Study shows exponential error reduction in multiclass classification without bias-variance trade-off.
problem Multiclass classification with margin conditions.
method Analysis of classification error under hard-margin conditions.
result Exponential decrease in classification error without bias-variance trade-off.
Paper explores robust regression methods and their bias-variance trade-off.
problem Understanding the trade-off between robust estimation and optimization methods.
method Examines traditional outlier-resistant robust estimation and robust optimization.
result Both methods follow converse strategies due to a bias-variance trade-off.
The paper explores the trade-off between bias and variance in high-dimensional models.
problem Understanding the unavoidable trade-off between bias and variance in high-dimensional statistical models.
method Proposes a general strategy to obtain lower bounds on the variance of estimators with a specified bias, and applies it to various statistical models.
result Shows the extent to which the bias-variance trade-off is unavoidable and quantifies the performance loss for methods that do not balance it.
In this paper, we provide a theoretical understanding of word embedding and its dimensionality. Motivated by the unitary-invariance of word embedding, we propose the Pairwise Inner Product (PIP) loss, a novel metric on the dissimilarity between word embeddings. Using techniques from matrix perturbation theory, we revea…
Hierarchical probabilistic models are able to use a large number of parameters to create a model with a high representation power. However, it is well known that increasing the number of parameters also increases the complexity of the model which leads to a bias-variance trade-off. Although it is a classical problem, t…
New algorithm offers costless model selection in contextual bandits.
problem Minimizing cumulative regret in stochastic contextual bandits.
method Gradually increasing class complexity and adapting to the simplest class with dominant estimation variance.
result Costless model selection is feasible under certain conditions, providing improved regret guarantees.
This paper analyzes bias-variance trade-off for clipped SFOMs, improving complexity guarantees for heavy-tailed noise.
problem Improving complexity guarantees for stochastic optimization methods with heavy-tailed noise.
method Novel analysis of bias-variance trade-off in gradient clipping for clipped SFOMs.
result Improved complexity guarantees for clipped SFOMs across various tail indices, including infinite mean noise.
Vector embedding is a foundational building block of many deep learning models, especially in natural language processing. In this paper, we present a theoretical framework for understanding the effect of dimensionality on vector embeddings. We observe that the distributional hypothesis, a governing principle of statis…
Breakthroughs in machine learning are rapidly changing science and society, yet our fundamental understanding of this technology has lagged far behind. Indeed, one of the central tenets of the field, the bias-variance trade-off, appears to be at odds with the observed behavior of methods used in the modern machine lear…
New insights into bias and variance in over-parameterized models.
problem Understanding bias and variance in over-parameterized models.
method Analytic expressions derived from statistical physics for two minimal models.
result Over-parameterized models can overfit even in noiseless conditions.
Paper tackles bias-variance trade-off in missing data, proposing a dynamic framework.
problem Missing data in practical applications deteriorates model performance.
method Develops a fine-grained dynamic learning framework to jointly optimize bias and variance.
result Theoretical and empirical validation of joint bias-variance optimization.
The paper develops asymptotic theory for QRF variable importance, revealing a bias-variance trade-off.
problem Challenges in statistical inference for QRF variable importance due to non-smoothness and bias-variance trade-off.
method Developed asymptotic theory using pinball loss and Knight's identity, uncovered phase transition phenomenon, derived asymptotic bias.
result Theoretical foundation for understanding QRF inference limitations in high-dimensional settings.
FlexAE addresses bias-variance trade-off in RAEs by learning latent priors.
problem Improving generation quality of deterministic AE models.
method Introducing flexibly learnable latent priors in WAEs to optimize the latent distribution.
result FlexAE achieves state-of-the-art performance in AE-based generative models.
Paper analyzes LPSA algorithm for constrained optimization, revealing phase transitions and bias-variance trade-offs.
problem Optimization problems with linear constraints.
method Loopless projection stochastic approximation (LPSA) with jump diffusion approximation.
result LPSA trajectories converge to SDEs, revealing asymptotic behaviors and phase transitions.
