New method uses GANs and proper scoring rules for robust scatter estimation.
problem Robust scatter estimation in statistics.
method General learning via classification framework based on proper scoring rules.
result Proposed robust scatter estimators achieve minimax rate under Huber's contamination model.
Graph scattering transforms are stable to metric perturbations of network topology.
problem Stability of graph data representations under metric perturbations.
method Extending scattering transforms to network data using multiresolution graph wavelets and graph convolutions.
result Graph scattering transforms are stable to metric perturbations of the underlying network topology.
A large dimensional characterization of robust M-estimators of covariance (or scatter) is provided under the assumption that the dataset comprises independent (essentially Gaussian) legitimate samples as well as arbitrary deterministic samples, referred to as outliers. Building upon recent random matrix advances in the…
SBI provides more accurate pole positions than chi-squared minimization in model misspecification.
problem Accurate pole position estimation in pi-pi scattering models.
method Simulation Based Inference (SBI) method compared to chi-squared minimization.
result SBI leads to more robust predictions of pole positions in models of pi-pi scattering.
Paper proves min-vol NMF robust to noise under expanded condition.
problem Robustness of min-vol NMF to noise.
method Proved robustness under expanded sufficiently scattered condition.
result Proves min-vol NMF identifies groundtruth factors in noise.
Efficiently estimates covariance matrix for elliptical distributions under strong contamination.
problem Robust estimation of covariance matrix in the presence of adversarial corruptions.
method Proposes an algorithm that uses spatial sign of elliptical distributions and spectral covariance filtering.
result Achieves nearly optimal error guarantee for various elliptical distributions.
New deep learning model estimates scattering timescale of FRBs efficiently.
problem Estimating scattering timescale of fast radio bursts (FRBs) is a bottleneck.
method Multimodal Transformer Based Generic Mixture Density Network (MT-GMDN) that ingests dynamic spectrum and timeseries profile.
result Achieves 94% R2 on expected value of τ for measurable scattering. Paper proposes a new method for covariance estimation using M-estimators with eigenvalue shrinkage.
problem Estimating covariance matrices in heavy-tailed distributions.
method Replaces shrinkage sample covariance matrix with M-estimator of scatter matrix and optimizes shrinkage parameter.
result Shrinkage M-estimators outperform shrinkage SCM in heavy-tailed distributions.
KMRCD detects outliers in non-elliptical data using kernel trick.
problem Outlier detection in non-elliptical data.
method KMRCD estimator that uses kernel trick to compute robust covariance matrix in a feature space.
result KMRCD performs well in simulations and real-life data.
The paper establishes scattering theory for wave equations on Schwarzschild spacetime.
problem Defocusing semilinear wave equations on Schwarzschild spacetime.
method Combining energy and pointwise decay results with Sobolev embedding, constructing scattering operator.
result Construction of a scattering operator mapping past to future scattering data.
Scattering representations simplify SBI for images without extra compression.
problem Efficiently performing simulation-based inference on images with limited data.
method Use scattering representations for compression and learning, combined with spatial averaging and expressive density estimators.
result Scattering representations provide more information than traditional methods, without requiring additional simulations.
Study proves well-posedness and scattering for wave equations on hyperbolic spaces with singular data.
problem Proving well-posedness and scattering for wave equations on hyperbolic spaces with singular initial data.
method Using weak-Lp spaces and dispersive estimates on Lorentz spaces, the study establishes global well-posedness and exponential asymptotic stability. result Developed a scattering theory and constructed wave operators in a singular framework.
We introduce general scattering transforms as mathematical models of deep neural networks with l2 pooling. Scattering networks iteratively apply complex valued unitary operators, and the pooling is performed by a complex modulus. An expected scattering defines a contractive representation of a high-dimensional probabil…
New MHSNs extract multiscale features from complex data for robust classification.
problem Signal classification and domain classification on complex data.
method Layered structure with multiscale basis dictionaries, pooling operations, and invariant features.
result High-accuracy classification with fewer parameters than traditional graph neural networks.
