3,665 research outputs found
Symbolic Exact Inference for Discrete Probabilistic Programs
The computational burden of probabilistic inference remains a hurdle for
applying probabilistic programming languages to practical problems of interest.
In this work, we provide a semantic and algorithmic foundation for efficient
exact inference on discrete-valued finite-domain imperative probabilistic
programs. We leverage and generalize efficient inference procedures for
Bayesian networks, which exploit the structure of the network to decompose the
inference task, thereby avoiding full path enumeration. To do this, we first
compile probabilistic programs to a symbolic representation. Then we adapt
techniques from the probabilistic logic programming and artificial intelligence
communities in order to perform inference on the symbolic representation. We
formalize our approach, prove it sound, and experimentally validate it against
existing exact and approximate inference techniques. We show that our inference
approach is competitive with inference procedures specialized for Bayesian
networks, thereby expanding the class of probabilistic programs that can be
practically analyzed
Automated Experiment Design for Data-Efficient Verification of Parametric Markov Decision Processes
We present a new method for statistical verification of quantitative
properties over a partially unknown system with actions, utilising a
parameterised model (in this work, a parametric Markov decision process) and
data collected from experiments performed on the underlying system. We obtain
the confidence that the underlying system satisfies a given property, and show
that the method uses data efficiently and thus is robust to the amount of data
available. These characteristics are achieved by firstly exploiting parameter
synthesis to establish a feasible set of parameters for which the underlying
system will satisfy the property; secondly, by actively synthesising
experiments to increase amount of information in the collected data that is
relevant to the property; and finally propagating this information over the
model parameters, obtaining a confidence that reflects our belief whether or
not the system parameters lie in the feasible set, thereby solving the
verification problem.Comment: QEST 2017, 18 pages, 7 figure
How Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics of Deterministic Chaos
Symbolic dynamics has proven to be an invaluable tool in analyzing the
mechanisms that lead to unpredictability and random behavior in nonlinear
dynamical systems. Surprisingly, a discrete partition of continuous state space
can produce a coarse-grained description of the behavior that accurately
describes the invariant properties of an underlying chaotic attractor. In
particular, measures of the rate of information production--the topological and
metric entropy rates--can be estimated from the outputs of Markov or generating
partitions. Here we develop Bayesian inference for k-th order Markov chains as
a method to finding generating partitions and estimating entropy rates from
finite samples of discretized data produced by coarse-grained dynamical
systems.Comment: 8 pages, 1 figure; http://cse.ucdavis.edu/~cmg/compmech/pubs/hrct.ht
Quantum Theory and Determinism
Historically, appearance of the quantum theory led to a prevailing view that
Nature is indeterministic. The arguments for the indeterminism and proposals
for indeterministic and deterministic approaches are reviewed. These include
collapse theories, Bohmian Mechanics and the many-worlds interpretation. It is
argued that ontic interpretations of the quantum wave function provide simpler
and clearer physical explanation and that the many-worlds interpretation is the
most attractive since it provides a deterministic and local theory for our
physical Universe explaining the illusion of randomness and nonlocality in the
world we experience.Comment: Some references updated. Published online in Quantum Studies:
Mathematics and Foundation
Deep determinism and the assessment of mechanistic interaction between categorical and continuous variables
Our aim is to detect mechanistic interaction between the effects of two
causal factors on a binary response, as an aid to identifying situations where
the effects are mediated by a common mechanism. We propose a formalization of
mechanistic interaction which acknowledges asymmetries of the kind "factor A
interferes with factor B, but not viceversa". A class of tests for mechanistic
interaction is proposed, which works on discrete or continuous causal
variables, in any combination. Conditions under which these tests can be
applied under a generic regime of data collection, be it interventional or
observational, are discussed in terms of conditional independence assumptions
within the framework of Augmented Directed Graphs. The scientific relevance of
the method and the practicality of the graphical framework are illustrated with
the aid of two studies in coronary artery disease. Our analysis relies on the
"deep determinism" assumption that there exists some relevant set V - possibly
unobserved - of "context variables", such that the response Y is a
deterministic function of the values of V and of the causal factors of
interest. Caveats regarding this assumption in real studies are discussed.Comment: 20 pages including the four figures, plus two tables. Submitted to
"Biostatistics" on November 24, 201
- …