In this paper, we obtain generic bounds on the variances of estimation and prediction errors in time series analysis via an information-theoretic approach. It is seen in general that the error bounds are determined by the conditional entropy of the data point to be estimated or predicted given the side information or p…
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48 results for “prediction error bounds”
Generic Bounds on the Maximum Deviations in Sequential Prediction: An Information-Theoretic Analysiscs.LG
In this paper, we derive generic bounds on the maximum deviations in prediction errors for sequential prediction via an information-theoretic approach. The fundamental bounds are shown to depend only on the conditional entropy of the data point to be predicted given the previous data points. In the asymptotic case, the…
Paper derives PAC-Bayesian bounds for LTI systems learning from empirical data.
problem Characterizing predictive power of LTI systems learned from data.
method PAC-Bayesian bounds for LTI stochastic dynamical systems with inputs.
result Finite-sample error bounds for learning algorithms of LTI systems.
This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean square-error (MSE). This approach, however, does not take into account that the stat…
Time-series Random Process Complexity Ranking Using a Bound on Conditional Differential Entropyeess.SP
This paper improves entropy bounds for ranking time-series complexity.
problem Ranking the complexity of time series processes.
method Building on information theoretic bounds, the paper improves the upper bound of conditional differential entropy using Hadamard's inequality and covariance matrix properties.
result The improved bounds can be used to rank the complexity of time series processes.
Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only limited results on the distribution of this error. We prove tight high-probabil…
Paper proves a new lower bound on calibration error for binary prediction.
problem Proving a strong lower bound on calibration error for binary prediction.
method Developed two new techniques: early stopping and sidestepping.
result Proves an lower bound on calibration error.
Improved BO algorithms reduce prediction error under Gaussian noise.
problem Reducing prediction error in Bayesian optimization with Gaussian noise.
method Established new prediction error bounds for Gaussian process under frequentist setting.
result Proved improved convergence rates of cumulative regret for GP-UCB and GP-TS.
New bounds show multicalibration error is close to prediction error.
problem Addressing fairness in machine learning systems.
method Sample complexity bounds for uniform convergence of multicalibration error.
result Uniform convergence guarantees for multicalibration error, independent of prediction error.
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.
The study analyzes prediction errors in systems with memory kernels, providing bounds and stability results.
problem Prediction errors in stochastic dynamical systems with memory kernels.
method Analysis of generalized Langevin equations (GLEs) with Volterra equations, integrating synchronized noise coupling and weighted norms.
result Prediction discrepancies decay at a rate determined by the memory kernel's decay, quantitatively bounded by kernel estimation errors.
New decision-theoretic calibration error metric improves prediction reliability.
problem Improving the reliability of predictions for decision-making.
method Proposed Calibration Decision Loss (CDL) and an efficient algorithm to achieve near-optimal CDL.
result Near-optimal CDL guarantees vanishing payoff loss from miscalibration.
Paper proposes a new time series prediction method using weighted past data and optimization.
problem Predicting time series data with improved accuracy considering both deterministic and stochastic assumptions.
method The approach uses a weighted sum of past data, solving a constrained linear optimization problem to minimize an outer bound of prediction error.
result The method can outperform existing non-parametric methods in short-term forecasts.
The paper develops bounds for predictive values in binary classification.
problem Lack of confidence intervals for positive and negative predictive values.
method Bi-criterion framework and distribution-free large deviation and uniform convergence bounds.
result New bounds for predictive values without relying on concentration inequalities.
Neural network accuracy improves with denser training samples.
problem Improving neural network accuracy on unseen test samples.
method Bounding empirical training error smoothed across activation regions and using it to discard high-risk test samples.
result Discarding high-risk test samples based on error bounds improves prediction accuracy by up to 20%.
New method preserves unitarity for Schrödinger equation learning, reducing errors and improving time generalization.
problem Learning the evolution operator for time-dependent Schrödinger equation with varying Hamiltonians.
method Linear estimator preserving weak unitarity, with theoretical error bounds and time generalization.
result Achieves up to two orders of magnitude smaller relative errors than existing methods.
