Related papers: On local analysis
For the purposes of computational dialectology or other geographically bound text analysis tasks, texts must be annotated with their or their authors' location. Many texts are locatable through explicit labels but most have no explicit…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
We propose local polynomial estimators for the conditional mean of a continuous response when only pooled response data are collected under different pooling designs. Asymptotic properties of these estimators are investigated and compared.…
Locality is a fundamental principle used extensively in program and system optimization. It can be measured in many ways. This paper formalizes the metrics of locality into a measurement theory. The new theory includes the precise…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
In this Letter, we introduce a notion of local fraction for experiments taking place against arbitrary static causal backgrounds -- greatly generalising previous results on no-signalling scenarios -- and we explicitly formulate a linear…
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…
This article deals with plausible reasoning from incomplete knowledge about large-scale spatial properties. The availableinformation, consisting of a set of pointwise observations,is extrapolated to neighbour points. We make use of belief…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…
We study large partial sums, localized with respect to the sums of variances, of a sequence of centered random variables. An application is given to the distribution of prime factors of typical integers.
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…