Related papers: Minimax D-optimal designs for multivariate regress…
We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…
Optimal designs are required to make efficient statistical experiments. D-optimal designs for some models are calculated by using canonical moments. On the other hand, integrable systems are dynamical systems whose solutions can be written…
Systems with both quantitative and qualitative responses are widely encountered in many applications. Design of experiment methods are needed when experiments are conducted to study such systems. Classic experimental design methods are…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…
There is increasing interest in modeling high-dimensional longitudinal outcomes in applications such as developmental neuroimaging research. Growth curve model offers a useful tool to capture both the mean growth pattern across individuals,…
Despite tremendous advancements of machine learning models and algorithms in various application domains, they are known to be vulnerable to subtle, natural or intentionally crafted perturbations in future input data, known as adversarial…
Cumulative link models have been widely used for ordered categorical responses. Uniform allocation of experimental units is commonly used in practice, but often suffers from a lack of efficiency. We consider D-optimal designs with ordered…
Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on Factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices…
A framework based on iterative coordinate minimization (CM) is developed for stochastic convex optimization. Given that exact coordinate minimization is impossible due to the unknown stochastic nature of the objective function, the crux of…
A meta-model of the input-output data of a computationally expensive simulation is often employed for prediction, optimization, or sensitivity analysis purposes. Fitting is enabled by a designed experiment, and for computationally expensive…
In this work we focus on saturated $D$-optimal designs. Using recent results, we identify $D$-optimal designs with the solutions of an optimization problem with linear constraints. We introduce new objective functions based on the geometric…
A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting…
Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…
Minimax designs provide a uniform coverage of a design space $\mathcal{X} \subseteq \mathbb{R}^p$ by minimizing the maximum distance from any point in this space to its nearest design point. Although minimax designs have many useful…
This paper considers structural optimization under a reliability constraint, where the input distribution is only partially known. Specifically, when we only know that the expected value vector and the variance-covariance matrix of the…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
In the context of structured nonconvex optimization, we estimate the increase in minimum value for a decision that is robust to parameter perturbations as compared to the value of a nominal problem. The estimates rely on detailed…
We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…
Reinforcement Learning is a powerful framework for training agents to navigate different situations, but it is susceptible to changes in environmental dynamics. However, solving Markov Decision Processes that are robust to changes is…
Optimal experimental design is an essential subfield of statistics that maximizes the chances of experimental success. The D- and A-optimal design is a very challenging problem in the field of optimal design, namely minimizing the…