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Localized Uncertainty Quantification in Random Forests via Proximities
Jake S. Rhodes, Scott D. Brown, J. Riley Wilkinson
https://arxiv.org/abs/2509.22928 https://

Localized Uncertainty Quantification in Random Forests via Proximities
In machine learning, uncertainty quantification helps assess the reliability of model predictions, which is important in high-stakes scenarios. Traditional approaches often emphasize predictive accuracy, but there is a growing focus on incorporating uncertainty measures. This paper addresses localized uncertainty quantification in random forests. While current methods often rely on quantile regression or Monte Carlo techniques, we propose a new approach using naturally occurring test sets and s…

Unsupervised Conformal Inference: Bootstrapping and Alignment to Control LLM Uncertainty
Lingyou Pang, Lei Huang, Jianyu Lin, Tianyu Wang, Akira Horiguchi, Alexander Aue, Carey E. Priebe
https://arxiv.org/abs/2509.23002

Unsupervised Conformal Inference: Bootstrapping and Alignment to Control LLM Uncertainty
Deploying black-box LLMs requires managing uncertainty in the absence of token-level probability or true labels. We propose introducing an unsupervised conformal inference framework for generation, which integrates: generative models, incorporating: (i) an LLM-compatible atypical score derived from response-embedding Gram matrix, (ii) UCP combined with a bootstrapping variant (BB-UCP) that aggregates residuals to refine quantile precision while maintaining distribution-free, finite-sample cover…

On function-on-function linear quantile regression
Muge Mutis, Ufuk Beyaztas, Filiz Karaman, Han Lin Shang
https://arxiv.org/abs/2510.10792 https://arxiv.o…

On function-on-function linear quantile regression
We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms utilize functional partial quantile regression decomposition to effectively project the infinite-dimensional response and predictor variables onto a finite-dimensional space. Within this framework, the partial quantile regression components are approximated …

Risk level dependent Minimax Quantile lower bounds for Interactive Statistical Decision Making
Raghav Bongole, Amirreza Zamani, Tobias J. Oechtering, Mikael Skoglund
https://arxiv.org/abs/2510.05808

Risk level dependent Minimax Quantile lower bounds for Interactive Statistical Decision Making
Minimax risk and regret focus on expectation, missing rare failures critical in safety-critical bandits and reinforcement learning. Minimax quantiles capture these tails. Three strands of prior work motivate this study: minimax-quantile bounds restricted to non-interactive estimation; unified interactive analyses that focus on expected risk rather than risk level specific quantile bounds; and high-probability bandit bounds that still lack a quantile-specific toolkit for general interactive prot…

An efficient algorithm for kernel quantile regression
Shengxiang Deng, Xudong Li, Yangjing Zhang
https://arxiv.org/abs/2510.07929 https://arxiv.org/pdf/251…

An efficient algorithm for kernel quantile regression
Kernel Quantile Regression (KQR) extends classical quantile regression to nonlinear settings using kernel methods, offering powerful tools for modeling conditional distributions. However, its application to large-scale datasets is severely limited by the computational burden of the large, dense kernel matrix and the need to efficiently solve large, often ill-conditioned linear systems. Existing state-of-the-art solvers usually struggle with scalability. In this paper, we propose a novel and hig…

QDeepGR4J: Quantile-based ensemble of deep learning and GR4J hybrid rainfall-runoff models for extreme flow prediction with uncertainty quantification
Arpit Kapoor, Rohitash Chandra
https://arxiv.org/abs/2510.05453

QDeepGR4J: Quantile-based ensemble of deep learning and GR4J hybrid rainfall-runoff models for extreme flow prediction with uncertainty quantification
Conceptual rainfall-runoff models aid hydrologists and climate scientists in modelling streamflow to inform water management practices. Recent advances in deep learning have unravelled the potential for combining hydrological models with deep learning models for better interpretability and improved predictive performance. In our previous work, we introduced DeepGR4J, which enhanced the GR4J conceptual rainfall-runoff model using a deep learning model to serve as a surrogate for the routing comp…

