Related papers: MIND: Monge Inception Distance for Generative Mode…
We argue that the estimation of mutual information between high dimensional continuous random variables can be achieved by gradient descent over neural networks. We present a Mutual Information Neural Estimator (MINE) that is linearly…
Time-unconditional generative models learn time-independent denoising vector fields. But without time conditioning, the same noisy input may correspond to multiple noise levels and different denoising directions, which interferes with the…
Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the…
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…
Generative moment matching network (GMMN) is a deep generative model that differs from Generative Adversarial Network (GAN) by replacing the discriminator in GAN with a two-sample test based on kernel maximum mean discrepancy (MMD).…
Generative Adversarial Nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their formulation is also known to be hard to optimize and often not stable. While this is…
Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learning as they can, for…
Availability of large and diverse medical datasets is often challenged by privacy and data sharing restrictions. For successful application of machine learning techniques for disease diagnosis, prognosis, and precision medicine, large…
We investigate the training and performance of generative adversarial networks using the Maximum Mean Discrepancy (MMD) as critic, termed MMD GANs. As our main theoretical contribution, we clarify the situation with bias in GAN loss…
Quantifying the distance between datasets is a fundamental question in mathematics and machine learning. We propose \textit{magnitude distance}, a novel distance metric defined on finite datasets using the notion of the \emph{magnitude} of…
Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…
We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. This MMD, which is also known as energy distance, has several advantageous…
This note provides a chronological account of Fr\'echet distances, starting with Maurice Fr\'echet's 1906 doctoral thesis on distances in abstract sets and tracing the Fr\'echet distance between polygonal curves and its algorithmic…
Single-cell omics enable the profiles of cells, which contain large numbers of biological features, to be quantified. Cluster analysis, a dimensionality reduction process, is used to reduce the dimensions of the data to make it…
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…
While Large Language Models (LLMs) have emerged with remarkable capabilities in complex tasks through Chain-of-Thought reasoning, practical resource constraints have sparked interest in transferring these abilities to smaller models.…
For a given image generation problem, the intrinsic image manifold is often low dimensional. We use the intuition that it is much better to train the GAN generator by minimizing the distributional distance between real and generated images…
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
Leveraging the power of deep learning to design nanophotonic devices has been an area of active research in recent times, with Generative Adversarial Networks (GANs) being a popular choice alongside autoencoder-based methods. However, both…
We point out a limitation of the mutual information neural estimation (MINE) where the network fails to learn at the initial training phase, leading to slow convergence in the number of training iterations. To solve this problem, we propose…