New method uses neural networks for unbiased physical observable estimation.
problem Estimating physical observables with neural samplers.
method Asymptotically unbiased estimators for observables, including partition function-dependent ones.
result Superiority over existing methods in numerical experiments for the 2d Ising model.
New theory of sensitivity for unbiased estimators using Wasserstein geometry.
problem Estimating the instability of estimators under small perturbations.
method Developed a new theory based on Wasserstein geometry, analogous to classical Cramér-Rao theory.
result Wasserstein-Cramér-Rao lower bound for sensitivity of unbiased estimators.
Paper addresses high-dimensional linear regression with missing data, proposing efficient and nearly unbiased estimators.
problem High-dimensional linear regression with blockwise missing covariates and partially observed responses.
method Proposes a computationally efficient estimator and nearly unbiased debiased estimators using blockwise imputation and estimating equations.
result Asymptotically valid confidence intervals and statistical tests constructed based on debiased estimators.
This work improves texture segmentation by automatically tuning hyperparameters for Total-Variation.
problem The challenge is to automatically select hyperparameters for Total-Variation texture segmentation.
method The approach involves extending Stein's unbiased gradient estimator to handle correlated Gaussian noise, leading to an automatic tuning method.
result The method provides an automatic way to select hyperparameters for Total-Variation texture segmentation.
Stochastic EM with biased MCMC improves inference stability.
problem Intractable E-step in EM algorithm.
method Stochastic approximation with biased MCMC.
result ULA is more stable and sometimes faster than MALA.
We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has minimal variance among all unbiased estimators and is asymptotically normally dis…
New nonconvex penalty smooths at origin for deep learning.
problem Improving variable selection and bias in high-dimensional statistical learning.
method Developed a new nonconvex penalty function smooth at origin.
result Asymptotic bias of new penalty function vanishes exponentially fast.
The empirical practice of using factor models to adjust for shared, unobserved confounders, Z, in observational settings with multiple treatments, A, is widespread in fields including genetics, networks, medicine, and politics. Wang and Blei (2019, WB) formalizes these procedures and develops the …
In the presence of a layer of metaprobabilities (from uncertainty concerning the parameters), the asymptotic tail exponent corresponds to the lowest possible tail exponent regardless of its probability. The problem explains "Black Swan" effects, i.e., why measurements tend to chronically underestimate tail contribution…
A widely applicable Bayesian information criterion (Watanabe, 2013) is applicable for both regular and singular models in the model selection problem. This criterion tends to overestimate the log marginal likelihood. We identify an overestimating term of a widely applicable Bayesian information criterion. Adjustment of…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds a…
We present online boosting algorithms for multiclass classification with bandit feedback, where the learner only receives feedback about the correctness of its prediction. We propose an unbiased estimate of the loss using a randomized prediction, allowing the model to update its weak learners with limited information. …
EigenGame improves eigendecomposition by offering unbiased updates for larger datasets.
problem Minibatch bias in EigenGame limits convergence and parallelism.
method Proposed unbiased stochastic update for EigenGame.
result Asymptotic equivalence to EigenGame, greater parallelism, and improved performance.
Improved estimator reduces bias in statistical learning models.
problem Asymptotic bias in classic WDRO estimator.
method Adjusted Wasserstein distributionally robust estimator.
result Asymptotic unbiased estimator with smaller MSE.
Estimates proper calibration errors and refinement terms in probabilistic predictions.
problem Lack of a general estimator for proper calibration errors and refinement terms with known statistical properties.
method Proposes a method for consistent, asymptotically unbiased estimation of proper calibration errors and refinement terms.
result Proves the relation between refinement and f-divergences, implying information monotonicity in neural networks.
We propose and analyze a new stochastic gradient method, which we call Stochastic Unbiased Curvature-aided Gradient (SUCAG), for finite sum optimization problems. SUCAG constitutes an unbiased total gradient tracking technique that uses Hessian information to accelerate con- vergence. We analyze our method under the ge…
Federated learning method improves covariate shift adaptation for missing target values.
problem Missing target values in federated learning.
method Federated covariate shift adaptation algorithm for missing target output values.
result Asymptotically unbiased and efficient algorithm for federated learning.
