503 research outputs found
Value of information in the binary case and confusion matrix
The simplest Bayesian system used to illustrate ideas of probability theory is a coin and a boolean utility function. To illustrate ideas of hypothesis testing, estimation or optimal control, one needs to use at least two coins and a confusion matrix accounting for the utilities of four possible outcomes. Here we use such a system to illustrate the main ideas of Stratonovich’s value of information (VoI) theory in the context of a financial time-series forecast. We demonstrate how VoI can provide a theoretical upper bound on the accuracy of the forecasts facilitating the analysis and optimization of models
FPT-algorithms for some problems related to integer programming
In this paper, we present FPT-algorithms for special cases of the shortest
lattice vector, integer linear programming, and simplex width computation
problems, when matrices included in the problems' formulations are near square.
The parameter is the maximum absolute value of rank minors of the corresponding
matrices. Additionally, we present FPT-algorithms with respect to the same
parameter for the problems, when the matrices have no singular rank
sub-matrices.Comment: arXiv admin note: text overlap with arXiv:1710.00321 From author:
some minor corrections has been don
Faster Integer Points Counting in Parametric Polyhedra
In this paper, we consider the counting function for a parametric polyhedron , where . We give a new representation of ,
called a \emph{piece-wise step-polynomial with periodic coefficients}, which is
a generalization of piece-wise step-polynomials and integer/rational Ehrhart's
quasi-polynomials. It gives the fastest way to calculate in certain
scenarios. The most important cases are the following:
1) We show that, for the parametric polyhedron defined by a
standard-form system with a fixed number of equalities,
the function can be represented by a polynomial-time computable
function. In turn, such a representation of can be constructed by an
-time algorithm;
2) Assuming again that the number of equalities is fixed, we show that
integer/rational Ehrhart's quasi-polynomials of a polytope can be computed by
FPT-algorithms, parameterized by sub-determinants of or its elements;
3) Our representation of is more efficient than other known approaches,
if has bounded elements, especially if it is sparse in addition.
Additionally, we provide a discussion about possible applications in the area
of compiler optimization. In some "natural" assumptions on a program code, our
approach has the fastest complexity bounds
A density-based statistical analysis of graph clustering algorithm performance
This is a pre-copyedited, author-produced version of an article accepted for publication in
Journal of Complex Networks following peer review. The version of record: Pierre Miasnikof, Alexander Y Shestopaloff, Anthony J Bonner, Yuri Lawryshyn, Panos M Pardalos, A density-based statistical analysis of graph clustering algorithm performance, Journal of Complex Networks, Volume 8, Issue 3, June 2020, cnaa012, https://doi.org/10.1093/comnet/cnaa012
is available online at: https://doi.org/10.1093/comnet/cnaa012© 2020 The authors. Published by Oxford University Press. All rights reserved. We introduce graph clustering quality measures based on comparisons of global, intra- A nd inter-cluster densities, an accompanying statistical significance test and a step-by-step routine for clustering quality assessment. Our work is centred on the idea that well-clustered graphs will display a mean intra-cluster density that is higher than global density and mean inter-cluster density. We do not rely on any generative model for the null model graph. Our measures are shown to meet the axioms of a good clustering quality function. They have an intuitive graph-theoretic interpretation, a formal statistical interpretation and can be tested for significance. Empirical tests also show they are more responsive to graph structure, less likely to breakdown during numerical implementation and less sensitive to uncertainty in connectivity than the commonly used measures
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