Related papers: Profile Likelihood via Optimisation and Differenti…
Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the…
Fisher's likelihood is widely used for statistical inference for fixed unknowns. This paper aims to extend two important likelihood-based methods, namely the maximum likelihood procedure for point estimation and the confidence procedure for…
The hazard function is central to the formulation of commonly used survival regression models such as the proportional hazards and accelerated failure time models. However, these models rely on a shared baseline hazard, which, when…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…
Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic…
The generalized varying coefficient partially linear model with growing number of predictors arises in many contemporary scientific endeavor. In this paper we set foot on both theoretical and practical sides of profile likelihood estimation…
In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(\xi^{-1} \log(1/\beta))$ (for generalization error $\xi$ with confidence $1-\beta$). The private…
This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number…
A method of calculating probability values from a system of marginal constraints is presented. Previous systems for finding the probability of a single attribute have either made an independence assumption concerning the evidence or have…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional is constrained by a partial differential equation (PDE)…
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,…
We study high-confidence behavior-agnostic off-policy evaluation in reinforcement learning, where the goal is to estimate a confidence interval on a target policy's value, given only access to a static experience dataset collected by…
For any class of one-sided $1-\alpha$ confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two…
Many real-world optimization problems involve uncertain parameters with probability distributions that can be estimated using contextual feature information. In contrast to the standard approach of first estimating the distribution of…
This article describes posterior maximization for topic models, identifying computational and conceptual gains from inference under a non-standard parametrization. We then show that fitted parameters can be used as the basis for a novel…
We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution…