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We propose a new class of physics-informed neural networks, called Physics-Informed Generator-Encoder Adversarial Networks, to effectively address the challenges posed by forward, inverse, and mixed problems in stochastic differential…
Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…
Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics. However, a fundamental limitation has been that such models have typically been relatively inflexible, which recent work introducing…
Unlike conventional anomaly detection research that focuses on point anomalies, our goal is to detect anomalous collections of individual data points. In particular, we perform group anomaly detection (GAD) with an emphasis on irregular…
Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the…
Generative adversarial networks (GANs) are the state of the art in generative modeling. Unfortunately, most GAN methods are susceptible to mode collapse, meaning that they tend to capture only a subset of the modes of the true distribution.…
Applications based on image retrieval require editing and associating in intermediate spaces that are representative of the high-level concepts like objects and their relationships rather than dense, pixel-level representations like RGB…
This paper investigates continuous representations of steering vectors over frequency and microphone/source positions for augmented listening (e.g., spatial filtering and binaural rendering), enabling user-parameterized control of the…
We consider the problem of learning deep generative models from data. We formulate a method that generates an independent sample via a single feedforward pass through a multilayer perceptron, as in the recently proposed generative…
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…
Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…
Generating synthetic data for financial time series poses challenges, especially considering their non-stationary nature. Traditional statistical time series models normally assume weak stationarity. However, this assumption can constrain…
Generative adversarial networks (GANs) have been shown to produce realistic samples from high-dimensional distributions, but training them is considered hard. A possible explanation for training instabilities is the inherent imbalance…
Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based…
The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex…
This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined…
We introduce a novel edge tracing algorithm using Gaussian process regression. Our edge-based segmentation algorithm models an edge of interest using Gaussian process regression and iteratively searches the image for edge pixels in a…
Learning probabilistic models that can estimate the density of a given set of samples, and generate samples from that density, is one of the fundamental challenges in unsupervised machine learning. We introduce a new generative model based…
While standard generative adversarial networks (GANs) rely solely on training data to learn unknown probability distributions, physics-informed GANs (PI-GANs) encode physical laws in the form of stochastic partial differential equations…
Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can…