New approach uses Gaussian processes to learn and track complex systems with guaranteed accuracy.
problem Inaccurate first principle models for complex systems due to data complexity.
method Bayesian prediction error bound for Gaussian process regression, derived from kernel-based data density.
result Achieves vanishing tracking error with increasing data density, providing time-varying accuracy guarantees.
The paper bounds the mean absolute error in DNN vector-to-vector regression.
problem Bounding the mean absolute error in deep neural network based vector-to-vector regression.
method Error decomposition techniques in statistical learning theory and non-convex optimization theory were used to derive upper bounds for approximation, estimation, and optimization errors.
result Theoretical upper bounds for mean absolute error in DNN vector-to-vector regression were derived and validated experimentally.
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…
Non-asymptotic Optimal Prediction Error for Growing-dimensional Partially Functional Linear Modelsmath.ST
Study optimizes prediction error for growing-dimensional PFLM models.
problem Optimizing prediction error for growing-dimensional PFLM models.
method Penalized least-squares approach in RKHS with effective dimension consideration.
result Shows exact upper bound for excess prediction risk in non-asymptotic form.
GPR models epidemic spread on logarithmic scale.
problem Modeling and predicting epidemic spread for policy decisions.
method Gaussian process regression (GPR) on logarithmic scale of infected cases.
result GPR predictions have high probability of being within 95% confidence interval for 94.29% of data.
The study sets lower bounds on MMSE for inferring sensitive features from noisy data.
problem Estimating sensitive features from noisy observations of correlated features.
method Adversarial evaluation framework based on MMSE estimation with theoretical lower bounds.
result Derives closed-form bounds for linear models, showing optimality in noise variance.
Standard methods in supervised learning separate training and prediction: the model is fit independently of any test points it may encounter. However, can knowledge of the next test point be exploited to improve prediction accuracy? We address this question in the context of linear prediction, show…
Paper proposes a cost-sensitive conformal training method with provably controllable learning bounds.
problem Uncertainty quantification and learning bounds in conformal prediction.
method Cost-sensitive conformal training algorithm that minimizes the expected size of prediction sets using rank weighting.
result Theoretical analysis shows tightness between weighted objective and expected size of conformal prediction sets.
Paper analyzes Gibbs and Langevin Monte Carlo for interpolation regime, showing generalization from low errors.
problem Analyzing Gibbs and Langevin Monte Carlo in overparameterized interpolation regime.
method Data-dependent bounds and stability under approximation with Langevin Monte Carlo.
result Generalization is signaled by small training errors in noisy regime, with bounds stable under approximation.
Crowdsourcing is an effective tool for human-powered computation on many tasks challenging for computers. In this paper, we provide finite-sample exponential bounds on the error rate (in probability and in expectation) of hyperplane binary labeling rules under the Dawid-Skene crowdsourcing model. The bounds can be appl…
Nonparametric modeling approaches show very promising results in the area of system identification and control. A naturally provided model confidence is highly relevant for system-theoretical considerations to provide guarantees for application scenarios. Gaussian process regression represents one approach which provid…
Existing guarantees in terms of rigorous upper bounds on the generalization error for the original random forest algorithm, one of the most frequently used machine learning methods, are unsatisfying. We discuss and evaluate various PAC-Bayesian approaches to derive such bounds. The bounds do not require additional hold…
When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship between prediction error and ensemble size is unknown in practice. In the standar…
Efficiently refits black box predictions with wild refitting method.
problem Computing high-probability upper bounds on prediction errors.
method Three-step procedure: residuals, symmetrization, and solving a modified prediction problem.
result Wild refitting provides an upper bound on prediction error with high probability.
Improved efficient robust regression with near-linear time and subquadratic samples.
problem Robust linear regression with unknown covariance matrix under Gaussian covariates.
method Near-linear time algorithm using subquadratic samples, complemented by SQ and polynomial lower bounds.
result Achieves prediction error for , improving over prior works.
