In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian structural equation models that can be represented as Andersson-Madigan-Perlman cha…
Bayesian method recovers causal structure in SEMs with equal error variances.
problem Recovering causal structure in SEMs with equal error variances.
method Bayesian DAG selection method using g-priors and the key property of minimum expected squared errors.
result The method consistently recovers the true graph without additional distributional assumptions.
This paper optimizes portfolio selection by penalizing tracking error, improving Sharpe ratio.
problem Optimizing portfolio allocation with a penalty for deviation from a reference portfolio.
method Formulated as a McKean-Vlasov control problem, provides explicit solutions and asymptotic expansions.
result The penalized portfolio strategy outperforms standard mean-variance and reference portfolios in most cases.
Optimal sample complexity for learning Gaussian DAG models established.
problem Learning the structure of Gaussian DAG models from observational data.
method Established minimax optimal sample complexity for two settings: equal variances without ordering knowledge and general linear models with ordering knowledge.
result Optimal sample complexity n≍qlog(d/q) for both settings, matching undirected graphical models under equal variances. We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed acyclic graph describing the relationships between the variables. In Gaussian structu…
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…
Proposes a modified Morgan-Pitman test for evaluating variances in machine learning models.
problem Limited ability to account for sampling variability in model selection.
method Enhances the classic Morgan-Pitman test for robustness in non-linear models with heavy-tailed distributions or outliers.
result Demonstrates the test's effectiveness and practical utility in model evaluation and selection.
In this work, we study robust deep learning against abnormal training data from the perspective of example weighting built in empirical loss functions, i.e., gradient magnitude with respect to logits, an angle that is not thoroughly studied so far. Consequently, we have two key findings: (1) Mean Absolute Error (MAE) D…
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.
New proof shows how to identify DAGs with weakly increasing errors.
problem Identifying the true DAG in models with weakly increasing error variances.
method Minimum-trace DAG method and hill climbing algorithm with R2R neighborhood.
result Hill climbing algorithm without strict local optima under weakly increasing error variances.
Improved heteroscedastic regression using neural networks with provably accurate mean estimates and calibrated variance.
problem Optimizing neural network parameters for heteroscedastic regression leads to suboptimal mean and variance estimates.
method Two simple modifications to optimization to retain accuracy of mean-only models and offer best-in-class variance calibration.
result Mean estimates from the proposed method are provably as accurate as those from a homoscedastic model.
Proposes ENVAR for causal discovery in structural VAR models with equal noise variance.
problem Challenges in causal discovery from multivariate time series with contemporaneous effects.
method Introduces observational equivalence and the observational alignment discrepancy for structural VAR models with equal noise variance.
result Shows that multiple structural VAR parameterizations can induce the same stationary observed process law.
VRSMD improves SMD convergence and has implicit regularization.
problem Efficiently estimating models with large datasets.
method Variance reduction in stochastic mirror descent.
result VRSMD converges to the minimum mirror interpolant.
The paper analyzes continuous optimization for DAG structure learning and its limitations.
problem The performance of continuous structure learning approaches is not consistent after data standardization.
method Analysis of continuous optimization for DAG structure learning, focusing on equal and non-equal noise variances.
result Continuous structure learning approaches may not perform well after data standardization, especially with non-equal noise variances.
Study reduces emissions in portfolios with error-prone emissions data.
problem Portfolio optimization with firm-level emissions intensities measured inaccurately.
method Introduced a scope-specific penalty operator to rescale asset payoffs based on revenue-normalized emissions intensity.
result Reduces average Scope~1 emissions intensity by roughly 92% while maintaining similar Sharpe ratios.
Empirical evidence shows that ensembles, such as bagging, boosting, random and rotation forests, generally perform better in terms of their generalization error than individual classifiers. To explain this performance, Schapire et al. (1998) developed an upper bound on the generalization error of an ensemble based on t…
PPI++ outperforms gold-standard labels only if pseudo-labels are highly correlated.
problem Optimizing statistical estimation using noisy pseudo-labels.
method Exact finite-sample analysis of PPI++ on mean estimation problem.
result PPI++ has provably worse estimation error than gold-standard labels alone in some settings.