Nonparametric Vector Quantile Autoregression
Alberto Gonz\'alez-Sanz, Marc Hallin, Yisha Yao
https://arxiv.org/abs/2510.03166 https://arxiv.org/pdf/251…

Nonparametric Vector Quantile Autoregression
Prediction is a key issue in time series analysis. Just as classical mean regression models, classical autoregressive methods, yielding L$^2$ point-predictions, provide rather poor predictive summaries; a much more informative approach is based on quantile (auto)regression, where the whole distribution of future observations conditional on the past is consistently recovered. Since their introduction by Koenker and Xiao in 2006, autoregressive quantile autoregression methods have become a popula…

An efficient hybrid approach of quantile and expectile regression
Abdellah Atanane, Abdallah Mkhadri, Karim Oualkacha
https://arxiv.org/abs/2510.05268 https://

An efficient hybrid approach of quantile and expectile regression
Quantiles and expectiles are determined by different loss functions: asymmetric least absolute deviation for quantiles and asymmetric squared loss for expectiles. This distinction ensures that quantile regression methods are robust to outliers but somewhat less effective than expectile regression, especially for normally distributed data. However, expectile regression is vulnerable to lack of robustness, especially for heavy-tailed distributions. To address this trade-off between robustness and…

Quantile-Scaled Bayesian Optimization Using Rank-Only Feedback
Tunde Fahd Egunjobi
https://arxiv.org/abs/2510.03277 https://arxiv.org/pdf/2510.03277…

Quantile-Scaled Bayesian Optimization Using Rank-Only Feedback
Bayesian Optimization (BO) is widely used for optimizing expensive black-box functions, particularly in hyperparameter tuning. However, standard BO assumes access to precise objective values, which may be unavailable, noisy, or unreliable in real-world settings where only relative or rank-based feedback can be obtained. In this study, we propose Quantile-Scaled Bayesian Optimization (QS-BO), a principled rank-based optimization framework. QS-BO converts ranks into heteroscedastic Gaussian targe…

Mean and quantile regression in the copula setting: properties, sharp bounds and a note on estimation
Henrik Kaiser, Wolfgang Trutschnig
https://arxiv.org/abs/2510.03804 https:/…

Mean and quantile regression in the copula setting: properties, sharp bounds and a note on estimation
Driven by the interest on how uniformity of marginal distributions propa\-gates to properties of regression functions, in this contribution we tackle the following questions: Given a $(d-1)$-dimensional random vector $\textbf{X}$ and a random variable $Y$ such that all univariate marginals of $(\textbf{X},Y)$ are uniformly distributed on $[0,1]$, how large can the average absolute deviation of the mean and the quantile regression function of $Y$ given $\textbf{X}$ from the value $\frac{1}{2}$ b…

A Data-Adaptive Factor Model Using Composite Quantile Approach
Seeun Park, Hee-Seok Oh
https://arxiv.org/abs/2510.00558 https://arxiv.org/pdf/2510.00558

A Data-Adaptive Factor Model Using Composite Quantile Approach
This paper proposes a data-adaptive factor model (DAFM), a novel framework for extracting common factors that explain the structures of high-dimensional data. DAFM adopts a composite quantile strategy to adaptively capture the full distributional structure of the data, thereby enhancing estimation accuracy and revealing latent patterns that are invisible to conventional factor models. In this paper, we develop a practical algorithm for estimating DAFM by minimizing an objective function based o…

Non-Asymptotic Analysis of Efficiency in Conformalized Regression
Yunzhen Yao, Lie He, Michael Gastpar
https://arxiv.org/abs/2510.07093 https://arxiv.org/p…

Non-Asymptotic Analysis of Efficiency in Conformalized Regression
Conformal prediction provides prediction sets with coverage guarantees. The informativeness of conformal prediction depends on its efficiency, typically quantified by the expected size of the prediction set. Prior work on the efficiency of conformalized regression commonly treats the miscoverage level $α$ as a fixed constant. In this work, we establish non-asymptotic bounds on the deviation of the prediction set length from the oracle interval length for conformalized quantile and median regre…

