We introduce the speculate-correct method to derive error bounds for local classifiers. Using it, we show that k nearest neighbor classifiers, in spite of their famously fractured decision boundaries, have exponential error bounds with O(sqrt((k + ln n) / n)) error bound range for n in-sample examples.
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48 results for “error-bounded”
PAC-Bayesian bounds for stochastic LTI systems derived.
problem Error bounds for stochastic LTI systems.
method PAC-Bayesian theory applied to autonomous stochastic LTI models.
result Error bounds for stochastic LTI systems derived.
PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Modelsstat.ML
Paper derives an error bound for stochastic LTI systems.
problem Stochastic LTI systems with inputs in control engineering and econometrics.
method PAC-Bayesian-Like error bound derivation.
result Derived an error bound for stochastic LTI systems.
A new error bound improves safety in Bayesian optimization.
problem Ensuring safety in Bayesian optimization with probabilistic models.
method Introducing a novel error bound using Wiener kernel regression for Gaussian processes and noise.
result The new error bound provides larger safety regions than previous methods.
In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a well-chosen temperature parameter. Second, the error bound also holds for training data t…
This paper addresses error bounds and posterior variance for Gaussian process regression.
problem Deriving performance guarantees for Gaussian process regression without prior knowledge.
method Lipschitz continuity and analysis of posterior variance function.
result Uniform error bounds for Gaussian process regression are derived.
Error bounds based on worst likely assignments use permutation tests to validate classifiers. Worst likely assignments can produce effective bounds even for data sets with 100 or fewer training examples. This paper introduces a statistic for use in the permutation tests of worst likely assignments that improves error b…
We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary symmetric submodular function. Arbitrary non-symmetric submodular functions can be…
Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for solving optimization problems. In this paper, we present a new framework for establis…
The paper offers error bounds for quantized dynamical models.
problem Accuracy of dynamical models from dependent data sequences.
method Developed uniform error bounds for quantized models and imperfect optimization algorithms.
result Unified bounds for slow and fast rates, scaling with model encoding bits.
Study error bounds in evaluating distributional computational graphs.
problem Error analysis in evaluating graphs with inputs as probability distributions.
method Establish non-asymptotic error bounds using Wasserstein-1 distance.
result Non-asymptotic error bounds for discretization errors in distributional computational graphs.
This paper examines error bounds for deep learning classifiers with noisy labels.
problem Understanding the performance of classifiers trained on noisy data.
method Derives error bounds for excess risk, decomposing it into statistical and approximation errors. Uses independent block construction for statistical dependencies and vector-valued setting for approximation error.
result Established theoretical results for error bounds in deep learning with noisy labels, mitigating the impact of high-dimensional input spaces.
Derives error bounds for stochastic iterative algorithms using Stein's method.
problem Bounding errors in stochastic iterative algorithms like SGD and SGLD.
method Uses infinite-dimensional Stein's method of exchangeable pairs to derive functional approximation error bounds.
result Establishes non-asymptotic error bounds for algorithm sample paths and variance of iterate averages.
New approach uses interpolation models and error bounds for verifiable scientific machine learning.
problem Challenges in verifying and validating modern scientific machine learning workflows.
method Combines multiple standard interpolation techniques with error bounds for efficient computation and comparative performance analysis.
result Error bounds for interpolation techniques can be computed or estimated efficiently, aiding in validation goals.
Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure and uniform error bounds have been derived, which allow safe control based on thes…
Paper improves uncertainty quantification in PINNs using error bounds and solution bundles.
problem Uncertainty quantification in PINNs for differential equation systems.
method Two-step procedure with Bayesian Neural Networks and heteroscedastic variance.
result Improved uncertainty estimation over PINNs solutions in differential equation systems.
We derive generalization error bounds for stationary univariate autoregressive (AR) models. We show that imposing stationarity is enough to control the Gaussian complexity without further regularization. This lets us use structural risk minimization for model selection. We demonstrate our methods by predicting interest…
We develop a technique for deriving data-dependent error bounds for transductive learning algorithms based on transductive Rademacher complexity. Our technique is based on a novel general error bound for transduction in terms of transductive Rademacher complexity, together with a novel bounding technique for Rademacher…
New error bounds for flow matching methods using deterministic sampling.
problem Improving the accuracy of flow matching methods for generating probability distributions.
method Derived error bounds for flow matching methods under deterministic sampling conditions.
result Presented error bounds for flow matching methods using loss and regularity conditions.
