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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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101203304405 · Jun 202019922001200920172026
48 results for bias terms

New analysis shows bias term affects conditions for benign overfitting in linear classifiers.

problem Understanding conditions for good generalization in linear classifiers with bias terms.
method Extending Hashimoto et al.'s results to include bias terms, analyzing covariance structure and label noise.
result Benign overfitting persists in linear classifiers with bias terms, with new constraints on data's covariance structure.

Study proposes a new method to estimate bias-correction term for ATE estimation.

problem Estimating the bias-correction term for ATE estimation.
method Directly estimating the bias-correction term by minimizing Bregman divergence.
result Automatic covariate balancing property achieved through specific model choices.

Paper analyzes LSA algorithm bias and error bounds with RR extrapolation.

problem Analyzing bias and high-order error bounds of LSA with Markovian noise.
method Polyak-Ruppert averaging, linearization, Richardson-Romberg extrapolation.
result RR extrapolation effectively cancels the leading bias term.

This work shows how penalising bias terms in norm regularisation leads to sparse solutions.

problem Understanding the relation between parameter norm regularization and the sparsity of neural network solutions.
method Analyzes one hidden ReLU layer networks with unidimensional data, showing the norm required for function representation and the importance of the bias term's norm.
result Penalising the bias terms in regularisation leads to sparse solutions, enforcing the uniqueness and sparsity of the minimal norm interpolator.

Gradient descent struggles with learning a single neuron with bias.

problem Learning a single neuron with a bias term in the realizable setting with ReLU activation.
method Theoretical study using gradient descent, characterizing critical points, and providing convergence guarantees.
result Gradient descent faces significant challenges in learning a single neuron with bias, unlike the bias-less case.

Study on bias and extrapolation in LSA with Markovian data, showing bias reduction with Richardson-Romberg extrapolation.

problem Bias in LSA with constant stepsizes and Markovian data.
method Viewing LSA as a Markov chain, proving convergence and bias expansion, and applying Richardson-Romberg extrapolation.
result Bias is proportional to the stepsize up to higher order terms, and Richardson-Romberg extrapolation reduces the bias.

New method reduces bias in incomplete data using deliberate missingness.

problem Systematic gradient biases in incomplete data for stochastic learning.
method Richardson-SGD debiasing procedure with deliberate missingness.
result Reduces gradient bias from O(p)O(\|p\|) to O(p2)O(\|p\|^2).

A hybrid strategy forecasts short-term loads using Warm-start Gradient Tree Boosting.

problem Lack of effective short-term load forecasting methods.
method Hybrid strategy integrating four different inference models: tree-based ensemble method Warm-start Gradient Tree Boosting (WGTB).
result Demonstrates effectiveness of hybrid strategy on real datasets.

New framework explains neural network bias in solving differential equations.

problem Understanding and controlling the bias in PINNs for differential equations.
method Deriving an integro-differential equation from PINNs and GPR equivalence.
result PINN predictions are influenced by a kernel term reflecting architecture choices.

We show how to convert ICL in linearized transformers into model weights.

problem Making in-context learning interpretable and permanent in large language models.
method Demonstrates equivalence between ICL and bias terms in linearized transformers, and develops ICLCA for exact conversion.
result Exact conversion of in-context learning into model weights is possible for linearized transformers.

Deep learning models show bias and variance are aligned, not in trade-off.

problem The classical bias-variance trade-off in deep learning models.
method Empirical evidence and theoretical analysis of bias and variance in deep learning models.
result Squared bias is approximately equal to variance for correctly classified sample points in deep learning models.

We study the implicit bias of generic optimization methods, such as mirror descent, natural gradient descent, and steepest descent with respect to different potentials and norms, when optimizing underdetermined linear regression or separable linear classification problems. We explore the question of whether the specifi…

2018-02-22abs ↗pdf ↗

The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.

problem The distribution of holonomy on compact hyperbolic 3-manifolds is not uniformly distributed.
method An asymptotic count of closed geodesics by their length and holonomy, and analysis of spectral parameters.
result A normalized, smoothed bias count of holonomy is distributed according to a probability distribution, controlled by the number of zero spectral parameters.

