estimating high-dimensional non-Gaussian models with non-linear relationships.
method Uses Stein's identities and thresholding for robust estimation.
result Achieves near-optimal statistical rate of convergence in various settings.
AR-Flow VAE improves blind source separation with flexible autoregressive priors.
problem Unsupervised blind source separation of latent signals from mixtures.
method AR-Flow VAE uses autoregressive flows to model latent sources, enhancing flexibility and capturing complex dependencies.
result AR-Flow VAE effectively separates latent sources, demonstrating improved performance over conventional methods.
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.
Real world systems typically feature a variety of different dependency types and topologies that complicate model selection for probabilistic graphical models. We introduce the ensemble-of-forests model, a generalization of the ensemble-of-trees model. Our model enables structure learning of Markov random fields (MRF) …
We improve DGP models by using importance-weighted variational inference for better accuracy.
problem Accurate modeling of non-Gaussian marginals in deep Gaussian processes.
method Introduced noisy latent covariates and an importance-weighted objective for variational inference.
result The importance-weighted objective consistently outperforms classical variational inference, especially for deeper models.
Study how neural networks learn from non-Gaussian data models.
problem Understanding neural network learning dynamics with non-Gaussian data.
method Developed a two-layer neural network with Hermite polynomial activations to control high-order cumulants.
result Neural networks progressively learn high-order cumulants after capturing low-order statistics.
In this paper, we generalize Huber's criterion to multichannel sparse recovery problem of complex-valued measurements where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vec…
Develops a cumulant-based algorithm for optimizing investment portfolios.
problem Optimizing investment portfolios with low variability in non-Gaussian data.
method Alternating Least Square method applied to 2nd-6th cumulants of multidimensional random variables.
result The algorithm outperforms benchmarks and other methods during recent crashes.
Paper uses optimal transport for Bayesian filtering, deriving new EnKF and FPF formulations.
problem Bayesian filtering for nonlinear systems with non-Gaussian observations.
method Optimal transport theory applied to Bayes' law, constructing Brenier maps.
result New variational formulations of EnKF and FPF for non-Gaussian settings.
A nonlinear channel estimator using complex Least Square Support Vector Machines (LS-SVM) is proposed for pilot-aided OFDM system and applied to Long Term Evolution (LTE) downlink under high mobility conditions. The estimation algorithm makes use of the reference signals to estimate the total frequency response of the …
The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems wi…
PCA can detect a low-rank signal but is suboptimal for non-Gaussian matrices and synchronization problems.
problem Understanding the optimal and suboptimal performance of PCA in spiked random matrix models.
method Analysis of spiked random matrix models, including Gaussian and non-Gaussian Wigner ensembles, and synchronization problems.
result PCA achieves optimal detection for Gaussian Wigner ensembles under benign priors but is suboptimal for non-Gaussian matrices and synchronization problems.
The paper analyzes the non-Gaussian behavior of inflation and unemployment over 70 years using multifractal methods.
problem Capturing unusual fluctuations in inflation and unemployment over long periods.
method Coupled multifractal approach to analyze non-Gaussian distributions of inflation and unemployment over 70 years.
result The non-Gaussianity of unemployment is noticeable only for periods smaller than 1 year, while inflation's non-Gaussianity persists across all time scales.
Proposes a hierarchical deep generative model for natural images.
problem Analyzing piecewise smooth signals like natural images.
method Hierarchical deep generative model with alternating minimization algorithm.
result Demonstrates the model's representation capabilities and classification performance.
PDGMM-VAE uses adaptive priors for better ICA recovery.
problem Nonlinear ICA recovery of latent source signals.
method Adaptive per-dimension Gaussian mixture model priors in a variational autoencoder.
result PDGMM-VAE effectively recovers source-specific non-Gaussian marginals.
Finite-width neural networks use non-Gaussian priors, extending Gaussian process theory.
problem Understanding the behavior of neural networks with finite width.
method Perturbative extension of Gaussian process theory to finite-width neural networks, tracking preactivation distributions.
result Non-Gaussian processes as priors in finite-width neural networks.
Study of asymmetric rank-one tensor models with non-Gaussian noise.
problem Analyzing maximum-likelihood estimators for asymmetric rank-one tensor models.
method Spectrally separated branch analysis, resolvent methods, cumulant expansions, Efron-Stein-type variance bounds.
result Asymptotic singular value and mode-wise alignments are robust to non-Gaussian noise.
Proposes a new complex Gaussian distribution for better modeling of complex-valued signals.
problem Limited ability of Gaussian distribution to represent diverse amplitude characteristics.
method Introduces a power-weighted noncentral complex Gaussian distribution on the complex plane.
result Consistently outperforms conventional distributions in log-likelihood for speech power spectra.
Novel NGCA algorithm finds non-Gaussian subspace without iterative steps.
problem Identifying a linear subspace with non-Gaussian projected data.
method Log-density gradient estimation for eigenvalue decomposition.
result Identified subspace converges to true subspace at optimal rate.
Paper solves NGCA problem with polynomial time and sample complexity.
problem Finding a low-dimensional subspace where data follows a non-gaussian distribution.
method Proposes Reweighted PCA algorithm to solve NGCA.
result Algorithm recovers at least one direction in the subspace with polynomial sample and time complexity.
Semi-supervised learning improves prediction using unlabeled data.
problem Improving prediction performance using unlabeled data.
method General methodology for semi-supervised Empirical Risk Minimization (ERM) focusing on generalized linear regression.
result Adaptive SSL can achieve substantial improvement over supervised and null models in various settings.
ICA reveals deep learning's feature learning mechanisms from non-Gaussian data.
problem Understanding feature learning from non-Gaussian inputs in deep neural networks.
method Investigates ICA and SGD on synthetic and real data.
result FastICA requires n≳d4 samples for single non-Gaussian direction recovery, while SGD outperforms and optimised SGD reaches n≳d2. Improves graph-based active learning for non-Gaussian models.
problem Efficiently selecting data points for labeling in graph-based semi-supervised learning.
method Approximates non-Gaussian distributions, introduces rank-one update and model change acquisition function.
result Enhanced active learning for graph-based SSL under non-Gaussian models.
This research develops an evolutionary approach to discover non-Gaussian stochastic dynamical systems.
problem Discovering explicit governing equations of stochastic dynamical systems with Lévy noise from data.
method ESSR approach using genetic programming, sparse regression, and nonlocal Kramers-Moyal formulas.
result The approach effectively extracts non-Gaussian stochastic dynamical systems from sample path data.
Extends option pricing theory for informed traders.
problem Empirical evidence for non-Gaussian returns, long-range dependence, volatility clustering, and asymmetric information.
method Extended option pricing theory to account for these factors.
result Improved understanding of option pricing for informed traders.
New algorithm for learning causal structures with disjoint cycles in linear non-Gaussian models.
problem Learning causal structures with cycles in linear non-Gaussian models.
method Characterizing when graphs determine the same model, using quadratic and cubic polynomial relations, and a strategy of decorrelating cycles and multivariate regression.
result Consistent and computationally efficient algorithm for learning causal structures with disjoint cycles.