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* Informatik-Oberseminar
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Zeit: Freitag, 11. Oktober 2024, 15:30 Uhr
Ort: Raum 5053.2 (großer B-IT-Hörsaal), Informatikzentrum, E2, Ahornstr. 55
Referentin: Bahare Salmani Barzoki, M.Sc.
Lehrstuhl für Softwaremodellierung und Verifikation (Informatik 2)
Thema: Probabilistic Model Checking and Parameter Tuning for Bayesian
Networks
Abstract:
Probabilistic reasoning is a key to handling uncertainties and making
decisions based on partial observations. Bayesian networks (BNs) are
popular probabilisticgraphical models in probabilistic decision-making
and AI and have a wide range of applications, including machine
learning, medicine, gene regulatory networks, and robotics. They combine
the notions from probability theory and graph theory and enablea
succinct representation of joint probability distributions.A Bayesian
network is composed of a directed acyclic graph over a set of random
variables and a set of conditional probability tables ---CPTs for short.
The primary task in Bayesian networks is probabilistic inference, that
is, to compute a conditional probability of a joint valuation for a
subset of random variables given an observation.
Probabilistic model checking is a field in computer science that
isfocusedon analyzing stochastic systems with respect toa set of
formally defined properties. The stochastic systems are typically Markov
models, and the properties of interest are probabilistic extensions of
LTL of CTL. The properties are mostly reducedto a pivotal task,
computing reachability probabilities: whatis the probability of reaching
a set of target states? Recent advancements in the field consider the
parametric extensions of the Markov models, where a subset of the
probabilities in the model are unknown and target various synthesis
problems including/feasibility checking/: is there a satisfying
instantiation that satisfies the given constraint?,/region
verification/: are all instantiations in a /region/ satisfy the given
constraint, and /parameter space partitioning/: split the entire
n-dimensional parameter space to sets of satisfying, rejecting, and
unknown subregions w.r.t. the given constraint.
In this dissertation, we present a new approach based on /probabilistic
model checking/ for inference and parameter tuning in Bayesian networks.
The dissertation is categorizedinto two main settings: the
/non-parametric/ and the /parametric/. In the non-parametric setting,we
focus on the classical Bayesian networks, where the model is fully
specified.We present mappings from Bayesian networks to discrete-time
Markov chains and mathematically reduce performing conditional inference
in the BN to computing reachability probabilities in Markov chains.
Thisenables the use of state-of-the-art algorithms for computing
reachability probabilities and the optimization techniques thereof,
e.g., bisimulation minimization for exact inference in BNs. We exploit
the explicit and symbolic methods from probabilistic model checking and
empirically evaluate our framework for Bayesian inference against the
state-of-the-art /weighted model counting. /In the parametric setting,we
define /parametric Bayesian networks (pBNs)/, where a subset of CPT
entries are unknown polynomials rather than concrete probabilities.We
build upon the synthesis techniques for parametric Markov chains and
address problems /sensitivity analysis/, /ratio/difference parameter
tuning/ from the BN literature, and /parameter space partitioning/from
pMC literature. Finally, we focus on the problem
/minimal-distanceparameter tunin/g, where the objective is to find the
instantiationu for the unknown parameters that satisfy the constraint of
interest while minimally deviating from the original instantiation u_0
in an original reference model. The motivation is to minimally disturb
the statistical information in the original model.
Our detailed experimental evaluations indicate that our parameter
synthesis techniques can treat parameter synthesis for Bayesian networks
(with hundreds of unknown parameters) that go beyond the capabilities of
the existing techniques. We lift the severe restrictions in the
literature on the number of unknown parameters, the global dependencies
between the parameters, and the form of obtained solutions.
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