Improved TD learning reduces variance and bias errors.
problem Inefficient optimization variance in TD learning.
method Proposed a mathematically solid analysis of VRTD, showing linear convergence rate and reduced variance and bias errors.
result VRTD converges to a fixed-point solution with reduced variance and bias errors compared to vanilla TD.
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.
This paper addresses error bounds and posterior variance for Gaussian process regression.
problem Deriving performance guarantees for Gaussian process regression without prior knowledge.
method Lipschitz continuity and analysis of posterior variance function.
result Uniform error bounds for Gaussian process regression are derived.
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose the natural lasso estimator for the error variance, which maximizes a penalized …
This work uses ANOVA to understand how different factors contribute to test error in machine learning models.
problem Understanding why overparametrized models generalize well despite potentially fitting noise.
method Analysis of variance (ANOVA) to decompose test error into components of variance.
result The interaction between training samples and initialization can dominate variance, and there are phase transitions in variance behavior.
Optimal estimator derived for partially observable LTI systems.
problem Optimal estimator for partially observable LTI systems.
method State-space representation for derivation of optimal estimator.
result Derivation of minimum error variance estimator for partially observable LTI systems.
The paper reconciles two conflicting fairness criteria in algorithmic risk scores.
problem How to reconcile calibration and equal error rates in algorithmic risk scores.
method Derive necessary and sufficient conditions for existence of calibrated scores achieving equal error rates, then present an algorithm to find the most accurate score subject to both criteria.
result The method can eliminate error disparities while maintaining calibration and improve profit in credit lending.
Stochastic gradient descent updates parameters with summation gradient computed from a random data batch. This summation will lead to unbalanced training process if the data we obtained is unbalanced. To address this issue, this paper takes the error variance and error mean both into consideration. The adaptively adjus…
Paper proposes diagnostics for error and variance estimation in randomized matrix computations.
problem Safe use of randomized matrix algorithms in applications.
method Leave-one-out error estimator and jackknife resampling method.
result Provides rapid diagnostics to assess quality of randomized matrix computations.
Optimizes embedding accuracy for data variance and error.
problem Efficiently embedding data while minimizing distortion.
method Uses Johnson-Lindenstrauss embeddings with orthogonal matrices and singular-value latent variables.
result Achieves best accuracy in variance, mean-squared error, and length distortion.
Proposes reducing random error in stochastic optimization by variance regularization.
problem Random error accumulation in stochastic optimization algorithms.
method Regularizes learning-rate based on mini-batch variances.
result Speeds up convergence and stabilizes stochastic optimization.
The bias-variance tradeoff tells us that as model complexity increases, bias falls and variances increases, leading to a U-shaped test error curve. However, recent empirical results with over-parameterized neural networks are marked by a striking absence of the classic U-shaped test error curve: test error keeps decrea…
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 presents a method to reduce prediction variance of DNNs for unknown systems.
problem Uncertainty in DNN predictions due to high variance.
method Ensemble averaging of multiple DNN models trained independently.
result Reduction in variance of DNN predictions, improving reliability.
In this work, we consider the identifiability assumption of Gaussian linear structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that linear Gaussian structural equation models are fully identifiable if all error va…
Scaling laws in linear regression explain model performance improvements with size and data.
problem Disagreement between empirical neural scaling laws and conventional wisdom on variance error.
method Infinite dimensional linear regression setup, one-pass SGD, Gaussian prior, power-law spectrum.
result Variance error is dominated by other errors, disappearing from the bound due to SGD's implicit regularization.
Investigates portfolio optimization with and without gearing constraints.
problem Improving portfolio weights for better alignment with expected returns.
method Extends the alpha-weight angle bound to include gearing constraints and uses theoretical arguments and simulations.
result Equally weighted portfolios are not preferable to mean-variance portfolios even with poor forecast ability and a badly conditioned covariance matrix.
