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 research highlights the secrecy potential of nonlinear generative models and their all-or-nothing phase transition.
problem Secrecy potential of nonlinear generative models in statistical learning.
method Replica method to derive asymptotic normalized cross entropy and statistical decoupling of Bayesian estimator.
result Strictly nonlinear models exhibit an all-or-nothing phase transition, leading to perfect secrecy.
FBMS R package simplifies Bayesian model selection and averaging.
problem Complex regression settings with multi-modal posterior landscapes.
method Efficient MJMCMC and GMJMCMC algorithms for Bayesian model exploration.
result FBMS effectively handles Bayesian generalized linear and nonlinear models.
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.
Flexible model for complex relationships using Bayesian nonparametrics.
problem Complex relationships between variables not well captured by simple models.
method Hierarchical generation of nonlinear features, Bayesian inference, variable selection.
result Find interpretable models with a small set of important features.
Bayesian framework improves robustness in nonlinear regression models.
problem Measurement error, model misspecification, and distributional misspecification in regression analyses.
method Joint Dirichlet process prior on latent covariate-response distribution, updating with posterior pseudo-samples.
result Improved stability and consistency in estimators under increasing measurement error.
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.
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.
A new flow-based Bayesian filter tackles high-dimensional nonlinear stochastic systems.
problem Bayesian filtering for high-dimensional nonlinear systems is challenging due to non-Gaussian distributions and computational limitations.
method Integrates normalizing flows to construct a latent linear state-space model with efficient density estimation and sampling.
result Demonstrates superior accuracy and efficiency in numerical experiments.
Bayesian state and parameter estimation for nonlinear models using variational methods.
problem Estimating states and parameters for nonlinear state-space models.
method Variational approach to approximate the intractable Bayesian distribution, resulting in an optimisation problem.
result The proposed method efficiently computes Bayesian estimates for nonlinear models, outperforming Hamiltonian Monte Carlo in numerical examples.
Kernel-based Bayesian filter for nonlinear systems using infinite-dimensional operators.
problem Modeling and predicting nonlinear dynamical systems.
method Functional Bayesian perspective, reproducing kernel Hilbert space, Gaussian kernel.
result Effective approximation and accurate results for nonlinear systems.
Bayesian model uses simple functions to forecast macroeconomic data.
problem Forecasting large datasets in macroeconomics with complex nonlinear relationships.
method Sum of simple two-component location mixtures, logistic function threshold, conjugate priors.
result Accurate point and density forecasts in US macroeconomic aggregates.
Bayesian filtering approach identifies nonlinear restoring forces in dynamic systems.
problem Identification of nonlinear dynamic systems in engineering.
method Modeling the nonlinear restoring force as a Gaussian process, converting it to a state-space model, and inferring internal states and the nonlinear restoring force through filtering and smoothing.
result The approach effectively identifies nonlinear restoring forces in both simulated and experimental datasets.
Bayesian methods solve complex nonlinear PDEs efficiently.
problem Solving nonlinear PDEs with high computational cost.
method Bayesian inference with approximate likelihood based on discretization.
result Probabilistic uncertainty quantification for PDE solutions is feasible.
Bayesian inference with deep, weakly nonlinear networks is solved rigorously.
problem Bayesian inference with neural networks of specific structure.
method Perturbative analysis of fully connected neural networks with a shaped nonlinearity.
result Neural network Bayesian inference can be equivalent to kernel methods under certain conditions.
Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep learning models have become more common, RNNs have been used to forecast increasingl…
Proposes a new method for nonlinear Bayesian updates using ensemble kernel regression.
problem Nonlinear and non-Gaussian Bayesian updates for complex systems.
method Combines Kalman filtering for observed components and kernel density estimation for unobserved components, with subsampling and clustering.
result Reduces estimation errors in highly nonlinear scenarios compared to standard linear updates.
Develops CLDS models to model neural activity with nonlinear dynamics.
problem Complex, nonlinear dynamics in neural population activity.
method Conditionally Linear Dynamical System (CLDS) models using Gaussian Process (GP) priors.
result CLDS models can perform well even in data-limited conditions.
