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.
The paper improves the empirical bootstrap method for non-normal estimators.
problem Theoretical properties of empirical bootstrap for non-asymptotically normal estimators.
method Establishing limiting distribution, deriving consistency conditions, proposing alternative methods.
result The empirical bootstrap method can be asymptotically consistent under stability conditions.
Proposes a private empirical bootstrap for Gaussian Differential Privacy.
problem Quantifying uncertainty in massive data under Differential Privacy.
method Gaussian Differential Private Bootstrap by Subsampling.
result Consistent and efficient private inference method.
Develops statistical confidence sets for multidimensional scaling.
problem Statistical uncertainty in multidimensional scaling of noisy data.
method Formal statistical framework, distributional convergence results, uniform confidence sets, bootstrap procedures.
result Construction of reliable confidence sets for latent configurations in multidimensional scaling.
A new method reduces bootstrap simulation cost and improves accuracy.
problem Efficiently simulating input uncertainty with large sample sizes.
method Orthogonal Bootstrap: Decomposes into Infinitesimal Jackknife and orthogonal parts.
result Significantly reduces computational cost and maintains accuracy.
Optimizes a small set of centroid points to approximate bootstrap distribution.
problem Computational inefficiency of standard bootstrap methods in large-scale machine learning.
method Explicitly optimizes a small set of high quality centroid points to approximate the ideal bootstrap distribution.
result Accurately estimates uncertainty with a small number of bootstrap centroids, outperforming i.i.d. sampling.
The bootstrap provides a simple and powerful means of assessing the quality of estimators. However, in settings involving large datasets, the computation of bootstrap-based quantities can be prohibitively demanding. As an alternative, we present the Bag of Little Bootstraps (BLB), a new procedure which incorporates fea…
We investigate the use of bootstrapping in the bandit setting. We first show that the commonly used non-parametric bootstrapping (NPB) procedure can be provably inefficient and establish a near-linear lower bound on the regret incurred by it under the bandit model with Bernoulli rewards. We show that NPB with an approp…
Validates network bootstraps for uncertainty quantification in network visualisation.
problem Quantifying uncertainty in network embeddings when only a single observation is available.
method Statistical indistinguishable embeddings using k-nearest neighbour smoothing, validated by an exchangeable network test.
result Proposes a principled, distribution-free network bootstrap that passes the exchangeable network test.
A new clustering method using Bayesian techniques improves robustness and interpretability.
problem Improving clustering techniques for better robustness and interpretability.
method The paper proposes a novel Bayesian clustering method using the proper Bayesian bootstrap, which combines k-means clustering and ensemble clustering.
result The method provides clear indication on the optimal number of clusters and a better representation of the clustered data.
Neural Bootstrapper reduces bootstrapping cost for deep neural networks.
problem Computational burden in bootstrapping deep neural networks.
method Neural Bootstrapper learns to generate bootstrapped neural networks through single model training.
result Neural Bootstrapper outperforms bagging methods with lower computational cost.
The bootstrap provides a simple and powerful means of assessing the quality of estimators. However, in settings involving large datasets---which are increasingly prevalent---the computation of bootstrap-based quantities can be prohibitively demanding computationally. While variants such as subsampling and the m out o…
The paper analyzes bootstrap ensemble classifiers in high-dimensional settings.
problem Performance of bootstrap ensemble classifiers in high-dimensional data.
method Random Matrix Theory applied to LSSVM ensemble.
result Strategies to optimize performance of LSSVM ensemble.
New method for efficient inference in large datasets.
problem Statistical inference in massive datasets.
method Combines divide-and-conquer method and empirical likelihood.
result Reduces computation burden and demonstrates effectiveness.
Data augmented bootstrap unifies various confidence interval construction methods.
problem Constructing confidence intervals from data transformations.
method Data augmented bootstrap (DAB) framework.
result Establishes theoretical coverage results for DAB methods.
We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an estimator based on a ratio of realized power variations. Our new resampling method,…
In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A simple method is to linearly average the parameters of the local models, which, howev…
GANs generate samples from time series data.
problem Resampling dependent time series data.
method Generative Adversarial Networks (GANs) for time series resampling.
result GANs can outperform traditional bootstrapping methods in time series resampling.
Generating realistic asset-class scenarios from time series and curves
problem Simulating realistic trajectories for asset classes
method Combining parametric and resampling techniques
result More coherent and realistic simulations of yield-curve dynamics
Non-parametric bootstrap improves robust portfolio and trading strategy optimization.
problem Mitigating uncertainty in expected returns and covariances in financial decision-making.
method Non-parametric bootstrap framework for robust optimization without distributional assumptions.
result Improved out-of-sample performance with smoother, more stable results.
A new estimator combines bootstrapping and rollout methods in RL.
problem Combining strengths of bootstrapping and rollout methods in RL.
method Subgraph Bellman operators and fixed point solving.
result Upper bound on error approaches optimal TD variance with additional term.
This paper examines the use of a residual bootstrap for bias correction in machine learning regression methods. Accounting for bias is an important obstacle in recent efforts to develop statistical inference for machine learning methods. We demonstrate empirically that the proposed bootstrap bias correction can lead to…
In this paper, we detail the main simulation methods used in practice to measure one-year reserve risk, and describe the bootstrap method providing an empirical distribution of the Claims Development Result (CDR) whose variance is identical to the closed-form expression of the prediction error proposed by Wüthrich et a…
GBEST model improves survival analysis for small datasets.
problem Challenges in survival analysis, especially with small data.
method Bayesian bootstrap and Beta Stacy bootstrap methods integrated into bagging tree models.
result GBEST model outperforms classical survival models in predictive performance and stability.
SGD improves generalization by using gradient variability as a proxy for data randomness.
problem Improving generalization in machine learning models trained with stochastic gradient descent.
method Bootstrap perspective on SGD, analyzing gradient variability and algorithmic variability.
result SGD avoids spurious solutions and improves generalization by implicitly regularizing the trace of the gradient covariance matrix.
Private statistical inference methods improve confidence interval lengths.
problem Constructing private confidence intervals with differential privacy.
method Proposed two private variants of non-parametric bootstrap.
result Achieve similar coverage accuracy to non-private methods with shorter intervals.
This work uses statistical bootstrapping to provide accurate confidence intervals for policy value in reinforcement learning.
problem Bias in estimating policy value using empirical transitions and rewards.
method Statistical bootstrapping to produce calibrated confidence intervals for the true policy value.
result Statistical bootstrapping can yield correct confidence intervals under certain conditions, and mechanisms are proposed to mitigate these conditions.
The study identifies extremal dependence in financial markets using a bootstrap-based testing procedure.
problem Accurately identifying extremal dependence in multivariate heavy-tailed financial data.
method Bootstrap-based testing procedure applied to U.S. and Chinese stock returns.
result The U.S. exhibits more isolated clustering of dependent assets compared to China.
Deep ensembles effectively capture epistemic uncertainty through training stochasticity, providing a frequentist perspective.
problem Understanding and quantifying epistemic uncertainty in machine learning models.
method Bootstrap-based estimator and decomposition of deep ensembles into data variability and training stochasticity.
result Deep ensembles primarily capture training stochasticity, explaining their effectiveness in quantifying epistemic uncertainty.
The intention of this paper is to estimate a Bayesian distribution-free chain ladder (DFCL) model using approximate Bayesian computation (ABC) methodology. We demonstrate how to estimate quantities of interest in claims reserving and compare the estimates to those obtained from classical and credibility approaches. In …
We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which the method is valid. We show the asymptotic refinements of the proposed procedure,…
TD learning reduces interference, leading to better generalization.
problem Understanding and reducing interference in TD learning for better generalization.
method Analyzing the inner product of gradients as interference, comparing TD and supervised learning, and examining the dynamics of interference and bootstrapping.
result TD learning leads to low-interference, under-generalizing parameters, while supervised learning does the opposite.
BAWS adapts window size for financial risk forecasting.
problem Adaptive selection of look-back window for financial risk modeling.
method Data-driven online learning method using bootstrap-based adaptive window selection (BAWS).
result BAWS improves risk forecasting, especially in data with structural changes.
