Related papers: Best Subset Binary Prediction
This paper presents a computationally efficient method for binary classification using Manski's (1975,1985) maximum score model when covariates are discretely distributed and parameters are partially but not point identified. We establish…
Manski's celebrated maximum score estimator for the discrete choice model, which is an optimal linear discriminator, has been the focus of much investigation in both the econometrics and statistics literatures, but its behavior under…
This paper develops maximum score estimation of preference parameters in the binary choice model under uncertainty in which the decision rule is affected by conditional expectations. The preference parameters are estimated in two stages: we…
In this paper, we propose a novel Mixed-Integer Non-Linear Optimization formulation to construct a risk score, where we optimize the logistic loss with sparsity constraints. Previous approaches are typically designed to handle binary…
In this paper we study the applicability of the bootstrap to do inference on Manski's maximum score estimator under the full generality of the model. We propose three new, model-based bootstrap procedures for this problem and show their…
The maximum score estimator of Manski (1975) provides an elegant approach to estimate slope coefficient in binary choice models without requiring parametric assumptions on the error distribution. However, under i.i.d. sampling, it admits a…
Binary optimization has a wide range of applications in combinatorial optimization problems such as MaxCut, MIMO detection, and MaxSAT. However, these problems are typically NP-hard due to the binary constraints. We develop a novel…
Let $(Y,X_1,...,X_m)$ be a random vector. It is desired to predict $Y$ based on $(X_1,...,X_m)$. Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the…
We provide a finite sample inference method for the structural parameters of a semiparametric binary response model under a conditional median restriction originally studied by Manski (1975, 1985). Our inference method is valid for any…
The maximum score method (Manski, 1975, 1985) is a powerful approach for binary choice models, yet it is known to face both practical and theoretical challenges. In particular, the estimator converges at a slower-than-root-$n$ rate to a…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…
Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…
We consider selecting the top-$m$ alternatives from a finite number of alternatives via Monte Carlo simulation. Under a Bayesian framework, we formulate the sampling decision as a stochastic dynamic programming problem, and develop a…
We present a fully probabilistic approach for solving binary optimization problems with black-box objective functions and with budget constraints. In the probabilistic approach, the optimization variable is viewed as a random variable and…
Multinomial logistic regression models allow one to predict the risk of a categorical outcome with more than 2 categories. When developing such a model, researchers should ensure the number of participants (n) is appropriate relative to the…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…
This paper considers a variation of the full-information secretary problem where the random variables to be observed are independent but not necessary identically distributed. The main result is a sharp lower bound for the optimal win…
The paper is about developing a solver for maximizing a real-valued function of binary variables. The solver relies on an algorithm that estimates the optimal objective-function value of instances from the underlying distribution of…