A new optimizer, MVO, improves nonlinear regression performance.
problem Finding optimal coefficients in nonlinear regression models.
method Multi-Verse Optimizer (MVO) compared to Particle Swarm Optimizer (PSO).
result MVO statistically outperforms PSO in 10 nonlinear regression problems.
New framework IIA identifies innovations in general nonlinear vector autoregressive processes.
problem Limited generality of NVAR models due to additive innovation assumption.
method Independent Innovation Analysis (IIA) framework, assuming mutual independence and modulation by an auxiliary variable.
result Guarantees identifiability of innovations with arbitrary nonlinearities, up to permutation and component-wise invertible nonlinearities.
Multiview analysis aims at extracting shared latent components from data samples that are acquired in different domains, e.g., image, text, and audio. Classic multiview analysis, e.g., canonical correlation analysis (CCA), tackles this problem via matching the linearly transformed views in a certain latent domain. More…
Kernel discriminant analysis uses nonlinear embeddings to improve classification.
problem Limited effectiveness of linear discriminant analysis in capturing nonlinear features.
method Study of nonlinear embeddings in kernel discriminant analysis using polynomial and Gaussian kernels, solving generalized eigenvalue problems.
result Polynomial and Gaussian discriminants capture class differences through population moments and randomized projections.
D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.
problem Analyzing nonlinear dynamical systems with probabilistic understanding.
method Combines deep learning and probabilistic modeling, using KL annealing and normalizing flows.
result Captures latent dynamics in sequential datasets with improved convergence and flexibility.
NKI integrates obfuscated datasets using nonlinear kernels for improved data collaboration.
problem Privacy-preserving data collaboration with reduced reconstruction risk.
method Formulates linear kernel integration, kernelizes it, and introduces graph regularization and centering constraints.
result NKI improves classification accuracy over existing linear integration methods under nonlinear dimensionality reduction.
This paper reviews nonlinear ICA for disentangled representations in unsupervised learning.
problem Finding useful disentangled representations in unsupervised deep learning.
method Review of nonlinear ICA theory and algorithms for disentanglement.
result Nonlinear ICA can be shown to estimate useful disentangled representations.
Proposes neural dynamic mode decomposition for end-to-end modeling of nonlinear dynamics.
problem Understanding and modeling nonlinear dynamical systems.
method Trains neural networks to minimize forecast error based on spectral decomposition in the lifted space.
result Demonstrates effectiveness in eigenvalue estimation and forecast performance.
Geometric analysis of nonlinear dynamics applied to financial time series.
problem Understanding dynamic properties of financial time series.
method Nonparametric filtering method to estimate vector fields and their derivatives from nonlinear oscillation models.
result Vector fields and their derivatives provide insights into the dynamic properties of financial time series.
Proposes a Koopman operator method for time-dependent reliability analysis of nonlinear systems.
problem Challenges in time-dependent reliability analysis of nonlinear dynamical systems.
method Koopman operator approach for transforming nonlinear systems into linear ones, combined with deep learning for intrinsic coordinates.
result Robust and generalizable approach for time-dependent reliability analysis, superior to purely data-driven methods.
This work examines the stability of GD and SGD near minima, revealing nonlinear dynamics that differ from linear analysis.
problem The stability of optimization algorithms like GD and SGD near minima is not well understood.
method The authors derive an exact criterion for stable oscillations of GD near minima in the multivariate setting, considering high-order derivatives.
result Nonlinear dynamics can diverge in expectation even if a single batch is unstable, challenging linear analysis.
Characterizes Hessian eigenspectra for realistic nonlinear models.
problem Understanding Hessian eigenspectra in realistic nonlinear models.
method Deterministic equivalent techniques from random matrix theory.
result Hessian can have qualitatively different spectral behaviors.
Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the …
Sensor data analysis plays a key role in health assessment of critical equipment. Such data are multivariate and exhibit nonlinear relationships. This paper describes how one can exploit nonlinear dimension reduction techniques, such as the t-distributed stochastic neighbor embedding (t-SNE) and kernel principal compon…
Study adapts β-TCVAE for fMRI to recover nonlinear brain components.
problem Capturing nonlinear brain dynamics in fMRI data.
method Adapted β-TCVAE framework for fMRI data. result Recovery of meaningful nonlinear spatial components in fMRI data.