Algorithm estimates common mean from Gaussian variables with unknown variances.
problem Estimating common mean from Gaussian variables with different unknown variances.
method Intuitive and efficient algorithm using Subset-of-Signals model as benchmark.
result Improved estimation error by polynomial factors compared to previous work.
In training speech recognition systems, labeling audio clips can be expensive, and not all data is equally valuable. Active learning aims to label only the most informative samples to reduce cost. For speech recognition, confidence scores and other likelihood-based active learning methods have been shown to be effectiv…
Generalizes bias-variance decomposition for Bregman divergences.
problem No specific problem stated; generalization of bias-variance for Bregman divergences.
method Provided a generalization of the bias-variance decomposition for Bregman divergences.
result A clear, standalone derivation of the bias-variance decomposition for Bregman divergences.
Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{é}r-Rao lower bound (efficiency bound), which is the minimum possible variance for an unbiased estimator. However, obtaining such MLE solution requires calculating t…
The paper examines prediction and estimation risks of ridgeless least squares under general error assumptions.
problem Prediction and estimation risks of ridgeless least squares under realistic error structures.
method Analysis of prediction and estimation risks under general regression error assumptions, including clustered or serial dependence.
result The benefits of overparameterization extend to time series, panel, and grouped data.
Paper solves dynamic portfolio selection using generative models.
problem Dynamic mean-variance portfolio selection problem in a model-free manner.
method Adaptive training and sampling methods for diffusion models, quantification bounds using adapted Wasserstein metric.
result Proposes a policy gradient algorithm that outperforms baselines on real data.
Analyzes error sources in global feature effect estimation methods.
problem Unexplored error sources in global feature effect estimation methods.
method Systematic, estimator-level analysis of bias and variance.
result Holdout data is theoretically cleanest, but estimation variance depends on sample size and model characteristics.
The paper develops estimators for variance in graph structures using fused lasso.
problem Variance estimation in graph-structured problems.
method Developed linear time estimator for homoscedastic case and total variation regularization estimator for heteroscedastic case.
result Minimax rates and consistency for variance estimation in various graph structures.
Proposes σ-PCA to learn identifiable linear transformations without whitening.
problem Cannot identify axes with equal variances in PCA.
method Unified model for linear and nonlinear PCA, introducing a missing piece to eliminate rotational indeterminacy.
result Eliminates subspace rotational indeterminacy in PCA.
There exist a number of reinforcement learning algorithms which learnby climbing the gradient of expected reward. Their long-runconvergence has been proved, even in partially observableenvironments with non-deterministic actions, and without the need fora system model. However, the variance of the gradient estimator ha…
The paper analyzes sparse high-dimensional linear regression with random design and unknown error variance, providing adaptiveness and concentration rates.
problem Sparse high-dimensional linear regression with random design and unknown error variance.
method Analysis of posterior concentration rates, employing techniques to address model misspecification.
result Adaptiveness and concentration rates of the posterior for sparse high-dimensional linear regression.
Proposes a new framework to optimize portfolios with reduced estimation errors.
problem Estimation errors in multiperiod mean-variance portfolio optimization.
method Reference-regulated multiperiod mean-variance (RRMV) framework.
result Improves portfolio stability and out-of-sample Sharpe ratios.
Optimizer memory affects learning rate sensitivity in shuffle order, impacting fine-tuning noise.
problem Optimizer memory affects the learning rate sensitivity in shuffle order, leading to fine-tuning noise.
method Isolated the mechanism of fixed-clock optimizer memory affecting the learning rate sensitivity in shuffle order, deriving a fit-free way to size the noise.
result Fixed-clock optimizers like AdamW produce a larger first-order noise channel compared to memoryless optimizers, affecting fine-tuning comparisons.
It has been noted in existing literature that over-parameterization in ReLU networks generally improves performance. While there could be several factors involved behind this, we prove some desirable theoretical properties at initialization which may be enjoyed by ReLU networks. Specifically, it is known that He initia…