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.
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48 results for “error analysis”
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.
CD-RCA method identifies causal relationships in prediction errors without predefined graphs.
problem Challenges in diagnosing prediction errors due to lack of transparency in black-box models.
method Causal-Discovery-based Root-Cause Analysis (CD-RCA) method that estimates causal relationships without predefined causal graphs.
result CD-RCA outperforms heuristic attribution methods in identifying variable contributions to prediction errors.
This work gives a simultaneous analysis of both the ordinary least squares estimator and the ridge regression estimator in the random design setting under mild assumptions on the covariate/response distributions. In particular, the analysis provides sharp results on the ``out-of-sample'' prediction error, as opposed to…
Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This paper presents generalizations of such estimation error analysis on all four aspe…
The paper analyzes CycleGAN's error components for unpaired data generation.
problem Analyzing approximation and estimation errors in CycleGAN for unpaired data.
method Decomposes risk into approximation and estimation errors, analyzing each separately and considering their trade-offs.
result Theoretical insights into CycleGAN's performance through error analysis.
This paper analyzes hedge errors in Black-Scholes models using finite difference techniques.
problem Accurate hedging strategies in dynamic market environments.
method Asymptotic approach and finite difference techniques.
result Reduction of hedge errors and enhancement of option pricing model robustness.
The study provides a comprehensive error analysis for diffusion models.
problem Understanding the accuracy and design of diffusion-based generative models.
method Conducts a non-asymptotic convergence analysis and sampling error analysis for diffusion models.
result Theoretical insights into designing effective training and sampling processes for diffusion models.
Sharp analysis of out-of-distribution error in overparameterized models with importance weights.
problem Understanding and quantifying the degradation of performance in overparameterized models when faced with underrepresented data.
method Sharp analysis of an overparameterized Gaussian mixture model with spurious features and cost-sensitive interpolating solutions incorporating importance weights.
result Characterization of a novel tradeoff between worst-case robustness and average accuracy as a function of importance weight magnitude.
Principal Component Analysis (PCA) is the most common nonparametric method for estimating the volatility structure of Gaussian interest rate models. One major difficulty in the estimation of these models is the fact that forward rate curves are not directly observable from the market so that non-trivial observational e…
Study analyzes error in neural network solving PDEs, providing convergence and error bounds.
problem Error analysis of neural network solving PDEs.
method Three-layer tanh neural network with projected gradient descent (PGD).
result Comprehensive error analysis including approximation, generalization, and optimization errors.
This work analyzes discrete diffusion models using stochastic integrals, providing error bounds and insights.
problem Error analysis for discrete diffusion models remains less understood.
method Proposes a comprehensive framework based on Lévy-type stochastic integrals.
result Obtains the first error bound for the -leaping scheme in KL divergence.
The paper analyzes the stability of an observer error in a vibrating string system.
problem Stability analysis of observer error in a vibrating string system.
method Abstract Cauchy problem reformulation and application of LaSalle's invariance principle for infinite-dimensional systems.
result The observer error is asymptotically stable.
A model order reduction framework reduces financial risk analysis models efficiently.
problem Simulating high-dimensional financial risk models.
method Adaptive greedy sampling based on POD and surrogate modeling.
result Reduced models provide significant speedup with excellent accuracy.
This paper reviews methods for constructing confidence intervals for error rates in 1:1 matching tasks.
problem Challenges in assessing uncertainty of error rates in matching algorithms, especially when data are dependent and error rates are low.
method Derives and examines statistical properties of methods for constructing confidence intervals for error rates in 1:1 matching tasks.
result Coverage and interval width vary with sample size, error rates, and data dependence.
Analysis of Trade-offs in Fair Principal Component Analysis Based on Multi-objective Optimizationcs.LG
This paper tackles fairness in PCA by balancing it with reconstruction error.
problem Fairness concerns in PCA due to different group representation errors.
method A multi-objective optimization approach to balance fairness and reconstruction error.
result Achieving fairness with minimal loss in reconstruction error.