Improved time series causal discovery with bootstrap aggregation and confidence measures.
problem Uncertainty estimation in time series causal discovery.
method Bootstrap aggregation and confidence measures for time series causal discovery.
result Bagged-PCMCI+ improves precision and recall compared to PCMCI+.
We address the problem of Bayesian structure learning for domains with hundreds of variables by employing non-parametric bootstrap, recursively. We propose a method that covers both model averaging and model selection in the same framework. The proposed method deals with the main weakness of constraint-based learning--…
Sampling with replacement occurs in many settings in machine learning, notably in the bagging ensemble technique and the .632+ validation scheme. The number of unique original items in a bootstrap sample can have an important role in the behaviour of prediction models learned on it. Indeed, there are uncontrived exampl…
New method for estimating high-dimensional binary time series coefficients.
problem Statistical inference for high-dimensional binary time series.
method Post-selection estimator and second-order wild bootstrap algorithm.
result Good finite-sample performance of the proposed method.
This study evaluates methods for constructing prediction intervals with neural networks.
problem Lack of confidence measures in neural network predictions limits their applicability.
method Two-step experiment using bootstrapping and conformal inference methods.
result Cross-conformal method provides best performance with reasonable computational burden.
AR-Sieve Bootstrap improves Random Forest time series prediction accuracy.
problem Inaccurate time series prediction due to inadequate resampling methods.
method Combines Random Forest with AR-Sieve Bootstrap for better resampling.
result AR-Sieve Bootstrap leads to more accurate predictions compared to other methods.
We consider the performance of the bootstrap in high-dimensions for the setting of linear regression, where p<n but p/n is not close to zero. We consider ordinary least-squares as well as robust regression methods and adopt a minimalist performance requirement: can the bootstrap give us good confidence intervals fo…
New bootstraps improve speed and accuracy for graph count functionals.
problem Efficiently counting subgraphs in large graphs.
method Developed two types of multiplier bootstraps: a fast, approximate linear one and a quadratic one for denser graphs.
result Both bootstraps provide valid inference and higher-order accuracy under different graph sparsity conditions.
New method corrects bias in estimating entropic risk for better decision-making.
problem Underestimation of entropic risk when data are limited.
method Parametric bootstrap procedure to overestimate entropic risk.
result Corrected method provides better risk estimates, leading to improved decision-making.
We compare the model-free reinforcement learning with the model-based approaches through the lens of the expressive power of neural networks for policies, Q-functions, and dynamics. We show, theoretically and empirically, that even for one-dimensional continuous state space, there are many MDPs whose optimal Q-func…
Three bootstrap tests compare categorical time series generating processes.
problem Testing equality of generating processes in categorical time series.
method Proposes three tests using dissimilarity measures and bootstrap methods.
result Advantages and disadvantages of each bootstrap method discussed.
New methods improve uncertainty in machine learning predictions for asset returns.
problem Uncertainty in machine learning predictions for asset returns.
method Developed new methods to construct forecast confidence intervals for expected returns from neural networks.
result Neural network forecasts of expected returns have the same asymptotic distribution as classic nonparametric methods, enabling standard error calculation.
E-QRGMM accelerates uncertainty quantification in simulations.
problem Challenges in covariate-dependent uncertainty quantification.
method Integrates cubic Hermite interpolation with gradient estimation.
result Substantially improves computational efficiency and accuracy.
Bootstrap method for Markov chains in reinforcement learning.
problem Distributional consistency in finite controlled Markov chains with unknown control policies.
method Model-based bootstrap with novel LLN and CLT for visitation counts and transition increments.
result Asymptotically valid confidence intervals for value and Q-functions in offline RL. The paper assesses conditions for the uniqueness of k-means clustering.
problem Conditions for the uniqueness of k-means clustering.
method Analyzes the choice of k and provides necessary and sufficient conditions for uniqueness.
result Determines the asymptotic distribution of the within cluster sum of squares (WCSS) and provides a bootstrap test for uniqueness.