Next talk of the Seminar (14:30, Room Sousa Pinto)
12/06/2024: “Generalization of the Belief
Propagation Algorithm”
Joana Martins (CIDMA, Universidade de Aveiro)
The Belief
Propagation (BP) Algorithm is an inference algorithm with applications to any system that can be represented as a factor
graph. Meanwhile, algorithms such the forward/backward algorithm, the
Viterbi algorithm, the iterative “turbo” decoding algorithm, the Kalman
filter and certain fast Fourier transform algorithms are also specific
instances of the BP algorithm.
In this seminar it will be presented a
generalization of the BP Algorithm so it can be applied
to broader variety of inference problems. For that we define a 'Lset
theory', based on a fuzzy logic and the concept of membership functions, as
well as a 'Smeasurable space', based on the concept of measurable spaces and
aggregation functions. A 'generalised' factor graph will then be defined
from a pair of aggregations functions (which satisfy certain conditions but
that can be different to the sum and product functions of the standard
factor graph). Such a factor graph can be more particularly called a
'measurable factor graph' if defined on a Smeasurable space (in the
standard case, on a probability space).
This Seminar is supported in part by the
Portuguese Foundation for Science and Technology (FCT  Fundação para a Ciência e a Tecnologia),
through CIDMA  Center for Research and Development in Mathematics and
Applications, within project UIDB/04106/2020
(https://doi.org/10.54499/UIDB/04106/2020).