A contraction analysis improves model-based RL's error recovery.
problem Theoretical understanding of model-based reinforcement learning.
method Contraction analysis applied to both stochastic and deterministic state transitions.
result Error reduction in cumulative reward using branched rollouts.
This paper analyzes errors in Shapley value-based model explanations.
problem Biased or unreliable explanations from existing SVA methods.
method Error theoretical analysis framework decomposing errors into observation and structural biases.
result Trade-off between observation and structural biases in SVA explanations.
Implicit biases in multitask and continual learning from a backward error analysis perspectivestat.ML
The study analyzes implicit biases in neural networks using backward error analysis.
problem Analyzing implicit biases in multitask and continual learning settings.
method Backward error analysis to compute implicit training biases, deriving modified losses with three terms.
result The conflict term, measuring gradient alignment, is a new quantity in continual learning.
This research analyzes the error convergence rate of GAN models.
problem Understanding the error convergence rate of GAN models.
method Applying Talagrand inequality and Borel-Cantelli lemma to establish a tight convergence rate.
result Established a tight convergence rate for the error of GAN models.
Analysis of Minimax Error Rate for Crowdsourcing and Its Application to Worker Clustering Modelstat.ML
While crowdsourcing has become an important means to label data, there is great interest in estimating the ground truth from unreliable labels produced by crowdworkers. The Dawid and Skene (DS) model is one of the most well-known models in the study of crowdsourcing. Despite its practical popularity, theoretical error …
Paper analyzes ECE bias and provides bounds for its estimation.
problem Understanding the estimation bias in ECE for machine learning models.
method Information-theoretic approach to analyze bias in uniform mass and uniform width binning strategies.
result Established upper bounds on ECE estimation bias and optimal number of bins.
We analyze errors in filtering algorithms using optimal transport.
problem Estimation errors in optimal transport-based filtering algorithms.
method Systematic analysis of estimation errors for conditional Brenier maps.
result Demonstrates effectiveness and practical potential of the optimal transport filtering algorithm.
This paper analyzes error feedback in compressed federated learning for non-convex optimization problems.
problem Reducing communication cost in federated learning with biased gradient compression.
method Proposes Fed-EF, a compressed federated learning scheme with error feedback, and analyzes its convergence rate and performance under partial client participation.
result Fed-EF can match the convergence rate of full-precision FL under data heterogeneity with a linear speedup and no extra slow-down factor due to stale error compensation.
The paper analyzes errors in mechanical systems with external forces.
problem Error analysis of mechanical systems with external forces.
method Analysis of variational integrators with contact order for discrete mechanical systems.
result The contact order of the integrator is the same as the contact order of the original systems.
In spite of the accomplishments of deep learning based algorithms in numerous applications and very broad corresponding research interest, at the moment there is still no rigorous understanding of the reasons why such algorithms produce useful results in certain situations. A thorough mathematical analysis of deep lear…
New method tackles composite optimization with error feedback.
problem Challenges in distributed machine learning training and message compression.
method Combines Dual Averaging with EControl for composite optimization.
result First strong convergence analysis for composite optimization with error feedback.
This paper analyzes error bounds for biased SMC samplers in conditional sampling.
problem Analyzing error bounds for biased SMC samplers in conditional sampling.
method Develops a non-asymptotic error analysis for SMC samplers with biased mutation kernels.
result Derives the first non-asymptotic error bound for conditional sampling with score-based diffusion models.
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…
Finite Sample Guarantees for Distributed Online Parameter Estimation with Communication Costseess.SY
The paper provides bounds on estimation error in a distributed online learning setting.
problem Estimating an unknown parameter in a distributed and online manner with finite sample guarantees.
method Proposes a distributed online estimation algorithm that improves accuracy through communication, providing non-asymptotic bounds on estimation error.
result Demonstrates a trade-off between estimation error and communication costs, and determines a stopping time for communication based on desired accuracy.
Paper analyzes online tensorial ICA convergence with stochastic approximation.
problem Online tensorial ICA convergence analysis.
method Stochastic approximation for nonconvex optimization.
result Sharp finite-sample error bound of .
