New approach avoids excess empirical risk in domain generalization.
problem Learning models that generalize to unseen distributions from diverse data sets.
method Minimizes penalty under constraint of optimal empirical risk, leveraging rate-distortion theory.
result Significant improvements in domain generalization performance across multiple methods.
Neural Empirical Bayes estimates source distributions from noisy simulations.
problem Estimating source distributions from noisy, simulated data.
method Uses neural density estimators to estimate a prior or source distribution over uncorrupted samples, then performs posterior inference.
result Recovering ground truth source distributions up to symmetries.
PROBE algorithm efficiently solves sparse high-dimensional linear regression.
problem Sparse high-dimensional linear regression models with complex parameter spaces.
method Partitioned empirical Bayes ECM algorithm for computationally efficient MAP estimation.
result PROBE algorithm provides robust and efficient coordinate-wise optimization.
New method estimates Schrödinger bridge potentials via empirical risk minimization.
problem Estimating Schrödinger bridge potentials from samples.
method Rewriting Schrödinger system as a fixed-point equation and estimating the potential via empirical risk minimization.
result Uniform concentration of empirical risk around population counterpart under sub-Gaussian assumptions.
We address the problem of algorithmic fairness: ensuring that sensitive variables do not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint into the learning problem. It encourages the conditional risk of the learned clas…
A non-parametric method for evaluation of the aggregate loss distribution (ALD) by combining and numerically inverting the empirical characteristic functions (CFs) is presented and illustrated. This approach to evaluate ALD is based on purely non-parametric considerations, i.e., based on the empirical CFs of frequency …
Empirical model tackles decision problems without specifying states of the world.
problem Decision problems under uncertainty with inaccessible states of the world.
method Empirical approach using observed act--consequence pairs as model primitives.
result Optimality in empirical decision problems addressed using protocol-based empirical choice functions.
VIB balances empirical and Bayesian approaches in predictive models.
problem Balancing empirical and Bayesian methods in predictive models.
method VIB as a compromise between empirical and Bayesian objectives.
result VIB minimizes risks due to finite sampling of targets.
Generative Adversarial Networks create realistic financial correlation matrices.
problem Creating realistic financial correlation matrices for practical applications.
method Generative Adversarial Networks (GANs) to model correlation matrices.
result GANs can recover known stylized facts about empirical correlation matrices.
Proposes MOPED method for choosing priors in Bayesian DNNs.
problem Challenges in specifying meaningful priors for deep neural networks.
method Two-stage hierarchical modeling with empirical Bayes.
result MOPED enables scalable variational inference and reliable uncertainty quantification.
Corrects sample selection bias in empirical risk minimization using importance sampling.
problem Statistical learning with biased training data.
method Weighted empirical risk minimization using importance sampling.
result Generalization capacity preserved with estimated importance weights.
A new method approximates expected empirical loss for stochastic deep learning tasks.
problem Determining optimal step sizes for stochastic gradient descent in deep learning.
method Applying one-dimensional function fitting to noisy losses of vertical cross sections to approximate expected empirical loss.
result The method leads to a robust and straightforward optimization method that performs well across datasets and architectures.
This research uses empirical copulas to price quanto options, showing significant differences from traditional models.
problem The dependence relation between currency and asset prices affects quanto option pricing.
method Empirical copulas are used to model the dependence between currency and asset prices.
result Empirical copulas provide non-negligible pricing differences compared to traditional models.
Bayesian Empirical Bayes extends EB to complex structures using probabilistic symmetry.
problem Improving simultaneous inference in complex settings like arrays and graphs.
method Generalized empirical Bayes approach based on probabilistic symmetry.
result BEB outperforms existing methods in denoising arrays and spatial data.
We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach builds off of techniques for distributionally robust optimization and Owen's empiric…
Recent work shows GRW approaches do not improve over ERM in distributional shift.
problem Improving robustness to distributional shift in machine learning models.
method Generalized Reweighting (GRW) algorithms, which iteratively update model parameters based on reweighting of training samples.
result GRW approaches do not significantly improve over ERM in real applications with distribution shift.
Flexible empirical Bayes for large-scale multiple linear regression.
problem Large-scale multiple linear regression with flexible priors and efficient computation.
method Adaptive shrinkage priors combined with variational approximations for hyperparameter estimation.
result The posterior mean from the empirical Bayes method solves a penalized regression problem.
