mailitics

Tag: estimation

  • Partition Function Estimation under Bounded f-Divergence

    Partition Function Estimation under Bounded f-Divergence arXiv:2602.23535v1 Announce Type: new Abstract: We study the statistical complexity of estimating partition functions given sample access to a proposal distribution and an unnormalized density ratio for a target distribution. While partition function estimation is a classical problem, existing guarantees typically rely on structural assumptions about the domain or…

  • Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models

    Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models arXiv:2602.17830v1 Announce Type: new Abstract: We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate drift estimation as a denoising problem conditional on previous…

  • Privacy utility trade offs for parameter estimation in degree heterogeneous higher order networks

    Privacy utility trade offs for parameter estimation in degree heterogeneous higher order networks arXiv:2602.03948v1 Announce Type: new Abstract: In sensitive applications involving relational datasets, protecting information about individual links from adversarial queries is of paramount importance. In many such settings, the available data are summarized solely through the degrees of the nodes in the network.…

  • Constrained Density Estimation via Optimal Transport

    Constrained Density Estimation via Optimal Transport arXiv:2601.06830v1 Announce Type: new Abstract: A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of functions adopts or exceeds given values. The framework…

  • Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contamination

    Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contamination arXiv:2512.09266v1 Announce Type: new Abstract: We examine the non-asymptotic properties of robust density ratio estimation (DRE) in contaminated settings. Weighted DRE is the most promising among existing methods, exhibiting doubly strong robustness from an asymptotic perspective. This study demonstrates that Weighted DRE achieves sparse…

  • Estimation of Stochastic Optimal Transport Maps

    Estimation of Stochastic Optimal Transport Maps arXiv:2512.09499v1 Announce Type: new Abstract: The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing statistical theory for OT map estimation is quite restricted, hinging on Brenier’s theorem (quadratic cost,…

  • Gradient Boosted Mixed Models: Flexible Joint Estimation of Mean and Variance Components for Clustered Data

    Gradient Boosted Mixed Models: Flexible Joint Estimation of Mean and Variance Components for Clustered Data arXiv:2511.00217v1 Announce Type: new Abstract: Linear mixed models are widely used for clustered data, but their reliance on parametric forms limits flexibility in complex and high-dimensional settings. In contrast, gradient boosting methods achieve high predictive accuracy through nonparametric estimation, but…

  • The Minimax Lower Bound of Kernel Stein Discrepancy Estimation

    The Minimax Lower Bound of Kernel Stein Discrepancy Estimation arXiv:2510.15058v1 Announce Type: new Abstract: Kernel Stein discrepancies (KSDs) have emerged as a powerful tool for quantifying goodness-of-fit over the last decade, featuring numerous successful applications. To the best of our knowledge, all existing KSD estimators with known rate achieve $sqrt n$-convergence. In this work, we…

  • 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…

  • Robust variational neural posterior estimation for simulation-based inference

    Robust variational neural posterior estimation for simulation-based inference arXiv:2509.05724v1 Announce Type: new Abstract: Recent advances in neural density estimation have enabled powerful simulation-based inference (SBI) methods that can flexibly approximate Bayesian inference for intractable stochastic models. Although these methods have demonstrated reliable posterior estimation when the simulator accurately represents the underlying data generative process (GDP),…

  • 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…

  • Understanding and Improving the Shampoo Optimizer via Kullback-Leibler Minimization

    Understanding and Improving the Shampoo Optimizer via Kullback-Leibler Minimization arXiv:2509.03378v1 Announce Type: new Abstract: As an adaptive method, Shampoo employs a structured second-moment estimation, and its effectiveness has attracted growing attention. Prior work has primarily analyzed its estimation scheme through the Frobenius norm. Motivated by the natural connection between the second moment and a covariance…

  • Fundamental limits of distributed covariance matrix estimation via a conditional strong data processing inequality

    Fundamental limits of distributed covariance matrix estimation via a conditional strong data processing inequality arXiv:2507.16953v1 Announce Type: new Abstract: Estimating high-dimensional covariance matrices is a key task across many fields. This paper explores the theoretical limits of distributed covariance estimation in a feature-split setting, where communication between agents is constrained. Specifically, we study a scenario…

