Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic elimination of partially continuous aggregation functions in
  directed graphical models   In Statistical Relational Artificial Intelligence, a branch of AI and machine
learning which combines the logical and statistical schools of AI, one uses the
concept {\em para\-metrized probabilistic graphical model (PPGM)} to model
(conditional) dependencies between random variables and to make probabilistic
inferences about events on a space of "possible worlds". The set of possible
worlds with underlying domain $D$ (a set of objects) can be represented by the
set $\mathbf{W}_D$ of all first-order structures (for a suitable signature)
with domain $D$. Using a formal logic we can describe events on $\mathbf{W}_D$.
By combining a logic and a PPGM we can also define a probability distribution
$\mathbb{P}_D$ on $\mathbf{W}_D$ and use it to compute the probability of an
event. We consider a logic, denoted $PLA$, with truth values in the unit
interval, which uses aggregation functions, such as arithmetic mean, geometric
mean, maximum and minimum instead of quantifiers. However we face the problem
of computational efficiency and this problem is an obstacle to the wider use of
methods from Statistical Relational AI in practical applications. We address
this problem by proving that the described probability will, under certain
assumptions on the PPGM and the sentence $\varphi$, converge as the size of $D$
tends to infinity. The convergence result is obtained by showing that every
formula $\varphi(x_1, \ldots, x_k)$ which contains only "admissible"
aggregation functions (e.g. arithmetic and geometric mean, max and min) is
asymptotically equivalent to a formula $\psi(x_1, \ldots, x_k)$ without
aggregation functions.

15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph