26 research outputs found
Visual characterization of associative quasitrivial nondecreasing operations on finite chains
In this paper we provide visual characterization of associative quasitrivial
nondecreasing operations on finite chains. We also provide a characterization
of bisymmetric quasitrivial nondecreasing binary operations on finite chains.
Finally, we estimate the number of functions belonging to the previous classes.Comment: 25 pages, 18 Figure
Fitting aggregation operators to data
Theoretical advances in modelling aggregation of information produced a wide range of aggregation operators, applicable to almost every practical problem. The most important classes of aggregation operators include triangular norms, uninorms, generalised means and OWA operators.With such a variety, an important practical problem has emerged: how to fit the parameters/ weights of these families of aggregation operators to observed data? How to estimate quantitatively whether a given class of operators is suitable as a model in a given practical setting? Aggregation operators are rather special classes of functions, and thus they require specialised regression techniques, which would enforce important theoretical properties, like commutativity or associativity. My presentation will address this issue in detail, and will discuss various regression methods applicable specifically to t-norms, uninorms and generalised means. I will also demonstrate software implementing these regression techniques, which would allow practitioners to paste their data and obtain optimal parameters of the chosen family of operators.<br /
Learning Aggregation Functions
Learning on sets is increasingly gaining attention in the machine learning
community, due to its widespread applicability. Typically, representations over
sets are computed by using fixed aggregation functions such as sum or maximum.
However, recent results showed that universal function representation by sum-
(or max-) decomposition requires either highly discontinuous (and thus poorly
learnable) mappings, or a latent dimension equal to the maximum number of
elements in the set. To mitigate this problem, we introduce a learnable
aggregation function (LAF) for sets of arbitrary cardinality. LAF can
approximate several extensively used aggregators (such as average, sum,
maximum) as well as more complex functions (e.g., variance and skewness). We
report experiments on semi-synthetic and real data showing that LAF outperforms
state-of-the-art sum- (max-) decomposition architectures such as DeepSets and
library-based architectures like Principal Neighborhood Aggregation, and can be
effectively combined with attention-based architectures.Comment: Extended version (with proof appendix) of paper that is to appear in
Proceedings of IJCAI 202
Visual characterization of associative quasitrivial nondecreasing functions on finite chains
In this paper we provide visual characterization of associative quasitrivial nondecreasing operations on finite chains. We also provide a characterization of bisymmetric quasitrivial nondecreasing binary operations on finite chains. Finally, we estimate the number of functions belonging to the previous classes