New nonlinear smoothers improve state estimation in chaotic systems.
problem Improving state estimation in chaotic dynamical systems with non-Gaussian behavior.
method Developed nonlinear backward ensemble transport smoothers with parameterization and regularization of transport maps.
result Nonlinear smoothers yield lower estimation error than conventional methods for comparable model evaluations.
BGM-IV uses AI to estimate causal effects in complex data.
problem Estimating causal effects in high-dimensional, nonlinear settings with endogeneity.
method Structured latent generative modeling for posterior inference in a causally structured latent space.
result BGM-IV outperforms existing methods in high-dimensional covariate regimes.
BINDy uses Bayesian methods to identify nonlinear dynamics from data.
problem Learning sparse representations of complex dynamics from data.
method Bayesian treatment of dictionary learning system identification using reversible-jump Markov-chain Monte-Carlo.
result BINDy produces models that are sparse in model space rather than parameter space.
Paper introduces ps-BART for estimating nonlinear ATE and CATE in continuous treatments.
problem Estimating ATE and CATE in continuous treatments with nonlinear relationships.
method Generalized ps-BART model for nonparametric estimation.
result ps-BART outperforms BCF model in highly nonlinear settings.
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.
Bayesian framework for robust model discovery from noisy data.
problem Robust model discovery from noisy, sparse and irregular observations of nonlinear systems.
method Bayesian differential programming using Hamiltonian Monte Carlo and sparsity-promoting priors.
result Efficient inference of posterior distributions over plausible models with quantified uncertainty.
Bayesian sOED uses PG reinforcement learning for efficient experiment design.
problem Optimizing sequential experiments for nonlinear models with limited data.
method Formulated as POMDP, solved via PG methods with neural network parameterization.
result Demonstrated advantages over batch and greedy designs in contaminant source inversion.
Framework models multiscale dynamics with Bayesian learning for regime changes.
problem Analyzing complex interactions between fast and slow processes.
method Hierarchical state-space modeling with Sequential Monte Carlo.
result Bayesian approach accurately tracks state transitions and identifies switching dynamics.
Bayesian neural networks improve macroeconomic forecasting and model nonlinearities.
problem Handling small T, big K macroeconomic datasets with temporal dependence.
method Developed Bayesian neural networks with mixture activation functions, shrinkage priors, and stochastic volatility.
result BNNs produce precise density forecasts, often better than other methods.
Paper introduces XBART for nonlinear regression, outperforming XGBoost.
problem Nonlinear regression problems, especially in speed and accuracy.
method Combines Bayesian modeling and recursive partitioning for efficient, accurate predictions.
result XBART provides faster and more accurate predictions than XGBoost.
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an optimization problem over an appropriately selected family of distributions. The…
A framework detects nonlinear and interaction effects in epidemiological data with uncertainty quantification.
problem Lack of reliable inference for ML-discovered nonlinearities and interactions in epidemiological data.
method Combines Bayesian sparse regression, tree ensembles, and Shapley values.
result Valid uncertainty quantification for feature effects at the individual level.
We introduce GP-FNARX: a new model for nonlinear system identification based on a nonlinear autoregressive exogenous model (NARX) with filtered regressors (F) where the nonlinear regression problem is tackled using sparse Gaussian processes (GP). We integrate data pre-processing with system identification into a fully …
A new method for Bayesian neural networks using probabilistic backpropagation.
problem Approximating posterior distributions in Bayesian neural networks.
method Variational Expectation Propagation (VEP) with probabilistic backpropagation.
result Efficient algorithm for approximate integration over posterior distributions.
We propose a general statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups. Our motivation comes from neuroscience, where an important problem is to identify, within a large assembly of neurons, subsets that respond similarly to a stimulu…
A novel model uses ODE-based random features to model nonlinear dynamical systems.
problem Modeling highly nonlinear dynamical systems with uncertainty quantification.
method Compositions of physics-informed random features derived from ODEs, combined with deep Gaussian processes and approximate Bayesian inference.
result The model effectively captures nonlinear behavior in real-world multivariate time series data and achieves comparable performance to other models on benchmark tasks.
