The paper examines Gaussian process means under misspecified likelihoods and smoothness.
problem Accuracy of Gaussian process approximations under misspecified smoothness and likelihood.
method Analysis of Gaussian process properties under misspecified conditions.
result The accuracy of Gaussian process approximations is influenced by experimental design and kernel choice.
This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We pr…
Nyström subsampling with Tikhonov regularization for covariate shift adaptation under misspecified case
problem Adaptation to misspecified covariate shift
method Regularized Nyström subsampling with Tikhonov regularization
result Upper bounds on excess risk
Study non-asymptotic bounds for robust estimators under misspecified models.
problem Evaluate performance of robust estimators under adversarial conditions.
method Propose a general approach to adversarial risk analysis, including investigations on generalization and approximation errors.
result Establish non-asymptotic upper bounds for adversarial excess risk under Lipschitz loss functions.
This paper studies a Nyström type subsampling approach to large kernel learning methods in the misspecified case, where the target function is not assumed to belong to the reproducing kernel Hilbert space generated by the underlying kernel. This case is less understood, in spite of its practical importance. To model su…
Kernel-based quadrature rules are becoming important in machine learning and statistics, as they achieve super- n \sqrt{n} n convergence rates in numerical integration, and thus provide alternatives to Monte Carlo integration in challenging settings where integrands are expensive to evaluate or where integrands are high d…
New algorithm optimizes smooth functions with Hölder exponent > 1.
problem Optimizing smooth functions with unknown Hölder exponent > 1.
method Two-layer algorithms using misspecified linear/polynomial bandit algorithms in bins.
result Regret bound of O ~ ( T d + α d + 2 α ) \tilde{O}(T^{\frac{d+\alpha}{d+2\alpha}}) O ~ ( T d + 2 α d + α ) for α > 1 \alpha > 1 α > 1 . Statistical inference for misspecified contextual bandits is challenging due to adaptivity issues.
problem Statistical inference for misspecified contextual bandits
method Inverse-probability-weighted Z-estimation framework
result Consistent and asymptotically normal estimator with sandwich variance estimator
The paper examines when importance weighting is needed for nonparametric and misspecified models.
problem When is importance weighting correction needed for covariate shift adaptation?
method Analysis of IW-corrected kernel ridge regression in various settings.
result The importance weighting correction is needed for nonparametric and misspecified models to obtain the best approximation of the true unknown function.
New PG losses improve decision optimization in misspecified models.
problem Improving decision optimization in models that are not perfectly specified.
method Introducing Perturbation Gradient (PG) losses to connect decision loss with directional derivatives and optimizing using gradient techniques.
result PG losses yield best-in-class policies asymptotically, even in misspecified settings.
Proposes m-POT to improve m-OT's misspecified mappings issue.
problem Misspecified mappings in mini-batch optimal transport.
method Partial optimal transport (POT) between mini-batch empirical measures.
result m-POT alleviates incorrect mappings compared to current methods.
New diagnostic method detects misspecified models in inverse PDE problems.
problem Misleading residual-norm diagnostics in inverse PDE problems.
method Structure-sensitive sequential diagnostic using e-processes.
result Rejects fitted models that produce biased predictions.
New methods for CI testing under model misspecification.
problem Challenges in CI testing with misspecified models.
method Proposes new approximations and upper bounds for testing errors of regression-based CI tests.
result Introduces the Rao-Blackwellized Predictor Test (RBPT) robust against misspecified inductive biases.
Reward hacking exploits misspecified rewards, affecting agent capabilities and true performance.
problem Reward hacking in RL models exploiting reward misspecifications.
method Constructed four RL environments with misspecified rewards; analyzed agent capabilities and behavior.
result More capable agents exploit reward misspecifications, achieving higher proxy reward but lower true reward.
Study on sequential prediction with log-loss, focusing on well-specified and misspecified cases.
problem Sequential prediction with log-loss under different specification conditions.
method Analysis of cumulative regret in well-specified and misspecified cases for a Gaussian location hypothesis class.
result Cumulative regrets in well-specified and misspecified cases asymptotically coincide for the d d d -dimensional Gaussian location hypothesis class. Stochastic Gradient Descent improved for various Hilbert scales and misspecified models.
problem Understanding and optimizing SGD in Hilbert scales for machine learning.
method Extending SGD analysis to Hilbert scales, including Sobolev and Diffusion spaces, and showing the effects of smoothness and preconditioning.
result Violation of smoothness assumption affects learning rate; preconditioning in Hilbert scales reduces the number of iterations for misspecified models.
