This paper analyzes error in SKI for Gaussian Processes, providing conditions for linear time inference.
problem Lack of rigorous theoretical error analysis for SKI.
method Proved error bounds for SKI Gram matrix, examined error effects, provided practical guidelines.
result Identified two dimensionality regimes for SKI's scalability-accuracy trade-offs.
The paper analyzes the probabilistic structure of DDPMs and bounds their sampling error.
problem Understanding and controlling errors in discrete-time DDPMs.
method Structural analysis of score functions, Schrödinger's problem, and FBSDEs.
result Explicit upper bound for total variation distance between sampling and target distributions.
Proposes a model combining difference-attention and error-correction LSTMs for improved time series prediction.
problem Improving accuracy in time series prediction.
method Combines difference-attention LSTM and error-correction LSTM in a cascade approach.
result Improves prediction accuracy in time series.
The paper introduces a method to model error correlations in multivariate time series forecasting.
problem Accurate modeling of error correlations for reliable uncertainty quantification.
method Plug-and-play method that learns error covariance over multiple steps using low-rank-plus-diagonal and independent latent temporal processes.
result Improves predictive accuracy and uncertainty quantification without significantly increasing parameter size.
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.
Proposes adjusting neural network errors for time series forecasting.
problem Autocorrelated errors in neural networks for time series.
method Jointly learn autocorrelation coefficient with model parameters.
result Enhances performance in almost all time series forecasting cases.
Improved deep probabilistic time series forecasting by learning error autocorrelation.
problem Simplification of time-independent error process and lack of serial correlation in existing models.
method Proposes a training method that incorporates error autocorrelation to enhance probabilistic forecasting accuracy.
result Improves predictive accuracy and uncertainty quantification across multiple datasets.
iTimER learns from reconstruction errors to represent irregularly sampled time series.
problem Learning from irregularly sampled time series with missing data.
method iTimER models reconstruction errors as a proxy for unobserved values, using a mixup strategy and a Wasserstein metric.
result iTimER outperforms state-of-the-art methods in classification, interpolation, and forecasting tasks.
ECI improves time series prediction uncertainty quantification by smoothing miscoverage error.
problem Challenges in uncertainty quantification for time series prediction due to temporal dependence and distribution shift.
method Error-quantified Conformal Inference (ECI) by smoothing quantile loss function and introducing adaptive feedback scale.
result ECI achieves valid miscoverage control and tighter prediction sets than existing methods.
Analyzes the generalization and training errors of the random feature model over time.
problem Understanding the temporal behavior of generalization and training errors in deep learning.
method Uses Cauchy complex integral representations and random matrix methods based on linear pencils.
result Analytical solution of the full time-evolution path of generalization and training errors.
New method calibrates asynchronous, error-prone covariates for longitudinal data.
problem Estimation biases and slow convergence in analyzing time-varying covariates with measurement error.
method Functional calibration approach based on functional principal component analysis.
result Asymptotically unbiased and consistent estimators for time-invariant coefficients; optimal convergence rate for time-varying coefficients.
Paper presents a method to reduce prediction variance of DNNs for unknown systems.
problem Uncertainty in DNN predictions due to high variance.
method Ensemble averaging of multiple DNN models trained independently.
result Reduction in variance of DNN predictions, improving reliability.
Study shows label errors impact model disparity metrics, proposing mitigation methods.
problem Impact of label errors on model disparity metrics.
method Empirical study, characterizing label error effects; proposing estimation and relabeling methods.
result Label errors significantly affect model disparity metrics, particularly for minority groups.
Time series forecasting gets much attention due to its impact on many practical applications. Higher-order neural network with recurrent feedback is a powerful technique which used successfully for forecasting. It maintains fast learning and the ability to learn the dynamics of the series over time. For that, in this p…
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.
Variant of mSSA improves time series prediction error.
problem Improve prediction error in multivariate time series.
method Introduce spatio-temporal factor model, establish prediction error scaling.
result Prediction error scales as 1 / √(min(N, T)T).