Improved multi-group learning with group-realizable concepts.
problem Enhancing multi-group learning efficiency.
method Empirical risk minimization over group-realizable concepts.
result Improved sample complexity in group-realizable settings.
Empirical study finds robust optimization can improve portfolio performance in Indian markets.
problem Comparing robust optimization to Markowitz model for portfolio performance.
method Three robust optimization models (box, ellipsoidal, separable uncertainty sets) tested on Indian market data.
result Robust optimization can be a viable alternative to Markowitz model in real market setups.
We study compressing empirical measures in finite RKHSs using convex optimization.
problem Efficiently approximating empirical measures in high-dimensional spaces.
method Convex optimization and lower bounds on ball size.
result High probability lower bounds on ball size under various conditions.
An empirical method to determine kernel definiteness.
problem Determining definiteness of kernels is time-consuming and requires effort.
method Empirical approach using sampling and optimization with evolutionary algorithms.
result Empirical method can disprove definiteness and estimate likelihood of indefinite matrices.
A new sequential method estimates Poisson means in streaming data, achieving optimality and efficiency.
problem Estimating Poisson means in a streaming, or online, framework.
method A quasi-Bayesian approach based on Newton's algorithm for a sequential estimate.
result Established frequentist guarantees including consistency and asymptotic optimality.
Enhances normal mean estimation with side info using NIT approach.
problem Compound estimation of normal means with side information.
method Empirical Bayes, nonparametric integrative Tweedie (NIT) approach.
result NIT approach improves estimation risk and convergence rate with increasing auxiliary data.
Disputes the empirical Fisher approximation for natural gradient descent.
problem The empirical Fisher approximation fails to capture second-order information in general.
method Comparison of empirical Fisher and Fisher information matrices.
result The empirical Fisher does not generally approximate the Fisher or Hessian.
Large-scale kernel approximation is an important problem in machine learning research. Approaches using random Fourier features have become increasingly popular [Rahimi and Recht, 2007], where kernel approximation is treated as empirical mean estimation via Monte Carlo (MC) or Quasi-Monte Carlo (QMC) integration [Yang …
New method for high-dimensional linear regression using empirical Bayes.
problem Estimating prior in high-dimensional linear regression.
method Variational empirical Bayes approach with NPMLE and mean field approximation.
result Established asymptotic consistency and computational efficiency of the method.
Unified approach to private statistics from empirical to population data.
problem Divided focus on empirical vs population statistics in private statistics.
method Unified methods for both types of statistics.
result Methods for empirical statistics can be applied to population statistics.
Aggregates probability models using Wasserstein space and variational approach.
problem Model aggregation in the Wasserstein space of distributions.
method Data-driven calibration framework based on Γ Γ Γ -convergence. result Empirical minimizers converge to the minimizers of the actual problem.
The Basel II internal ratings-based (IRB) approach to capital adequacy for credit risk implements an asymptotic single risk factor (ASRF) model. Measurements from the ASRF model of the prevailing state of Australia's economy and the level of capitalisation of its banking sector find general agreement with macroeconomic…
A new learning method uses data to learn from large model sets.
problem Learning with large sets of candidate models where uniform convergence is hard.
method Data-dependent learning that incorporates empirical data less reliant on prior assumptions.
result Demonstrates improved generalization in various learning assumptions.
Empirical mode modeling improves state-space analysis of noisy data.
problem Analyzing nonlinear systems with noisy data.
method Combining empirical mode decomposition with empirical dynamic modeling.
result Empirical mode modeling enhances state-space representations in noisy data.
Flexible Bayesian approach for generalized linear models, especially for sparse logistic regression.
problem Sparse logistic regression challenges in machine learning.
method Empirical Bayes approach with mean-field variational inference, tuning-free and scalable.
result Superior predictive performance in sparse logistic regression compared to existing methods.
This paper reviews and analyzes various modeling approaches for financial index tracking.
problem Efficient replication of market index performance in financial markets.
method Categorization into three frameworks: optimization, statistical, and machine learning; empirical study on S&P 500 dataset.
result Optimization-based models deliver the most precise index tracking, statistical-based models achieve the strongest return-risk balance, and data-driven models provide competitive performance.
