We carefully study how well minimizing convex surrogate loss functions, corresponds to minimizing the misclassification error rate for the problem of binary classification with linear predictors. In particular, we show that amongst all convex surrogate losses, the hinge loss gives essentially the best possible bound, o…
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48 results for “error minimization”
Sharp bounds on ERM's minimal error in regression.
problem Understanding ERM's performance in regression tasks.
method Sharp lower bounds for ERM in random and fixed design settings.
result ERM's performance depends on the global or local complexity of the model.
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.
New fairness concept extends minimax fairness to lexicographic fairness.
problem Fairness in supervised learning, especially lexicographic fairness.
method Introduced approximate lexifairness, derived algorithms for finding solutions, and proved generalization bounds.
result Proved that approximate lexifairness on training data implies approximate lexifairness on true distribution.
Paper introduces a new cost function to improve deep learning model generalization.
problem Overfitting and poor extrapolation of deep learning models.
method Introduces a 'whitening' cost function based on the Ljung-Box statistic.
result Significant improvement in generalization for RNNs and image autoencoders.
We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error (MAE) regression. We also show that, under some asumptions, universal consisten…
New online learning algorithm combines PA and TER for binary classification.
problem Binary classification with non-separable data and data imbalance.
method Online Passive-Aggressive (PA) and Total-Error-Rate (TER) learning combined into PATER algorithm.
result PATER algorithms outperform existing online learning algorithms in efficiency and effectiveness.
Upper bounds for CV errors apply to lasso and other models.
problem Bounding CV errors for lasso and similar models.
method Rademacher complexity and Orlicz- norm.
result Upper bounds are tight and stable for lasso.
We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless…
MEVA aggregates model predictions to improve accuracy without needing model details.
problem Improving model accuracy by combining multiple models.
method Non-intrusive, data-driven framework that treats models as black boxes and optimizes aggregation methods.
result MVA outperforms MEA in estimating aggregated predictions, enhancing robustness and accuracy.
Noise makes data unlearnable by tricking models.
problem Unauthorized exploitation of personal data by deep learning models.
method Error-minimizing noise to reduce training examples' learnability.
result Error-minimizing noise can make training examples unlearnable by deep learning models.
We address the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem analytically in the case of two populations, with a uniform bonus-malus on the zones whe…
Hallucinations in models are mislinked estimates, not errors.
problem Hallucinations in generative models as failures to link estimates to plausible causes.
method Formalized hallucinations, showed even optimal estimators hallucinate, provided a general lower bound on hallucinate rate, reframed hallucination as structural misalignment, and experimentally supported theory.
result Hallucinations are structural misalignments between loss minimization and human-acceptable outputs, leading to estimation errors.
This study explains how different training methods affect the minimizer of neural networks.
problem How training methods influence the minimizer of neural networks.
method Explains how initialization size, adaptive optimization (AdaGrad), and stochastic mini-batch training affect the minimizer.
result Different training methods lead to different minimizers, even in overparameterized networks.
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…
Paper shows how gradient concentration helps in learning from inexact data.
problem Learning from inexact and stochastic training data.
method Combines probabilistic gradient concentration with inexact optimization techniques.
result Derives sharp test error guarantees for learning.
On the Loss Landscape Geometry of Regularized Deep Matrix Factorization: Uniqueness and Sharpnessstat.ML
The paper studies the loss landscape of regularized deep matrix factorization, revealing unique and sharp minimizers.
problem Understanding the loss landscape and minimizers of regularized deep matrix factorization problems.
method Theoretical analysis of -regularized deep matrix factorization/deep linear network training problems with squared-error loss.
result The unique end-to-end minimizer exists for all target matrices except for a set of Lebesgue measure zero.
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…
This technical note extends recent results on the computational complexity of globally minimizing the error of piecewise-affine models to the related problem of minimizing the error of switching linear regression models. In particular, we show that, on the one hand the problem is NP-hard, but on the other hand, it admi…
Optimal AFs minimize RFR test error and sensitivity.
problem Finding optimal AFs for RFR to minimize test error and sensitivity.
method Closed-form solution for AFs minimizing test error and sensitivity under different functional parsimony.
result Optimal AFs can be linear, saturated linear, or Hermite polynomial expressions.
We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has minimal variance among all unbiased estimators and is asymptotically normally dis…
An Exponential Factorization Machine with Percentage Error Minimization to Retail Sales Forecastingcs.LG
New model predicts sales of new products with short life cycles.
problem Forecasting sales of new products with short lead times and life cycles.
method Developed an exponential factorization machine (EFM) to consider attributes and pairwise interactions.
result EFM model outperforms existing models in terms of MAPE and MAE.
Study of estimation errors in surrogate loss minimizers, providing stronger guarantees than existing methods.
problem Estimation errors in surrogate loss minimizers for various hypothesis sets.
method Detailed study of -consistency estimation error bounds, proving general theorems for distribution-dependent and independent settings.
result Explicit bounds for zero-one and adversarial losses, showing enhancements under distributional assumptions.
