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Many modern spatial models express the stochastic variation component as a basis expansion with random coefficients. Low rank models, approximate spectral decompositions, multiresolution representations, stochastic partial differential…
Deep generative models (DGMs) have the potential to revolutionize diagnostic imaging. Generative adversarial networks (GANs) are one kind of DGM which are widely employed. The overarching problem with deploying GANs, and other DGMs, in any…
Large sparse linear systems of equations are ubiquitous in science and engineering, such as those arising from discretizations of partial differential equations. Algebraic multigrid (AMG) methods are one of the most common methods of…
Stochastic and conditional simulation methods have been effective towards producing realistic realizations and simulations of spatial numerical models that share equal probability of occurrence. Application of these methods are valuable…
We study the structure of the ground states of local stoquastic Hamiltonians and show that under mild assumptions the following distributions can efficiently approximate one another: (a) distributions arising from ground states of…
Interior point methods solve small to medium sized problems to high accuracy in a reasonable amount of time. However, for larger problems as well as stochastic problems, one needs to use first-order methods such as stochastic gradient…
State-space models (SSMs) are a powerful statistical tool for modelling time-varying systems via a latent state. In these models, the latent state is never directly observed. Instead, a sequence of observations related to the state is…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
We demonstrate the use of conditional autoregressive generative models (van den Oord et al., 2016a) over a discrete latent space (van den Oord et al., 2017b) for forward planning with MCTS. In order to test this method, we introduce a new…
In this contribution we deal with the problem of learning an undirected graph which encodes the conditional dependence relationship between variables of a complex system, given a set of observations of this system. This is a very central…
Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics. We give the first randomized polynomial-time algorithm for finding ground states of gapped one-dimensional Hamiltonians: it outputs an…
Large collections of coupled, heterogeneous agents can manifest complex dynamical behavior presenting difficulties for simulation and analysis. However, if the collective dynamics lie on a low-dimensional manifold then the original…
Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling…
Latent-based image generative models, such as Latent Diffusion Models (LDMs) and Mask Image Models (MIMs), have achieved notable success in image generation tasks. These models typically leverage reconstructive autoencoders like VQGAN or…
We demonstrate in this paper that a generative model can be designed to perform classification tasks under challenging settings, including adversarial attacks and input distribution shifts. Specifically, we propose a conditional variational…
In this paper we propose an identification procedure of a sparse graphical model associated to a Gaussian stationary stochastic process. The identification paradigm exploits the approximation of autoregressive processes through reciprocal…
Artificial neural networks have been recently introduced as a general ansatz to compactly represent many- body wave functions. In conjunction with Variational Monte Carlo, this ansatz has been applied to find Hamil- tonian ground states and…
The increasing availability and accessibility of numerous overhead images allows us to estimate and assess the spatial arrangement of groups of geospatial target objects, which can benefit many applications, such as traffic monitoring and…
Autoregressive (AR) models based on next-scale prediction are rapidly emerging as a powerful tool for image generation, but they face a critical weakness: information inconsistencies between patches across timesteps introduced by…
Machine learning has emerged recently as a powerful tool for predicting properties of quantum many-body systems. For many ground states of gapped Hamiltonians, generative models can learn from measurements of a single quantum state to…