Defines simplicity of non-linear mappings using information geometry.
problem Finding a simple yet effective non-linear mapping from latent to observation space.
method Formalizes simplicity through information geometry, independent of empirical data.
result Proves basic properties of the defined simplicity measure.
Bayesian non-linear matrix completion tackles large, sparse data.
problem Predict missing elements in large, sparsely observed matrices.
method Bayesian Gaussian process latent variable models with data-parallel distributed computation.
result Scalable Bayesian non-linear matrix completion outperforms linear methods.
Efficient estimator for non-linear regression problems using convex programming.
problem Non-linear regression problems with difference of convex (DC) non-linearities.
method Formulated as a convex program, using an approximation oracle for gradients.
result Produces accurate estimates with high probability under certain assumptions.
Proposes a method to infer causal relationships using non-linear ICA.
problem Inferring causal relationships between variables with non-linear dependencies.
method Non-linear ICA to recover latent disturbances and infer causal direction.
result Demonstrates the effectiveness of the method through simulation and neuroimaging data.
We study two inverse problems on a globally hyperbolic Lorentzian manifold (M,g). The problems are: 1. Passive observations in spacetime: Consider observations in a neighborhood V⊂M of a time-like geodesic μ. Under natural causality conditions, we reconstruct the conformal type of the unknown open, relativ…
Develops goodness-of-fit tests for noisy submanifold samples.
problem Testing non-linear models on noisy submanifold samples.
method Non-linear least-square problem solution and χ2 distribution application. result Residual follows χ2 distribution with parameters related to model order and dimension. Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional observations. In these cases, system identification, i.e., finding the measurement map…
Agents learn state ambiguity from non-linear sensor data using Gaussian approximations.
problem Learning state representation from non-linear sensor data.
method Second-order Taylor approximation of Gaussian distribution for non-linear measurement functions.
result Induces a preference for states based on inferability from observations.
This paper conditions non-linear infinite-dimensional diffusion processes.
problem Conditioning non-linear and infinite-dimensional diffusion processes.
method Infinite-dimensional Girsanov's theorem to condition function-valued stochastic processes.
result Conditioning of non-linear infinite-dimensional diffusion processes is achieved.
A new decision tree variant improves linear model performance.
problem Improving decision tree performance on non-linear data.
method Extremely random tree with non-linear data transformation and linear observer.
result Outperforms linear models on benchmark dataset.
SSL framework identifies non-linear systems without labeled data.
problem System identification in non-linear environments without labeled data.
method Dynamics contrastive learning framework.
result SSL can identify non-linear dynamics in latent space.
New method disentangles perceptual uncertainty and behavioral costs in partially observable systems.
problem Tackles inverse optimal control for non-linear partially observable systems.
method Probabilistic approach using maximum causal entropy formulations and local linearization.
result Disentangles perceptual factors and behavioral costs in sequential decision-making.
Paper uses non-linear dimension reduction for better economic forecasting.
problem Analyzing economic effects of shocks in large datasets.
method Non-linear dimension reduction in factor-augmented vector autoregressions.
result Non-linear dimension reduction techniques improve forecasting, especially in volatile data.
Matrix completion works well for smooth non-linear structures, even without low-rank assumptions.
problem Matrix completion for smooth non-linear structures.
method Nuclear-norm penalization for matrices lying in a low-dimensional non-linear manifold.
result Nuclear-norm penalization is minimax rate optimal for recovering smooth non-linear matrices with missing data.
Study Tikhonov regularization for non-linear inverse problems to improve image reconstruction accuracy.
problem Reconstructing quantities from noisy, non-linearly transformed observations.
method Tikhonov regularization using reproducing kernel Hilbert spaces.
result Developed optimal convergence rates for the estimator.
Study predicts evolution patterns for pretzel knots, revealing abrupt transitions and hidden non-linearity.
problem Predicting evolution of Khovanov polynomials for pretzel knots.
method Conjectured explicit evolution formulas, revealed abrupt transitions, and identified additional Lyapunov exponents.
result Abrupt transitions and hidden non-linearity in evolution of Khovanov polynomials for thick knots.