Bayesian framework integrates prior and data knowledge for nonlinear dynamical systems.
problem Fusing diverse prior knowledge with data for accurate model learning.
method General-purpose Bayesian inference and learning framework combining explicit and implicit prior knowledge.
result Efficient parameter marginalization and closed-form densities for online and offline inference.
Two models predict net loan losses using Bayesian and frequentist regression.
problem Predicting net loan losses using financial and sociological data.
method Bayesian and frequentist regression analysis.
result Improved understanding of net loan loss relationships.
Bayesian model learns physics laws from data with uncertainty quantification.
problem Lack of uncertainty in discovering governing physical laws from data.
method Bayesian approach with leaf and root modules, Gaussian process for operators, automatic differentiation.
result Quantifies reliability of learned physics laws and propagates uncertainty.
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to repres…
We propose a fast inference method for Bayesian nonlinear support vector machines that leverages stochastic variational inference and inducing points. Our experiments show that the proposed method is faster than competing Bayesian approaches and scales easily to millions of data points. It provides additional features …
Study nonconcave portfolio choice with smooth ambiguity and Bayesian learning.
problem Nonconcave portfolio choice under smooth ambiguity and Bayesian learning.
method Developed a general framework for dynamic, non-concave asset allocation.
result Dynamic consistency achieved through a robust representation.
Bayesian non-linear latent variable modeling for complex data.
problem Inference for GPLVMs is computationally limited and often leads to overfitting or underestimates uncertainty.
method Approximate Gaussian process mappings with random Fourier features for MCMC inference.
result Generalized RFLVMs perform well on various data types and applications.
Bayesian GAMs improve predictive performance for high-dimensional data.
problem Sparse regularization in GAMs leads to excess shrinkage and difficulty in selecting nonlinear effects.
method Developed a novel spike-and-slab LASSO prior and scalable EM-Coordinate Descent algorithm.
result Improved predictive and computational performance compared to existing models.
nFBST tests neural networks using Bayesian methods.
problem Traditional significance testing struggles with complex nonlinear relationships.
method nFBST uses Bayesian neural networks to test neural networks.
result nFBST can test global, local, and instance-wise significance.
Expands experimental design for causal discovery from limited data.
problem Challenges in causal discovery from observational and interventional data.
method Bayesian optimal experimental design incorporating recent advances in causal discovery.
result Active causal discovery of large, nonlinear SCMs with both intervention target and value selection.
This paper tackles Bayesian system identification with probabilistic numerical methods.
problem Accurately modeling nonlinear dynamic systems from noisy data.
method Probabilistic Sequential Monte Carlo (SMC) combined with probabilistic numerical integration.
result Efficient identification of latent states and system parameters from noisy measurements.
Generative Bayesian Filtering improves inference in complex models without explicit density evaluations.
problem Performing posterior inference in complex nonlinear and non-Gaussian state-space models.
method Generative Bayesian Filtering (GBF) extends GBC to dynamic settings using deep neural networks for recursive posterior inference. Generative-Gibbs sampler bypasses density evaluations for parameter learning.
result GBF significantly outperforms likelihood-free approaches in accuracy and robustness for intractable state-space models.
The paper proposes a semi-parametric Bayesian network model using Gaussian Processes and Horseshoe priors.
problem Learning semi-parametric relationships in Expert Bayesian Networks with minimal nonlinear components.
method Uses Gaussian Processes and Horseshoe priors to model relationships, prioritizes modifying expert graphs, and generates diverse graphs.
result Models outperform state-of-the-art semi-parametric Bayesian Network models in synthetic and real-world datasets.
The paper analyzes methods for sparse Bayesian regression in nonlinear system identification.
problem Learning sparse models in Bayesian regression with nonlinear applications.
method Two classes of methods: regularization and thresholding based, built on automatic relevance determination (ARD).
result Analytical demonstration of favorable performance with sparse solutions in linear problems.