Extends importance sampling to nonlinear models using adjoint operators.
problem Lack of tools for identifying important data points in nonlinear models.
method Introduces adjoint operator for nonlinear maps, generalizes norm and leverage scores.
result Generalized scores provide approximation guarantees for nonlinear mappings.
Nonlinear MCMC improves Bayesian machine learning sampling.
problem Sampling problems in Bayesian machine learning.
method Nonlinear MCMC technique with convergence guarantees.
result Improves sampling in Bayesian neural networks.
This paper analyzes the sample complexity of two timescale reinforcement learning algorithms.
problem Analyzing the sample complexity of two timescale reinforcement learning algorithms.
method Non-asymptotic analysis of linear and nonlinear TDC and Greedy-GQ algorithms under Markovian sampling with constant stepsize.
result The paper provides non-asymptotic convergence results for two timescale linear and nonlinear TDC and Greedy-GQ algorithms.
Unified framework for ensemble sampling in nonlinear contextual bandits with provable regret bounds.
problem Efficient exploration in nonlinear contextual bandits with unknown feature dimensions.
method Developed GLM-ES and Neural-ES for generalized linear and neural contextual bandits, respectively, using maximum likelihood estimation on randomly perturbed data.
result Unified high-probability frequentist regret bounds for GLM-ES and Neural-ES, matching state-of-the-art results.
This work improves sample efficiency in meta-learning for nonlinear tasks.
problem Learning complex tasks efficiently with limited data.
method Subspace-based representations for nonlinear tasks.
result Subspace-based representations can be learned efficiently and improve future task performance.
New method learns nonlinear systems from single finite trajectory samples.
problem Learning stabilizable nonlinear systems from single finite trajectory samples.
method Gradient-based algorithms with noise-sensitive uniform convergence guarantees.
result Efficient learning of general nonlinear systems with high accuracy and small sample complexity.
Novel method for nonlinear data assimilation using Langevin sampling.
problem Nonlinear data assimilation challenges in Bayesian filtering.
method Score-based sequential Langevin sampling (SSLS) with dynamic models and annealing.
result Asymptotic stability and error bounds for local posterior sampling.
CAG method predicts nonlinear solid mechanics responses in real-time with high accuracy and efficiency.
problem Real-time prediction of nonlinear solid mechanics responses.
method Clustering adaptive Gaussian process regression (CAG) method.
result Offers predictions within a second with high precision using only 20 samples.
Optimistic estimate predicts best fitting performance of nonlinear models.
problem Evaluating the potential of nonlinear models in fitting.
method Proposes an optimistic estimate to quantify the smallest sample size for fitting nonlinear models.
result Predicts specific subsets of targets that can be fitted at overparameterization.
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.
In this paper we investigate the adaptive market efficiency of the agricultural commodity futures market, using a sample of eight futures contracts. Using a battery of nonlinear tests, we uncover the nonlinear serial dependence in the returns series. We run the Hinich portmanteau bicorrelation test to uncover the momen…
New method identifies latent components in nonlinear mixtures without stringent assumptions.
problem Unraveling latent components in nonlinearly mixed data.
method Constrained autoencoder-based algorithm for identifiability under relaxed assumptions.
result Comprehensive sample complexity results and new identifiability conditions.
RichID learns optimal control policies from nonlinear observations.
problem Continuous control with unknown nonlinearity in system model.
method RichID algorithm using a least-squares regression oracle.
result First provable sample complexity guarantee for continuous control.
We consider the demixing problem of two (or more) structured high-dimensional vectors from a limited number of nonlinear observations where this nonlinearity is due to either a periodic or an aperiodic function. We study certain families of structured superposition models, and propose a method which provably recovers t…
Method estimates parameters of complex nonlinear systems.
problem Parameter estimation for nonlinear systems with derivative states.
method Regularized linear regression using differentiation filtering and least squares.
result Finite-sample bound on mean absolute error of estimation.
CDSSL improves representation quality by integrating linear and nonlinear dependencies.
problem Scarcity of labeled data and neglect of nonlinear dependencies in SSL.
method CDSSL combines linear correlations and nonlinear dependencies using HSIC in RKHS.
result CDSSL enhances representation quality on diverse benchmarks.
