Related papers: Bayesian optimal experimental design with Wasserst…
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…
We study Bayesian histograms for distribution estimation on $[0,1]^d$ under the Wasserstein $W_v, 1 \leq v < \infty$ distance in the i.i.d sampling regime. We newly show that when $d < 2v$, histograms possess a special \textit{memory…
Under a generalised estimating equation analysis approach, approximate design theory is used to determine Bayesian D-optimal designs. For two examples, considering simple exchangeable and exponential decay correlation structures, we compare…
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…
This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample…
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.…
Evolutionary algorithms (EAs) are promising approaches for non-differentiable or strongly multimodal topology optimization problems, but they often suffer from the curse of dimensionality, generally leading to low-resolution optimized…
The sliced Wasserstein (SW) distance has been widely recognized as a statistically effective and computationally efficient metric between two probability measures. A key component of the SW distance is the slicing distribution. There are…
Computing expected information gain (EIG) from prior to posterior (equivalently, mutual information between candidate observations and model parameters or other quantities of interest) is a fundamental challenge in Bayesian optimal…
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…
We introduce a framework for Bayesian experimental design (BED) with implicit models, where the data-generating distribution is intractable but sampling from it is still possible. In order to find optimal experimental designs for such…
Model selection and order selection problems frequently arise in statistical practice. A popular approach to addressing these problems in the frequentist setting involves information criteria based on penalised maxima of log-likelihoods for…
Regression loss design is an essential topic for oriented object detection. Due to the periodicity of the angle and the ambiguity of width and height definition, traditional L1-distance loss and its variants have been suffered from the…
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…
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Bayesian optimal experimental design (BOED) selects experiments to maximize information gain about model parameters. However, in decision-critical settings, reducing parameter uncertainty does not necessarily improve downstream decisions,…
Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…
We develop a framework for goal-oriented optimal design of experiments (GOODE) for large-scale Bayesian linear inverse problems governed by PDEs. This framework differs from classical Bayesian optimal design of experiments (ODE) in the…
Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be…