It has been recently shown that a large class of balanced graph cuts allows for an exact relaxation into a nonlinear eigenproblem. We review briefly some of these results and propose a family of algorithms to compute nonlinear eigenvectors which encompasses previous work as special cases. We provide a detailed analysis…
New methods integrate nonlinear, sparse, and multi-view aspects for high-dimensional data analysis.
problem Integrating nonlinear dependence, sparsity, and multi-view data in high-dimensional datasets.
method Proposes HSIC-SGCCA, SA-KGCCA, and TS-KGCCA methods for multi-view high-dimensional data analysis.
result HSIC-SGCCA outperforms competing methods in multi-view variable selection.
Nonlinear analysis has played a prominent role in the recent developments in geometry and topology. The study of the Yang-Mills equation and its cousins gave rise to the Donaldson invariants and more recently, the Seiberg-Witten invariants. Those invariants have enabled us to prove a number of striking results for low …
DeepONet accelerates reliability analysis of stochastic nonlinear systems.
problem Time-dependent reliability analysis of systems with stochastic forcing.
method DeepONet, a novel operator network, learns function-to-function mappings.
result DeepONet efficiently and accurately predicts system responses.
CNN identifies nonlinear human posture control models efficiently.
problem Identifying nonlinear human posture control models.
method Convolutional Neural Networks (CNN) for model identification.
result Efficiently identifies nonlinear human posture control models.
Improved stability analysis of neural network systems using Zames-Falb multipliers.
problem Analyzing stability of linear systems with neural network nonlinearities.
method Using integral quadratic constraints, sector-bounded and slope-restricted structure, and acausal Zames-Falb multipliers.
result Flexible and versatile framework for stability analysis with improved computational efficiency.
Deep-RLS uses deep learning to improve PCA for better source separation.
problem Improving PCA for better source separation in nonlinear systems.
method Inspired by RLS, Deep-RLS unfolds RLS iterations into a deep neural network.
result Deep-RLS significantly improves accuracy in recovering source signals.
This paper describes a new neuroimaging analysis toolbox that allows for the modeling of nonlinear effects at the voxel level, overcoming limitations of methods based on linear models like the GLM. We illustrate its features using a relevant example in which distinct nonlinear trajectories of Alzheimer's disease relate…
New method for separating mixed signals with nonlinear functions.
problem Recovering source signals from nonlinear mixtures.
method Optimisation-based function approximation to minimize mutual statistical dependence.
result The method can recover source signals from nonlinear mixtures under certain conditions.
In this paper, we address the problem of hidden common variables discovery from multimodal data sets of nonlinear high-dimensional observations. We present a metric based on local applications of canonical correlation analysis (CCA) and incorporate it in a kernel-based manifold learning technique.We show that this metr…
Harmonic maps from Riemann surfaces arise from a conformally invariant variational problem. Therefore, on one hand, they are intimately connected with moduli spaces of Riemann surfaces, and on the other hand, because the conformal group is noncompact, constitute a prototype for the formation of singularities, the so-ca…
New PDEs of mixed type emerge in fluid mechanics and geometry.
problem Analysis of nonlinear PDEs of mixed type.
method Through historical problems and recent trends.
result Many PDEs are of mixed type, requiring new analysis.
A new method for efficient nonlinear process monitoring using random Bernoulli features.
problem High computational demands and real-time responsiveness in online monitoring systems.
method Random Bernoulli principal component analysis to capture nonlinear patterns efficiently.
result The proposed methods offer excellent scalability and reduced computational complexity.
In this dissertation, the main goal is visualisation of financial time series. We expect that visualisation of financial time series will be a useful auxiliary for technical analysis. Firstly, we review the technical analysis methods and test our trading rules, which are built by the essential concepts of technical ana…
Kernel learning FBSDE filter improves nonlinear filtering efficiency.
problem Nonlinear filtering problem in high-dimensional systems.
method Iterative and adaptive meshfree approach using forward backward SDE and KDE.
result Rigorous convergence analysis provided, supporting empirical results.
Paper analyzes and proves convergence of a new method for solving complex PDEs.
problem Solving high-dimensional nonlinear PDEs and PIDEs with random neural networks.
method Random deep splitting method using random neural networks.
result The method converges to the unique viscosity solution of nonlinear PDEs and PIDEs.
