Related papers: Wasserstein Logistic Regression with Mixed Feature…
Logistic regression is the most commonly used method for constructing predictive models for binary responses. One significant drawback to this approach, however, is that the asymptotes of the logistic response function are fixed at 0 and 1,…
Composite quantile regression has been used to obtain robust estimators of regression coefficients in linear models with good statistical efficiency. By revealing an intrinsic link between the composite quantile regression loss function and…
Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences. Existing data-driven non-parametric…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
In this paper, we develop a simulation-based framework for regularized logistic regression, exploiting two novel results for scale mixtures of normals. By carefully choosing a hierarchical model for the likelihood by one type of mixture,…
Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…
Robust estimators and Wald-type tests are developed for the multinomial logistic regression based on $\phi$-divergence measures. The robustness of the proposed estimators and tests is proved through the study of their influence functions…
We study the cyclic inventory routing problem that involves joint decisions on vehicle routing and inventory replenishment on an infinite, cyclic horizon. It considers a single warehouse and a set of geographically dispersed retailers. We…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
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…
We study a class of distributionally robust games where agents are allowed to heterogeneously choose their risk aversion with respect to distributional shifts of the uncertainty. In our formulation, heterogeneous Wasserstein ball…
Algorithmic robust statistics has traditionally focused on the contamination model where a small fraction of the samples are arbitrarily corrupted. We consider a recent contamination model that combines two kinds of corruptions: (i) small…
A data-driven MPC scheme is proposed to safely control constrained stochastic linear systems using distributionally robust optimization. Distributionally robust constraints based on the Wasserstein metric are imposed to bound the state…
We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…
The problem of learning functions over spaces of probabilities - or distribution regression - is gaining significant interest in the machine learning community. A key challenge behind this problem is to identify a suitable representation…
We present a Distributionally Robust Optimization (DRO) approach to estimate a robustified regression plane in a linear regression setting, when the observed samples are potentially contaminated with adversarially corrupted outliers. Our…
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…
In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A…
Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are…
This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…