We introduce the Statistical Equilibrium of Optimistic Beliefs (SE-OB) for mixed extension finite normal-form games, drawing insights from discrete choice theory. Departing conventional best responders Nash equilibrium and better quantal response equilibrium, we reconceptualize player behavior as that optimistic responders. In this setting, players assume their expected payoffs are subject to random perturbations, form beliefs by selecting distribution perturbations maximizes highest...

Algorithms are now routinely used to make consequential decisions that affect human lives. Examples include college admissions, medical interventions or law enforcement. While algorithms empower us harness all information hidden in vast amounts of data, they may inadvertently amplify existing biases the available datasets. This concern has sparked increasing interest fair machine learning, which aims quantify and mitigate algorithmic discrimination. Indeed, learning models should undergo...

We propose a distributionally robust logistic regression model with an unfairness penalty that prevents discrimination respect to sensitive attributes such as gender or ethnicity. This is equivalent tractable convex optimization problem if Wasserstein ball centered at the empirical distribution on training data used distributional uncertainty and new measure incentivize equalized opportunities. demonstrate resulting classifier improves fairness marginal loss of predictive accuracy both...

Abstract Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems ubiquitous in statistics, machine learning computer vision, however, this perception has not yet received theoretical justification. To fill gap, we prove that computing measure supported on two points Lebesgue standard hypercube is already $$\#$$ <mml:math...

We propose a change detection algorithm for hyperspectral images by properly extending the description of commonly used mutual information metric in monochrome to images. The newly extended additional spectral dimension accumulates effects all bands statistical relation between pixels two at same location. In order avoid blurring kind distortions maps resulting from usage fixed size kernels during calculation previous literature, proposed method first applies an oversegmentation and then,...

Linear-Quadratic-Gaussian (LQG) control is a fundamental paradigm that studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling system with linear dynamics imperfect observations, subject to additive noise, the goal of minimizing quadratic cost function for state variables. In this work, we consider generalization discrete-time, finite-horizon LQG problem, where noise distributions are unknown belong Wasserstein ambiguity sets...

.We study the computational complexity of optimal transport problem that evaluates Wasserstein distance between distributions two \(K\) -dimensional discrete random vectors. The best known algorithms for this run in polynomial time maximum number atoms distributions. However, if components either vector are independent, then can be exponential even though size description scales linearly with . We prove described is #P-hard all first independent uniform Bernoulli variables, while second has...

Özet—In this paper, a novel solution to the problem of unsupervised change detection in bitemporal satellite images is presented. Information measures, which are well-known and commonly-used literature, result unsharp maps masks without well defined boundaries as local computation. In proposed method, mutual information with joint distributions computed within over-segments after image registration, radiometric correction some preprocessing steps observed eliminate prob­lem sharpness....

Follow-The-Regularized-Leader (FTRL) algorithms often enjoy optimal regret for adversarial as well stochastic bandit problems and allow a streamlined analysis. Nonetheless, FTRL require the solution of an optimization problem in every iteration are thus computationally challenging. In contrast, Follow-The-Perturbed-Leader (FTPL) achieve computational efficiency by perturbing estimates rewards arms, but their analysis is cumbersome. We propose new FTPL algorithm that generates policies both...

In the past few years, there has been considerable interest in two prominent approaches for Distributionally Robust Optimization (DRO): Divergence-based and Wasserstein-based methods. The divergence approach models misspecification terms of likelihood ratios, while latter it through a measure distance or cost actual outcomes. Building upon these advances, this paper introduces novel that unifies methods into single framework based on optimal transport (OT) with conditional moment...

We study supervised learning problems for predicting properties of individuals who belong to one two demographic groups, and we seek predictors that are fair according statistical parity. This means the distributions predictions within groups should be close with respect Kolmogorov distance, fairness is achieved by penalizing dissimilarity these in objective function problem. In this paper, showcase conceptual computational benefits measuring unfairness integral probability metrics (IPMs)...

Algorithms are now routinely used to make consequential decisions that affect human lives. Examples include college admissions, medical interventions or law enforcement. While algorithms empower us harness all information hidden in vast amounts of data, they may inadvertently amplify existing biases the available datasets. This concern has sparked increasing interest fair machine learning, which aims quantify and mitigate algorithmic discrimination. Indeed, learning models should undergo...

We study the computational complexity of optimal transport problem that evaluates Wasserstein distance between distributions two K-dimensional discrete random vectors. The best known algorithms for this run in polynomial time maximum number atoms distributions. However, if components either vector are independent, then can be exponential K even though size description scales linearly with K. prove described is #P-hard all first independent uniform Bernoulli variables, while second has merely...

Least squares estimators, when trained on a few target domain samples, may predict poorly. Supervised adaptation aims to improve the predictive accuracy by exploiting additional labeled training samples from source distribution that is close distribution. Given available data, we investigate novel strategies synthesize family of least estimator experts are robust with regard moment conditions. When these conditions specified using Kullback-Leibler or Wasserstein-type divergences, can find...

Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems ubiquitous in statistics, machine learning computer vision, however, this perception has not yet received theoretical justification. To fill gap, we prove that computing measure supported on two points Lebesgue standard hypercube is already #P-hard. This insight prompts...