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A stationary stochastic geometric model is proposed for analyzing the data compression method used in one-bit compressed sensing. The data set is an unconstrained stationary set, for instance all of $\mathbb{R}^n$ or a stationary Poisson…
The design and application of regression-free tensor network representations for integration is presented. Tensor network methods are demonstrated to outperform Monte Carlo for test problems, and exponential convergence is shown to be…
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
Importance sampling is one of the most widely used variance reduction strategies in Monte Carlo rendering. In this paper, we propose a novel importance sampling technique that uses a neural network to learn how to sample from a desired…
A powerful and well-established tool for free-energy estimation is Bennett's acceptance ratio method. Central properties of this estimator, which employs samples of work values of a forward and its time reversed process, are known: for…
Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…
Sampling complex free energy surfaces is one of the main challenges of modern atomistic simulation methods. The presence of kinetic bottlenecks in such surfaces often renders a direct approach useless. A popular strategy is to identify a…
Ordinary stochastic neural networks mostly rely on the expected values of their weights to make predictions, whereas the induced noise is mostly used to capture the uncertainty, prevent overfitting and slightly boost the performance through…
In this work a general approach to compute a compressed representation of the exponential $\exp(h)$ of a high-dimensional function $h$ is presented. Such exponential functions play an important role in several problems in Uncertainty…
Energy-Based Models (EBMs) provide a flexible framework for generative modeling, but their training remains theoretically challenging due to the need to approximate normalization constants and efficiently sample from complex, multi-modal…
Can we leverage high-resolution information without the unsustainable quadratic complexity to input scale? We propose Traversal Network (TNet), a novel multi-scale hard-attention architecture, which traverses image scale-space in a top-down…
We apply tensor networks to counting statistics for the stochastic particle transport in an out-of-equilibrium diffusive system. This system is composed of a one-dimensional channel in contact with two particle reservoirs at the ends. Two…
Inspired by coarse-graining approaches used in physics, we show how similar algorithms can be adapted for data. The resulting algorithms are based on layered tree tensor networks and scale linearly with both the dimension of the input and…
Observables in random tensor theory are polynomials in the entries of a tensor of rank $d$ which are invariant under $U(N)^d$. It is notoriously difficult to evaluate the expectations of such polynomials, even in the Gaussian distribution.…
When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…
Network estimation and variable selection have been extensively studied in the statistical literature, but only recently have those two challenges been addressed simultaneously. In this paper, we seek to develop a novel method to…
Estimating the uncertainty in deep neural network predictions is crucial for many real-world applications. A common approach to model uncertainty is to choose a parametric distribution and fit the data to it using maximum likelihood…
Fueled by the expressive power of deep neural networks, normalizing flows have achieved spectacular success in generative modeling, or learning to draw new samples from a distribution given a finite dataset of training samples. Normalizing…