Paper explores using bootstrap methods to improve SGD's stability and robustness.
problem Improving the stability and robustness of SGD.
method Investigates empirical bootstrap approaches for SGD from algorithmic stability and statistical robustness perspectives.
result Demonstrates construction of purely distribution-free confidence intervals using bootstrap SGD.
BERT outperforms traditional machine learning in text classification tasks.
problem Comparing BERT to traditional machine learning methods for text classification.
method Empirical testing of BERT against TF-IDF-based machine learning models in various scenarios.
result BERT demonstrates superior performance and independence from text features.
Study compares model-free valuation to actual financial outcomes, finds it slightly conservative.
problem Evaluating the quality of model-free valuation approaches for financial derivatives.
method Empirical analysis using historical option prices from S&P 500 constituents.
result Model-free valuation approaches are only marginally more conservative than industry-standard models.
We analyze differences between two information-theoretically motivated approaches to statistical inference and model selection: the Minimum Description Length (MDL) principle, and the Minimum Message Length (MML) principle. Based on this analysis, we present two revised versions of MML: a pointwise estimator which give…
A new one-step method for covariate shift adaptation.
problem Real-world data often violates the assumption of same distribution for training and test samples.
method Proposes a one-step optimization approach to jointly learn the model and weights.
result The proposed method achieves a generalization error bound and is empirically effective.
We introduce performance-based regularization (PBR), a new approach to addressing estimation risk in data-driven optimization, to mean-CVaR portfolio optimization. We assume the available log-return data is iid, and detail the approach for two cases: nonparametric and parametric (the log-return distribution belongs in …
Introduces BPEL for EL, enhancing flexibility and using MCMC for inference.
problem Computational challenges in EL methods.
method Bayesian Penalized Empirical Likelihood (BPEL) framework with MCMC sampling.
result Enhanced flexibility and practicality of EL methods with MCMC.
Analyzes empirical risk minimization in finance, showing effectiveness and generalization issues.
problem Analyzing empirical risk minimization in finance for optimal hedging and investment decisions.
method Classical statistical machine learning techniques and non-asymptotic estimates based on Rademacher complexity.
result Over-training leads to anticipative decisions, but non-asymptotic estimates show convergence for large training sets.
Empirical moment matrix reveals properties of point clouds.
problem Uncovering properties of point clouds, especially those with singular support.
method Combining statistics, real algebraic geometry, and approximation theory.
result The empirical moment matrix provides insights into data analysis.
Improved privacy-preserving linear regression via iterative Hessian mixing.
problem Differentially private linear regression with improved accuracy and efficiency.
method Iterative Hessian Mixing (IHM) for differentially private ordinary least squares (DP-OLS).
result IHM provides better utility guarantees and outperforms AdaSSP in empirical evaluations.
Gradient-based optimization improves variational empirical Bayes regression.
problem Sparse, large-scale multiple regression models.
method Gradient-based optimization (GradVI) for variational empirical Bayes (VEB) regression.
result GradVI produces similar predictive performance to CAVI but converges faster and is faster in certain settings.
Improved sample complexity for diffusion models without needing empirical risk minimizers.
problem Theoretical limitations in sample complexity for diffusion models.
method Structured decomposition of score estimation error, eliminating dependence on neural network parameters.
result Achieved sample complexity bound of O(ε^(-4)) without empirical risk minimizer access.
Distributional reinforcement learning (distributional RL) has seen empirical success in complex Markov Decision Processes (MDPs) in the setting of nonlinear function approximation. However, there are many different ways in which one can leverage the distributional approach to reinforcement learning. In this paper, we p…
New method for neural network uncertainty quantification using empirical Neural Tangent Kernel.
problem Accurately quantify uncertainty in neural network predictions.
method Post-hoc, sampling-based approach using gradient-descent on linearized networks.
result Method effectively approximates Gaussian process posterior and outperforms existing methods in efficiency and accuracy.
Paper proposes an algorithm to reduce hypothesis space for faster convergence in high-dimensional settings.
problem Over-conservativeness of existing regularization approaches in high-dimensional settings.
method Empirical hypothesis space reduction to achieve faster convergence without dependence on the size of the hypothesis space.
result Achieves faster convergence of generalization error O ( log n / n ) O(\sqrt{\log n/n}) O ( log n / n ) independent of the dimension d d d .