The paper analyzes the bias-variance tradeoff for Bregman divergences.

problem Understanding the bias-variance tradeoff for Bregman divergences.
method Analyzes the bias-variance tradeoff through operations in dual space.
result Derives several results including a generalized law of total variance and ensembling operations.

The bias potential model explains how generative models can generalize or memorize samples.

problem Understanding and achieving generalization in generative models like GANs.
method Introducing the bias potential model to analyze the behavior of generative models.
result Dimension-independent generalization accuracy can be achieved with early stopping in the bias potential model.

Deep learning models can have low bias and variance, contrary to classical theory.

problem Understanding the performance of deep learning models at high complexity.
method Developed a fine-grained bias-variance decomposition for random feature kernel regression, analyzing the effects of sampling, initialization, and labels.
result The variance terms exhibit non-monotonic behavior and can diverge at the interpolation boundary, even in the absence of label noise.

New method reduces bias in estimating causal effects from discretized variables.

problem Bias in estimating causal effects from discretized continuous variables.
method Proposes a bias-reduced functional that evaluates outcome regression at within-bin conditional means.
result Demonstrates substantial bias reduction and near-nominal confidence interval coverage.

UCBMQ improves Q-learning by adding momentum to correct bias and limit regret.

problem Improving Q-learning's bias and regret in reinforcement learning.
method UCBMQ combines Q-learning with an upper confidence bound and momentum term.
result UCBMQ guarantees a regret of O(H3SAT+H4SA)O(\sqrt{H^3SAT}+ H^4 S A ) with a linear second-order term in SS.

Mitigates bias in text classification by weighting instances.

problem Unintended biases in text classification datasets based on demographic terms.
method Instance weighting to recover non-discrimination distribution.
result Effective mitigation of unintended biases without sacrificing generalization.

New method controls bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin.

problem Bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin samplers.
method Delocalization of bias technique applied to these samplers.
result Control W2W_2 bias with O(K)O(\sqrt{K}) integration steps for high-dimensional distributions.

In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze existing solutions including finite-difference (FD) estimators and continuous relaxatio…

2018-09-29abs ↗pdf ↗

Jointly correct bias fields and reconstruct undersampled MRI images.

problem Recovering fully sampled MRI images from undersampled data while accounting for bias field differences.
method An unsupervised learning-based reconstruction algorithm combined with a N4-based bias field estimation method in a joint optimization scheme.
result The proposed method improves reconstruction quality, both visually and in terms of RMSE.

Paper analyzes convergence of decentralized algorithms with noise and bias.

problem Finite time convergence analysis of decentralized stochastic approximation schemes.
method Separated iterates into consensual parts and consensus error; bounded consensus error in terms of stationarity.
result Decentralized SA scheme converges at O(logT/T){\cal O}(\log T/ \sqrt{T} ) rate.

Deep convolutional networks can be understood through kernel methods, providing insights into their inductive bias.

problem Understanding the functional space and inductive bias of deep convolutional networks.
method Using kernel methods to analyze simple hierarchical kernels with convolution and pooling layers.
result The RKHS consists of additive models of interaction terms between patches, and pooling layers encourage spatial similarities.

Adversarial training leads to large generalization gap, decomposed into bias and variance.

problem Understanding the large generalization gap in adversarially trained models.
method Bias-Variance decomposition of test risk as a function of adversarial perturbation radius.
result Bias increases monotonically with adversarial perturbation radius and is dominant in test risk.

SGD in linear regression overfits but performs well due to bias-variance trade-off.

problem Understanding overfitting in SGD for linear regression.
method Constant-stepsize SGD with iterate averaging or tail averaging, analyzing full eigenspectrum of data covariance matrix.
result Sharp excess risk bounds revealing bias-variance decomposition for SGD in linear regression.

The paper analyzes optimal implicit bias in linear regression for over-parameterized models.

problem Finding the best generalization performance in over-parameterized linear regression.
method Asymptotic analysis of generalization performance for convex functions/potentials.
result Optimal implicit bias that achieves the best generalization error under certain conditions.