Study evaluates machine learning for predicting treatment effects in observational studies.
problem Challenges in measuring treatment effects due to confounding bias in observational studies.
method Simulated two scenarios with and without confounding, using linear and non-linear relationships. Used machine learning models (linear regression, lasso regression, random forest) to predict counterfactuals and treatment effects.
result Machine learning models perform well under linearity but poorly under non-linearity, even in the presence of confounding.
Improved particle filters enhance vehicle tracking accuracy.
problem Particle filters struggle with frequent, informative observations.
method Proposes particle filters that sample around recent observations.
result Significant improvement in accuracy and efficiency.
Improved Kalman filter for non-linear, non-Gaussian data.
problem Estimating hidden variables with non-linear, non-Gaussian observations.
method Reproduces and extends Burkhart et al.'s discriminative Kalman filter.
result Enhanced filter performance for complex observation models.
Gaussian processes improve system identification models.
problem Improving system identification models for non-linear dynamics.
method Using Gaussian processes to create time series prediction models.
result Gaussian processes enhance model accuracy in system identification.
New framework selects features from noisy data with hidden variables.
problem Feature selection from noisy data with hidden variables.
method Developed a mathematical framework for feature selection from real-world data with non-linear observations.
result Successful variable selection possible even without knowing model parameters.
In this pre-print we explore the multi-fractal properties of 1 minute traded volume of the equities which compose the Dow Jones 30. We also evaluate the weights of linear and non-linear dependences in the multi-fractal structure of the observable. Our results show that the multi-fractal nature of traded volume comes es…
DREAM model improves computational efficiency for non-linear effects in relational event models.
problem Efficiently modeling non-linear effects in dynamic relational networks.
method Introduces Deep Relational Event Additive Model (DREAM) using Neural Additive Models.
result Demonstrates superior computational efficiency compared to traditional REM approaches.
Theoretical analysis of deep neural networks for time series data.
problem Theoretical development for deep neural networks on temporally dependent observations is lacking.
method Established non-asymptotic bounds for prediction error of deep neural networks under mixing-type assumptions.
result Deep neural networks can model non-linear time series data with additional logarithmic factors due to dependence.
New filters for non-linear systems achieve closed-form solutions.
problem Intractability of Bayesian filtering for non-linear systems.
method Gaussian PSD Models for efficient closed-form filtering.
result Closed-form filtering with strong theoretical guarantees and adaptive error.
Paper establishes limits for accurately estimating low-rank matrices from noisy, non-linear data.
problem Estimating low-rank matrices from noisy, non-linear observations.
method Proves strong universality result with equivalent Gaussian model and effective prior parameters.
result Signal-to-noise ratio requirement grows as $N^{ rac 12 (1-1/k_F)}$ for accurate reconstruction.
We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financia…
The paper provides guarantees for learning switching non-linear systems from a single trajectory.
problem Learning non-linear dynamical systems with switching dynamics.
method Non-asymptotic bounds derived under stability assumptions for i.i.d. switching modes.
result Explicit convergence rates for Hölder and linear function classes based on effective sample size.
Adversarial Regression uses GANs for non-linear regression with uncertainty estimation.
problem Performing high-dimensional non-linear regression with uncertainty estimation.
method Conditional Generative Adversarial Network (CGAN) approach.
result CGANs provide an approximate predictive distribution for new observations.
New technique finds globally optimal symbolic equations.
problem Finding globally optimal mathematical expressions.
method Formulated a mixed integer non-linear program (MINLP).
result Guaranteed global optimality in symbolic regression.
Broadens Jourdain and Martini's method to non-linear stochastic processes.
problem Applying pricing methods to non-linear stochastic processes.
method Analyzes from probabilistic and analytic viewpoints, extending Jourdain and Martini's method.
result Broadens applicability of pricing methods to non-linear frameworks.