In this work a robust clustering algorithm for stationary time series is proposed. The algorithm is based on the use of estimated spectral densities, which are considered as functional data, as the basic characteristic of stationary time series for clustering purposes. A robust algorithm for functional data is then app…
Deep learning solves wave-based inverse problems, including super-resolution imaging.
problem Solving inverse wave scattering problems across all length scales.
method Wide-band butterfly network coupled with dynamic noise injection.
result Framework successfully solves super-resolution imaging problems.
Real data often contain anomalous cases, also known as outliers. These may spoil the resulting analysis but they may also contain valuable information. In either case, the ability to detect such anomalies is essential. A useful tool for this purpose is robust statistics, which aims to detect the outliers by first fitti…
We present a sparse and invariant representation with low asymptotic complexity for robust unsupervised transient and onset zone detection in noisy environments. This unsupervised approach is based on wavelet transforms and leverages the scattering network from Mallat et al. by deriving frequency invariance. This frequ…
Charts are an excellent way to convey patterns and trends in data, but they do not facilitate further modeling of the data or close inspection of individual data points. We present a fully automated system for extracting the numerical values of data points from images of scatter plots. We use deep learning techniques t…
In this paper, we propose a novel linear discriminant analysis criterion via the Bhattacharyya error bound estimation based on a novel L1-norm (L1BLDA) and L2-norm (L2BLDA). Both L1BLDA and L2BLDA maximize the between-class scatters which are measured by the weighted pairwise distances of class means and meanwhile mini…
T-Rex uses EM to fit robust factor models in noisy data.
problem Robustly fitting factor models in high-dimensional data with heavy tails and outliers.
method Expectation-Maximization (EM) algorithm based on Tyler's M-estimator for elliptical distributions.
result Demonstrates robustness in direction-of-arrival estimation and subspace recovery.
This paper proposes a new framework to regularize the highly ill-posed and non-linear phase retrieval problem through deep generative priors using simple gradient descent algorithm. We experimentally show effectiveness of proposed algorithm for random Gaussian measurements (practically relevant in imaging through scatt…
Bayesian Scattering offers a simple baseline for image data uncertainty.
problem Lack of interpretable, mathematically grounded uncertainty quantification methods for image data.
method Coupling wavelet scattering transform with a simple probabilistic head.
result Bayesian Scattering provides sensible uncertainty estimates under distribution shifts.
We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity…
Novel method uses Gaussian process to estimate particle sizes from scattering data.
problem Estimating particle size distributions from noisy optical scattering measurements.
method Constrained Gaussian process regression with normalization constraints.
result Accurately reconstructs particle size distributions from noisy data.
Enhances DSN with multi-family wavelet transforms and sparsity.
problem Improving interpretability and expressive power of DSN.
method Multi-family wavelet transforms and optimal thresholding.
result Enhanced robustness and diversity of scattering coefficients.
BCV method helps estimate clusters and hyper-parameters in large data sets.
problem Determining the number of clusters in large-scale data.
method Bi-cross validation (BCV) for spectral clustering.
result BCV directly applies to spectral clustering for estimating clusters and hyper-parameters.
Explains Fisher and Kernel Fisher Discriminant Analysis with examples and comparisons.
problem Classifying data with different features and dimensions.
method Projection and reconstruction, scatters analysis, PCA comparison, Fisher forest.
result Equivalence of Fisher and Linear Discriminant Analysis, effectiveness of Fisher forest.
Paper introduces a robust generative model using weighted conjugate feature duality.
problem Training generative models can be affected by contamination, leading to noisy data.
method Introduces weighted conjugate feature duality in the framework of Restricted Kernel Machines (RKMs) to fine-tune the latent space.
result The weighted RKM is capable of generating clean images when training data is contaminated.
Unified geometric scattering model for measure spaces.
problem Improving CNNs for non-Euclidean data.
method Unified geometric scattering model for measure spaces.
result Unified model includes previous work and applies to more general settings.
We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization problems. Recently, it was shown that the underlying principle behind their succ…
This work defines observation-specific explanations for black-box models.
problem Assigning importance to data points in black-box model predictions.
method Surrogate model construction using scattered data approximation and orthogonal matching pursuit.
result Validated approach on simulated and real-world datasets.
