Bayesian method improves predictions in overparameterized nonlinear regression.
problem Understanding overparameterization in nonlinear regression models.
method Bayesian framework with adaptive prior considering data spectral structure.
result Posterior contraction established for generalized linear and single-neuron models, demonstrating prediction consistency.
This paper extends performative prediction to nonlinear cases.
problem Performative prediction's effectiveness is limited by linear assumptions in real-world applications.
method Formulated a maximum margin approach loss function and extended it to nonlinear spaces using kernel methods.
result Derived conditions for performative stability in both linear and nonlinear cases.
Two new Koopman models improve nonlinear system prediction.
problem Predicting nonlinear, nonconvex dynamic systems.
method Convex and Extended Koopman Models using deep learning.
result Significantly improved predictive performance.
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.
GO-OED maximizes predictive information gain on nonlinear QoIs.
problem Maximizing information gain on nonlinear predictive quantities.
method Nested Monte Carlo estimator, Markov chain Monte Carlo, kernel density estimation, Bayesian optimization.
result GO-OED outperforms conventional OED in nonlinear settings.
Extends nonlinear filtering to predictable jump times.
problem Filtering with jumps in both signal and observation, especially when jump times are known.
method Derive Kushner-Stratonovich and Zakai equations for predictable discontinuities.
result Extends classical nonlinear filtering results to a setting with predictable discontinuities.
Controller seeks informative system observations to predict nonlinear dynamics.
problem Predicting nonlinear dynamics with uncertain parameters.
method Expected free energy minimization for balancing goal state and informative observations.
result Controller improves performance in uncertain parameter scenarios.
Proposes a method to reveal nonlinearities in tensor data.
problem Capturing nonlinear relationships in high-dimensional tensor data.
method Linear tensor projection method to maximize prediction accuracy.
result Effective in revealing nonlinear relationships in tensor data.
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…
New insights and algorithms improve prediction models with time-series privileged information.
problem Efficient learning of nonlinear prediction models with limited data.
method Generalization of LuPI to nonlinear tasks, using random features and representation learning.
result Theoretical and empirical evidence supports the use of privileged time-series information for nonlinear prediction.
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…
A framework uses preprocessing to improve psychiatric questionnaire predictions while maintaining interpretability.
problem Weak predictive accuracy and limited interpretability of psychiatric questionnaires.
method Two-stage method: stable preprocessing followed by a linear mapping.
result REFINE outperforms other interpretable approaches in psychiatric and non-psychiatric prediction tasks.
Novel autoencoder method approximates Koopman operator in low dimensions.
problem Challenges in approximating finite Koopman operators using data-driven methods.
method Mori-Zwanzig autoencoder (MZ-AE) for robust Koopman operator approximation.
result Improved predictive capability and robust long-term statistical performance.
This paper improves fund net value prediction using ARIMA-LSTM hybrid model.
problem Inaccurate prediction of fund net value due to linear characteristics of models.
method ARIMA-LSTM hybrid model: ARIMA for linear characteristics, LSTM for nonlinear.
result Hybrid model shows higher accuracy in predicting fund net value.
DeepRSCN models nonlinear systems using stochastic configurations.
problem Modeling nonlinear dynamic systems efficiently.
method Incrementally constructed deep reservoir computing framework with random parameters and online weight updates.
result DeepRSCN outperforms single-layer networks in efficiency, learning, and generalization.
Predictability enables efficient parallelization of nonlinear models.
problem Understanding which nonlinear state space models can be efficiently parallelized.
method Established a relationship between system dynamics and optimization problem conditioning, quantified by the largest Lyapunov exponent.
result Predictable systems can be evaluated in O((logT)2) time, improving over conventional sequential approaches. We reveal a model rank that predicts successful recovery of target functions at overparameterization.
problem Understanding the mysterious good generalization performance of overparameterized nonlinear models.
method Rank stratification and linear stability theory for general nonlinear models.
result Linearly stable functions are preferred by nonlinear training, and model rank predicts minimal training data size.
Researchers develop a method to control nonlinear systems with Koopman operator regression.
problem Controlling nonlinear systems with finite action spaces.
method Koopman operator regression for dynamics estimation and model predictive control for control.
result The method yields a linear switching predictive model for control.
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.
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 analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear…
Study uses machine learning to predict nonlinear seismic brace behavior.
problem Predicting nonlinear seismic response of structural braces.
method State-of-the-art machine learning techniques, specifically LSTM, were used.
result LSTM method effectively captures nonlinear brace behavior.
Spectral methods predict long-term signals from linear and nonlinear systems.
problem Forecasting temporal signals from linear and nonlinear systems with arbitrary sampling.
method Introduces a spectral algorithm for linear signals and extends it to nonlinear systems using Koopman theory.
result The spectral methods achieve high accuracy in forecasting and uncertainty quantification.
New method linearizes nonlinear coupled oscillators on graphs.
problem Predicting global synchronization in nonlinear coupled oscillators on graphs.
method Latent dynamic filters learned through supervised matrix factorization.
result Latent dynamics filters enable effective prediction of global synchronization.
