arXiv research

We find a convex model for traditional nonlinear regression under L2 loss.

New algorithms estimate Jacobian matrices for large-scale machine learning.

Method improves SINDy for noisy nonlinear systems.

This paper presents regression models obtained from a process of blind prediction of peptide binding affinity from provided descriptors for several distinct datasets as part of the 2006 Comparative Evaluation of Prediction Algorithms (COEPRA) contest. This paper finds that kernel partial least squares, a nonlinear part…

Deep-RLS uses deep learning to improve PCA for better source separation.

JAXFit speeds up curve fitting on GPUs.

Generalization in nonlinear least squares can be studied via algorithmic stability and effective dimension.

We learn linear models from nonlinear systems using multiple trajectories and regularization.

The paper provides a non-asymptotic error bound for linear system identification under nonlinear policies.

PGD algorithms solve nonlinear inverse problems with generative priors using noisy measurements.

A new method estimates parameters of complex models using ordinary least squares.

We identify linear models from nonlinear systems with initialization constraints.

Develops Lagrange-Hamilton geometry for COVID-19 disease dynamics.

Bayesian system ID improves robustness to sparse, noisy data.

We study the problem of recovering a structured signal $\mathbf{x}_0$ from high-dimensional data $\mathbf{y}_i=f(\mathbf{a}_i^T\mathbf{x}_0)$ for some nonlinear (and potentially unknown) link function $f$, when the regressors $\mathbf{a}_i$ are iid Gaussian. Brillinger (1982) showed that ordinary least-squares estimate…

Method estimates parameters of complex nonlinear systems.

This book introduces linear models and their theories rigorously.

Smooth, globally PŁ functions are essentially nonlinear least-squares.

Unified theory and debiasing framework for random oblique projections in high dimensions.

The paper proposes a least squares method for binary compressive sampling with low intrinsic dimension signals.

New method learns low-dimensional models for systems with non-polynomial terms.

Improved real-time UAV terrain following with RVM-RLS filter.

Develops geometry for Lotka-Volterra model of species competition.

Machine learning can improve 2SLS first stage predictions, but nonlinear methods often introduce bias.

Optimizes prediction error method for time-varying models.

Bayesian method improves online NARMAX model identification.

Proposes KAR for nonlinear causal discovery using kernel methods.

WENDy now estimates nonlinear ODEs with noisy data.

Unified multi-view learning framework using OPLS with regularization and deep extensions.

Stochastic VB improves nonlinear model inference speed and accuracy.

Functional PLS improves prediction and inference for scalar responses from functional predictors.

We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top β^* ) + ε$, where $f$ is nonlinear. To recover $β^*$, we propose an $\ell_1$-regularized least-squares estimator. Unlike classical linear regression, the correspondin…

A tutorial on non-asymptotic system identification methods.

This study defines a multivariate Self--Exciting Threshold Autoregressive with eXogenous input (MSETARX) models and present an estimation procedure for the parameters. The conditions for stationarity of the nonlinear MSETARX models is provided. In particular, the efficiency of an adaptive parameter estimation algorithm…

ADMM algorithm solves nonlinear matrix decompositions efficiently.

We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty. We propose that these uncertainties can be estimated from (conditioned on) past…

Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often need to prepare nonlinear observables manually according to the underlying dynami…

RichID learns optimal control policies from nonlinear observations.

A novel algorithm converges for solving a specific matrix decomposition problem.

A new tensor completion method using tensor networks with Tucker wrapper.

We study the estimation of $β$ for the nonlinear model $y = f(X\sp{\top}β) + ε$ when $f$ is a nonlinear transformation that is known, $β$ has sparse nonzero coordinates, and the number of observations can be much smaller than that of parameters ($n\ll p$). We show that in order to bound the $L_2$ error of the $L_0$ reg…

We present ADMM-Softmax, an alternating direction method of multipliers (ADMM) for solving multinomial logistic regression (MLR) problems. Our method is geared toward supervised classification tasks with many examples and features. It decouples the nonlinear optimization problem in MLR into three steps that can be solv…

Paper addresses identifiability and asymptotics of ODE systems from noisy data.

New method designs experiments robustly for nonlinear estimation, improving parameter knowledge.

We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows us to numerically solve stochastic control problems with controlled volatility,…

Papers learn from data to make decisions without interacting, improving on previous methods.

Simplifies neural regression by combining two sub-networks for predictions and uncertainties.

The paper proposes a new system ID method from noisy data.