Related papers: Computing Rare Probabilities of Voltage Collapse
This paper introduces a versatile approach for computing the risk of collision specifically tailored for scenarios featuring low relative encounter velocities, but with potential applicability across a wide range of situations. The…
A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question naturally lends itself to a probabilistic formulation, by…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
We are interested in bounding probabilities of rare events in the context of computer experiments. These rare events depend on the output of a physical model with random input variables. Since the model is only known through an expensive…
The climate system is a complex, chaotic system with many degrees of freedom and variability on a vast range of temporal and spatial scales. Attaining a deeper level of understanding of its dynamical processes is a scientific challenge of…
Randomized singular value decomposition (RSVD) is a class of computationally efficient algorithms for computing the truncated SVD of large data matrices. Given an $m \times n$ matrix $\widehat{{\mathbf M}}$, the prototypical RSVD algorithm…
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
Variational inference has become one of the most widely used methods in latent variable modeling. In its basic form, variational inference employs a fully factorized variational distribution and minimizes its KL divergence to the posterior.…
Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. This leads in some cases to symmetry-broken space-time…
Accurately estimating the probability of failure in engineering systems under uncertainty is a fundamental challenge, particularly in high-dimensional settings and for rare events. Conventional reliability analysis methods often become…
The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on $\mathbb{R}^d$, and edges are independently drawn with probability depending on the locations of the two end…
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…
The standard Large Deviation Theory (LDT) is mathematically illustrated by the Boltzmann-Gibbs factor which describes the thermal equilibrium of short-range-interacting many-body Hamiltonian systems, the velocity distribution of which is…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…
We analyze the \textit{Large Deviation Probability (LDP)} of linear factor models generated from non-identically distributed components with \textit{regularly-varying} tails, a large subclass of heavy tailed distributions. An efficient…
Multivariate linear regressions are widely used statistical tools in many applications to model the associations between multiple related responses and a set of predictors. To infer such associations, it is often of interest to test the…
Estimating the probability of failure is a critical step in developing safety-critical autonomous systems. Direct estimation methods such as Monte Carlo sampling are often impractical due to the rarity of failures in these systems. Existing…
We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our…
In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an $\epsilon$-stochastic stationary point, where the expected violations of both constraints and…
Demand for high-performance, robust, and safe autonomous systems has grown substantially in recent years. These objectives motivate the desire for efficient safety-theoretic reasoning that can be embedded in core decision-making tasks such…