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Tag: variance

  • Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Data

    Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Data arXiv:2602.23602v1 Announce Type: new Abstract: Heteroscedasticity — where the variance of a variable changes with other variables — is pervasive in real data, and elucidating why it arises from the perspective of statistical moments is crucial in scientific knowledge discovery and decision-making. However,…

  • A General Weighting Theory for Ensemble Learning: Beyond Variance Reduction via Spectral and Geometric Structure

    A General Weighting Theory for Ensemble Learning: Beyond Variance Reduction via Spectral and Geometric Structure arXiv:2512.22286v1 Announce Type: new Abstract: Ensemble learning is traditionally justified as a variance-reduction strategy, explaining its strong performance for unstable predictors such as decision trees. This explanation, however, does not account for ensembles constructed from intrinsically stable estimators-including smoothing splines,…

  • On the Effect of Regularization on Nonparametric Mean-Variance Regression

    On the Effect of Regularization on Nonparametric Mean-Variance Regression arXiv:2511.22004v1 Announce Type: new Abstract: Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty quantification. However, overparameterized mean-variance models struggle with signal-to-noise…

  • Variance-Bounded Evaluation without Ground Truth: VB-Score

    Variance-Bounded Evaluation without Ground Truth: VB-Score arXiv:2509.22751v1 Announce Type: new Abstract: Reliable evaluation is a central challenge in machine learning when tasks lack ground truth labels or involve ambiguity and noise. Conventional frameworks, rooted in the Cranfield paradigm and label-based metrics, fail in such cases because they cannot assess how robustly a system performs under…

  • Jackknife Variance Estimation for H’ajek-Dominated Generalized U-Statistics

    Jackknife Variance Estimation for H’ajek-Dominated Generalized U-Statistics arXiv:2509.12356v1 Announce Type: cross Abstract: We prove ratio-consistency of the jackknife variance estimator, and certain variants, for a broad class of generalized U-statistics whose variance is asymptotically dominated by their H’ajek projection, with the classical fixed-order case recovered as a special instance. This H’ajek projection dominance condition unifies…

  • Uncertainty Estimation using Variance-Gated Distributions

    Uncertainty Estimation using Variance-Gated Distributions arXiv:2509.08846v1 Announce Type: cross Abstract: Evaluation of per-sample uncertainty quantification from neural networks is essential for decision-making involving high-risk applications. A common approach is to use the predictive distribution from Bayesian or approximation models and decompose the corresponding predictive uncertainty into epistemic (model-related) and aleatoric (data-related) components. However, additive decomposition…

  • Optimal Variance and Covariance Estimation under Differential Privacy in the Add-Remove Model and Beyond

    Optimal Variance and Covariance Estimation under Differential Privacy in the Add-Remove Model and Beyond arXiv:2509.04919v1 Announce Type: new Abstract: In this paper, we study the problem of estimating the variance and covariance of datasets under differential privacy in the add-remove model. While estimation in the swap model has been extensively studied in the literature, the…

  • A Scalable Gradient-Based Optimization Framework for Sparse Minimum-Variance Portfolio Selection

    A Scalable Gradient-Based Optimization Framework for Sparse Minimum-Variance Portfolio Selection arXiv:2505.10099v1 Announce Type: new Abstract: Portfolio optimization involves selecting asset weights to minimize a risk-reward objective, such as the portfolio variance in the classical minimum-variance framework. Sparse portfolio selection extends this by imposing a cardinality constraint: only $k$ assets from a universe of $p$ may…

  • Variance Reduction via Resampling and Experience Replay

    Variance Reduction via Resampling and Experience Replay arXiv:2502.00520v1 Announce Type: new Abstract: Experience replay is a foundational technique in reinforcement learning that enhances learning stability by storing past experiences in a replay buffer and reusing them during training. Despite its practical success, its theoretical properties remain underexplored. In this paper, we present a theoretical framework…

  • On weight and variance uncertainty in neural networks for regression tasks

    On weight and variance uncertainty in neural networks for regression tasks arXiv:2501.04272v1 Announce Type: new Abstract: We consider the problem of weight uncertainty proposed by [Blundell et al. (2015). Weight uncertainty in neural network. In International conference on machine learning, 1613-1622, PMLR.] in neural networks {(NNs)} specialized for regression tasks. {We further} investigate the effect…

  • Confidence Interval Construction and Conditional Variance Estimation with Dense ReLU Networks

    Confidence Interval Construction and Conditional Variance Estimation with Dense ReLU Networks arXiv:2412.20355v1 Announce Type: new Abstract: This paper addresses the problems of conditional variance estimation and confidence interval construction in nonparametric regression using dense networks with the Rectified Linear Unit (ReLU) activation function. We present a residual-based framework for conditional variance estimation, deriving nonasymptotic bounds…

  • On the Precise Asymptotics and Refined Regret of the Variance-Aware UCB Algorithm

    On the Precise Asymptotics and Refined Regret of the Variance-Aware UCB Algorithm arXiv:2412.08843v1 Announce Type: new Abstract: In this paper, we study the behavior of the Upper Confidence Bound-Variance (UCB-V) algorithm for Multi-Armed Bandit (MAB) problems, a variant of the canonical Upper Confidence Bound (UCB) algorithm that incorporates variance estimates into its decision-making process. More…