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The exact estimation of latent variable models with big data is known to be challenging. The latents have to be integrated out numerically, and the dimension of the latent variables increases with the sample size. This paper develops a…
We propose a new method for simulating QCD at finite density, where interesting phases such as the color superconductivity phase is conjectured to appear. The method is based on a general factorization property of distribution functions of…
A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of U(1) groups are studied. After identifying general conditions which such representations should satisfy, several…
It is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified extension of the path integral (in the…
The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions, such as when there is some sparsity…
In high dimensional settings, density estimation algorithms rely crucially on their inductive bias. Despite recent empirical success, the inductive bias of deep generative models is not well understood. In this paper we propose a framework…
A master equation for the Kardar-Parisi-Zhang (KPZ) equation in 2+1 dimensions is developed. In the fully nonlinear regime we derive the finite time scale of the singularity formation in terms of the characteristics of forcing. The exact…
This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…
In the context of unitary evolution of a generic quantum system interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus, we adduce a general theoretical…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…
Stochastic kriging has been widely employed for simulation metamodeling to predict the response surface of complex simulation models. However, its use is limited to cases where the design space is low-dimensional because, in general, the…
The standard (``fine-grained'') interpretation of quantum density functional theory, in which densities are specified with infinitely-fine spatial resolution, is mathematically unruly. Here, a coarse-grained version of DFT, featuring…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
The ratio of two densities provides a direct characterization of their differences. We consider the two-sample comparison problem by estimating this ratio given i.i.d. observations from two distributions. To this end, we propose additive…
One reason for the well known fact that the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit has been identified long ago: it is insufficient decay of the probability density either near infinity or…
Finite mixture of Gaussian distributions provide a flexible semi-parametric methodology for density estimation when the variables under investigation have no boundaries. However, in practical applications variables may be partially bounded…
Langevin dynamics has found a large number of applications in sampling, optimization and estimation. Preconditioning the gradient in the dynamics with the covariance - an idea that originated in literature related to solving estimation and…
In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining is an important technique to reduce the dimensionality of the problem. We will study and quantify the coarse-graining error between the coarse-grained…
Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte-Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle…