Related papers: Optimal quantisation of probability measures using…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
We analyse the performance of several iterative algorithms for the quantisation of a probability measure $\mu$, based on the minimisation of a Maximum Mean Discrepancy (MMD). Our analysis includes kernel herding, greedy MMD minimisation and…
Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum…
We propose a method to optimize the representation and distinguishability of samples from two probability distributions, by maximizing the estimated power of a statistical test based on the maximum mean discrepancy (MMD). This optimized MMD…
Maximum mean discrepancy (MMD) has been widely employed to measure the distance between probability distributions. In this paper, we propose using MMD to solve continuous multi-objective optimization problems (MOPs). For solving MOPs, a…
We propose a novel deterministic sampling method to approximate a target distribution $\rho^*$ by minimizing the kernel discrepancy, also known as the Maximum Mean Discrepancy (MMD). By employing the general \emph{energetic variational…
The maximum mean discrepancy (MMD) is a kernel-based distance between probability distributions useful in many applications (Gretton et al. 2012), bearing a simple estimator with pleasing computational and statistical properties. Being able…
Covariate shifts are a common problem in predictive modeling on real-world problems. This paper proposes addressing the covariate shift problem by minimizing Maximum Mean Discrepancy (MMD) statistics between the training and test sets in…
The maximum mean discrepancy (MMD) is a kernel-based nonparametric statistic for two-sample testing, whose inferential accuracy depends critically on variance characterization. Existing work provides various finite-sample estimators of the…
Bayesian Neural Networks (BNNs) are trained to optimize an entire distribution over their weights instead of a single set, having significant advantages in terms of, e.g., interpretability, multi-task learning, and calibration. Because of…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
One of the most well-known and simplest models for diversity maximization is the Max-Min Diversification (MMD) model, which has been extensively studied in the data mining and database literature. In this paper, we initiate the study of the…
The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…
In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates. To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a…
Detecting changes is of fundamental importance when analyzing data streams and has many applications, e.g., in predictive maintenance, fraud detection, or medicine. A principled approach to detect changes is to compare the distributions of…
This paper is motivated by addressing open questions in distributionally robust chance-constrained programs (DRCCP) using the popular Wasserstein ambiguity sets. Specifically, the computational techniques for those programs typically place…