Paper analyzes LSA algorithm bias and error bounds with RR extrapolation.
problem Analyzing bias and high-order error bounds of LSA with Markovian noise.
method Polyak-Ruppert averaging, linearization, Richardson-Romberg extrapolation.
result RR extrapolation effectively cancels the leading bias term.
Suppose some classifiers are selected from a set of hypothesis classifiers to form an equally-weighted ensemble that selects a member classifier at random for each input example. Then the ensemble has an error bound consisting of the average error bound for the member classifiers, a term for selectivity that varies fro…
Study on Transfer Elastic Net error bounds and grouping effect.
problem Estimation error and grouping effect in Transfer Elastic Net.
method Derives non-asymptotic error bound and examines grouping effect scenarios.
result Effective error bounds and grouping effect observed in Transfer Elastic Net.
Sharp 2-Wasserstein bounds for DDPMs derived from Föllmer process.
problem Sampling error bounds for DDPMs in 2-Wasserstein distance.
method Lipschitz-type conditions on score function, Föllmer process, and log-concave target distributions.
result Sharp upper bounds for DDPMs in 2-Wasserstein distance, optimal in dimension and steps.
This note provides an error bound for the Hartman-Watson integral's leading term.
problem Bounding the error of the leading term of the Hartman-Watson integral.
method Asymptotic expansion analysis focusing on the regime constant.
result The error term is bounded uniformly as .
Paper addresses generalization error bounds for learning with censored feedback.
problem Impact of censored feedback on generalization error bounds.
method Derives an extension of DKW inequality for non-IID data due to censored feedback and uses it to bound generalization error.
result Existing generalization error bounds fail to account for censored feedback, necessitating new bounds.
Estimating the Convex Hull of the Image of a Set with Smooth Boundary: Error Bounds and Applicationsmath.OC
Estimates convex hulls of smooth function images with error bounds.
problem Estimating the convex hull of the image of a smooth boundary set.
method Using submersion properties and sampling inputs, derive bounds on Hausdorff distance.
result New tighter and more general error bounds for geometric inference.
The paper provides tighter error bounds for GPR under bounded support noise.
problem Rigorous error quantification for safety-critical applications with bounded noise.
method Using concentration inequalities and low complexity assumptions in RKHS, the paper derives probabilistic and deterministic error bounds for GPR.
result The derived error bounds are substantially tighter than existing state-of-the-art bounds and are particularly well-suited for GPR with neural network kernels.
The success of deep learning has led to a rising interest in the generalization property of the stochastic gradient descent (SGD) method, and stability is one popular approach to study it. Existing works based on stability have studied nonconvex loss functions, but only considered the generalization error of the SGD in…
Study improves error bounds for sparse regression with heavy-tailed covariates.
problem Estimating sparse coefficients in linear regression with heavy-tailed covariates.
method Employed an -penalized Huber regression method.
result Error bound identical to Gaussian case for -subexponential covariates.
End-to-end algorithm for controlling bilinear systems with probabilistic noise.
problem Controlling bilinear systems with noisy data.
method Proposes an end-to-end algorithm using statistical learning theory and robust controller design.
result Derived finite sample identification error bounds and structurally suitable for control.
Study Hodge Laplacians for manifold data, improving error bounds.
problem Approximating Laplace-Beltrami operator on differential forms.
method Higher-order graph Laplacians (Hodge Laplacians) as approximations.
result High-probability error bound for Dirichlet forms.
New bounds quantify estimation error in kernel-based system identification with unknown hyperparameters.
problem Inaccurate error bounds for kernel-based system identification with unknown hyperparameters.
method Construct a high-probability set for true hyperparameters from marginal likelihood, then find worst-case posterior covariance.
result Proposed bounds contain true model with high probability and verified in simulations.