We address structured covariance estimation in elliptical distributions by assuming that the covariance is a priori known to belong to a given convex set, e.g., the set of Toeplitz or banded matrices. We consider the General Method of Moments (GMM) optimization applied to robust Tyler's scatter M-estimator subject to t…
Geometric approach solves maximum likelihood for Cauchy-like distributions.
problem Estimating center and scatter robustly from heavy-tailed data.
method Geodesic convexity and symmetry spaces of noncompact type.
result Efficient numerical solution for robust estimates of location and spread.
Study fourth order Schrödinger equation on Cartan-Hadamard manifolds, proving existence, scattering, and blow-up results.
problem Fourth order Schrödinger equation with mixed dispersion on Cartan-Hadamard manifolds.
method Fourier transform for hyperbolic space, weighted Strichartz estimates for rotationally symmetric manifolds, localized virial argument.
result Existence, scattering, and blow-up results for the equation.
This paper solves the convergence problem for estimating MGGD parameters with a convex formulation.
problem Establishing convergence properties for estimating MGGD parameters with unknown mean and precision matrix.
method Proposes a convex formulation with well-established convergence properties for robust estimation in noisy scenarios.
result Demonstrates improved accuracy in precision and covariance matrix estimation compared to existing methods.
Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution ena…
We introduce multiscale invariant dictionaries to estimate quantum chemical energies of organic molecules, from training databases. Molecular energies are invariant to isometric atomic displacements, and are Lipschitz continuous to molecular deformations. Similarly to density functional theory (DFT), the molecule is re…
Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.
problem Improving discriminant analysis for multilabel classification with enhanced dimensionality and robustness.
method Unified algebraic and statistical analysis of multilabel Fisher discriminants with Stiefel orthogonality constraints.
result Equivalence of four Fisher objectives under the Stiefel constraint and improved discriminant dimensionality.
Generative networks have made it possible to generate meaningful signals such as images and texts from simple noise. Recently, generative methods based on GAN and VAE were developed for graphs and graph signals. However, the mathematical properties of these methods are unclear, and training good generative models is di…
Geometric wavelet scattering on manifolds improves neural network understanding.
problem Improving neural network understanding on manifold and graph domains.
method Defining a geometric scattering transform based on wavelet filters and nonlinearities.
result Generalizes deformation stability and local translation invariance to manifolds.
We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be computable. This paper will demonstrate the potential of the scattering symplect…
Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.
problem Improving discriminant analysis for multilabel classification with enhanced dimensionality and robustness.
method Unified theoretical analysis of multilabel Fisher discriminants with algebraic and statistical guarantees.
result Unified characterization of multilabel Fisher objectives and their equivalence under orthogonality constraints.
Paper explains scattering diagrams' role in mirror symmetry.
problem Reconstruction problem in mirror symmetry.
method Introduction of scattering diagrams and their role in SYZ and HMS conjectures.
result Scattering diagrams help in understanding mirror symmetry.
Paper proposes a new model for multivariate risk measures using Wasserstein barycenters.
problem Estimating robust multivariate risk measures in financial markets.
method Wasserstein barycenters of probability measures, copulas, Value at Risk models.
result The new model provides realistic VaR forecasts in both common and volatile periods.
New method uses broken scattering to uniquely identify Finsler manifolds.
problem Identifying Finsler manifolds from scattering data.
method Uses broken scattering relation to compare geodesics.
result Two reversible Finsler manifolds with the same broken scattering relation are isometric.
GSAN learns adaptive node representations using geometric scattering and attention.
problem Oversmoothing in node representation learning.
method Attention-based architecture integrating geometric scattering and GCN channels.
result GSAN outperforms previous networks in semi-supervised node classification.
New method learns soliton dynamics from scattering data without assuming known equations.
problem Deriving soliton dynamics from scattering data without prior knowledge.
method Combining IST with weak-form system identification for data-driven discovery.
result Effective soliton dynamics models derived from observed scattering data.