robust statistics

Distributionally Risk-Receptive and Robust Multistage Stochastic Integer Programs and Interdiction Models

  • Sumin Kang
  • Manish Bansal
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , , , , , ,

    In this paper, we study distributionally risk-receptive and distributionally robust (or risk-averse) multistage stochastic mixed-integer programs (denoted by DRR- and DRO-MSIPs). We present cutting plane-based and reformulation-based approaches for solving DRR- and DRO-MSIPs without and with decision-dependent uncertainty to optimality. We show that these approaches are finitely convergent with probability one. Furthermore, we introduce generalizations … Read more

    Distributionally Favorable Optimization: A Framework for Data-driven Decision-making with Endogenous Outliers

  • Nan Jiang
  • Weijun Xie
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    A typical data-driven stochastic program aims to seek the best decision that minimizes the sum of a deterministic cost function and an expected recourse function under a given distribution. Recently, much success has been witnessed in the development of Distributionally Robust Optimization (DRO), which considers the worst-case expected recourse function under the least favorable probability … Read more

    General risk measures for robust machine learning

  • Émilie Chouzenoux
  • Jean-Christophe Pesquet
  • Henri Gérard
    • Categories Convex Optimization, Robust Optimization, Stochastic Programming Tags , , , , ,

    A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often estimated from training sets, which may lead to poor out-of-sample performance. In this work, we … Read more

    Fast Robust Methods for Singular State-Space Models

  • Aleksandr Y. Aravkin
  • James V. Burke
  • Sarah Webster
  • Jonathan Jonker
  • Gianluigi Pillonetto
    • Categories Control Applications, Nonsmooth Optimization, Statistics Tags , ,

    State-space models are used in a wide range of time series analysis applications. Kalman filtering and smoothing are work-horse algorithms in these settings. While classic algorithms assume Gaussian errors to simplify estimation, recent advances use a broad range of optimization formulations to allow outlier-robust estimation, as well as constraints to capture prior information. Here we … Read more

    Portfolio Selection with Robust Estimation

  • Victor DeMiguel
  • Francisco Javier Nogales
    • Categories Finance and Economics, Robust Optimization Tags , , ,

    Mean-variance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly out-of-sample due to estimation error. Moreover, it is commonly accepted that estimation error in the sample mean is much larger than in the sample covariance matrix. For this reason, practitioners and researchers have recently focused on the minimum-variance portfolio, which … Read more