This work analyzes the stability of graph filters under large perturbations.
problem Stability of graph filters under large edge rewires.
method Proves a bound on stability using frequency response and community structure.
result Graph filter stability depends on perturbation to community structure.
Gradient filters track moving parameters under noisy data and misspecification.
problem Tracking multidimensional time-varying parameters under noisy observations and model misspecification.
method Gradient-based filters update parameters using the gradient of a postulated objective function, evaluated at either the predicted or updated parameters.
result Novel sufficient conditions for exponential stability of the filtered parameter path, and finite-sample and asymptotic mean squared error bounds.
We investigate the convergence and stability properties of the decoupled extended Kalman filter learning algorithm (DEKF) within the long-short term memory network (LSTM) based online learning framework. For this purpose, we model DEKF as a perturbed extended Kalman filter and derive sufficient conditions for its stabi…
Develops inverse EKF for non-linear systems with stability guarantees and learning unknown dynamics.
problem Estimating adversary's Kalman-filtered estimates in highly non-linear systems.
method Proposes inverse extended Kalman filter (I-EKF) for second-order, Gaussian sum, and dithered forward models. Uses reproducing kernel Hilbert space for learning unknown dynamics.
result Derives theoretical stability guarantees for inverse second-order EKF.
This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to another. One example is in graph convolutional neural networks (ConvNets), where the…
We study the stability vis a vis adversarial noise of matrix factorization algorithm for matrix completion. In particular, our results include: (I) we bound the gap between the solution matrix of the factorization method and the ground truth in terms of root mean square error; (II) we treat the matrix factorization as …
The paper stabilizes PD term structures under forecast uncertainty using a Kalman filter with an anchored observation model.
problem Stable estimation of lifetime PDs under forecast uncertainty.
method Reformulated in state-space framework, introduced an anchored observation model.
result Asymptotic stochastic stability of error dynamics, leading to smoother projections.
In this work, we study stability of distributed filtering of Markov chains with finite state space, partially observed in conditionally Gaussian noise. We consider a nonlinear filtering scheme over a Distributed Network of Agents (DNA), which relies on the distributed evaluation of the likelihood part of the centralize…
Stable algebraic filters improve neural network performance.
problem Improving neural network stability to deformations.
method Analyzed stability of algebraic filters and neural networks under deformations of the homomorphism.
result Stable algebraic filters have frequency responses whose derivative is inversely proportional to frequency.
Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the Decomposed Convolutional Filters network (DCFNet), where the expansion coefficient…
GNNs generalize CNNs for graph data, showing equivariance and stability.
problem Processing signals on graphs.
method Graph convolutional filters, nonlinearities, stacked layers.
result GNNs converge to graphon neural networks under graph convergence.
The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an Itô stochastic differential equation (SDE), and the measurements are obtained at discrete time instants. We propose novel Taylor moment expansion (TME) Gaussian …
Develops inverse extended Kalman filter for predicting adversarial steps.
problem Predicting adversarial Kalman filter estimates from limited information.
method Proposes inverse extended Kalman filter (I-EKF) for non-linear systems with unknown inputs.
result Derives I-EKF with theoretical stability guarantees and consistency proofs.
Develops inverse unscented Kalman filter for non-linear systems.
problem Estimating defender's state in adversarial settings.
method Formulated inverse unscented Kalman filter (I-UKF) and reproducing kernel Hilbert space-based UKF (RKHS-UKF).
result Proposed filters are conservative estimators with upper-bounded error covariance.
Explicit encoding of group actions in deep features makes it possible for convolutional neural networks (CNNs) to handle global deformations of images, which is critical to success in many vision tasks. This paper proposes to decompose the convolutional filters over joint steerable bases across the space and the group …
The paper explores stability and generalization of deep GCNs.
problem Understanding the stability and generalization of deep GCNs from a theoretical perspective.
method Theoretical analysis of stability and generalization properties of deep GCNs.
result The stability and generalization of deep GCNs are influenced by the maximum absolute eigenvalue of the graph filter operators and the depth of the network.
