4,092 research outputs found
Probabilistic Programming Concepts
A multitude of different probabilistic programming languages exists today,
all extending a traditional programming language with primitives to support
modeling of complex, structured probability distributions. Each of these
languages employs its own probabilistic primitives, and comes with a particular
syntax, semantics and inference procedure. This makes it hard to understand the
underlying programming concepts and appreciate the differences between the
different languages. To obtain a better understanding of probabilistic
programming, we identify a number of core programming concepts underlying the
primitives used by various probabilistic languages, discuss the execution
mechanisms that they require and use these to position state-of-the-art
probabilistic languages and their implementation. While doing so, we focus on
probabilistic extensions of logic programming languages such as Prolog, which
have been developed since more than 20 years
Reasoning about Independence in Probabilistic Models of Relational Data
We extend the theory of d-separation to cases in which data instances are not
independent and identically distributed. We show that applying the rules of
d-separation directly to the structure of probabilistic models of relational
data inaccurately infers conditional independence. We introduce relational
d-separation, a theory for deriving conditional independence facts from
relational models. We provide a new representation, the abstract ground graph,
that enables a sound, complete, and computationally efficient method for
answering d-separation queries about relational models, and we present
empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related
wor
Projectivity revisited
The behaviour of statistical relational representations across differently
sized domains has become a focal area of research from both a modelling and a
complexity viewpoint.Recently, projectivity of a family of distributions
emerged as a key property, ensuring that marginal probabilities are independent
of the domain size. However, the formalisation used currently assumes that the
domain is characterised only by its size. This contribution extends the notion
of projectivity from families of distributions indexed by domain size to
functors taking extensional data from a database. This makes projectivity
available for the large range of applications taking structured input. We
transfer key known results on projective families of distributions to the new
setting. This includes a characterisation of projective fragments in different
statistical relational formalisms as well as a general representation theorem
for projective families of distributions. Furthermore, we prove a
correspondence between projectivity and distributions on countably infinite
domains, which we use to unify and generalise earlier work on statistical
relational representations in infinite domains. Finally, we use the extended
notion of projectivity to define a further strengthening, which we call
-projectivity, and which allows the use of the same representation in
different modes while retaining projectivity.Comment: 30 page
Semantics, Modelling, and the Problem of Representation of Meaning -- a Brief Survey of Recent Literature
Over the past 50 years many have debated what representation should be used
to capture the meaning of natural language utterances. Recently new needs of
such representations have been raised in research. Here I survey some of the
interesting representations suggested to answer for these new needs.Comment: 15 pages, no figure
- …