Neural Optimal Transport Meets Multivariate Conformal Prediction
Vladimir Kondratyev, Alexander Fishkov, Nikita Kotelevskii, Mahmoud Hegazy, Remi Flamary, Maxim Panov, Eric Moulines
https://arxiv.org/abs/2509.25444

Neural Optimal Transport Meets Multivariate Conformal Prediction
We propose a framework for conditional vector quantile regression (CVQR) that combines neural optimal transport with amortized optimization, and apply it to multivariate conformal prediction. Classical quantile regression does not extend naturally to multivariate responses, while existing approaches often ignore the geometry of joint distributions. Our method parametrizes the conditional vector quantile function as the gradient of a convex potential implemented by an input-convex neural network…

Differentially Private Learning of Exponential Distributions: Adaptive Algorithms and Tight Bounds
Bar Mahpud, Or Sheffet
https://arxiv.org/abs/2510.00790 https://

Differentially Private Learning of Exponential Distributions: Adaptive Algorithms and Tight Bounds
We study the problem of learning exponential distributions under differential privacy. Given $n$ i.i.d.\ samples from $\mathrm{Exp}(λ)$, the goal is to privately estimate $λ$ so that the learned distribution is close in total variation distance to the truth. We present two complementary pure DP algorithms: one adapts the classical maximum likelihood estimator via clipping and Laplace noise, while the other leverages the fact that the $(1-1/e)$-quantile equals $1/λ$. Each method excels in a d…

Comparative Analysis of Parameterized Action Actor-Critic Reinforcement Learning Algorithms for Web Search Match Plan Generation
Ubayd Bapoo, Clement N Nyirenda
https://arxiv.org/abs/2510.03064

Comparative Analysis of Parameterized Action Actor-Critic Reinforcement Learning Algorithms for Web Search Match Plan Generation
This study evaluates the performance of Soft Actor Critic (SAC), Greedy Actor Critic (GAC), and Truncated Quantile Critics (TQC) in high-dimensional decision-making tasks using fully observable environments. The focus is on parametrized action (PA) spaces, eliminating the need for recurrent networks, with benchmarks Platform-v0 and Goal-v0 testing discrete actions linked to continuous action-parameter spaces. Hyperparameter optimization was performed with Microsoft NNI, ensuring reproducibility…

Optimal placement of wind farms via quantile constraint learning
Wenxiu Feng, Antonio Alc\'antara, Carlos Ruiz
https://arxiv.org/abs/2510.01093 https://

Optimal placement of wind farms via quantile constraint learning
Wind farm placement arranges the size and the location of multiple wind farms within a given region. The power output is highly related to the wind speed on spatial and temporal levels, which can be modeled by advanced data-driven approaches. To this end, we use a probabilistic neural network as a surrogate that accounts for the spatiotemporal correlations of wind speed. This neural network uses ReLU activation functions so that it can be reformulated as mixed-integer linear set of constraints …

Adapting Noise to Data: Generative Flows from 1D Processes
Jannis Chemseddine, Gregor Kornhardt, Richard Duong, Gabriele Steidl
https://arxiv.org/abs/2510.12636 https://

Adapting Noise to Data: Generative Flows from 1D Processes
We introduce a general framework for constructing generative models using one-dimensional noising processes. Beyond diffusion processes, we outline examples that demonstrate the flexibility of our approach. Motivated by this, we propose a novel framework in which the 1D processes themselves are learnable, achieved by parameterizing the noise distribution through quantile functions that adapt to the data. Our construction integrates seamlessly with standard objectives, including Flow Matching an…

Replaced article(s) found for stat.ME. https://arxiv.org/list/stat.ME/new
[1/1]:
- Multiscale Quantile Regression with Local Error Control
Zhi Liu, Housen Li
ht…

Crosslisted article(s) found for math.ST. https://arxiv.org/list/math.ST/new
[1/1]:
- Quantile-Scaled Bayesian Optimization Using Rank-Only Feedback
Tunde Fahd Egunjobi