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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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172343515686 · Jun 202019922001200920172026
48 results for Weighted error measures

Robust variable selection for high-dimensional data with missing and measurement errors.

problem Missing data and measurement errors confound data distribution.
method Exponential loss function with inverse probability weighting and additive error models.
result The Atan punishment method improves robust variable selection.

New weighted Lasso estimates improve logistic regression performance with measurement error.

problem Improper Lasso estimates in sparse logistic regression with equal penalties.
method Proposed weighted Lasso estimates using McDiarmid inequality for non-asymptotic oracle inequalities.
result Finite sample behavior illustrated by non-asymptotic oracle inequalities for estimation and prediction errors.

Gaussian process regression helps approximate Bayesian inverse problems efficiently.

problem Computational intractability of Bayesian posterior distributions in inverse problems.
method Gaussian process regression to build a surrogate model for the likelihood.
result Error between true and approximate posterior can be bounded by weighted L2L^2-norm error between true and approximate likelihood.

The paper analyzes constrained optimal portfolios in high dimensions using novel statistical learning techniques.

problem Forming optimal portfolios with constraints in high-dimensional asset spaces.
method CROWN method integrating factor models with nodewise regression for estimation in large dimensions.
result Demonstrates estimation consistency and convergence rates for constrained portfolio weights, risk, and Sharpe Ratio.

We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We prove the existence of an optimal MAPE model and we show the universal consistency of Empirical Risk Minimization based on the MAPE. We also show that finding the best model under…

2016-05-09abs ↗pdf ↗

Biases in observational data of treatments pose a major challenge to estimating expected treatment outcomes in different populations. An important technique that accounts for these biases is reweighting samples to minimize the discrepancy between treatment groups. We present a novel reweighting approach that uses bi-le…

2018-10-17abs ↗pdf ↗

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…

2015-06-12abs ↗pdf ↗

Study proposes method to estimate causal effects from noisy treatment data.

problem Estimating causal effects from noisy treatment data without side information.
method Deep latent variable model with neural network parameterization and amortized importance-weighted variational objective.
result Causal effect estimates are identifiable without side information and measurement error variance knowledge.

Neural networks improve nonparametric regression with measurement errors.

problem Nonparametric regression with measurement errors.
method Proposes a neural network design using FNN, normalizing flow, and inference network.
result Neural network approach is more flexible and superior or comparable to classical methods.

Neural networks can approximate rectifiable measures with small error.

problem Approximating complex rectifiable measures using neural networks.
method Using ReLU neural networks to approximate (countably) m-rectifiable measures as push-forwards of the Lebesgue measure.
result The approximation error in terms of Wasserstein distance can be made arbitrarily small.

CWGD measures gradient diversity weighted by curvature, improving SGD convergence.

problem Gradient noise in high-curvature directions is underestimated by standard methods.
method CWGD weights gradient diversity by the inverse square root of the Hessian.
result CWGD-Cosine reduces optimization error by up to 20% compared to standard cosine annealing.

Paper introduces a novel error measure for neural networks integrating statistical and information theory.

problem No single error measure is universally best for neural network training.
method Developed a novel error measure EExpAbsE_{ExpAbs} and integrated it into the Levenberg-Marquardt algorithm.
result Self-adaptive, dynamic learning algorithm improves both model accuracy and training process.

AdapDISCOM tackles high-dimensional multimodal data with missingness and errors, improving prediction and biomarker selection.

problem High-dimensional multimodal data with block-wise missingness and measurement errors.
method AdapDISCOM introduces modality-specific weighting schemes to address heterogeneity and error magnitudes.
result AdapDISCOM consistently outperforms existing methods under heterogeneous contamination and heavy-tailed distributions.

New risk measure and quadrangle improve financial decision-making.

problem Heterogeneous risk assessments among analysts.
method Established analytical characterizations of WGRM and incorporated FRQ into WRQ.
result WGRM and WRQ framework improves risk-adjusted performance and downside resilience.

The paper provides theoretical guarantees for optimized sampling in compressed sensing, showing error vanishes with more measurements.

problem Theoretical and practical improvements in compressed sensing with optimized sampling schemes.
method Theoretical analysis and empirical experiments with optimized sampling schemes for subsampled unitary matrices.
result The error caused by measurement noise vanishes with an increasing number of measurements for optimized sampling schemes, assuming Gaussian noise.

We study the total least squares (TLS) problem that generalizes least squares regression by allowing measurement errors in both dependent and independent variables. TLS is widely used in applied fields including computer vision, system identification and econometrics. The special case when all dependent and independent…

2014-06-01abs ↗pdf ↗

Study recovers community structure from coarse graph measurements.

problem Community recovery from low-resolution graph measurements.
method Formalized coarsening process of graph measurements, developed conditions for perfect recovery.
result Simple and closed-form asymptotic conditions for perfect recovery of coarse graph communities.

New findings on neural networks with non-negative weights and low training error.

problem Does a low training error imply a small outer norm for two-layer neural networks?
method Covering number argument and fat-shattering dimension analysis.
result For non-negative output weights, low training error guarantees a well-controlled outer norm.

PIE-PINN estimates elastic properties from noisy, low-res displacement data.

problem Estimating heterogeneous elastic properties from low-resolution, noisy data.
method Probabilistic Physics-Informed Neural Network (PIE-PINN) framework combining B-spline and hierarchical scale model.
result Robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data.

A new weighted MCC measure improves classifier performance evaluation.

problem Lack of measures sensitive to observation weights in multiclass classification.
method Proposes weighted versions of Pearson-Matthews Correlation Coefficient (MCC) for binary and multiclass classification.
result Weighted MCC values are higher for classifiers that perform better on highly weighted observations.

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.

Proposes HeteroJIVE for joint subspace estimation in multi-view data with statistical and structural heterogeneity.

problem Joint subspace estimation in multi-view data with varying statistical and structural heterogeneity.
method HeteroJIVE: A weighted two-stage spectral algorithm addressing statistical and structural heterogeneity.
result HeteroJIVE achieves the O(K1/2)O(K^{-1/2}) rate without iterative refinement, validating the oracle-optimal weighting scheme.

This paper analyzes SGD with increasingly weighted averaging for optimization and generalization.

problem Improving optimization and generalization for non-strongly convex objectives.
method Comprehensive analysis of increasingly weighted averaging schemes for convex, strongly convex, and non-convex objectives.
result The weight αα affects both optimization and generalization errors, revealing a trade-off.

We propose a novel method for compressed sensing recovery using untrained deep generative models. Our method is based on the recently proposed Deep Image Prior (DIP), wherein the convolutional weights of the network are optimized to match the observed measurements. We show that this approach can be applied to solve any…

2018-06-17abs ↗pdf ↗

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.

The paper proposes a method to improve random forest classification accuracy by weighting trees based on their decision path reliability.

problem Random forests' uniform voting fails to correct errors in regions where incorrect tree representations outnumber correct ones.
method The paper introduces using the structural pattern of each tree's decision path as an instance-adaptive reliability signal to identify and weight more reliable trees.
result Using the proposed method yields a statistically significant accuracy improvement over RF on 36 binary classification benchmarks.

New neural network rates for unbounded domains with weighted Sobolev spaces.

problem Improving neural network approximation rates for unbounded domains.
method Embedding results for weighted Fourier-Lebesgue spaces in weighted Sobolev spaces, followed by asymptotic approximation rates.
result Asymptotic approximation rates for shallow neural networks without curse of dimensionality for unbounded domains and Muckenhoupt weights.

Study excess capacity in neural networks using Rademacher complexity.

problem Understanding how much capacity deep networks have beyond what's needed for classification.
method Unified Rademacher complexity bounds for function composition and convolutional layers, considering Lipschitz constants and initialization norms.
result There is substantial excess capacity per task, and capacity can be kept similar across different tasks.

Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is evaluated on the estimated mixture instead of the (unknown) true one, then it is impor…

2017-10-09abs ↗pdf ↗

New weighted surface area measures for convex bodies with applications.

problem Generalizing surface area measures to weighted Borel measures.
method Formulating and analyzing weighted surface area measures, proving integral formula and Bézout-type inequality.
result New integral formula for mixed measure of three bodies, generalizing Bézout-type inequality.

Method measures weight similarity in neural networks using normalization and statistical inference.

problem Quantifying weight similarity in non-convex neural networks.
method Chain normalization rule and hypothesis-training-testing statistical inference.
result Weights of identical neural networks converge to similar local solutions.