Related papers: Confidence Intervals for Stochastic Arithmetic
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity…
We consider the prospect of a processor that can perform interval arithmetic at the same speed as conventional floating-point arithmetic. This makes it possible for all arithmetic to be performed with the superior security of interval…
In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…
Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distribution, and Monte Carlo sampling…
The age of big data has produced data sets that are computationally expensive to analyze and store. Algorithmic leveraging proposes that we sample observations from the original data set to generate a representative data set and then…
Security-Constrained Unit Commitment (SCUC) is one of the most significant problems in secure and optimal operation of modern electricity markets. New sources of uncertainties such as wind speed volatility and price-sensitive loads impose…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
Scientific computing programs often undergo aggressive compiler optimization to achieve high performance and efficient resource utilization. While performance is critical, we also need to ensure that these optimizations are correct. In this…
Machine learning models are often evaluated using point estimates of performance metrics such as accuracy, F1 score, or mean squared error. Such summaries fail to capture the inherent variability induced by stochastic elements of the…
Floating-point program errors can lead to severe consequences, particularly in critical domains such as military applications. Only a small subset of inputs may induce substantial floating-point errors, prompting researchers to develop…
Factor analysis (FA) and principal component analysis (PCA) are popular statistical methods for summarizing and explaining the variability in multivariate datasets. By default, FA and PCA assume the number of components or factors to be…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…
Fault Tree Analysis (FTA) is a well-established method in failure analysis and is widely used in safety and reliability assessments. While FTA tools enable users to manage complex analyses effectively, they can sometimes obscure the…
For scientific computations on a digital computer the set of real number is usually approximated by a finite set F of "floating-point" numbers. We compare the numerical accuracy possible with difference choices of F having approximately the…
From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things…
Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…
Program verification techniques typically focus on finding counter-examples that violate properties of a program. Constraint programming offers a convenient way to verify programs by modeling their state transformations and specifying…
Reliable and secure human-machine communication is fundamental to IoT and cyber-physical ecosystems, where smartphones and wearables commonly serve as authentication controllers. PIN-based authentication can be viewed as a low-bandwidth…