A new method improves super learner validation efficiency.
problem Improving the efficiency of super learner validation.
method Bootstrap Bias Corrected Cross Validation applied to Super Learning.
result Bootstrap Bias Corrected Cross Validation proved efficient and cost-effective.
A novel bootstrap method improves concept drift detection in predictive models.
problem Detecting changes in predictive relationships (concept drift) in data-driven applications.
method Developed a nested bootstrap procedure to calibrate control limits using the entire initial sample.
result The method yields more accurate baseline models and faster CL setup times.
Cross-validation estimates model performance on unseen data, not training data.
problem Understanding how cross-validation estimates prediction error and its limitations.
method Analyzing linear models and popular prediction error estimates, introducing nested cross-validation.
result Cross-validation estimates the average prediction error of models fit on other unseen training sets, not the model at hand.
The correct use of model evaluation, model selection, and algorithm selection techniques is vital in academic machine learning research as well as in many industrial settings. This article reviews different techniques that can be used for each of these three subtasks and discusses the main advantages and disadvantages …
Study cobordisms of nested manifolds and their invariants.
problem Understanding cobordisms of nested manifolds and their invariants.
method Identify a nested analog of the Pontryagin-Thom construction and find spaces homotopy equivalent to nested Pontryagin-Thom spaces.
result Discover nested cobordism invariants and provide an alternative proof of Wall's splitting result.
Quantum algorithm speeds up nested expectation estimation by nearly quadratically.
problem Estimating repeatedly nested expectations with quantum computing.
method Proposes a quantum algorithm achieving nearly quadratic speedup over classical methods.
result Achieves nearly quadratic speedup for RNEs, up to logarithmic factors.
Improved nested simulation for financial risk measurement.
problem Efficiently estimating nested risk measures in financial engineering.
method Reusing inner simulation outputs to improve efficiency and accuracy.
result The proposed approach outperforms standard nested simulation and regression methods.
Scalable tools for nested optimization in deep learning.
problem Solving nested optimization problems on a large scale in deep learning.
method Building scalable tools for bilevel optimization.
result Tools for nested optimization scale to deep learning setups.
Paper proposes a new estimator for nested expectations with faster convergence.
problem Estimating nested expectations is computationally challenging.
method Nested kernel quadrature estimators with proof of faster convergence rate.
result The proposed method requires fewer samples for accurate estimation.
Unified SGD method improves convergence for nested optimization problems.
problem Stochastic nested optimization problems.
method ALTERNATE dESCEN (ALSET) method leveraging hidden smoothness.
result Requires O(ε−2) samples to achieve an ε-stationary point. Let R be an o-minimal expansion of the real field, and let L(R) be the language consisting of all nested Rolle leaves over R. We call a set nested subpfaffian over R if it is the projection of a boolean combination of definable sets and nested Rolle leaves over R. Assuming that R admits analytic cell decomposition, we …
Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves involve calculation of a separate, nested, estimation. We investigate the statistica…
Develops a method for learning proposals in nested importance samplers.
problem Improving sampling quality in complex distributions.
method Nested Variational Inference (NVI) using forward or reverse KL divergence.
result Optimizing nested objectives leads to improved sample quality.
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.
Solving real-world problems, particularly with deep learning, relies on the availability of abundant, quality data. In this paper we develop a novel framework that maximises the utility of time-series datasets that contain only small quantities of expertly-labelled data, larger quantities of weakly (or coarsely) labell…
Nested model averaging improves high-dimensional linear regression performance.
problem High-dimensional linear regression with predictor ordering impact.
method Combining model averaging with regularized estimators on the solution path.
result Nested model averaging with lasso and SLOPE outperforms competing methods.
Gradient-guided nested sampling improves posterior inference efficiency.
problem Efficiently sampling from complex posterior distributions.
method Gradient-guided nested sampling combining differentiable programming, Hamiltonian slice sampling, clustering, mode separation, dynamic nested sampling, and parallelization.
result Significantly faster mode discovery and more accurate partition function estimates.
Nested Slice Sampling accelerates Nested Sampling for GPU acceleration.
problem Challenging inference for complex, multimodal targets.
method Vectorized Nested Slice Sampling using Hit-and-Run Slice Sampling.
result NSS maintains accurate evidence estimates and high-quality posterior samples, robust on multimodal problems.
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.
New discrete cobordism category for nested manifolds and relations to algebraic structures.
problem Discrete cobordism category for nested manifolds.
method Stratified Morse theory, Cyl-objects, doubling construction, cylindrical bar construction.
result Relations between Cyl-objects and algebraic structures like Temperley-Lieb algebras.