The development of algorithms for unsupervised pattern recognition by nonlinear clustering is a notable problem in data science. Markov clustering (MCL) is a renowned algorithm that simulates stochastic flows on a network of sample similarities to detect the structural organization of clusters in the data, but it has n…
Stochastic VB improves nonlinear model inference speed and accuracy.
problem Bayesian inference of nonlinear models from noisy data.
method Stochastic Variational Bayesian (VB) inference for nonlinear models.
result Stochastic VB achieves comparable parameter recovery to analytical solution but is faster.
We identify linear models from nonlinear systems with initialization constraints.
problem Identifying linear models from nonlinear systems with initialization constraints.
method Multiple trajectories-based deterministic data acquisition algorithm followed by regularized least squares.
result We provide a finite sample error bound on the learned linearized dynamics.
This paper analyzes a simplified strategy for nonlinear control using local linear models and iLQR updates.
problem Nonlinear policy optimization in control systems.
method Iterative estimation of local linear models and iLQR-like policy updates.
result Demonstrates polynomial sample complexity and overcomes exponential problem horizon dependence.
INGB improves oversampling for noisy imbalanced datasets.
problem Imbalanced, noisy, and complex datasets in classification problems.
method INGB uses granular balls to simulate spatial distribution and informed entropy for optimization, followed by nonlinear oversampling.
result INGB outperforms traditional linear sampling frameworks and algorithms on complex datasets.
New RL approach tackles non-linear MDPs without linear assumptions.
problem Sample efficiency in RL for complex, nonlinear MDPs with continuous states.
method Introduces EPW condition to relax linear structure requirements; provides sample-efficient RL algorithm.
result EPW condition allows solving MDPs without linear assumptions, including Atari games.
The paper uses machine learning to forecast macroeconomic outcomes with high-dimensional data.
problem Forecasting the full conditional distribution of macroeconomic outcomes.
method Systematically integrating three key principles: high-dimensional data with regularization, rigorous out-of-sample validation, and incorporating nonlinearities.
result Regularization via shrinkage is essential to control model complexity, while nonlinearities yield limited improvements in predictive accuracy.
Improved bounds for function approximation in nonlinear sets.
problem Achieving high probability error with limited samples in nonlinear function approximation.
method Restricting model class to a neighbourhood of the best approximation and estimating sample complexity using tangent and normal spaces' complexities and curvature.
result Improved worst-case bounds for sample complexity in more general sets like tensor networks and neural networks.
Finslerian graph neural networks recover nonlinear diffusion geometry
problem Graph neural networks on point clouds
method Estimates of the Finsler Laplacian
result Recovery of Finsler geometry
Quantum dynamics algorithm learns manifold from data.
problem Learning manifolds from high-dimensional datasets.
method Simulation of quantum dynamics on a graph embedding of data.
result Algorithm reveals connections between data sampling and quantization.
Extends linear classification framework to nonlinear SVM-based ranking problems.
problem Maximizing performance on relevant samples in ranking problems.
method Dualization, kernel addition, componentwise dual ascent method.
result General framework for nonlinear classifiers in ranking problems.
Three-layer networks learn complex hierarchical polynomials of multiple nonlinear features.
problem Understanding how neural networks learn hierarchical features of multiple nonlinear inputs.
method Examine a broad class of functions using three-layer neural networks, showing complete recovery and efficient learning.
result Three-layer neural networks trained via gradient descent can learn hierarchical polynomials of multiple nonlinear features efficiently.
New method for nonlinear Granger causality improves predictive relationships.
problem Challenges in applying Granger causality to nonlinear data.
method Permutation of covariate set, artificial neural networks, consistent variance estimation.
result Permutation method outperforms other techniques in predicting nonlinear relationships.
In this paper we study the problem of recovering a structured but unknown parameter θ∗ from n nonlinear observations of the form yi=f(⟨xi,θ∗⟩) for i=1,2,…,n. We develop a framework for characterizing time-data tradeoffs for a variety of parameter estimation algorithms when…
FNOs learn solution operators of dissipative equations efficiently via spectral methods.
problem Learning and approximation of solution operators for dissipative equations.
method Introducing spectral methods and deriving FNO approximation bounds and sample complexity guarantees.
result Polynomial sample complexity guarantees for FNOs learning solution operators of dissipative equations.
Kernel measures similarity of nonlinear causal structures in heterogeneous populations.
problem Learning causal structure in populations with diverse underlying structures.
method Distance covariance-based kernel for measuring similarity of causal structures.
result Kernel enables clustering of homogeneous subpopulations for causal structure learning.