New approach tackles nonidentifiability in nonlinear blind source separation.
problem Nonidentifiability in nonlinear blind source separation.
method Independent mechanism analysis, incorporating causal assumptions.
result Empirical and theoretical evidence shows improved identifiability.
Extends deep learning for nonlinear Cox regression variable selection.
problem Variable selection for nonlinear Cox regression model.
method Extends LassoNet to survival data for nonlinear Cox model.
result Valid and effective method demonstrated through simulations.
The purpose of this research article is to discover how the econophysics analysis can complement the econometrics models in application to the risk management in the central banks and financial institutions, operating within the nonlinear dynamical financial system. We consider the modern risk management models and sho…
The paper reviews identifiability in linear and nonlinear models, from Gaussian to non-Gaussian.
problem Identifiability issues in latent-variable and structural-equation models, especially in nonlinear cases.
method Review of identifiability theory for linear and nonlinear models, including factor analysis and structural equation models.
result Even nonparametric nonlinear models can be estimated with additional assumptions.
MediEncoder learns nonlinear representations for causal mediation analysis.
problem High-dimensional noisy covariates and mediators in biomedical studies.
method Coupled encoder-decoder architecture with cross-factor network.
result Improves estimation accuracy in high-dimensional causal mediation analysis.
Nonlinear independent component analysis (ICA) is a general framework for unsupervised representation learning, and aimed at recovering the latent variables in data. Recent practical methods perform nonlinear ICA by solving a series of classification problems based on logistic regression. However, it is well-known that…
DDICA separates nonlinear mixed signals robustly.
problem Blind source separation of nonlinear mixed signals.
method Deep deterministic neural network with matrix-based entropy function.
result DDICA effectively separates independent components with high accuracy.
Word2vec analysis reveals spectral underpinnings.
problem Lack of theoretical justification for word2vec.
method Rigorous spectral analysis of word2vec's nonlinear functional.
result Word2vec may be primarily driven by spectral method.
Using the scalar curvature of the product manifold S^{2}X R and the complete group classification of nonlinear Poisson equation on (pseudo) Riemannian manifolds, we extend the previous results on symmetry analysis of homogeneous wave equation obtained by H. Azad and M. T. Mustafa [H. Azad and M. T. Mustafa, Symmetry an…
We address the problem of distinguishing cause from effect in bivariate setting. Based on recent developments in nonlinear independent component analysis (ICA), we train nonparametrically general nonlinear causal models that allow non-additive noise. Further, we build an ensemble framework, namely Causal Mosaic, which …
PGPCA improves PCA for nonlinear data in neuroscience.
problem Nonlinear data distribution in neuroscience.
method Developed PGPCA for nonlinear manifolds, incorporating EM algorithm.
result PGPCA outperforms PPCA in modeling data around nonlinear manifolds.
New method identifies latent components in PNL mixtures without strong assumptions.
problem Identifying latent components in PNL mixtures under unknown nonlinear functions.
method Carefully designed UML criterion to identify a null space associated with the mixing system.
result Identification/removal of unknown nonlinearity under minimal conditions.
Independent Component Analysis (ICA) aims to find a coordinate system in which the components of the data are independent. In this paper we construct a new nonlinear ICA model, called WICA, which obtains better and more stable results than other algorithms. A crucial tool is given by a new efficient method of verifying…
We learn linear models from nonlinear systems using multiple trajectories and regularization.
problem Identifying linear models from data when the underlying dynamics are nonlinear.
method Multiple trajectories data acquisition followed by regularized least squares.
result Learn linearized dynamics with arbitrarily small error given enough samples.
Paper extends ICA to ISA with auxiliary variables for better speech representation learning.
problem Learning unsupervised speech representations with independent subspaces.
method Theoretical framework of nonlinear ISA with auxiliary variables.
result Proposes an algorithm to learn speech representations with independent subspaces.
Novel algorithm identifies nonlinear Granger causal relationships using kernel ridge regression.
problem Identification of nonlinear Granger causal relationships.
method Flexible plug-in architecture with kernel ridge regression using radial basis function.
result Kernel ridge regression in mlcausality achieves competitive AUC scores and more finely calibrated p-values.
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the monitored process is linear, nonlinear PCA models, such as autoencoder models and kern…