Paper tackles fairness in CCA by minimizing correlation disparity error.
problem Fairness issues in CCA.
method Framework to minimize correlation disparity error in CCA.
result Reduces correlation disparity error without sacrificing CCA accuracy.
In this work, we present a novel upper bound of target error to address the problem for unsupervised domain adaptation. Recent studies reveal that a deep neural network can learn transferable features which generalize well to novel tasks. Furthermore, a theory proposed by Ben-David et al. (2010) provides a upper bound …
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.
Study shows how neural networks generalize with minimal training data.
problem Understanding how neural networks generalize with limited data.
method Mean-field analysis of KL-regularized empirical risk minimization.
result Generalization error rate is for large .
The paper explores why a specific type of predictor works well in noisy data.
problem Understanding why a specific type of predictor (minimum-norm interpolator) works well in noisy data.
method The paper uses uniform convergence and zero-error predictors in a norm ball to explain the success of the minimum-norm interpolator.
result The minimum-norm interpolator is consistent, and this can be explained by uniform convergence of zero-error predictors in a norm ball.
Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Accesscs.LG
Improved sample complexity for diffusion models without needing empirical risk minimizers.
problem Theoretical limitations in sample complexity for diffusion models.
method Structured decomposition of score estimation error, eliminating dependence on neural network parameters.
result Achieved sample complexity bound of O(ε^(-4)) without empirical risk minimizer access.
New method for distributional off-policy evaluation using Bellman residual minimization.
problem Learning return distribution from offline data generated by a different policy.
method Energy Bellman Residual Minimizer (EBRM) method.
result Established finite-sample error bound for EBRM estimator.
We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error (MAE) regression. We show that universal consistency of Empirical Risk Minimiza…
This work proves -regularized ERM controls smCE without post-hoc correction.
problem Calibration of predicted probabilities in machine learning models.
method Canonical -regularized empirical risk minimization.
result Theoretical proof that smCE is controlled by ERM without post-hoc correction.
Minimizes indecisions in selective classification to control misclassification rates.
problem Controlling misclassification rates in high-risk scenarios.
method Using indecisions to control misclassification rates, even below Bayes optimal.
result Control of misclassification rates to any user-specified level, even below Bayes optimal.
On the Minimal Adversarial Perturbation for Deep Neural Networks with Provable Estimation Errorcs.LG
Paper proposes methods to estimate minimal adversarial perturbations for deep neural networks.
problem Quantifying robustness of deep neural networks against adversarial attacks.
method Proposes two lightweight strategies to find minimal adversarial perturbation.
result Approximates theoretical distance for samples close to classification boundary, providing robustness guarantees.
A new method for the unsupervised learning of sparse representations using autoencoders is proposed and implemented by ordering the output of the hidden units by their activation value and progressively reconstructing the input in this order. This can be done efficiently in parallel with the use of cumulative sums and …
The paper improves tensor completion bounds using spectral gap.
problem Theoretical limitations in tensor completion, especially for deterministic sampling.
method Bounding the generalization error of tensor completion methods using spectral gap.
result Improved bounds on tensor completion error, reducing rank dependence.
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…
The reactions of the human body to physical exercise, psychophysiological stress and heart diseases are reflected in heart rate variability (HRV). Thus, continuous monitoring of HRV can contribute to determining and predicting issues in well-being and mental health. HRV can be measured in everyday life by consumer wear…
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.
Passive investing can incur hidden costs due to market timing inefficiencies.
problem Hidden costs in passive investing due to market timing inefficiencies.
method Analysis of passive investing strategies, including gradual share acquisition and post-announcement trading.
result Post-announcement trading can earn significant profits, often exceeding 1%.
Paper tackles MLR prediction error without assuming realizable models.
problem Prediction error in mixture of linear regressions without realizable assumptions.
method Developed algorithms for list-decoding MLR predictions and minimized empirical risk.
result Alternating minimization algorithm finds best fit lines in non-realizable settings.
We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold of dimension at most seven, can degenerate. Loosely speaking, our results show …
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…
Regularization of minimization for dealing with outliers and noise in Statistics and Signal Recoverymath.OC
We study the robustness properties of norm minimization for the classical linear regression problem with a given design matrix and contamination restricted to the dependent variable. We perform a fine error analysis of the estimator for measurements errors consisting of outliers coupled with noise. We…
Study on double descent behavior in two-layer neural networks for binary classification.
problem Understanding the double descent phenomenon in model test error.
method Two-layer neural network with ReLU activation for binary classification. Quantified model size by sample-to-dimension ratio. Empirical risk minimization using Convex Gaussian Min Max Theorem.
result Observed and investigated the double descent behavior of model test error.
New method bounds high-dimensional regression without estimating design covariance.
problem High-dimensional linear regression with random design.
method Error-in-operator approach that incorporates design covariance into empirical risk minimization.
result Dimension-free bounds on excess prediction risk derived.
Bayesian regression underestimates parameter uncertainties in noisy models.
problem Parameter uncertainties are underestimated in Bayesian regression for imperfect models.
method Analyzed and designed an ansatz to correct for misspecification in near-deterministic surrogate models.
result Posterior distributions must cover all training points to avoid divergent generalization error.
Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether the regression assumptions are me…