Study uses DNNs for real-time EM inversion, highlighting model errors and proposing solutions.
problem Model errors in DNNs affect real-time geosteering decisions in EM measurements.
method Bayesian ensemble smoothing with DNNs for thousands of model evaluations, identifying multimodality.
result Model errors can lead to biased estimates, necessitating error reduction techniques.
Neural CDEs correct errors in learned time-series models for better forecasting.
problem Error accumulation in multi-step forecasts of learned time-series models.
method Predictor-Corrector framework with a neural controlled differential equation.
result The proposed framework consistently improves forecasting performance across various models.
Continuous-time PCD for MLE with explicit error bounds.
problem Maximum likelihood estimation of unnormalised densities.
method Continuous-time formulation as coupled SDEs, deriving UiT bounds.
result Explicit error bounds between PCD iterates and MLE solution.
This work finds a point with small test error in polynomial time for mildly overparameterized neural nets.
problem Achieving small test error in mildly overparameterized neural networks.
method The work shows that the landscape of loss functions with explicit regularization has a property that all local minima and certain stationary points achieve small test error. It also proves the existence of polynomial time algorithms for finding such points in convolutional and fully connected neural nets.
result Polynomial time algorithms exist for finding points with small test error in mildly overparameterized neural nets.
TD learning reduces prediction error in Markov chain problems.
problem Estimating value functions in Markov chains with temporal inconsistency.
method Temporal difference learning minimizes temporal inconsistency between successive estimates.
result TD learning can significantly reduce mean-squared error in value estimates.
Langevin dynamics fails to produce accurate samples even with small score function errors.
problem Robustness of Langevin dynamics to score function errors.
method Analysis of Langevin dynamics and score function errors.
result Langevin dynamics produces a distribution far from the target distribution in TV distance even with small L2 errors in the score function. Improved error estimate for SGLD sampling algorithm.
problem Establishing a precise error bound for SGLD.
method Sharp uniform-in-time error estimate for SGLD under mild assumptions.
result Uniform-in-time O(η2) bound for KL-divergence between SGLD and Langevin diffusion. 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.
Unified framework for blending ML and mechanistic models in dynamical systems.
problem Learning dynamical systems from noisy, partially observed data.
method A unifying framework that combines mechanistic and machine learning approaches.
result Proves that hybrid models can learn memory-dependent model error.
Derives EoM for DNNs to describe GD dynamics precisely.
problem Gaps between differential equations and actual DNN learning dynamics due to discretization error.
method Starts from GF, derives counter term to cancel discretization error, obtains EoM.
result EoM precisely describes GD dynamics of DNNs, highlights differences between continuous and discrete GD.
This paper studies the problem of error-runtime trade-off, typically encountered in decentralized training based on stochastic gradient descent (SGD) using a given network. While a denser (sparser) network topology results in faster (slower) error convergence in terms of iterations, it incurs more (less) communication …
The paper analyzes error propagation in dynamic programming for stochastic control and option pricing.
problem Error propagation in dynamic programming for stochastic control and option pricing.
method Formulated a general dynamic programming framework, used RKHSs for nonparametric regression, and Monte Carlo subsampling for estimating continuation value.
result Proposed a rigorous error decomposition and control mechanism for error propagation in dynamic programming.
New error bound for diffusion models without dimensionality constraints.
problem Error estimation in diffusion generative models without dimensionality constraints.
method Derive dimension-free error bound using a smooth test functional.
result Explicit, dimension-free bound on generated vs true data distributions.
SGLDiff approximates Bayesian posterior distributions with subsampling error.
problem Approximating Bayesian posterior distributions in large-scale data settings.
method Stochastic Gradient Langevin Diffusion (SGLDiff) with subsampling.
result The Wasserstein distance between the posterior and SGLDiff's limiting distribution is bounded by a fractional power of the mean waiting time.
Paper proposes RAN for better anomaly detection in time series data.
problem Anomaly detection algorithms often fail to accurately detect anomalies due to incomplete reconstruction of anomaly data.
method RAN uses adversarial learning and latent vector-constrained Autoencoder to ensure consistent reconstruction of anomaly data.
result RAN outperforms other algorithms in detecting meaningful anomalies with higher AUC-ROC scores.