Suppose an investor aims at Delta hedging a European contingent claim h ( S ( T ) ) h(S(T)) h ( S ( T )) in a jump-diffusion model, but incorrectly specifies the stock price's volatility and jump sensitivity, so that any hedging strategy is calculated under a misspecified model. When does the erroneously computed strategy super-replicate the t…
Improved algorithm for misspecified MLMDPs with bounded regret and space/time complexities.
problem Misspecified linear Markov decision processes.
method Proposes an algorithm with three desirable properties: bounded regret, bounded space/time complexities, and no need for misspecification input.
result Regret scales as K max { ε e x t m i s , ε e x t t o l } K \max \{ \varepsilon_{ ext{mis}}, \varepsilon_{ ext{tol}} \} K max { ε e x t mi s , ε e x t t o l } , improving existing bounds. New method improves GP uncertainty quantification for misspecified priors.
problem Uncertainty quantification for GPs under incorrect priors.
method Constructs a confidence sequence using martingale techniques.
result Empirically outperforms standard GP methods in robustness and utility for Bayesian Optimization.
Framework predicts responses in misspecified systems using GPLFM and BNNs.
problem Predicting responses in dynamical systems with model misspecification.
method Integrates GPLFM and BNNs for uncertainty-aware inference and prediction.
result Systematic propagation of uncertainty from diagnosis to prediction.
SATL adapts to varying smoothness in hypothesis transfer learning.
problem Fixed kernel regularization fails in varying smoothness settings.
method Proposes SATL, a two-phase KRR algorithm with adaptive Gaussian kernels.
result SATL achieves minimax optimality with matching upper and lower bounds.
Self-consistency improves the accuracy of model comparison methods.
problem Improving the accuracy of model comparison methods when simulation models are misspecified.
method Supplement traditional simulation-based training with a self-consistency loss on unlabeled real data.
result Self-consistency training improves model comparison accuracy, especially in open-world scenarios.
We consider a class of misspecified dynamical models where the governing term is only approximately known. Under the assumption that observations of the system's evolution are accessible for various initial conditions, our goal is to infer a non-parametric correction to the misspecified driving term such as to faithful…
Improved classifier for PU data using logistic regression.
problem Analysis of Positive Unlabeled data under SCAR assumption.
method Fitting misspecified logistic regression model to PU data.
result The classifier performs on par or better than competitors on real data sets.
The paper studies the robust maximization of utility of terminal wealth in the diffusion financial market model. The underlying model consists with risky tradable asset, whose price is described by diffusion process with misspecified trend and volatility coefficients, and non-tradable asset with a known parameter. The …
Bayesian algorithms perform well even with misspecified priors, especially in meta-learning.
problem Performance degradation of Bayesian algorithms with misspecified priors.
method Thompson sampling and meta-learning analysis with misspecified priors.
result Thompson sampling's performance degrades gracefully with misspecification, with a bound of i l d e O ( H 2 ε ) ilde{\mathcal{O}}(H^2 ε) i l d e O ( H 2 ε ) . New algorithms for optimizing functions with noisy feedback, even when the model is misspecified.
problem Optimizing a black-box function with noisy bandit feedback, especially when the model is misspecified.
method Developed two algorithms based on Gaussian process methods: EC-GP-UCB and Phased GP Uncertainty Sampling.
result Achieved optimal dependence on misspecification error without prior knowledge, and effective in stochastic contextual settings.
New method for adaptive estimation and inference in econometric models without knowing smoothness.
problem Adaptive estimation and inference in ill-posed linear inverse problems with unknown smoothness.
method Discrepancy principle-based framework for adaptive hyperparameter selection.
result Achieves optimal rates in weak and strong metrics for linear functionals.
Paper analyzes spectral algorithms under covariate shift, providing convergence rates.
problem Addressing distributional mismatch in regression models.
method Incorporates importance weights into spectral algorithms in RKHS.
result Establishes minimax-optimal convergence rates for misspecified cases.
Existing nonconvex statistical optimization theory and methods crucially rely on the correct specification of the underlying "true" statistical models. To address this issue, we take a first step towards taming model misspecification by studying the high-dimensional sparse phase retrieval problem with misspecified link…
Riemannian flows model curved spaces better.
problem Normalizing flows misspecified on curved spaces.
method Riemannian continuous normalizing flows using ODE solutions.
result Improves modeling on spheres, torii, and hyperbolic spaces.
