arXiv research

New method identifies key genes affecting phenotypes in biological systems.

We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may be readily extended to nonlinear systems - with a reasonable expectation of suc…

SOAD model improves data assimilation for nonlinear systems.

RichID learns optimal control policies from nonlinear observations.

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…

Detects model misspecifications in causal models using observational data.

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…

Study on conditioning Gaussian measures on nonlinear observations, including representer theorem and mode estimation.

Researchers identify latent variables and causal structures from nonlinear hierarchical models.

Controller seeks informative system observations to predict nonlinear dynamics.

Method learns dynamics from noisy partial observations.

Algorithm learns dynamics from past observations.

We observe that the comparison result of Barles-Biton-Ley for viscosity solutions of a class of nonlinear parabolic equations can be applied to a geometric fully nonlinear parabolic equation which arises from the graphic solutions for the Lagrangian mean curvature flow.

New methods generalize nonlinear ICA beyond structural sparsity.

New method recovers causal networks from short time-series data.

Filtering is a general name for inferring the states of a dynamical system given observations. The most common filtering approach is Gaussian Filtering (GF) where the distribution of the inferred states is a Gaussian whose mean is an affine function of the observations. There are two restrictions in this model: Gaussia…

A deep learning method solves nonlinear filtering problems efficiently.

Two algorithms for nonlinear systems with unknown inputs are compared and implemented.

Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local optimal transport principles is formulated to transform deterministically point…

DAISI improves data assimilation for complex systems with noisy observations.

KRCD detects unobserved confounders in nonlinear observational data.

New method solves robust matrix completion using nonlinear equations.

Study tackles nonlinear factor models with unknown monotone links from incomplete and noisy data.

The paper automates policy learning for nonlinear welfare criteria using machine learning and debiasing techniques.

New model combines ICA and HMM for unsupervised learning of nonstationary time series.

Machine learning techniques have recently received significant attention as promising approaches to deal with the optical channel impairments, and in particular, the nonlinear effects. In this work, a machine learning-based classification technique, known as the Parzen window (PW) classifier, is applied to mitigate the…

Develops VAEs for learning complex physical systems from data.

Proposes FunNoL for better curve classification and reconstruction in multivariate functional data.

In this paper we study the problem of recovering a structured but unknown parameter ${\bfθ}^*$ from $n$ nonlinear observations of the form $y_i=f(\langle {\bf{x}}_i,{\bfθ}^*\rangle)$ for $i=1,2,\ldots,n$. We develop a framework for characterizing time-data tradeoffs for a variety of parameter estimation algorithms when…

Proposes a new method for nonlinear Bayesian updates using ensemble kernel regression.

GD-VAEs learn dynamics from observations using geometric and topological information.

New method recovers sparse signals from nonlinear observations with robust error bounds.

This work uses a scalable approach to identify partially observed nonlinear systems.

NoLimits.jl: Flexible and Composable Nonlinear Mixed-Effects Modeling in Julia

Identifying the underlying directional relations from observational time series with nonlinear interactions and complex relational structures is key to a wide range of applications, yet remains a hard problem. In this work, we introduce a novel minimum predictive information regularization method to infer directional r…

This paper contains the technical foundations from stochastic differential geometry for the construction of geometrically intrinsic nonlinear recursive filters. A diffusion X on a manifold N is run for a time interval T, with a random initial condition. There is a single observation consisting of a nonlinear function o…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising meaningful models out of such observations in an automated fashion still remains an op…

Final part of a series on nonlinear observers on Riemannian metrics, establishing conditions for convergence.

The paper analyzes the observability of relative pose estimation using dual quaternions.

IMA addresses non-identifiability in nonlinear ICA by assuming orthogonal Jacobian columns.

Learning nonlinear dynamics from diffusion data is a challenging problem since the individuals observed may be different at different time points, generally following an aggregate behaviour. Existing work cannot handle the tasks well since they model such dynamics either directly on observations or enforce the availabi…

Extends nonlinear filtering to predictable jump times.

This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the pure components and t…

New approach tackles nonidentifiability in nonlinear blind source separation.

Novel method for nonlinear data assimilation using Langevin sampling.

Interpretable framework evaluates structure learning methods for causal discovery from observational data.

Improves LSTM performance by initializing states via manifold learning.

In nonlinear latent variable models or dynamic models, if we consider the latent variables as confounders (common causes), the noise dependencies imply further relations between the observed variables. Such models are then closely related to causal discovery in the presence of nonlinear confounders, which is a challeng…