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This paper deals with the problem of accurately determining guaranteed suboptimal values of an unknown cost function on the basis of noisy measurements. We consider a set-valued variant to regression where, instead of finding a best…

Optimization and Control · Mathematics 2024-07-29 Jaap Eising , Jorge Cortes

The shadow price of information has played a central role in stochastic optimization ever since its introduction by Rockafellar and Wets in the mid-seventies. This article studies the concept in an extended formulation of the problem and…

Optimization and Control · Mathematics 2016-01-21 Teemu Pennanen , Ari-Pekka Perkkiö

We develop a novel application of hybrid information divergences to analyze uncertainty in steady-state subsurface flow problems. These hybrid information divergences are non-intrusive, goal-oriented uncertainty quantification tools that…

Probability · Mathematics 2019-07-05 Eric Joseph Hall , Markos A. Katsoulakis

This paper is concerned with personalized pricing models aimed at maximizing the expected revenues or profits for a single item. While it is essential for personalized pricing to predict the purchase probabilities for each consumer, these…

Optimization and Control · Mathematics 2024-07-23 Shunnosuke Ikeda , Naoki Nishimura , Noriyoshi Sukegawa , Yuichi Takano

A seller sells an object over time but is uncertain how the buyer learns their willingness-to-pay. We consider informational robustness under \textit{limited commitment}, where the seller offers a price \textit{each period} to maximize…

Theoretical Economics · Economics 2025-09-10 Zihao Li , Jonathan Libgober , Xiaosheng Mu

We model an informed agent with information about the future value of an asset trying to maximize profits when subjected to a transaction cost as well as a market maker tasked with setting fair transaction prices. In a single auction model,…

Trading and Market Microstructure · Quantitative Finance 2020-07-29 Weston Barger , Ryan Donnelly

We consider a one-period Kyle (1985) framework where the insider can be subject to a penalty if she trades. We establish existence and uniqueness of equilibrium for virtually any penalty function when noise is uniform. In equilibrium, the…

Trading and Market Microstructure · Quantitative Finance 2018-09-21 Sylvain Carré , Pierre Collin-Dufresne , Franck Gabriel

We study statistical parameter estimation in the setting of data markets. A buyer seeks to estimate a parameter based on samples that can be purchased from competing providers that differ in their data quality and provision costs. When…

Computer Science and Game Theory · Computer Science 2026-04-13 Yuchen Hu , Martin J. Wainwright , Stephen Bates

Recently, many self-supervised learning methods for image reconstruction have been proposed that can learn from noisy data alone, bypassing the need for ground-truth references. Most existing methods cluster around two classes: i) Stein's…

Machine Learning · Statistics 2025-02-12 Julián Tachella , Mike Davies , Laurent Jacques

This paper tackles challenges in pricing and revenue projections due to consumer uncertainty. We propose a novel data-based approach for firms facing unknown consumer type distributions. Unlike existing methods, we assume firms only observe…

Theoretical Economics · Economics 2024-05-28 Duarte Gonçalves , Bruno A. Furtado

We study a single-buyer pricing problem with unreliable side information, motivated by the increasing use of AI-assisted decision-making and LLM-based predictions. The seller observes a private sample that may be either accurate (coinciding…

Computer Science and Game Theory · Computer Science 2026-04-06 Zhihao Gavin Tang , Yixin Tao , Shixin Wang

Prediction markets are often described as mechanisms that ``aggregate information'' into prices, yet the mapping from dispersed private information to observed market histories is typically noisy, endogenous, and shaped by heterogeneous and…

Mathematical Finance · Quantitative Finance 2026-01-28 Juan Pablo Madrigal-Cianci , Camilo Monsalve Maya , Lachlan Breakey

For multiple reasons -- such as avoiding overtraining from one data set or because of having received numerical estimates for some parameters in a model from an alternative source -- it is sometimes useful to divide a model's parameters…

Methodology · Statistics 2024-06-26 Yunrong Wan

We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…

Statistics Theory · Mathematics 2017-11-27 Oliver Lang , Michael Lunglmayr , Mario Huemer

Interference between treated and untreated units is a source of bias in marketplace experiments. In this paper, we specifically consider pricing interventions, in which a platform seeks to adjust base pricing levels at the marketplace level…

Optimization and Control · Mathematics 2025-02-27 Arthur Delarue , Kleanthis Karakolios

We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all…

Systems and Control · Electrical Eng. & Systems 2025-11-17 Martina Vanelli , Nima Monshizadeh , Julien M. Hendrickx

This paper discusses a class of uncertain optimization problems, in which unknown parameters are modeled by fuzzy intervals. The membership functions of the fuzzy intervals are interpreted as possibility distributions for the values of the…

Data Structures and Algorithms · Computer Science 2020-09-15 Adam Kasperski , Pawel Zielinski

In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations,…

Applications · Statistics 2019-11-20 Andrea Cappozzo , Francesca Greselin , Thomas Brendan Murphy

We develop a stochastic equilibrium model for an electricity market with asymmetric renewable energy forecasts. In our setting, market participants optimize their profits using public information about a conditional expectation of energy…

Optimization and Control · Mathematics 2020-05-26 Vladimir Dvorkin , Jalal Kazempour , Pierre Pinson

A major challenge in sparsity pattern estimation is that small modes are difficult to detect in the presence of noise. This problem is alleviated if one can observe samples from multiple realizations of the nonzero values for the same…

Information Theory · Computer Science 2011-07-29 Galen Reeves , Michael Gastpar
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