New algorithms for best arm identification in bandits robust to misspecified parameters.
problem Inconsistent learning performance of traditional MAB algorithms when parameters are misspecified.
method Proposes two classes of asymptotically near-optimal algorithms for statistically robust MAB under fixed-budget pure exploration.
result Establishes fundamental performance limits and proposes algorithms that are asymptotically near-optimal.
There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study these opportunities in a generic stochastic volatility model and exhibit the strateg…
Improves Bayesian predictive performance in misspecified models.
problem Misspecification gap between inferential and predictive risks.
method Develops a multi-sample loss (PAC m ^m m ) to bridge the gap. result Empirical study shows improved predictive distribution.
New method improves uncertainty quantification for large batch sizes and misspecified models.
problem Challenges in tuning algorithms for accurate uncertainty quantification in large batch sizes and misspecified models.
method Proposes new discrete-time approximations to SGD and SGLD, proving error bounds for practical tuning.
result Quantitative, non-asymptotic error bounds for accurate predictions of covariance and autocorrelation time.
RoPE framework calibrates misspecified simulators for reliable inference.
problem Misspecification compromises reliability of simulation-based inference.
method Data-driven calibration using optimal transport and a small calibration set.
result RoPE framework improves inference accuracy and uncertainty calibration.
Sharp bounds on ATE with unmeasured confounders, valid even when misspecified.
problem Bounding average treatment effects with unmeasured confounders.
method Distributionally robust optimization, double sharpness, double validity.
result Proposes estimators with robustness properties for valid bounds.
Bayesian metalearning improves performance in linear bandits with misspecified priors.
problem Improper priors lead to suboptimal performance in sequential decision-making.
method Proves performance bounds for metalearning priors in stochastic linear bandits and develops a metalearning algorithm.
result Metalearning can improve performance by learning the prior from multiple tasks.
Plug-in method improves performative prediction accuracy.
problem Learning under performative feedback with slow convergence rates.
method Plug-in performative optimization using models.
result Plug-in method can be superior to model-agnostic strategies.
Paper develops a method to predict spatial point processes with guarantees.
problem Predicting the number of events in space with uncertainty.
method Regularized method to learn spatial models with out-of-sample guarantees.
result Method provides valid prediction intervals even when model is misspecified.
A new method improves efficiency in finding optimal personalized treatment rules.
problem Heteroscedasticity and misspecified treatment-free effect models affect optimal ITR estimation.
method E-Learning framework that accounts for covariate-treatment dependent variance of residuals.
result E-Learning framework improves efficiency of optimal ITR estimation.
ACE improves GBI for simulators by approximating cost functions, making inference more efficient.
problem Inference for misspecified simulators is overly restrictive.
method Amortized cost estimation (ACE) for Generalized Bayesian Inference (GBI).
result ACE provides accurate cost predictions and more efficient inference.
Study optimizes learning rates for conditional mean embedding estimates.
problem Consistency of kernel ridge regression for conditional mean embedding.
method Adaptive statistical learning rate derived for misspecified setting.
result Upper bound matches optimal O ( log n / n ) O(\log n / n) O ( log n / n ) rates without assuming finite dimensionality. Nonparametric modeling approaches show very promising results in the area of system identification and control. A naturally provided model confidence is highly relevant for system-theoretical considerations to provide guarantees for application scenarios. Gaussian process regression represents one approach which provid…
Paper presents a machine learning method to improve significance tests for misspecified linear models.
problem Misspecification of linear assumptions in social science models leads to inaccurate significance levels.
method Apply machine learning to fit ground truth function, calculate linear approximation, and adjust the estimator.
result The method significantly outperforms linear regression for non-linear ground truth functions.
Proposes a method to improve SBI under model misspecification.
problem Unreliable inference from SBI methods under model misspecification.
method Introduces a regularized loss function to penalize statistics that increase model-data mismatch.
result Demonstrates superior performance and robust inference in misspecified scenarios.
New method infers causal effects without knowing control variables.
problem Inference errors when control variables are unknown.
method Proposes a method for inferring causal effects when control variables are unknown.
result Proves method yields asymptotically valid confidence intervals for average causal effects.
GES algorithm improves consistency for nonparametric DAG models.
problem Consistent estimation of nonparametric DAG models.
method Greedy equivalence search with new consistency proof for nonparametric families.
result Consistency of GES for general nonparametric DAG models with smooth factorization.