  • Applications of Density Estimation to Legal Theory

    Applications of Density Estimation to Legal Theory A brief analysis using density estimation to compare the two-verdict and three-verdict systems. The post Applications of Density Estimation to Legal Theory appeared first on Towards Data Science. Jimin Kang Go to original source

  • Non-Parametric Density Estimation: Theory and Applications

    Non-Parametric Density Estimation: Theory and Applications In this article, we’ll talk about what Density Estimation is and the role it plays in statistical analysis. We’ll analyze two popular density estimation methods, histograms and kernel density estimators, and analyze their theoretical properties as well as how they perform in practice. Finally, we’ll look at how density…

  • Fast Likelihood-Free Parameter Estimation for L’evy Processes

    Fast Likelihood-Free Parameter Estimation for L’evy Processes arXiv:2505.01639v1 Announce Type: new Abstract: L’evy processes are widely used in financial modeling due to their ability to capture discontinuities and heavy tails, which are common in high-frequency asset return data. However, parameter estimation remains a challenge when associated likelihoods are unavailable or costly to compute. We propose…

  • Statistical Learning for Heterogeneous Treatment Effects: Pretraining, Prognosis, and Prediction

    Statistical Learning for Heterogeneous Treatment Effects: Pretraining, Prognosis, and Prediction arXiv:2505.00310v1 Announce Type: new Abstract: Robust estimation of heterogeneous treatment effects is a fundamental challenge for optimal decision-making in domains ranging from personalized medicine to educational policy. In recent years, predictive machine learning has emerged as a valuable toolbox for causal estimation, enabling more flexible…

  • Causal rule ensemble approach for multi-arm data

    Causal rule ensemble approach for multi-arm data arXiv:2504.17166v1 Announce Type: new Abstract: Heterogeneous treatment effect (HTE) estimation is critical in medical research. It provides insights into how treatment effects vary among individuals, which can provide statistical evidence for precision medicine. While most existing methods focus on binary treatment situations, real-world applications often involve multiple interventions.…

  • Dose-finding design based on level set estimation in phase I cancer clinical trials

    Dose-finding design based on level set estimation in phase I cancer clinical trials arXiv:2504.09157v1 Announce Type: new Abstract: The primary objective of phase I cancer clinical trials is to evaluate the safety of a new experimental treatment and to find the maximum tolerated dose (MTD). We show that the MTD estimation problem can be regarded…

  • Density estimation via mixture discrepancy and moments

    Density estimation via mixture discrepancy and moments arXiv:2504.01570v1 Announce Type: new Abstract: With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed [D. Li, K. Yang, W. Wong, Advances in Neural Information Processing Systems (2016) 1099-1107] to learn an adaptive piecewise constant approximation…

  • A Meta-learner for Heterogeneous Effects in Difference-in-Differences

    A Meta-learner for Heterogeneous Effects in Difference-in-Differences arXiv:2502.04699v1 Announce Type: new Abstract: We address the problem of estimating heterogeneous treatment effects in panel data, adopting the popular Difference-in-Differences (DiD) framework under the conditional parallel trends assumption. We propose a novel doubly robust meta-learner for the Conditional Average Treatment Effect on the Treated (CATT), reducing the…

  • Median of Forests for Robust Density Estimation

    Median of Forests for Robust Density Estimation arXiv:2501.15157v1 Announce Type: new Abstract: Robust density estimation refers to the consistent estimation of the density function even when the data is contaminated by outliers. We find that existing forest density estimation at a certain point is inherently resistant to the outliers outside the cells containing the point,…

  • DPERC: Direct Parameter Estimation for Mixed Data

    DPERC: Direct Parameter Estimation for Mixed Data arXiv:2501.10540v1 Announce Type: new Abstract: The covariance matrix is a foundation in numerous statistical and machine-learning applications such as Principle Component Analysis, Correlation Heatmap, etc. However, missing values within datasets present a formidable obstacle to accurately estimating this matrix. While imputation methods offer one avenue for addressing this…

  • 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…

  • A Note on Estimation Error Bound and Grouping Effect of Transfer Elastic Net

    A Note on Estimation Error Bound and Grouping Effect of Transfer Elastic Net arXiv:2412.01010v1 Announce Type: new Abstract: The Transfer Elastic Net is an estimation method for linear regression models that combines $ell_1$ and $ell_2$ norm penalties to facilitate knowledge transfer. In this study, we derive a non-asymptotic $ell_2$ norm estimation error bound for the…