This paper analyzes SGD with biased gradients for deep learning models.
problem Analyzing SGD with biased gradients for deep learning models.
method Non-asymptotic analysis of SGD with adaptive steps for non-convex smooth functions.
result Adagrad, RMSProp, and AMSGRAD converge to critical points at a similar rate to unbiased case.
The paper offers precise bounds for averaged LSA iterates in linear systems.
problem Computing approximate solutions of linear systems with noisy observations.
method Finite-time analysis of LSA algorithms with Polyak-Ruppert averaging.
result Sharp high-probability bounds for averaged LSA iterates.
A new method for approximating softmax and Gaussian kernels with reduced error.
problem Approximating softmax and Gaussian kernels with low error.
method Simplex Random Features (SimRFs) and SimRFs+.
result SimRFs provide the smallest MSE among weight-independent geometrically-coupled PRF mechanisms.
New anomaly estimator reduces bias in MLE for normally distributed data.
problem Bias in Maximum Likelihood Estimation of structured anomalies.
method Derive a new anomaly estimator using a mixture model.
result New estimator is asymptotically unbiased regardless of anomaly family size.
Random Forest permutation importance measure is asymptotically unbiased in sparse regression models.
problem Challenges in selecting informative variables in high-dimensional regression problems.
method Theoretical guarantees and asymptotic unbiasedness of permutation importance measure under specific assumptions.
result Permutation importance measure in Random Forest is asymptotically unbiased.
Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions such as unbiased gradient estimates and convex objective function, which significan…
Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{é}r-Rao lower bound (efficiency bound), which is the minimum possible variance for an unbiased estimator. However, obtaining such MLE solution requires calculating t…
In this paper, we obtain a property of the expectation of the inverse of compound Wishart matrices which results from their orthogonal invariance. Using this property as well as results from random matrix theory (RMT), we derive the asymptotic effect of the noise induced by estimating the covariance matrix on computing…
AR-DAE approximates entropy gradient for machine learning models.
problem Intractable computation of entropy gradient for continuous distributions.
method Amortized residual denoising autoencoder (AR-DAE) to approximate entropy gradient.
result AR-DAE provides an unbiased gradient approximation for entropy.
We propose an estimator of prediction error using an approximate message passing (AMP) algorithm that can be applied to a broad range of sparse penalties. Following Stein's lemma, the estimator of the generalized degrees of freedom, which is a key quantity for the construction of the estimator of the prediction error, …
Synthetic construction of 3D complex bases.
problem Creating a complete set of unbiased bases in 3D complex space.
method Synthetic construction using complex projective trigonometry.
result Synthetic construction of mutually unbiased bases in C^3.
Unbiased wealth exchanges always lead to inequality.
problem Understanding wealth distribution in unbiased binary exchange systems.
method Analytical demonstration of unbiased binary exchanges leading to perfect inequality.
result Any system driven by unbiased binary exchanges will reach perfect inequality and zero mobility.
Develops asymptotic analysis for RandNLA sampling estimators in least-squares problems.
problem Lack of distributional information for RandNLA estimators in statistical inference.
method Asymptotic analysis of sampling estimators for least-squares problems in two settings.
result Sampling estimators are asymptotically normally distributed under mild conditions.
New unbiased methods for generating stochastic bridges with given extrema.
problem Generating unbiased stochastic bridges with a specified extremum.
method Comparison and generalization of two algorithms for Brownian bridges to other diffusions, and application to Ornstein-Uhlenbeck and unconstrained processes.
result Generalization of unbiased generation methods to other diffusions and application to various processes.
Dropout and RaM become equivalent in large ResNets as depth and width increase.
problem Improving performance in deep learning models.
method Comparing Dropout and Random Gradient Masking in ResNets.
result Dropout and RaM converge to the same large-scale limiting dynamics in ResNets.