We propose a new Bayesian tracking and parameter learning algorithm for non-linear non-Gaussian multiple target tracking (MTT) models. We design a Markov chain Monte Carlo (MCMC) algorithm to sample from the posterior distribution of the target states, birth and death times, and association of observations to targets, …
New approach to ODEs using Gaussian processes and Bayesian filtering.
problem Solving ordinary differential equations (ODEs) with probabilistic methods.
method Formulate ODE solutions as Gaussian process regression problems with non-linear measurement functions.
result Developed novel Gaussian solvers with favourable stability properties.
New algorithm recovers non-linear cause-effect relationships from mixed neuroimaging data.
problem Recovering meaningful cause-effect relationships from linearly mixed neuroimaging data.
method MERLiN (Mixture Effect Recovery in Linear Networks) algorithm, extended to handle non-linear cause-effect relationships.
result The algorithm can recover non-linear cause-effect relationships from linearly mixed neuroimaging data.
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.
Deep learning aids causal inference in complex settings.
problem Estimating heterogeneous treatment effects in non-linear, time-varying, and encoded confounders.
method Intuitive introduction to deep learning and causal inference, focusing on observational data.
result Maximizes accessibility to causal inference through deep learning.
Bayesian model merges multi-view latent models and kernel methods.
problem Handling high-dimensionality and non-linear issues in multi-view data.
method Combines probabilistic factor analysis with kernelized observations.
result Compact solutions for kernelized observations and feature selection.
Develops Poisson algebras for field theories using synthetic differential geometry.
problem Constructing Poisson algebras for non-linear field theories.
method Synthetic differential geometry and Cahiers topos model.
result Formulates a Poisson algebra for field theories, showing it forms a family of observables.
DKF improves state estimation in non-linear models.
problem State estimation in non-linear and non-Gaussian systems.
method Discriminative Kalman Filter (DKF) for Bayesian filtering.
result DKF outperforms standard Kalman filter in neural decoding.
Improves recommendation systems by adding non-linearity to matrix completion.
problem Predicting user interests from ratings and features using bilinear models is limiting.
method Applies non-linear activation functions on top of projected user/item features using gradient descent.
result Gradient descent can solve non-linear Inductive Matrix Completion problems effectively.
LOCA learns standardized data coordinates from measurements.
problem Learning invariant data coordinates from non-linearly deformed manifolds.
method LOCA, a LOcal Conformal Autoencoder, learns an isometric embedding.
result LOCA preserves geometric information while learning invariant coordinates.
Bayesian method estimates intervention effects in non-linear data.
problem Causal discovery from observational data with non-linear relationships.
method Gaussian Process Networks (GPN) with Bayesian estimation and Monte Carlo methods.
result Approach accurately identifies and reflects uncertainty of causal estimates.
Method estimates mixture components without discretizing parameters.
problem Learning from mixtures of continuous features with noise.
method Off-the-grid optimization method for continuous parameter space.
result Prediction error bound similar to Lasso predictor.
This study develops a multi-factor framework where not only market risk is considered but also potential changes in the investment opportunity set. Although previous studies find no clear evidence about a positive and significant relation between return and risk, favourable evidence can be obtained if a non-linear rela…
The paper uses Bayesian methods to infer hidden processes with unknown parameters.
problem Estimating hidden processes from noisy observations with unknown parameters.
method Variational Bayesian inference with autoregressive moving average (ARMA) and vector autoregressive (VAR) models, combined with sequential Monte Carlo (SMC) and importance sampling resampling (SISR).
result The proposed inference method accurately estimates hidden states from non-linear noisy observations.
Bayesian optimization improved for biased data.
problem Adversarial bias in observations, especially hidden confounders.
method Reduction to dueling bandits, information-directed sampling (IDS).
result First efficient kernelized algorithm with regret guarantees.
We investigate the joint dynamics of spot and implied volatility from an empirical perspective. We focus on the equity market with the SPX Index our underlying of choice. Using only observable quantities, we extract the instantaneous variance curves implied by the market and study their daily variations jointly with sp…
Diffusion Maps improves on Functional PCA for non-linear functional data.
problem Functional PCA's linear manifold assumption fails for non-linear functional data.
method Extends Diffusion Maps to functional data and compares it to Functional PCA.
result Diffusion Maps outperforms Functional PCA in non-linear functional data analysis.