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.
Nested sampling improved for arbitrary priors.
problem Technical obstacle to using nested sampling with arbitrary priors.
method Parametric bijectors trained on samples from a desired prior density.
result Nested sampling can be used with arbitrary priors.
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.
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.
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.
Efficiently bootstraps massive distributed data without over-resampling.
problem Statistical inference for massive distributed data.
method Distributed Bootstrap applied to gradients from worker machines.
result Proves optimal statistical efficiency with minimal communication.
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. 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.
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…
Study of loops in sums of Laplace eigenfunctions on surfaces.
problem Uniform bound for the number of nested loops in sums of Laplace eigenfunctions.
method Real-analytic category analysis and biharmonic function construction.
result Uniform bound for the number of rooted double nests in terms of surface, root, and spectral cutoff.
Enhances Bayesian model selection for high-dimensional problems.
problem Bayesian model selection for high-dimensional problems.
method Proximal nested sampling with data-driven priors.
result Improves model selection for log-convex likelihood models.
Nested learning improves model performance on multi-granular tasks.
problem Overconfident models and lack of fine-grained confidence in predictions.
method Introducing nested learning with a sequence of nested feature embeddings and explicit combination of outputs.
result Nested learning outperforms standard end-to-end training on various datasets.
Geometric observables detect financial regime shifts with high accuracy.
problem Detecting regime shifts in financial markets.
method Extracted four geometric observables from equity-index returns and evaluated them against various baseline methods.
result The Berry Phase Rate achieves an unbiased out-of-sample median Cohen's d of 0.72, significantly reducing false alarms.
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.
New DP bootstrap method for statistical inference with improved privacy and accuracy.
problem Lack of general techniques for conducting statistical inference under differential privacy.
method DP bootstrap procedure to infer sampling distribution and construct confidence intervals.
result DP bootstrap estimates provide consistent point estimates and asymptotically valid standard CIs.
NEST optimizes deep learning training by placing devices efficiently across networks and memory.
problem Inefficient device placement in distributed deep learning leads to high communication and memory overhead.
method NEST uses network-, compute-, and memory-aware dynamic programming to optimize device placement.
result NEST achieves up to 2.43 times higher throughput and better memory efficiency.
We propose doubly nested network(DNNet) where all neurons represent their own sub-models that solve the same task. Every sub-model is nested both layer-wise and channel-wise. While nesting sub-models layer-wise is straight-forward with deep-supervision as proposed in \cite{xie2015holistically}, channel-wise nesting has…
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.
A new bootstrapping method reduces key sizes and runtime in FHE.
problem Large plaintext evaluation in FHE increases bootstrapping complexity.
method New polynomial vector representation and monic monomial permutation matrices.
result Polynomial factor improvement in key size and constant factor in runtime.
New methods for estimating complex causal effects in econometrics.
problem Estimating causal parameters in short panel data models using nested nonparametric instrumental variable regression.
method Introducing techniques to limit ill-posedness in nested NPIV, providing explicit mean square rates and efficient inference.
result Explicit mean square rates for nested NPIV and efficient inference for causal parameters.
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…
A new algorithm improves stochastic linear bandit performance using residual bootstrap.
problem Improving performance in stochastic linear bandit problems.
method Residual bootstrap exploration to estimate mean reward and pull the arm with the highest estimate.
result Proposed algorithm exttt{LinReBoot} achieves high-probability sub-linear regret under mild conditions.
We formalize the notion of nesting probabilistic programming queries and investigate the resulting statistical implications. We demonstrate that while query nesting allows the definition of models which could not otherwise be expressed, such as those involving agents reasoning about other agents, existing systems take …
Sharp lower bound on GHHs' representation power of CPWL functions.
problem Proving the minimum number of nestings for GHHs to represent arbitrary CPWL functions.
method Using a key lemma about finite sums of periodic functions, proving necessity of n nestings.
result Proving necessity of n nestings for GHHs to achieve universal representation power.
Paper improves bootstrapping for off-policy reinforcement learning inference.
problem Improving bootstrapping for off-policy reinforcement learning inference.
method Proposes a bootstrapping FQE method for off-policy statistical inference and a subsampling procedure to improve runtime.
result Asymptotically efficient and distributionally consistent bootstrapping FQE method for off-policy inference.
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 develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable models to evaluating a probability generating function which contains many leve…