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Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

We derive a novel generative model from iterative Gaussian posterior inference. By treating the generated sample as an unknown variable, we can formulate the sampling process in the language of Bayesian probability. Our model uses a…

Most successful machine intelligence systems rely on gradient-based learning, which is made possible by backpropagation. Some systems are designed to aid us in interpreting data when explicit goals cannot be provided. These unsupervised…

Simulation-based Bayesian inference (SBI) methods are widely used for parameter estimation in complex models where evaluating the likelihood is challenging but generating simulations is relatively straightforward. However, these methods…

In recent years, there has been a remarkable development of simulation-based inference (SBI) algorithms, and they have now been applied across a wide range of astrophysical and cosmological analyses. There are a number of key advantages to…

Bayesian inference usually requires running potentially costly inference procedures separately for every new observation. In contrast, the idea of amortized Bayesian inference is to initially invest computational cost in training an…

Generative adversarial networks (GANs) have proven effective in modeling distributions of high-dimensional data. However, their training instability is a well-known hindrance to convergence, which results in practical challenges in their…

We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the…

We propose Graphical Generative Adversarial Networks (Graphical-GAN) to model structured data. Graphical-GAN conjoins the power of Bayesian networks on compactly representing the dependency structures among random variables and that of…

Probabilistic state estimation is essential for robots navigating uncertain environments. Accurately and efficiently managing uncertainty in estimated states is key to robust robotic operation. However, nonlinearities in robotic platforms…

We introduce GenAI-Powered Inference (GPI), a statistical framework for both causal and predictive inference using unstructured data, including text and images. GPI leverages open-source Generative Artificial Intelligence (GenAI) models --…

Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…

The Laser Interferometer Space Antenna (LISA) data stream will inevitably contain gaps due to maintenance and environmental disturbances, introducing nonstationarities and spectral leakage that compromise standard frequency-domain…

Recent advances in generative adversarial networks (GANs) have shown remarkable progress in generating high-quality images. However, this gain in performance depends on the availability of a large amount of training data. In limited data…

Generative adversarial networks (GANs) have attracted intense interest in the field of generative models. However, few investigations focusing either on the theoretical analysis or on algorithm design for the approximation ability of the…

Generative adversarial networks (GANs) are a powerful approach to unsupervised learning. They have achieved state-of-the-art performance in the image domain. However, GANs are limited in two ways. They often learn distributions with low…

Generative adversarial networks (GANs)successfully generate high quality data by learning amapping from a latent vector to the data. Various studies assert that the latent space of a GAN is semanticallymeaningful and can be utilized for…

The ability of the Generative Adversarial Networks (GANs) framework to learn generative models mapping from simple latent distributions to arbitrarily complex data distributions has been demonstrated empirically, with compelling results…

Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators, leading to unstable…

Generative adversarial networks (GANs) are a novel approach to generative modelling, a task whose goal it is to learn a distribution of real data points. They have often proved difficult to train: GANs are unlike many techniques in machine…