The paper introduces a fast algorithm for learning and forecasting nonlinear dynamics from noisy time series data.
problem Challenges in capturing nonlinear dynamics from noisy time series data.
method A projected nonlinear state-space model with kernel functions applied to projected lines.
result The model effectively learns and forecasts complex nonlinear dynamics with computational efficiency.
New methods learn sampling distributions for particle filters without supervision.
problem Designing accurate sampling distributions for nonlinear dynamical systems.
method Proposed four unsupervised learning methods for multivariate Gaussian and nonparametric distributions.
result Learned sampling distributions outperform designed ones in accuracy.
This paper presents a method for efficient density estimation in nonlinear systems.
problem Accurate representation of non-Gaussian distributions in nonlinear dynamical systems is challenging.
method Uses Seminonparametric (SNP) densities with probabilists' Hermite polynomial basis and Monte Carlo approximation for maximum likelihood estimation.
result Demonstrates that the method can accurately capture non-Gaussian density structure and compute quantiles using fewer samples than raw Monte Carlo.
The paper provides guarantees for learning nonlinear representations from multiple non-identically distributed data sources.
problem Learning from non-identically distributed and dependent data.
method Established statistical guarantees for learning general nonlinear representations from multiple data sources.
result The excess risk of the estimated function decays as a function of the sample complexity and task diversity.
Extends linear MDP to handle nonlinear rewards.
problem Restrictive linear MDP assumption limits real-world applicability.
method Proposes Generalized Linear MDP (GLMDP) with GLMs for rewards.
result Develops offline RL algorithms achieving suboptimality guarantees.
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.
Private method measures nonlinear correlations between data hosted across two entities.
problem Measuring nonlinear correlations between sensitive data hosted across multiple parties while preserving privacy.
method Differentially private estimator of distance correlation.
result First private estimator of nonlinear correlations in a multi-party setup.
New method finds basins of attraction without needing system models.
problem Determining basins of attraction (BoA) for nonlinear systems without prior knowledge.
method Hybrid Active Learning (HAL) method combining AST, AL, and DBS.
result Efficiently finds and labels boundary of BoA without model knowledge.
A new deep learning framework selects representative samples for unsupervised learning.
problem Selecting representative samples for unsupervised learning in non-linear data.
method DUAL framework using an encoder-decoder architecture to learn nonlinear embeddings and a selection block to choose representative samples.
result DUAL outperforms state-of-the-art methods in selecting representative samples for unsupervised learning.
Temporal Difference Learning analysis under non-i.i.d. data and nonlinear approximation.
problem Finite-sample behavior of TD(0) under non-i.i.d. data and nonlinear approximation.
method High-probability, finite-sample analysis of vanilla TD(0) on polynomially mixing Markov data, assuming Holder continuity and bounded generalized gradients.
result Bounds on the convergence rate of TD(0) with high probability, matching known i.i.d. rates and holding even with nonstationary initialization.
Several popular graph embedding techniques for representation learning and dimensionality reduction rely on performing computationally expensive eigendecompositions to derive a nonlinear transformation of the input data space. The resulting eigenvectors encode the embedding coordinates for the training samples only, an…
Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis testing and investigates potential differences in discriminant statistics between the…
A new method clusters heterogeneous subgroups for accurate causal learning.
problem Diverse causal relationships across different time spans, regions, or strategies.
method Nonlinear Causal Kernel Clustering
result Reduction in prediction error through enhanced causal learning.
Unified analysis for nonlinear parametric models in Bayesian optimization.
problem Limited theoretical guarantees for nonlinear parametric models in Bayesian optimization.
method Kernel-based framework for analyzing regularized nonlinear parametric models trained on adaptively collected data.
result Unified convergence guarantees for nonlinear acquisition and surrogate models.
New algorithm tackles stochastic optimization with inequality constraints.
problem Stochastic optimization with inequality constraints in various applications.
method Active-set stochastic sequential quadratic programming (StoSQP) with a differentiable exact augmented Lagrangian.
result Global convergence for any initialization, KKT residuals converge to zero almost surely.
New method recovers matrices with nonlinear structures using optimization on Grassmann manifold.
problem Recovering high-rank matrices with nonlinear structures like subspaces or clusters.
method Formulated as rank minimization of a nonlinear feature map, approximated by constrained non-convex optimization on the Grassmann manifold, using Riemannian and alternating minimization schemes.
result Global convergence and worst-case complexity bounds for alternating minimization scheme, leading to unique limit point.