Proposes CoDEAL for estimating heterogeneous treatment effects in panel data models.
problem Estimating heterogeneous treatment effects in causal panel data models with covariate effects.
method Covariate-Adjusted Deep Causal Learning (CoDEAL) integrating neural networks and autoencoders.
result Establishes theoretical guarantees and demonstrates compelling performance in simulations and real data.
Many machine learning algorithms require precise estimates of covariance matrices. The sample covariance matrix performs poorly in high-dimensional settings, which has stimulated the development of alternative methods, the majority based on factor models and shrinkage. Recent work of Ledoit and Wolf has extended the sh…
Improved LDA using a nonlinear covariance estimator for better performance.
problem Inefficient LDA when data covariance is ill-conditioned.
method Regularized LDA with a positive semidefinite ridge-type estimator of the inverse covariance matrix.
result The proposed NL-RLDA classifier outperforms state-of-the-art methods across multiple datasets.
MediEncoder learns nonlinear representations for causal mediation analysis.
problem High-dimensional noisy covariates and mediators in biomedical studies.
method Coupled encoder-decoder architecture with cross-factor network.
result Improves estimation accuracy in high-dimensional causal mediation analysis.
New covariance estimator for financial portfolios.
problem Estimating large financial covariances in non-stationary environments.
method Exponentially weighted averages and cross-validation for nonlinearly shrinking sample eigenvalues.
result Our estimator performs well in large dimensions compared to existing estimators.
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.
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.
This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). The main problem with such model is that we have to know the covariance matrix of the noise to get optimal estimator. however we show that, if we choose as cost function the logarithm of the determinant of t…
A new method quickly identifies key variables and interactions.
problem Identifying key variables and interactions in high-dimensional data.
method Kernel trick for sparse orthogonal decomposition in O(# covariates) time.
result Outperforms existing methods for large, high-dimensional data sets.
New method for nonlinear SDR of complex non-Euclidean data.
problem Nonlinear SDR for complex non-Euclidean random objects.
method Fréchet Cumulative Covariance (FCCov) and neural networks.
result Robust and unbiased nonlinear SDR for complex data.
Proposes a new AFT model for nonlinear survival data.
problem Limited ability of classical AFT models to represent nonlinear relationships and handle complex covariate structures.
method Structured nonparametric extension using Kolmogorov--Arnold representations and unified censoring-adjusted losses.
result Method captures nonlinear effects and recovers linear structure when appropriate.
Proposes a new estimator for weak instrumental variables in panel data models.
problem Weak instrumental variables due to ignored nonlinearities in panel data.
method Triangular simultaneous equation model with a nonlinear reduced form equation and a control function approach using Super Learner.
result The proposed SLCF estimator is consistent and asymptotically normal, achieving a parametric rate of convergence.
Proposes a partially linear structure to capture nonlinear relationships in mixture of experts models.
problem Suboptimal estimates due to linearity assumption in mixture of experts models.
method Introduces a partially linear structure that incorporates unspecified functions to capture nonlinear relationships.
result Establishes the identifiability of the proposed model under mild conditions and introduces a practical estimation algorithm.
New method tests independence with single nonstationary time series.
problem Testing independence in nonstationary nonlinear time series.
method Time-varying nonlinear regression, local long-run covariance estimation, strong Gaussian approximation.
result First framework for conditional independence testing with a single realization of a nonstationary nonlinear process.
In this paper, we introduce a new machine learning (ML) model for nonlinear regression called the Boosted Smooth Transition Regression Trees (BooST), which is a combination of boosting algorithms with smooth transition regression trees. The main advantage of the BooST model is the estimation of the derivatives (partial…
SCOPE estimator improves covariance and precision matrix estimation.
problem Estimating covariance and precision matrices accurately.
method Distributionally robust optimization with convex spectral divergence.
result SCOPE estimator reduces spectral bias and improves condition number.
