2,479 research outputs found
Encoding Markov Logic Networks in Possibilistic Logic
Markov logic uses weighted formulas to compactly encode a probability
distribution over possible worlds. Despite the use of logical formulas, Markov
logic networks (MLNs) can be difficult to interpret, due to the often
counter-intuitive meaning of their weights. To address this issue, we propose a
method to construct a possibilistic logic theory that exactly captures what can
be derived from a given MLN using maximum a posteriori (MAP) inference.
Unfortunately, the size of this theory is exponential in general. We therefore
also propose two methods which can derive compact theories that still capture
MAP inference, but only for specific types of evidence. These theories can be
used, among others, to make explicit the hidden assumptions underlying an MLN
or to explain the predictions it makes.Comment: Extended version of a paper appearing in UAI 201
Induction of Interpretable Possibilistic Logic Theories from Relational Data
The field of Statistical Relational Learning (SRL) is concerned with learning
probabilistic models from relational data. Learned SRL models are typically
represented using some kind of weighted logical formulas, which make them
considerably more interpretable than those obtained by e.g. neural networks. In
practice, however, these models are often still difficult to interpret
correctly, as they can contain many formulas that interact in non-trivial ways
and weights do not always have an intuitive meaning. To address this, we
propose a new SRL method which uses possibilistic logic to encode relational
models. Learned models are then essentially stratified classical theories,
which explicitly encode what can be derived with a given level of certainty.
Compared to Markov Logic Networks (MLNs), our method is faster and produces
considerably more interpretable models.Comment: Longer version of a paper appearing in IJCAI 201
Uncertainty Analysis of the Adequacy Assessment Model of a Distributed Generation System
Due to the inherent aleatory uncertainties in renewable generators, the
reliability/adequacy assessments of distributed generation (DG) systems have
been particularly focused on the probabilistic modeling of random behaviors,
given sufficient informative data. However, another type of uncertainty
(epistemic uncertainty) must be accounted for in the modeling, due to
incomplete knowledge of the phenomena and imprecise evaluation of the related
characteristic parameters. In circumstances of few informative data, this type
of uncertainty calls for alternative methods of representation, propagation,
analysis and interpretation. In this study, we make a first attempt to
identify, model, and jointly propagate aleatory and epistemic uncertainties in
the context of DG systems modeling for adequacy assessment. Probability and
possibility distributions are used to model the aleatory and epistemic
uncertainties, respectively. Evidence theory is used to incorporate the two
uncertainties under a single framework. Based on the plausibility and belief
functions of evidence theory, the hybrid propagation approach is introduced. A
demonstration is given on a DG system adapted from the IEEE 34 nodes
distribution test feeder. Compared to the pure probabilistic approach, it is
shown that the hybrid propagation is capable of explicitly expressing the
imprecision in the knowledge on the DG parameters into the final adequacy
values assessed. It also effectively captures the growth of uncertainties with
higher DG penetration levels
Belief Revision with Uncertain Inputs in the Possibilistic Setting
This paper discusses belief revision under uncertain inputs in the framework
of possibility theory. Revision can be based on two possible definitions of the
conditioning operation, one based on min operator which requires a purely
ordinal scale only, and another based on product, for which a richer structure
is needed, and which is a particular case of Dempster's rule of conditioning.
Besides, revision under uncertain inputs can be understood in two different
ways depending on whether the input is viewed, or not, as a constraint to
enforce. Moreover, it is shown that M.A. Williams' transmutations, originally
defined in the setting of Spohn's functions, can be captured in this framework,
as well as Boutilier's natural revision.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in
Artificial Intelligence (UAI1996
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