Related papers: Explicit factorization of external coordinates in …
The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with a partition function whose integrand is not positive. One way to simulate such a system is to use the factorization method where one enforces…
We present an extension of the functional renormalization group (FRG) framework developed to compute critical probability distributions of the order parameter to momentum-dependent observables. Focusing on the constraint effective action at…
We study probability measures induced by set functions with constraints. Such measures arise in a variety of real-world settings, where prior knowledge, resource limitations, or other pragmatic considerations impose constraints. We consider…
We study the geometrical meaning of higher-order terms in matrix models of Yang-Mills type in the semi-classical limit, generalizing recent results arXiv:1003.4132 to the case of 4-dimensional space-time geometries with general Poisson…
We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…
This article introduces a nonlinear generalized matrix factor model (GMFM) that allows for mixed-type variables, extending the scope of linear matrix factor models (LMFM) that are so far limited to handling continuous variables. We…
Current mathematical frameworks for predicting the flux state and macromolecular composition of the cell do not rely on thermodynamic constraints to determine the spontaneous direction of reactions. These predictions may be biologically…
Monte Carlo simulations of finite density systems are often plagued by the complex action problem. We point out that there exists certain non-commutativity in the zero chemical potential limit and the thermodynamic limit when one tries to…
A typical problem with Monte Carlo simulations in statistical physics is that they do not allow for a direct calculation of the free energy. For systems at criticality, this means that one cannot calculate the central charge in a Monte…
We discuss the $F$-matrices associated to the $R$-matrix of a general $N$-state vertex model whose statistical configurations encode $N-1$ U(1) symmetries. The factorization condition is shown for arbitrary weights being based only on the…
Markov Chain Monte Carlo (MCMC) underlies both statistical physics and combinatorial optimization, but mixes slowly near critical points and in rough landscapes. Parallel Tempering (PT) improves mixing by swapping replicas across…
The problem of estimating the probability p=P(g(X<0) is considered when X represents a multivariate stochastic input of a monotone function g. First, a heuristic method to bound p is formally described, involving a specialized design of…
We investigate a Gaussian mixture model (GMM) with component means constrained in a pre-selected subspace. Applications to classification and clustering are explored. An EM-type estimation algorithm is derived. We prove that the subspace…
Regularized linear regression under the $\ell_1$ penalty, such as the Lasso, has been shown to be effective in variable selection and sparse modeling. The sampling distribution of an $\ell_1$-penalized estimator $\hat{\beta}$ is hard to…
In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper, we focus on variance reduction for matrix…
The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They rely on knowledge of interevent probability density functions (PDFs) and on…
A growing body of research on probabilistic programs and causal models has highlighted the need to reason compositionally about model classes that extend directed graphical models. Both probabilistic programs and causal models define a…
We consider the perturbation of an electric potential due to an insulating inclusion with corners. This perturbation is known to admit a multipole expansion whose coefficients are linear combinations of generalized polarization tensors. We…
We report an essential improvement of the plain Fourier Monte Carlo algorithm that promises to be a powerful tool for investigating critical behavior in a large class of lattice models, in particular those containing microscopic or…
Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves…