Related papers: Optimal design for linear models via gradient flow
Current techniques for Out-of-Distribution (OoD) detection predominantly rely on quantifying predictive uncertainty and incorporating model regularization during the training phase, using either real or synthetic OoD samples. However,…
Bayesian optimal experimental design is a sub-field of statistics focused on developing methods to make efficient use of experimental resources. Any potential design is evaluated in terms of a utility function, such as the (theoretically…
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…
We present a Bayesian approach to identify optimal transformations that map model input points to low dimensional latent variables. The "projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to…
Optimal power flow (OPF) is a central problem in the operation of electric power systems. An OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering…
Optimal Power Flow (OPF) is a core optimization problem in power system operation and planning, aiming to minimize generation costs while satisfying physical constraints such as power flow equations, generator limits, and voltage limits.…
We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While…
Algorithms which compute locally optimal continuous designs often rely on a finite design space or on repeatedly solving a complex non-linear program. Both methods require extensive evaluations of the Jacobian Df of the underlying model.…
The design of an experiment can be always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the…
For computing efficient approximate designs of multifactor experiments, we propose a simple algorithm based on adaptive exploration of the grid of all combinations of factor levels. We demonstrate that the algorithm significantly…
We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show…
Minimizing functionals in the space of probability distributions can be done with Wasserstein gradient flows. To solve them numerically, a possible approach is to rely on the Jordan-Kinderlehrer-Otto (JKO) scheme which is analogous to 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…
This paper develops a generative model by minimizing the second-order Wasserstein loss (the $W_2$ loss) through a distribution-dependent ordinary differential equation (ODE), whose dynamics involves the Kantorovich potential associated with…
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…
We propose a variance-penalized formulation of Bayesian optimal experimental design for nonlinear models that augments the classical expected utility criterion with a penalty on utility variability, yielding a mean--variance objective that…
The goal of this paper is to make Optimal Experimental Design (OED) computationally feasible for problems involving significant computational expense. We focus exclusively on the Mean Objective Cost of Uncertainty (MOCU), which is a…
We propose efficient numerical schemes for implementing the natural gradient descent (NGD) for a broad range of metric spaces with applications to PDE-based optimization problems. Our technique represents the natural gradient direction as a…
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for…
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for…