MUSE provides unbiased stopping estimates for optimal problems.
problem Estimating the utility of optimal stopping problems.
method Backward recursive construction of the Multilevel Unbiased Stopping Estimator (MUSE).
result MUSE achieves ε-accuracy with O(1/ε^2) computational cost.
Randomized trials, also known as A/B tests, are used to select between two policies: a control and a treatment. Given a corresponding set of features, we can ideally learn an optimized policy P that maps the A/B test data features to action space and optimizes reward. However, although A/B testing provides an unbiased …
The paper derives an equation linking WAIC and WBIC for singular models.
problem In singular models, conventional criteria fail due to likelihood and posterior breakdown.
method Theoretical derivation linking WAIC and WBIC.
result An asymptotic equation linking WAIC and WBIC for singular models.
The paper analyzes the risk of CV-tuned regularized estimators and connects it to SURE.
problem Understanding the risk of CV-tuned regularized estimators.
method Derives asymptotic risk function of CV-tuned estimators and connects it to SURE.
result The risk function provides a more detailed picture of predictive performance than uniform bounds.
New algorithm finds unbiased subnetworks in biased datasets.
problem Finding unbiased subnetworks in biased neural networks.
method Debiased Contrastive Weight Pruning (DCWP) algorithm.
result DCWP significantly outperforms state-of-the-art debiasing methods.
Proposes unbiased estimators for training mixture of experts models.
problem Efficiently training large-scale mixture of experts models on modern hardware.
method Two unbiased estimators based on principled stochastic assignment procedures.
result Both estimators are more effective and robust than biased alternatives.
SUMO provides unbiased log marginal likelihood estimation for latent variable models.
problem Biased estimates of log marginal likelihood in latent variable models.
method Randomized truncation of infinite series for unbiased estimation.
result Models trained with SUMO give better test-set likelihoods than standard methods.
Unbiased methods for alpha-divergence minimization struggle in high dimensions.
problem The difficulty of unbiased alpha-divergence minimization in high dimensions.
method Signal-to-Noise Ratio (SNR) analysis of gradient estimators.
result The SNR of the gradient estimator worsens exponentially with dimensionality.
Stochastic Gradient Langevin Dynamics (SGLD) is a popular variant of Stochastic Gradient Descent, where properly scaled isotropic Gaussian noise is added to an unbiased estimate of the gradient at each iteration. This modest change allows SGLD to escape local minima and suffices to guarantee asymptotic convergence to g…
Unbiased gradient estimation for Markov chains
problem Estimating gradients of stationary means in Markov chains
method Propose new unbiased estimators
result Improves efficiency for slow mixing Markov chains
New unbiased gradient estimators for complex optimization problems.
problem Unbiased and variance-limited gradient estimation for conditional stochastic optimization.
method Developed multilevel Monte Carlo gradient estimators for conditional stochastic optimization problems.
result Unbiased and finite variance gradient estimators for conditional stochastic optimization problems.
In this paper, we introduce a new approach to constructing unbiased estimators when computing expectations of path functionals associated with stochastic differential equations (SDEs). Our randomization idea is closely related to multi-level Monte Carlo and provides a simple mechanism for constructing a finite variance…
Extends unbiased simulation method to Asian options.
problem Simulating path-dependent dynamics for Asian options.
method Extension of unbiased simulation method for SDEs to path-dependent dynamics.
result Extension applies to numerical resolution of path-dependent PDEs.
Developed unbiased estimators for Heston model with stochastic interest rates.
problem Estimating the Heston model with stochastic interest rates.
method Combined unbiased estimators with the Heston model and developed a semi-exact log-Euler scheme.
result Convergence rate of O(h) in the L2 norm for a wide range of models. New method for unbiased regression reduces excess risk.
problem Least squares regression with optimal solution and Hessian matrix.
method Averaged stochastic gradient descent with time-average estimator.
result Unbiased estimator with O(1/k) expected excess risk.
vqSGD reduces communication in distributed optimization with convergence guarantees.
problem Reduction of communication cost in distributed optimization.
method Vector quantization schemes based on convex hull of a point set.
result Asymptotic reduction in communication cost with convergence guarantees.