New method differentiates square-root Kalman filters robustly.
problem Gradient calculation issues in square-root Kalman filters.
method Closed-form chain rule derived from Gramian identity, resolves non-orthogonal and rank-deficient issues.
result Robust automatic differentiation for Kalman filters, resolving numerical stability and gradient issues.
Inspired by convolutional neural networks on 1D and 2D data, graph convolutional neural networks (GCNNs) have been developed for various learning tasks on graph data, and have shown superior performance on real-world datasets. Despite their success, there is a dearth of theoretical explorations of GCNN models such as t…
Collaborative filtering (CF) is a popular technique in today's recommender systems, and matrix approximation-based CF methods have achieved great success in both rating prediction and top-N recommendation tasks. However, real-world user-item rating matrices are typically sparse, incomplete and noisy, which introduce ch…
A new method for estimating adversarial strategies in nonlinear systems.
problem Inferring an intelligent adversarial agent's strategy in highly nonlinear systems.
method Formulated inverse cognition as a nonlinear Gaussian state-space model and developed an inverse UKF (IUKF) system.
result The estimation error of IUKF converges and closely follows the recursive Cramér-Rao lower bound.
GNNs improve graph signal discrimination by adding nonlinearities.
problem Improving graph signal discrimination in physical networks.
method Analyzing the discriminability of GNNs and their relation to graph filter banks.
result GNNs are at least as discriminative as linear graph filter banks.
New algorithms robustly estimate mean with near-optimal error rates.
problem Outlier robust mean estimation in high-dimensional data.
method Stability condition and iterative filtering algorithms.
result Optimal error rates with subgaussian rates for robust mean estimation.
The paper establishes a correspondence between Higgs torsors and connections on curves.
problem Establishing a correspondence between Higgs torsors and connections on curves.
method Introduced a stability condition on filtered Stokes local systems and used it to prove a one-to-one correspondence.
result One-to-one correspondence between stable meromorphic parahoric Higgs torsors and stable meromorphic parahoric connections.
One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions,…
Paper analyzes robustness of data-selective Volterra NLMS algorithm.
problem Robustness analysis of data-selective Volterra NLMS algorithm.
method The paper analyzes the local robustness and proposes a global bound for the error in the coefficient vector.
result The DS-VNLMS algorithm is robust against noise and improves parameter estimation for most iterations.
This paper studies when particle filtering is efficient for planning in partially observed systems.
problem The efficiency of particle filtering for planning in partially observed linear dynamical systems.
method Coupling of ideal and approximate sequences to bound particle complexity.
result Polynomially many particles suffice for stable systems to approximate optimal planning.
New graph convolution captures local features on non-Euclidean grids.
problem Capturing local features on irregular, coarse non-Euclidean grids.
method Low-rank learnable local filters in graph convolutions.
result Proves more expressive than previous spectral graph convolution methods.
Paper proposes a DNN-driven AF framework for improved generalization.
problem Generalization challenge in adaptive filtering.
method Structural embedding of DNN into AF system, using maximum likelihood as implicit cost function.
result Demonstrates improved generalization capability through extensive experiments.
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consist of the observations of the difference between the derivative …
Adaptive filters are applied in several electronic and communication devices like smartphones, advanced headphones, DSP chips, smart antenna, and teleconference systems. Also, they have application in many areas such as system identification, channel equalization, noise reduction, echo cancellation, interference cancel…
New filters improve radar target inference in complex scenarios.
problem Improving radar target inference in highly non-linear system models.
method Developed inverse cubature Kalman filter (I-CKF), inverse quadrature Kalman filter (I-QKF), and inverse cubature-quadrature Kalman filter (I-CQKF) for non-linear systems.
result Numerical experiments show improved estimation accuracy compared to existing methods.
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.