Recent works have derived non-asymptotic upper bounds for convergence of underdamped Langevin MCMC. We revisit these bound and consider introducing scaling terms in the underlying underdamped Langevin equation. In particular, we provide conditions under which an appropriate scaling allows to improve the error bounds in…
On -regularized estimation for nonlinear models that have sparse underlying linear structuresmath.ST
In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of -regularized estimation. In this note, we show that -regularized estimation in some important cases can achieve the same order of error bounds as those in the aforementioned …
New method improves privacy in linear regression with optimal error bounds.
problem Differentially private linear regression with suboptimal error bounds.
method One-pass mini-batch stochastic gradient descent (DP-AMBSSGD) with adaptive clipping.
result Nearly optimal error bounds in terms of key parameters like dimensionality, number of points, and noise standard deviation.
Unified framework for high-dimensional online learning with non-divergent error bounds and adaptive gains.
problem Divergence of error bounds in high-dimensional online learning as data batches increase.
method Asynchronous decomposition framework with summary statistics and dynamic regularization.
result Non-divergent error bounds and adaptive gains in sparse online optimization.
The paper improves error bounds for Bayesian quadrature in noisy settings.
problem Improving error bounds for Bayesian quadrature in noisy settings.
method Develops a two-step meta-algorithm to relate average-case quadrature error to -function approximation error.
result Provides new average-case results for various kernels and noise settings.
Paper establishes a universal growth rate for smooth surrogate losses in classification.
problem Analyzing growth rates of consistency bounds for various surrogate losses.
method Proves square-root growth rate for smooth margin-based losses; extends to multi-class classification.
result Demonstrates a universal square-root growth rate for smooth comp-sum and constrained losses.
In this paper we consider the cluster estimation problem under the Stochastic Block Model. We show that the semidefinite programming (SDP) formulation for this problem achieves an error rate that decays exponentially in the signal-to-noise ratio. The error bound implies weak recovery in the sparse graph regime with bou…
Study error bounds and optimal schedules for Masked Diffusions with factorized approximations.
problem Analyzing trade-offs between computation and accuracy in Masked Diffusion Models.
method Provided general error bounds and identified optimal schedules based on data distribution information profiles.
result Identified optimal schedule sizes for Masked Diffusion Models.
New error bounds for GANs with nonlinear objective functions derived.
problem Statistical consistency of GANs with nonlinear objective functions.
method Derivation of statistical error bounds for -GANs using Rademacher complexity.
result Proves the statistical consistency of -GANs.
In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling probabilities. The sampling dependent error bound (i) allows us to better understand the …
RQMC improves QMC by providing practical error bounds for financial applications.
problem Lack of practical error estimates in QMC methods.
method Combines Sobol LDS with randomized scrambling methods.
result RQMC outperforms standard QMC in convergence rates and provides error bounds.
This work uses sampling theory to analyze smoothness and error bounds of finite neural networks.
problem Analyzing the function space of finite neural networks and providing error bounds.
method Applying sampling theory to finite neural networks with non-expansive activation functions, considering both deterministic and random sampling.
result Novel error bounds for univariate neural networks under band-limited input assumption, highlighting the advantage of deterministic uniform sampling.
The paper tackles stock prediction models by improving their generalizability to out-of-sample domains using causal representation learning.
problem Low signal-to-noise ratio and nonstationary nature of financial markets lead to poor performance of stock prediction models.
method The paper investigates Domain Generalization techniques, focusing on causal representation learning to improve model generalizability. It introduces a novel error bound and a causal discovery technique to mitigate spurious correlations.
result The proposed approach enhances the generalizability of stock prediction models, as demonstrated by numerical results.
New sampling algorithms for complex distributions without log-concavity.
problem Efficient sampling from complex, high-dimensional distributions.
method Randomized splitting Langevin Monte Carlo (RSLMC) algorithm.
result Uniform-in-time error bounds for RSLMC and RLMC algorithms.
This work bounds classification error in machine learning for low Bayes error conditions.
problem Understanding the error mismatch between Bayes error and model-based classification error.
method Applying classification error bounds to study the relationship with Kullback-Leibler divergence and proposing a linear approximation for low Bayes error conditions.
result A linear approximation of the classification error bound for low Bayes error conditions is proposed.
This paper concerns error bounds for recursive equations subject to Markovian disturbances. Motivating examples abound within the fields of Markov chain Monte Carlo (MCMC) and Reinforcement Learning (RL), and many of these algorithms can be interpreted as special cases of stochastic approximation (SA). It is argued tha…