Related papers: On a Multiplicative Algorithm for Computing Bayesi…
We provide an optimization-based argument for the monotonicity of the multiplicative algorithm (MA) for a class of optimal experimental design problems considered in Yu (2010). Our proof avoids introducing auxiliary variables (or problems)…
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
We study a class of multiplicative algorithms introduced by Silvey et al. (1978) for computing D-optimal designs. Strict monotonicity is established for a variant considered by Titterington (1978). A formula for the rate of convergence is…
In this article, we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis. Monotonic convergence for a general class of multiplicative algorithms for $D$-optimality has been…
We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning…
Bayesian optimality criteria provide a robust design strategy to parameter misspecification. We develop an approximate design theory for Bayesian $D$-optimality for non-linear regression models with covariates subject to measurement errors.…
A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey,…
In experimental design, we are given $n$ vectors in $d$ dimensions, and our goal is to select $k\ll n$ of them to perform expensive measurements, e.g., to obtain labels/responses, for a linear regression task. Many statistical criteria have…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal…
We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the…
The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A…
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…
Iterative majorize-minimize (MM) (also called optimization transfer) algorithms solve challenging numerical optimization problems by solving a series of "easier" optimization problems that are constructed to guarantee monotonic descent of…
Finding methods for making generalizable predictions is a fundamental problem of machine learning. By looking into similarities between the prediction problem for unknown data and the lossless compression we have found an approach that…
In this paper, we derive optimality results for greedy Bayesian-network search algorithms that perform single-edge modifications at each step and use asymptotically consistent scoring criteria. Our results extend those of Meek (1997) and…
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but…
Experimental design is a classical statistics problem and its aim is to estimate an unknown $m$-dimensional vector $\beta$ from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental…
Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…