The paper addresses Qini curve estimation under clustered network interference.
problem Qini curves can be biased when interference is ignored in clustered network settings.
method Proposes three estimation strategies for clustered network interference.
result Identifies the most appropriate approach based on bias-variance trade-offs.
XEM improves multivariate time series classification with explainable models.
problem Multivariate time series classification challenges.
method Hybrid ensemble method combining explicit boosting-bagging and implicit divide-and-conquer.
result XEM outperforms state-of-the-art MTS classifiers on public datasets.
RS-PINN uses randomized smoothing to speed up high-dimensional PDE simulations without sacrificing accuracy.
problem High computational cost and bias in PINNs for high-dimensional PDEs.
method Introduces Gaussian noise for stochastic smoothing of PINNs, enabling Monte Carlo derivative approximation.
result Proposes bias correction techniques and a hybrid method to optimize the bias-variance trade-off.
Analyzes bias-variance in overparameterized linear models using random features.
problem Understanding bias-variance trade-off in overparameterized models.
method Zero-temperature cavity method and random matrix theory.
result Three phase transitions in the linear random features model.
Unified theory explains diversity in ensemble learning.
problem Explaining diversity in ensemble learning across various scenarios.
method Developed a framework revealing diversity as a hidden dimension in bias-variance decomposition.
result Proved exact bias-variance-diversity decompositions for multiple losses in regression and classification.
Optimizes weights for better model performance in shifting data.
problem Improper importance weighting leads to poor model performance in data shifts.
method Interprets weights as a bias-variance trade-off and optimizes them simultaneously with model parameters.
result Optimizing weights significantly improves model generalization performance.
New theory explains how overparametrized neural networks generalize well without bias-variance trade-off.
problem Overparametrized neural networks generalize well despite classical bias-variance trade-off.
method Nonasymptotic generalization theory for two-layer neural networks with ReLU activation, incorporating scaled variation regularization.
result Prediction bounds for all network widths reproduce the double descent phenomenon, and overparametrized models are nearly minimax optimal.
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.
Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE ex…
GCNs improve regression tasks by aggregating neighbor signals.
problem GCNs' statistical properties in regression tasks are poorly understood.
method Examined two GCN convolutions and their impact on learning error.
result GCNs have a bias-variance trade-off that depends on neighborhood size and topology.
This study optimizes model averaging for personalized collaborative learning.
problem Differences in data or objectives between nodes in federated learning.
method Weighted averaging between local and global models for scalar mean estimation.
result There is always some positive model averaging that reduces expected squared error.
AWNN improves matrix completion by adaptively weighting nearest neighbors.
problem Matrix completion with optimal nearest neighbor weights and radii selection.
method Adaptively weighted nearest neighbor method for matrix completion.
result Theoretical guarantees and synthetic experiments support the effectiveness of AWNN.
Study explores bias-variance in adversarial machine learning.
problem Understanding adversarial machine learning's impact on bias and variance.
method Investigates bias-variance trade-offs in deep neural networks using MSE and cross-entropy.
result Derives bias-variance trade-offs for classification and regression.
Study on neural networks' performance under different normalizations as N grows.
problem Characterizing neural networks' performance under various normalizations.
method Developed an asymptotic expansion to analyze statistical output of shallow neural networks.
result No bias-variance trade-off exists to leading order in N, and variance decreases as normalization approaches mean field.
Random Forests automatically prune a latent 'true' tree, explaining their overfitting without tuning.
problem Difficulty in building bad Random Forests and overfitting without apparent consequences.
method Bootstrap aggregation and model perturbation in Random Forests.
result Randomized ensembles implicitly perform optimal early stopping out-of-sample, explaining overfitting.
VRER selectively reuses past observations to reduce variance in policy optimization.
problem Lack of effective experience replay for accelerating policy optimization in complex systems.
method Variance Reduction Experience Replay (VRER) framework that selectively reuses informative samples.
result VRER reduces gradient variance and improves policy learning over state-of-the-art algorithms.