Cryptocurrencies show stable prices as a medium of exchange.
problem Price stability of cryptocurrencies as a medium of exchange.
method Filtered daily returns of major cryptocurrencies compared to major financial assets using Pearson correlations, dynamic time-warping method, and Black-Scholes model.
result Cryptocurrencies exhibit stable daily returns relative to major financial assets over the years 2016-2020.
Graph neural networks leverage graph filters to learn from network data.
problem Learning from network data with graph structure.
method Characterize graph neural networks using graph signal processing and graph convolutional filters.
result Graph neural networks have permutation equivariance and stability to topology changes.
EnCF improves data assimilation for implicit, non-smooth observations.
problem Data assimilation challenges with implicit, many-to-one observations.
method EnCF uses a stochastic controlled flow to update forecast distributions.
result EnCF outperforms Kalman filters for non-Gaussian, implicit observations.
ATPF combines PF and EnKF for better inference in complex systems.
problem Weight degeneracy in PF and approximation errors in EnKF.
method Adversarial learning to improve posterior matching and incorporate kernel methods for optimization.
result ATPF provides theoretical guarantees and practical advantages over PF and EnKF.
Develops 2-categorical methods for multi-parameter persistence.
problem Fundamental limitations of traditional persistence modules.
method 2-categorical structures to capture hierarchical interactions.
result New invariants effectively characterize multidimensional topological features.
New method controls linear systems with adversarial disturbances.
problem Controlling linear dynamical systems under adversarial conditions.
method Novel convex relaxation using spectral filters from Hankel matrix eigenvectors.
result Polylogarithmic running time improvement over prior methods.
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.
Spectral graph sparsification preserves geometry of GNN embeddings.
problem Maintaining geometric properties of graph neural network embeddings during sparsification.
method Proving spectral sparsification preserves squared pairwise distances, class means, and covariance structure in embedding space.
result Spectral sparsification preserves the geometry of learned embeddings in GNNs.
Constrained adaptive filtering algorithms inculding constrained least mean square (CLMS), constrained affine projection (CAP) and constrained recursive least squares (CRLS) have been extensively studied in many applications. Most existing constrained adaptive filtering algorithms are developed under mean square error (…
This paper is concerned with sequential filtering based stochastic optimization (FSO) approaches that leverage a probabilistic perspective to implement the incremental proximity method (IPM). The present FSO methods are derived based on the Kalman filter (KF) and the extended KF (EKF). In contrast with typical methods …
New method simplifies tomographic reconstruction using RKHS.
problem Tomographic reconstruction challenges.
method RKHS framework for X-ray transform.
result Sharp stability results without Fourier transform.
Controlled interacting particle systems such as the ensemble Kalman filter (EnKF) and the feedback particle filter (FPF) are numerical algorithms to approximate the solution of the nonlinear filtering problem in continuous time. The distinguishing feature of these algorithms is that the Bayesian update step is implemen…
The paper addresses instability in CNNs' first layer by proving max pooling's shift invariance.
problem Instability in CNNs' first layer, leading to sensitivity to small input shifts.
method Establishing conditions for max pooling's shift invariance and deriving a measure of stability.
result Max pooling approximates a nearly shift-invariant complex modulus under certain conditions.
This paper explores how balancing and filtering techniques affect predictive multiplicity in machine learning models.
problem Predictive multiplicity due to Rashomon effect in high-stakes environments.
method Investigates the impact of balancing and filtering techniques on predictive multiplicity using 21 real-world datasets.
result Data-centric AI strategies can mitigate predictive multiplicity, but preprocessing methods may introduce it.
Paper shows equivalence between MM and PH for n-D Morse functions.
problem Relationship between Mathematical Morphology and Persistent Homology.
method Examined pairing of extrema in Morse functions using dynamics and persistence.
result Equivalence proven between dynamics and persistence on n-D Morse functions.
Study explains Zipf's law using geometric mechanisms from a finite alphabet.
problem Explains Zipf's law in language without relying on linguistic elements.
method Uses the Full Combinatorial Word Model (FCWM) to generate geometric distributions of word lengths.
result Supports predictions of power-law rank-frequency curves, matching various languages.