Related papers: Sum-of-Squares & Gaussian Processes I: Certificati…
While most power system small-signal stability assessments rely on the reduced Jacobian, which depends non-linearly on the states, uncertain operating points introduce nontrivial hurdles in certifying the system's stability. In this paper,…
We give the first polynomial-time algorithm to estimate the mean of a $d$-variate probability distribution with bounded covariance from $\tilde{O}(d)$ independent samples subject to pure differential privacy. Prior algorithms for this…
Triangular map is a recent construct in probability theory that allows one to transform any source probability density function to any target density function. Based on triangular maps, we propose a general framework for high-dimensional…
The three and five-dimensional convex sets of two-level complex and quaternionic quantum systems are studied in the Bayesian thermostatistical framework introduced by Lavenda. Associated with a given parameterization of each such set is a…
Win statistics have gained increasing popularity as primary analysis methods for clinical trials with hierarchical endpoints (HEs) as primary endpoints. However, existing sample size and power calculation approaches in trial design still…
We introduce a spectral approach to characterizing the three-dimensional Edwards-Anderson spin glass. By analyzing the eigenvalue statistics of overlap matrices constructed from two-dimensional cross-sections, we identify a crossover from…
Deregulation of energy markets, penetration of renewables, advanced metering capabilities, and the urge for situational awareness, all call for system-wide power system state estimation (PSSE). Implementing a centralized estimator though is…
We calculate high-temperature graph expansions for the Ising spin glass model with 4 symmetric random distribution functions for its nearest neighbor interaction constants J_{ij}. Series for the Edwards-Anderson susceptibility \chi_EA are…
Accurate, global Potential Energy Surfaces (PES) expressed in sum-of-products (SOP) form are a prerequisite for efficient high-dimensional quantum dynamics simulations using the MCTDH method. This work introduces a methodology for…
We present an identity for an unbiased estimate of a general statistical distribution. The identity computes the distribution density from dividing a histogram sum over a local window by a correction factor from a mean-force integral, and…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
We consider a one-step replica symmetry breaking description of the Edwards-Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on…
We consider a random walk on a homogeneous space $G/\Lambda$ where $G$ is $\mathrm{SO}(2,1)$ or $\mathrm{SO}(3,1)$ and $\Lambda$ is a lattice. The walk is driven by a probability measure $\mu$ on $G$ whose support generates a Zariski-dense…
The Lasserre/Sum-of-Squares (SoS) hierarchy is a systematic procedure for constructing a sequence of increasingly tight semidefinite relaxations. It is known that the hierarchy converges to the 0/1 polytope in n levels and captures the…
A new method to simulate probability distributions in regions where the events are VERY unlikely (e.g. p ~ 10^{-40}) is presented. The basic idea is to represent the underlying probability space by the phase space of a physical system. The…
This paper introduces a general class of hierarchical nonparametric prior distributions. The random probability measures are constructed by a hierarchy of generalized species sampling processes with possibly non-diffuse base measures. The…
A Wright function based framework is proposed to combine and extend several distribution families. The $\alpha$-stable distribution is generalized by adding the degree of freedom parameter. The PDF of this two-sided super distribution…
We study the problem of computing weighted sum-of-squares (WSOS) certificates for positive polynomials over a compact semialgebraic set. Building on the theory of interior-point methods for convex optimization, we introduce the concept of…
The authors present empirical distributions for the halting time (measured by the number of iterations to reach a given accuracy) of optimization algorithms applied to two random systems: spin glasses and deep learning. Given an algorithm,…
We introduce Selective Greedy Equivalence Search (SGES), a restricted version of Greedy Equivalence Search (GES). SGES retains the asymptotic correctness of GES but, unlike GES, has polynomial performance guarantees. In particular, we show…