Kernel measures similarity of nonlinear causal structures in heterogeneous populations.
problem Learning causal structure in populations with diverse underlying structures.
method Distance covariance-based kernel for measuring similarity of causal structures.
result Kernel enables clustering of homogeneous subpopulations for causal structure learning.
We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte Carlo estimation of Geyer and Thompson (1992). The family is such that we can e…
Proposes estimators for complex dose-response curves using kernel methods.
problem Estimating complex dose-response curves with continuous treatments, mediators, and covariates.
method Kernel ridge regression with sequential kernel embedding technique.
result Simple estimators for mediated and time-varying dose response curves with nonasymptotic uniform rates.
Develops estimators for near-optimal linear regression under distribution shift.
problem Linear regression under distribution shift with scarce target domain data.
method Minimax linear risk estimators covering various transfer learning settings.
result Achieves near-optimal risk for linear regression problems under distribution shift.
Reservoir computer dimensions estimated using three methods.
problem Estimating the dimension of reservoir computer signals.
method Used three dimension estimation methods: false nearest neighbor, covariance, and Kaplan-Yorke.
result Signals in reservoir system exist on a low dimensional surface.
Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness for the model-free knockoffs procedure introduced recently in Candès, Fan, Jans…
Introduces intrinsic Riemannian cross-covariance for manifold-valued random objects.
problem Covariance estimation for random objects on Riemannian manifolds.
method Defines covariance and correlation via parallel transport.
result Proposed covariance is independent of coordinate choices.
Proposes a deep learning framework for interval-censored survival data.
problem Lack of deep learning methods for interval-censored survival data.
method Partially linear transformation models with DNN approximations for nonlinear effects.
result DNN estimator achieves minimax-optimal convergence and superior performance.
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a p-dimensional Gaussian random vector from n independent samples. The proposed model minimizes the worst case (maximum) of Stein's loss across all normal reference d…
GBMixed boosts mixed models for clustered data, estimating mean and variance flexibly.
problem Flexible estimation of mean and variance components in clustered data.
method Gradient Boosting framework for linear mixed models with likelihood-based gradients.
result GBMixed accurately recovers complex nonlinear fixed effects and covariances.
Develops DML for nonlinear panel data models with fixed effects.
problem Estimating causal effects in nonlinear panel data models with fixed effects.
method Double machine learning (DML) procedures for approximating nuisance functions.
result First-differencing yields the least constraints on fixed effects distribution.
FIDDLE uses deep learning to estimate ATE from complex data.
problem Estimating ATE from high-dimensional, correlated covariates with sparse nonlinear effects.
method Factor-augmented deep learning for propensity and outcome models.
result FIDDLE consistently estimates ATE under model misspecification and is semiparametrically efficient.
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…
Dual Bayesian Affine Estimators for Wiener-type state-space models
problem Estimating parameters in Wiener-type state-space models
method Fixed-point architecture combining two affine estimators
result Dual basis-parameter estimator achieves comparable parameter MSE to purely affine estimator
Bayesian framework for analyzing heterogeneous covariance data with a novel MoE-Wishart model.
problem Analyzing complex multivariate systems with varying covariance structures.
method Comprehensive Bayesian framework using mixture-of-experts Wishart model with predictor-dependent mixture weights.
result Accurate subpopulation recovery and estimation in heterogeneous covariance scenarios.
New kernel methods estimate complex causal relationships.
problem Estimating nonparametric causal functions like dose-response curves.
method Kernel ridge regression with decomposition property.
result Uniform consistency with finite sample rates proved.
The paper proposes AIS for Bayesian inversion of multioutput signals with covariance estimation.
problem Performing uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals.
method Adaptive Importance Sampling (AIS) scheme, split variables, frequentist approach for noise covariance, prior density over covariance matrix.
result Estimation of model parameters and covariance matrix of noise.
NoLimits.jl: Flexible and Composable Nonlinear Mixed-Effects Modeling in Julia
problem Flexible and composable nonlinear mixed-effects modeling
method Macro-based modeling language and unified interface
result Substantially expand the range of nonlinear mixed-effects models
CSTs improve stability in covariance spectrum analysis without training.
problem Stability and expressiveness in covariance spectrum analysis.
method Sequential application of covariance wavelet filters to input data.
result Stable and expressive hierarchical representations in low-data settings.
PSLR classifies functional data with scalar covariates using path signatures.
problem Classical functional logistic regression models have limitations in capturing nonlinear and cross-channel dependencies.
method PSLR uses truncated path signatures to create a basis-free representation of functional data.
result PSLR outperforms traditional functional classifiers in accuracy and robustness, especially under non-uniform sampling.
Active-set algorithm improves Cox regression for shape-restricted covariates.
problem Improving Cox regression for shape-restricted covariates.
method Shape-restricted inference using active-set optimization for spline basis expansion.
result Active-set algorithm produces accurate linear covariate effect estimates.
Extends deep learning for nonlinear Cox regression variable selection.
problem Variable selection for nonlinear Cox regression model.
method Extends LassoNet to survival data for nonlinear Cox model.
result Valid and effective method demonstrated through simulations.
The paper develops time-uniform inference methods for stochastic approximation parameters.
problem Statistical inference for parameters in stochastic approximation problems.
method Analysis of averaged iterates convergence rates and construction of asymptotic confidence sequences.
result Valid asymptotic confidence sequences for parameters in stochastic approximation problems.
Study on identifying and inferring nonlinear dynamics on unknown networks.
problem Identifying network structure in nonlinear dynamic systems with unknown interactions.
method Showed network structure is not generically identified, requiring sufficient spectral heterogeneity. Developed necessary and sufficient conditions for identification and proposed a semiparametric estimator.
result Necessary and sufficient conditions for identification of network structure in nonlinear dynamic systems.
Semi-parametric survival analysis methods like the Cox Proportional Hazards (CPH) regression (Cox, 1972) are a popular approach for survival analysis. These methods involve fitting of the log-proportional hazard as a function of the covariates and are convenient as they do not require estimation of the baseline hazard …
Combines BART and Gaussian process for spatial covariate prediction with uncertainty.
problem Improving spatial prediction models with nonlinear and interaction covariates.
method Bayesian Additive Regression Trees (BART) combined with Gaussian process for spatial dependence.
result Effective in reducing computational burden through INLA and MCMC.
New decompositions misattribute differences between populations, even when outcomes are identical.
problem Misattribution of differences between populations using common functional decompositions.
method Extending the Kitagawa-Oaxaca-Blinder decomposition to nonlinear functional decompositions.
result Functional ANOVA and Accumulated Local Effects can misattribute differences even when outcomes are identical in two populations.
Proposes using external data to improve predictions in medical applications with limited samples.
problem Small sample sizes and complex covariate-response relationships in medical data.
method Integrates external co-data into Bayesian Additive Regression Trees (BART) using an empirical Bayes framework.
result Improves prediction accuracy compared to standard BART, especially for nonlinear relationships.
Bayesian framework tackles measurement error in covariates.
problem Misleading inference due to corrupted covariates.
method Bayesian Nonparametric Learning framework robust to misspecification.
result General framework for Classical and Berkson error models.
This paper establishes that so-called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with Berkson-type measurement error in the regressors. An estimator is proposed and proven to be consistent. Its practical performance and feasibility are investigated via …
A new ML-based filter improves data assimilation for nonlinear systems.
problem Improving data assimilation for nonlinear systems using ensemble methods.
method Developed a machine learning-based conditional mean filter (ML-EnCMF) integrating ANN and linear functions.
result ML-EnCMF outperforms EnKF and likelihood-based EnCMF in nonlinear systems.
RFMs transition from linear to nonlinear under specific input-label correlation.
problem Understanding the transition from linear to nonlinear behavior in RFMs.
method Analyzing RFMs under spiked covariance designs, characterizing the interaction between anisotropy and input-label correlation.
result The RFM generalization error is governed by the strength of input-label correlation, leading to a clear nonlinear advantage above a specific boundary.