Measurement noise limits the advantage of nonlinear models over linear models in biomedical prediction
problem Nonlinear models vs. linear models in biomedical prediction
method Measurement reliability
result Measurement noise blurs the population-optimal predictor
This research improves dynamical systems understanding by identifying latent states and their nonlinear transitions.
problem Previous work on dynamical systems could not identify nonlinear transition dynamics, leading to unreliable predictions.
method Proposes a state-space modeling framework using variational auto-encoders to identify latent states and their nonlinear transition functions.
result Demonstrates high accuracy in recovering latent state dynamics and future prediction accuracy.
Enhances kernel regression with network data for better predictions.
problem Improving predictive power in high-dimensional data.
method Combines kernel regression with network cohesion data to model nonlinearities.
result Significantly better predictive performances in high-dimensional data.
MambaStock predicts stock prices with high accuracy using a state space model.
problem Inaccurate stock price predictions due to nonlinearity in stock market data.
method Mamba-based state space model with selection mechanism and scan module.
result MambaStock outperforms previous methods in stock price prediction accuracy.
The paper investigates non-linear and heavy-tailed predictability in transition-energy financial markets.
problem Incomplete representation of dependence structure in Gaussian-linear forecasting frameworks.
method Develops a hybrid forecasting framework combining Student-t Vector Autoregressions with nonlinear recurrent residual learning architectures.
result The proposed framework consistently improves predictive accuracy relative to conventional models, especially during macro-financial stress.
Panda predicts chaotic systems without retraining, showing emergent properties.
problem Predicting chaotic systems with small errors.
method Trained on a synthetic dataset of chaotic dynamical systems using evolutionary algorithms.
result Panda predicts unseen chaotic systems with zero-shot learning.
DiffSlack learns neural networks with nonlinear constraints via learnable slack variables.
problem Enforcing nonlinear inequality constraints in neural networks.
method DiffSlack reformulates inequalities as equalities with learnable slack variables, predicting them as part of the network output.
result DiffSlack achieves higher planning success rates and stronger geometric constraint satisfaction compared to existing methods.
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.
Combines Gaussian processes and polynomial chaos for stochastic control.
problem Uncertainties in dynamic models lead to performance issues in predictive control.
method Combines Gaussian processes with polynomial chaos expansions to estimate probability distributions of nonlinear functions.
result Demonstrates accurate approximation and closed-loop performance in stochastic nonlinear model predictive control.
Key to multitask learning is exploiting relationships between different tasks to improve prediction performance. If the relations are linear, regularization approaches can be used successfully. However, in practice assuming the tasks to be linearly related might be restrictive, and allowing for nonlinear structures is …
Hybrid model for online nonlinear prediction using LSTM and soft GBDT.
problem Online nonlinear prediction with manual feature selection and model selection issues.
method End-to-end architecture with LSTM for feature extraction and soft GBDT for regression, jointly optimized.
result Significant performance improvements over conventional methods on real datasets.
Proposes a framework to identify and correct model-form errors in nonlinear systems.
problem Model-form errors in nonlinear dynamical systems due to unknown or approximated governing equations.
method Uses a hybrid approach combining machine learning and Bayesian filtering to estimate and correct model-form errors.
result Improves the predictive capability of known but approximate governing equations for nonlinear dynamical systems.
NLR models often perform worse than LR for outlying input data in environmental sciences.
problem NLR models often give poor predictions for input data outside the training domain.
method Screened input data for outliers, using linear extrapolation for outliers based on NLR within the non-outlier domain.
result NLROR approach reduces poor extrapolation and tends to outperform NLR and LR for outliers. Transfer learning improves chaotic dynamics predictions with less data.
problem Efficiently predicting chaotic dynamics with limited data.
method Transfer learning for nonlinear dynamics, optimizing transfer rate and leveraging small-scale turbulence universality.
result Significantly more accurate inference of chaotic dynamics achieved.
DynNet models dynamic responses of linear and nonlinear systems with fewer variables and higher accuracy.
problem Predicting dynamic responses of linear and nonlinear systems.
method Physics-based recurrent neural network with optimized architecture and training techniques.
result Higher accuracy and fewer trainable variables compared to existing models.
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.
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.
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.
The study compares Euclidean and cosine distances in medical drug prescription prediction.
problem Comparing Euclidean and cosine distances in medical drug prescription prediction.
method Established geometric properties and compared distances in real-world medical data.
result Different distances lead to different optimizing nonlinear kernel embedding frameworks.
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.
Deep learning searches for nonlinear factors for predicting asset returns. Predictability is achieved via multiple layers of composite factors as opposed to additive ones. Viewed in this way, asset pricing studies can be revisited using multi-layer deep learners, such as rectified linear units (ReLU) or long-short-term…
Novel neural operator predicts complex spatiotemporal dynamics from partial observations.
problem Capturing complex operator dynamics in infinite-dimensional function spaces.
method Integrates Koopman operator theory with deep neural networks to approximate nonlinear operators between Banach spaces.
result BNO achieves robust zero-shot super-resolution in unsteady flow prediction and outperforms conventional methods.
We study the use of feedforward neural networks (FNN) to develop models of nonlinear dynamical systems from data. Emphasis is placed on predictions at long times, with limited data availability. Inspired by global stability analysis, and the observation of the strong correlation between the local error and the maximum …
We present a novel methodology for predicting future outcomes that uses small numbers of individuals participating in an imperfect information market. By determining their risk attitudes and performing a nonlinear aggregation of their predictions, we are able to assess the probability of the future outcome of an uncert…