Related papers: An Adaptive Algorithm based on High-Dimensional Fu…
The issue of determining not only an adequate dose but also a dosing frequency of a drug arises frequently in Phase II clinical trials. This results in the comparison of models which have some parameters in common. Planning such studies…
This paper presents a new and efficient method for the construction of optimal designs for regression models with dependent error processes. In contrast to most of the work in this field, which starts with a model for a finite number of…
The purpose of this short note is to show that the Christoffel-Darboux polynomial, useful in approximation theory and data science, arises naturally when deriving the dual to the problem of semi-algebraic D-optimal experimental design in…
The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large literature on empirical approaches to…
We consider the problem of identifying the most profitable product design from a finite set of candidates under unknown consumer preference. A standard approach to this problem follows a two-step strategy: First, estimate the preference of…
Optimal experimental design (OED) seeks experiments expected to yield the most useful data for some purpose. In practical circumstances where experiments are time-consuming or resource-intensive, OED can yield enormous savings. We pursue…
Consider the problem of constructing an experimental design, optimal for estimating parameters of a given statistical model with respect to a chosen criterion. To address this problem, the literature usually provides a single solution.…
Kernel Adaptive Filtering (KAF) are mathematically principled methods which search for a function in a Reproducing Kernel Hilbert Space. While they work well for tasks such as time series prediction and system identification they are…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…
Often computational models are too expensive to be solved in the entire domain of simulation, and a cheaper model would suffice away from the main zone of interest. We present for the concrete example of an evolution problem of advection…
Efficient algorithms for searching for optimal saturated designs are widely available. They maximize a given efficiency measure (such as D-optimality) and provide an optimum design. Nevertheless, they do not guarantee a \emph{global}…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
We propose an algorithm for an optimal adaptive selection of points from the design domain of input random variables that are needed for an accurate estimation of failure probability and the determination of the boundary between safe and…
We study a standard distributed optimization framework where $N$ networked nodes collaboratively minimize the sum of their local convex costs. The main body of existing work considers the described problem when the underling network is…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
Computing derivatives is a crucial subroutine in computer science and related fields as it provides a local characterization of a function's steepest directions of ascent or descent. In this work, we recognize that derivatives are often not…
In random allocation rules, typically first an optimal fractional point is calculated via solving a linear program. The calculated point represents a fractional assignment of objects or more generally packages of objects to agents. In order…
Modeling real processes often results in several suitable models. In order to be able to distinguish, or discriminate, which model best represents a phenomenon, one is interested, e.g., in so-called T-optimal designs. These consist of the…
Modern advanced manufacturing and advanced materials design often require searches of relatively high-dimensional process control parameter spaces for settings that result in optimal structure, property, and performance parameters. The…
We study a continuous-time, infinite-horizon dynamic bipartite matching problem. Suppliers arrive according to a Poisson process; while waiting, they may abandon the queue at a uniform rate. Customers on the other hand must be matched upon…