Unified error analysis for discrete flow models.
problem Error analysis of discrete flow models.
method Stochastic calculus theory, Girsanov theorem, generator matching, uniformization.
result First error analysis for discrete flow models.
The paper examines prediction and estimation risks of ridgeless least squares under general error assumptions.
problem Prediction and estimation risks of ridgeless least squares under realistic error structures.
method Analysis of prediction and estimation risks under general regression error assumptions, including clustered or serial dependence.
result The benefits of overparameterization extend to time series, panel, and grouped data.
New algorithm learns value and advantage functions for continuous-time Markov processes without structural assumptions.
problem Learning value and advantage functions for continuous-time Markov processes without structural assumptions.
method Proposes Sobolev-prox fitted q-learning algorithm based on Hilbert-space positive definiteness and boundedness properties of Bellman operators. result Identifies ellipticity as a key structural property enabling reinforcement learning for Markov diffusions.
New approach shapes error distribution in long-term forecasting.
problem Disparate error distributions in recent transformer models.
method Loss shaping constraints to respect upper bounds on loss at each time-step.
result Competitive average performance with shaped error distribution.
MACER accelerates error repair by modularly identifying and applying fixes.
problem Automated compilation error repair for novice programmers.
method Modular segregation of repair process into identification and application, using discriminative learning techniques.
result MACER outperforms existing methods by 20% on popular errors and is competitive on all error types.
We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local bounds. In doing so, we prove for the first time that the Lie-Butcher theory of Lie group integrators leads to global error estimates.
Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.
problem Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination.
method Near-optimal algorithms with optimal error guarantees, achieving sample complexity n=ildeO(d/ε2) and almost linear runtime. result First sample near-optimal and almost linear-time algorithms with optimal error guarantees for both problems.
Enhanced TSFMs improve time series forecasting accuracy and reliability.
problem Variance, bias, and uncertainty in TSFMs' predictions on real data.
method Statistical and ensemble techniques including bagging, stacking, residual modeling, and prediction intervals.
result Hybrid models consistently outperform standalone TSFMs across multiple horizons.
Artificial Intelligence (AI) systems sometimes make errors and will make errors in the future, from time to time. These errors are usually unexpected, and can lead to dramatic consequences. Intensive development of AI and its practical applications makes the problem of errors more important. Total re-engineering of the…
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…
Optimizes prediction error method for time-varying models.
problem Achieving optimal prediction error rates for time-varying models.
method Nonlinear least squares method for time-varying parametric models.
result First rate-optimal non-asymptotic analysis for time-varying models.
This paper provides a mathematical foundation for deep neural networks solving PDEs.
problem Mathematical foundation for deep neural networks solving high-dimensional PDEs.
method Decomposed generalization error into approximation and training errors; derived gradient flow in the wide network limit.
result Generalization error tends to zero as the number of neurons and training time tend to infinity.
A method for noise reduction in functional time series using FPCA.
problem Noise contamination in functional time series.
method Extending FPCA to separate signal and noise components.
result Optimal projection minimizes mean integrated squared error.
A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than observed in simulations, a deficit that is repaired with the help of a new past-future…
Develops a Bayesian method for causal inference with partly censored time-to-event data.
problem Estimating causal effects with unobserved confounders and measurement errors in partly censored time-to-event data.
method Semiparametric Bayesian instrumental variable analysis using a two-stage Dirichlet process mixture model.
result The proposed method outperforms competing methods in simulations and real-world data analysis.
Proposes a non-autoregressive Transformer for time series forecasting.
problem Autoregressive errors and spatial-temporal dependencies in time series forecasting.
method Introduces a Non-Autoregressive Transformer with a learned temporal influence map.
result Demonstrates state-of-the-art performance on time series forecasting datasets.
K-DAREK improves KKANs for efficient function approximation with robust error bounds.
problem Efficient function approximation with uncertainty quantification for large-scale problems.
method Developed a novel learning algorithm, K-DAREK, for KKANs.
result Established robust error bounds that are distance-aware, improving efficiency and scalability.