Related papers: Local Optimization of Black-Box Function with High…
Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…
Some real-world problems revolve to solve the optimization problem \max_{x\in\mathcal{X}}f\left(x\right) where f\left(.\right) is a black-box function and X might be the set of non-vectorial objects (e.g., distributions) where we can only…
Constraining Beyond the Standard Model theories usually involves scanning highly multi-dimensional parameter spaces and check observable predictions against experimental bounds and theoretical constraints. Such task is often timely and…
Bayesian optimisation (BO) is a standard approach for sample-efficient global optimisation of expensive black-box functions, yet its scalability to high dimensions remains challenging. Here, we investigate nonlinear dimensionality reduction…
We present a tutorial on reduced-rank signal processing, design methods and algorithms for dimensionality reduction, and cover a number of important applications. A general framework based on linear algebra and linear estimation is employed…
Many expensive black-box optimisation problems are sensitive to their inputs. In these problems it makes more sense to locate a region of good designs, than a single-possibly fragile-optimal design. Expensive black-box functions can be…
Many planning applications involve complex relationships defined on high-dimensional, continuous variables. For example, robotic manipulation requires planning with kinematic, collision, visibility, and motion constraints involving robot…
This paper explores the extension of dimension reduction (DR) techniques to the multi-dimension case by using the Einstein product. Our focus lies on graph-based methods, encompassing both linear and nonlinear approaches, within both…
We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…
Design optimisation potentially leads to lightweight aircraft structures with lower environmental impact. Due to the high number of design variables and constraints, these problems are ordinarily solved using gradient-based optimisation…
In this thesis, I explore the possibilities of conducting Bayesian optimization techniques in high dimensional domains. Although high dimensional domains can be defined to be between hundreds and thousands of dimensions, we will primarily…
This work focuses on the space-time reduced-order modeling (ROM) method for solving large-scale uncertainty quantification (UQ) problems with multiple random coefficients. In contrast with the traditional space ROM approach, which performs…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
To reduce complexity and achieve scalable performance in high-dimensional black-box settings, we propose a distributed method for nonconvex derivative-free optimization of continuous variables with an additively separable objective, subject…
High-dimensional classification has become an increasingly important problem. In this paper we propose a "Multivariate Adaptive Stochastic Search" (MASS) approach which first reduces the dimension of the data space and then applies a…
Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive…
Sufficient dimension reduction (SDR) using distance covariance (DCOV) was recently proposed as an approach to dimension-reduction problems. Compared with other SDR methods, it is model-free without estimating link function and does not…
In numerous applications across all science and engineering areas, there are optimization problems where both the objective function and the constraints have no closed-form expression or are too complex to be managed analytically, that they…
Black-box optimizers that explore in parameter space have often been shown to outperform more sophisticated action space exploration methods developed specifically for the reinforcement learning problem. We examine these black-box methods…