39,085 research outputs found
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Optimisation of Mobile Communication Networks - OMCO NET
The mini conference “Optimisation of Mobile Communication Networks” focuses on advanced methods for search and optimisation applied to wireless communication networks. It is sponsored by Research & Enterprise Fund Southampton Solent University.
The conference strives to widen knowledge on advanced search methods capable of optimisation of wireless communications networks. The aim is to provide a forum for exchange of recent knowledge, new ideas and trends in this progressive and challenging area. The conference will popularise new successful approaches on resolving hard tasks such as minimisation of transmit power, cooperative and optimal routing
Delineating Parameter Unidentifiabilities in Complex Models
Scientists use mathematical modelling to understand and predict the
properties of complex physical systems. In highly parameterised models there
often exist relationships between parameters over which model predictions are
identical, or nearly so. These are known as structural or practical
unidentifiabilities, respectively. They are hard to diagnose and make reliable
parameter estimation from data impossible. They furthermore imply the existence
of an underlying model simplification. We describe a scalable method for
detecting unidentifiabilities, and the functional relations defining them, for
generic models. This allows for model simplification, and appreciation of which
parameters (or functions thereof) cannot be estimated from data. Our algorithm
can identify features such as redundant mechanisms and fast timescale
subsystems, as well as the regimes in which such approximations are valid. We
base our algorithm on a novel quantification of regional parametric
sensitivity: multiscale sloppiness. Traditionally, the link between parametric
sensitivity and the conditioning of the parameter estimation problem is made
locally, through the Fisher Information Matrix. This is valid in the regime of
infinitesimal measurement uncertainty. We demonstrate the duality between
multiscale sloppiness and the geometry of confidence regions surrounding
parameter estimates made where measurement uncertainty is non-negligible.
Further theoretical relationships are provided linking multiscale sloppiness to
the Likelihood-ratio test. From this, we show that a local sensitivity analysis
(as typically done) is insufficient for determining the reliability of
parameter estimation, even with simple (non)linear systems. Our algorithm
provides a tractable alternative. We finally apply our methods to a
large-scale, benchmark Systems Biology model of NF-B, uncovering
previously unknown unidentifiabilities
Robust distributed linear programming
This paper presents a robust, distributed algorithm to solve general linear
programs. The algorithm design builds on the characterization of the solutions
of the linear program as saddle points of a modified Lagrangian function. We
show that the resulting continuous-time saddle-point algorithm is provably
correct but, in general, not distributed because of a global parameter
associated with the nonsmooth exact penalty function employed to encode the
inequality constraints of the linear program. This motivates the design of a
discontinuous saddle-point dynamics that, while enjoying the same convergence
guarantees, is fully distributed and scalable with the dimension of the
solution vector. We also characterize the robustness against disturbances and
link failures of the proposed dynamics. Specifically, we show that it is
integral-input-to-state stable but not input-to-state stable. The latter fact
is a consequence of a more general result, that we also establish, which states
that no algorithmic solution for linear programming is input-to-state stable
when uncertainty in the problem data affects the dynamics as a disturbance. Our
results allow us to establish the resilience of the proposed distributed
dynamics to disturbances of finite variation and recurrently disconnected
communication among the agents. Simulations in an optimal control application
illustrate the results
Optimization. An attempt at describing the State of the Art
This paper is an attempt at describing the State of the Art of the vast field of continuous optimization. We will survey deterministic and stochastic methods as well as hybrid approaches in their application to single objective and multiobjective optimization. We study the parameters of optimization algorithms and possibilities for tuning them. Finally, we discuss several methods for using approximate models for computationally expensive problems
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