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Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance),…

In recent years, Generative Adversarial Networks (GANs) have drawn a lot of attentions for learning the underlying distribution of data in various applications. Despite their wide applicability, training GANs is notoriously difficult. This…

The text generated by neural language models is not as good as the real text. This means that their distributions are different. Generative Adversarial Nets (GAN) are used to alleviate it. However, some researchers argue that GAN variants…

Implicit Generative Models (IGMs) such as GANs have emerged as effective data-driven models for generating samples, particularly images. In this paper, we formulate the problem of learning an IGM as minimizing the expected distance between…

Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…

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…

Class imbalance in supervised classification often degrades model performance by biasing predictions toward the majority class, particularly in critical applications such as medical diagnosis and fraud detection. Traditional oversampling…

This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed. GAN is applied to…

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…

In recent years, machine learning has achieved impressive results across different application areas. However, machine learning algorithms do not necessarily perform well on a new domain with a different distribution than its training set.…

We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects…

This paper studies the distribution estimation of contaminated data by the MoM-GAN method, which combines generative adversarial net (GAN) and median-of-mean (MoM) estimation. We use a deep neural network (DNN) with a ReLU activation…

Generative neural samplers are probabilistic models that implement sampling using feedforward neural networks: they take a random input vector and produce a sample from a probability distribution defined by the network weights. These models…

Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare…

The collected data from industrial machines are often imbalanced, which poses a negative effect on learning algorithms. However, this problem becomes more challenging for a mixed type of data or while there is overlapping between classes.…

We propose two novel nonparametric two-sample kernel tests based on the Maximum Mean Discrepancy (MMD). First, for a fixed kernel, we construct an MMD test using either permutations or a wild bootstrap, two popular numerical procedures to…

We propose novel statistics which maximise the power of a two-sample test based on the Maximum Mean Discrepancy (MMD), by adapting over the set of kernels used in defining it. For finite sets, this reduces to combining (normalised) MMD…

Understanding how two datasets differ can help us determine whether one dataset under-represents certain sub-populations, and provides insights into how well models will generalize across datasets. Representative points selected by a…

Generative Adversarial Networks (GANs) are a widely-used tool for generative modeling of complex data. Despite their empirical success, the training of GANs is not fully understood due to the min-max optimization of the generator and…

Generative Adversarial Networks (GANs), as a framework for estimating generative models via an adversarial process, have attracted huge attention and have proven to be powerful in a variety of tasks. However, training GANs is well known for…