Related papers: Extending the optimum interval method
Singular Spectrum Analysis and many other subspace-based methods of signal processing are implicitly relying on the assumption of close proximity of unperturbed and perturbed signal subspaces extracted by the Singular Value Decomposition of…
We propose an approach to rapidly find the upper limit of separability between datasets that is directly applicable to HEP classification problems. The most common HEP classification task is to use $n$ values (variables) for an object…
Finding upper limits on the rate of events from a proposed process in the presence of unknown backgrounds is an often encountered problem in the search for rare processes. Methods based on unusually large "gaps", or spacings, in the event…
The goal of this paper is to increase our understanding of the fundamental performance limits of mobile and Delay Tolerant Networks (DTNs), where end-to-end multi-hop paths may not exist and communication routes may only be available…
In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the…
In this paper, a new method for investigating Dirichlet's divisor problem is developed. For this purpose, integer points under the graph of a hyperbola are studied. Since many investigations in this direction focus on direct estimates of…
We study the problem of designing interval-valued observers that simultaneously estimate the system state and learn an unknown dynamic model for partially unknown nonlinear systems with dynamic unknown inputs and bounded noise signals.…
The block maxima method is a classical and widely applied statistical method for time series extremes. It has recently been found that respective estimators whose asymptotics are driven by empirical means can be improved by using sliding…
Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…
We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…
Bayesian optimization is normally performed within fixed variable bounds. In cases like hyperparameter tuning for machine learning algorithms, setting the variable bounds is not trivial. It is hard to guarantee that any fixed bounds will…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the…
We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…
The problem of detecting new signals in the presence of an unknown background is ubiquitous in scientific discoveries and is especially prominent in the physical sciences. Most solutions proposed thus far to address the problem focus on…
Fisher's likelihood is widely used for statistical inference for fixed unknowns. This paper aims to extend two important likelihood-based methods, namely the maximum likelihood procedure for point estimation and the confidence procedure for…
The method is described and tested for analysis of statistical parameters of reduced neutron widths distributions accounting for possibility of coexistence of superposition of some functions with non-zero mean values of neutron amplitude…
Sequential decision making under uncertainty is studied in a mixed observability domain. The goal is to maximize the amount of information obtained on a partially observable stochastic process under constraints imposed by a fully observable…
An optimal bound on the quantiles of a certain kind of distributions is given. Such a bound is used in applications to Berry--Esseen-type bounds for nonlinear statistics.