New bounds predict deep learning generalization better than existing methods.
problem Predicting generalization errors for deep learning models.
method Function-based PAC-Bayesian bounds that meet multiple desiderata.
result The new bound performs significantly better than existing parameter-based PAC-Bayes bounds.
Improved bounds for continuous functions in online learning.
problem Generalizing mistake-bound model to continuous real-valued functions.
method Investigating the class of absolutely continuous functions with bounded derivative, proving bounds on prediction errors.
result Proved that for with , the bound on the worst-case sum of the powers of prediction errors is $Θ(ε^{- rac{1}{2}})$, independent of .
We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the Wasserstein metric. We go on to prove an error bound for the value-function estimate arisi…
A new metric predicts model performance on unseen data.
problem Predicting performance on out-of-distribution data without labels.
method Uses model predictions to pseudo-label data, trains a new model, and measures difference from in-distribution models.
result Empirically outperforms existing methods on image and text classification tasks.
Study tightens bounds for interpolating noisy data using minimum l1-norm.
problem Predicting noisy data with minimum l1-norm interpolation.
method Provided matching upper and lower bounds for prediction error.
result Tight consistency up to negligible terms for .
Proposes a non-crossing deep neural network quantile regression method.
problem Quantile crossing in nonparametric quantile regression.
method Non-crossing constraints via rectified linear unit penalty function.
result Established non-asymptotic upper bounds for excess risk.
Prediction intervals are a valuable way of quantifying uncertainty in regression problems. Good prediction intervals should be both correct, containing the actual value between the lower and upper bound at least a target percentage of the time; and tight, having a small mean width of the bounds. Many prior techniques f…
The study analyzes robustness of estimators in linear models with adversarial errors.
problem Analyzing robustness of estimators in linear models with adversarial errors.
method Develops a general theory for minimum norm interpolating estimators and RERM in linear models without conditions on errors.
result Quantitative bound for the prediction error relating it to Rademacher complexity, norm of minimum norm interpolator of errors, and subdifferential size.
New bounds for adaptive control in high dimensions without fixed state space.
problem Adaptive control of linear systems in high or infinite dimensions.
method Novel perturbation bound for certainty equivalence, scaling with prediction error.
result First regret bounds for LQR in infinite dimensional systems, independent of ambient dimension.
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item is closer to item than item ". Ordinal constraints like this often come from human judgments. To account for errors and variation in jud…
Optimal multiclass U-calibration error found to be Θ(√KT).
problem Online multiclass U-calibration with low regret for all bounded proper losses.
method Follow-the-Perturbed-Leader algorithm and lower bound construction.
result Optimal U-calibration error is Θ(√KT).
The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task. Predictive sparse coding algorithms recently have demonstrated impressive perform…
This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators' to a distribution over the true error. The variance of this distribution can be…
The paper analyzes prediction error in nonstationary settings using weighted risk minimization.
problem Prediction under distribution drift and nonstationary conditions.
method General decomposition of excess risk into learning and drift terms, proving oracle inequalities under mixing conditions.
result Oracle inequalities for the learning error, providing bounds that hold uniformly over arbitrary weight classes.
Random forests are stable and provide reliable prediction intervals.
problem Stability and reliability of random forest prediction intervals.
method Established stability under mild conditions and proved coverage bounds.
result Non-asymptotic lower and upper bounds for prediction interval coverage.
Develops bounds predicting deep learning generalization using optimal transport.
problem Discrepancy between theoretical error bounds and empirical observations in deep learning.
method Margin-based generalization bounds with optimal transport costs.
result Theoretical bounds robustly predict generalization error on large datasets.
The paper assesses quality measures for machine learning models using cross-validation.
problem Evaluating the accuracy and robustness of quality measures for machine learning models.
method Cross-validation approach to estimate prediction error and quantify explained variation. Confidence bounds and local quality measures derived from residuals.
result The reliability and robustness of quality measures are assessed through numerical examples and confidence bounds.