Novel Fréchet regression method handles errors-in-variables with low-rank covariates.
problem Regression with noisy and limited covariate data.
method Combines global Fréchet regression and principal component regression for low-rank structure.
result Improved efficiency and accuracy in high-dimensional and noisy data settings.
Measurement error in the observed values of the variables can greatly change the output of various causal discovery methods. This problem has received much attention in multiple fields, but it is not clear to what extent the causal model for the measurement-error-free variables can be identified in the presence of meas…
Paper develops an online learning algorithm for functional data models.
problem Recovering slope functions or predictors in functional data models.
method Online regularized learning algorithm in reproducing kernel Hilbert spaces with polynomially decaying step-size.
result Established fast convergence rates for estimation error without capacity assumption.
This article analyzes the weak error of SGD optimization schemes.
problem Analyzing the error in SGD optimization schemes with respect to a test function.
method Weak error analysis for SGD type optimization schemes.
result The weak error decays at the same speed as in the strong sense.
CNFs learn distributions from samples with error bounds.
problem Learning probability distributions from finite samples.
method Continuous normalizing flows with linear interpolation and flow matching objective function.
result Non-asymptotic error bounds for distribution estimator in Wasserstein-2 distance.
Two derivations of PCA for distributional data.
problem PCA for datasets of distributions.
method Two derivations: variance maximization and reconstruction error minimization.
result Closed-form solution for distributional PCA.
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…
This work analyzes how different layers in deep neural networks contribute to generalization error.
problem Understanding the role of each layer in deep neural networks for generalization.
method Spectral analysis, Neural Tangent Kernel, Hermite polynomials, Spherical Harmonics.
result Initial layers in deep neural networks have a larger bias towards high-frequency functions.
This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are considered. Focusing on the fundamental problem of separating a two-class Gauss…
DFM models are analyzed for generating distributions with provable convergence.
problem Training DFM models to generate distributions that match true data.
method Theoretical analysis decomposes error into approximation and estimation errors.
result DFM models converge to true data distribution as training set size increases.
Double Q-learning has the same mean-squared error as Q-learning under certain conditions.
problem Comparing the mean-squared error of Double Q-learning and Q-learning.
method Theoretical analysis based on Lyapunov equations for both tabular and linear function approximation settings.
result The asymptotic mean-squared error of Double Q-learning is exactly equal to that of Q-learning under specific conditions.
A unified error analysis for randomized low-rank approximation with application to data assimilationmath.NA
Unified error analysis for low-rank approximation improves data assimilation performance.
problem Analyzing the error in low-rank approximation methods for data assimilation.
method Unified stochastic analysis framework for Frobenius norm error bounds on centered and non-standard Gaussian matrices.
result Unified bounds provide clearer interpretations and enable better practical choices for covariance matrices.
Proposes improved classification via transfer learning with regularized linear discriminant analysis.
problem High dimensionality and small sample sizes lead to poor classification performance.
method Regularized random-effects linear discriminant analysis, combining ridge estimates from target and source models.
result Explicit derivation of asymptotic weights and classification error rates in high-dimensional settings.
We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of refining time-grids to reduce statistical approximation errors in an adaptive and…
Paper proposes a fast stochastic algorithm for neural network quantization with error bounds.
problem Error analysis for quantized neural networks with non-convex loss functions and nonlinear activations.
method Greedy path-following mechanism combined with stochastic quantizer.
result Established full-network error bounds for quantized neural networks.
Recent theoretical work has guaranteed that overparameterized networks trained by gradient descent achieve arbitrarily low training error, and sometimes even low test error. The required width, however, is always polynomial in at least one of the sample size , the (inverse) target error , and the (inverse) fail…
Generative models improve inverse problems by providing tailored priors.
problem Analyzing the error in inverse problems solved with generative priors.
method Quantitative error bounds for minimum Wasserstein-2 generative models.
result The error in the posterior due to the generative prior is bounded by the prior's error in Wasserstein-1 distance.