Paper introduces a new power-dominance axis in estimator design.
problem Estimator design trade-off between bias and variance.
method Introduces a third power regime, `power-dominant', with an unavoidable error penalty.
result Any estimator in the `power-dominant' regime is structurally sub-optimal.
We analyze Gibbs-based transfer learning algorithms using information theory.
problem Understanding the generalization error of transfer learning.
method Information-theoretic analysis focusing on α-weighted-ERM and two-stage-ERM. result Exact characterization of generalization behavior using conditional symmetrized KL information.
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.
Kernel-smoothed scores improve diffusion models by reducing memorization.
problem Diffusion models can memorize training data, leading to biased samples.
method Interpret empirical score as noisy version of true score, kernel-smoothed.
result Kernel-smoothing reduces variance and improves generalization.
In this paper, we study the performance of extremum estimators from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. By adapting the classical concentration inequalities, we derive upper bounds on the empirical out-of-sample prediction e…
Gradient boosting for spatial regression models improves prediction accuracy.
problem Spatial data with autoregressive disturbances.
method Model-based gradient boosting algorithm for spatial regression models.
result Improves prediction accuracy on out-of-sample spatial data.
A new method interpolates between sampling and variational inference using stochastic mixtures.
problem Combining the strengths of sampling and variational inference methods.
method Develops a framework using stochastic mixtures of simple component distributions to interpolate between sampling and variational inference.
result Improves on both sampling and variational inference methods by reducing bias and variance.
Causal forests use honesty to reduce overfitting, but it can also reduce accuracy, especially with large datasets.
problem Causal forests' honesty can reduce accuracy of individual treatment effects.
method Using honest estimation to divide data into two samples, one for subgroup definition and another for effect estimation.
result Honest estimation can reduce accuracy by requiring 27% more data to match performance of non-honest models.
The classical bias-variance trade-off predicts that bias decreases and variance increase with model complexity, leading to a U-shaped risk curve. Recent work calls this into question for neural networks and other over-parameterized models, for which it is often observed that larger models generalize better. We provide …
Neural estimator improves mutual information estimation in high dimensions.
problem Estimating mutual information in high dimensions is challenging.
method Parametrizing conditional densities with normalizing flows and using block autoregressive structure.
result Improved mutual information estimation on benchmark tasks.
This paper improves generative models by using data scaling and theoretical analysis.
problem Challenges in selecting noise distributions for stable learning in generative models.
method Introduces Scale-GAN, which uses data scaling and variance-based regularization.
result Data scaling controls the bias-variance trade-off and improves stability and accuracy.
Improves Gaussian process regression without bias.
problem Bias in Gaussian process regression estimates.
method Adaptive computation selection to minimize bias.
result Guaranteed small bias in log marginal likelihood estimates.
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.
Reinforcement learning methods carry a well known bias-variance trade-off in n-step algorithms for optimal control. Unfortunately, this has rarely been addressed in current research. This trade-off principle holds independent of the choice of the algorithm, such as n-step SARSA, n-step Expected SARSA or n-step Tree bac…
New bandit algorithm works without realizability assumption.
problem Contextual bandit problems without realizability assumption.
method Computes a constrained regression problem in every epoch, ensuring similar regret guarantees as realizability-based algorithms.
result Ensures similar regret guarantees as realizability-based algorithms, up to a misspecification term.
Dealing with high variance is a significant challenge in model-free reinforcement learning (RL). Existing methods are unreliable, exhibiting high variance in performance from run to run using different initializations/seeds. Focusing on problems arising in continuous control, we propose a functional regularization appr…
Ensemble methods for classification and clustering have been effectively used for decades, while ensemble learning for outlier detection has only been studied recently. In this work, we design a new ensemble approach for outlier detection in multi-dimensional point data, which provides improved accuracy by reducing err…
Temporal Difference learning or TD(λ) is a fundamental algorithm in the field of reinforcement learning. However, setting TD's λ parameter, which controls the timescale of TD updates, is generally left up to the practitioner. We formalize the λ selection problem as a bias-variance trade-off where the solution is …