Publications de Soroosh Shafieezadeh Abadeh

Bridging Bayesian and Minimax Mean Square Error Estimation via Wasserstein Distributionally Robust Optimization

Peyman Mohajerin Esfahani, Viet Anh Nguyen, Daniel Kuhn, Soroosh Shafieezadeh Abadeh

We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zero-sum game between a statistician choosing a ...

2023

Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Bahar Taskesen

Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, ...

2023

Discrete Optimal Transport with Independent Marginals is #P-Hard

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Bahar Taskesen

We study the computational complexity of the optimal transport problem that evaluates the Wasser- stein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in th ...

2023

Wasserstein Distributionally Robust Learning

Soroosh Shafieezadeh Abadeh

Many decision problems in science, engineering, and economics are affected by uncertainty, which is typically modeled by a random variable governed by an unknown probability distribution. For many practical applications, the probability distribution is onl ...

EPFL2020

Regularization via Mass Transportation

Peyman Mohajerin Esfahani, Daniel Kuhn, Soroosh Shafieezadeh Abadeh

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, ...

2019

Calculating Optimistic Likelihoods Using (Geodesically) Convex Optimization

Viet Anh Nguyen, Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Wolfram Wiesemann

A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data, which makes them s ...

2019

Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

Viet Anh Nguyen, Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Wolfram Wiesemann

The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of the likelihood ...

2019

Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning

Peyman Mohajerin Esfahani, Viet Anh Nguyen, Daniel Kuhn, Soroosh Shafieezadeh Abadeh

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely many training s ...

2019

Wasserstein Distributionally Robust Kalman Filtering

Peyman Mohajerin Esfahani, Viet Anh Nguyen, Daniel Kuhn, Soroosh Shafieezadeh Abadeh

We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash equilibrium. Despit ...

2018

Data-Driven Inverse Optimization with Incomplete Information

Peyman Mohajerin Esfahani, Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Grani Adiwena Hanasusanto

In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent's objective function that best explains a historical ...

2018

Evolving Takagi-Sugeno model based on online Gustafson-Kessel algorithm and kernel recursive least square method

Soroosh Shafieezadeh Abadeh

In this paper, we introduce an evolving system utilizing sparse weighted kernel least square as local models and online Gustafson-Kessel clustering algorithm for structure identification. Our proposed online clustering algorithm forms elliptical clusters w ...

2016

Distributionally Robust Logistic Regression

Peyman Mohajerin Esfahani, Daniel Kuhn, Soroosh Shafieezadeh Abadeh

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ...

2015