333 research outputs found
Quantum Inference on Bayesian Networks
Performing exact inference on Bayesian networks is known to be #P-hard.
Typically approximate inference techniques are used instead to sample from the
distribution on query variables given the values of evidence variables.
Classically, a single unbiased sample is obtained from a Bayesian network on
variables with at most parents per node in time
, depending critically on , the probability the
evidence might occur in the first place. By implementing a quantum version of
rejection sampling, we obtain a square-root speedup, taking
time per sample. We exploit the Bayesian
network's graph structure to efficiently construct a quantum state, a q-sample,
representing the intended classical distribution, and also to efficiently apply
amplitude amplification, the source of our speedup. Thus, our speedup is
notable as it is unrelativized -- we count primitive operations and require no
blackbox oracle queries.Comment: 8 pages, 3 figures. Submitted to PR
Broadcasting on Random Directed Acyclic Graphs
We study a generalization of the well-known model of broadcasting on trees.
Consider a directed acyclic graph (DAG) with a unique source vertex , and
suppose all other vertices have indegree . Let the vertices at
distance from be called layer . At layer , is given a random
bit. At layer , each vertex receives bits from its parents in
layer , which are transmitted along independent binary symmetric channel
edges, and combines them using a -ary Boolean processing function. The goal
is to reconstruct with probability of error bounded away from using
the values of all vertices at an arbitrarily deep layer. This question is
closely related to models of reliable computation and storage, and information
flow in biological networks.
In this paper, we analyze randomly constructed DAGs, for which we show that
broadcasting is only possible if the noise level is below a certain degree and
function dependent critical threshold. For , and random DAGs with
layer sizes and majority processing functions, we identify the
critical threshold. For , we establish a similar result for NAND
processing functions. We also prove a partial converse for odd
illustrating that the identified thresholds are impossible to improve by
selecting different processing functions if the decoder is restricted to using
a single vertex.
Finally, for any noise level, we construct explicit DAGs (using expander
graphs) with bounded degree and layer sizes admitting
reconstruction. In particular, we show that such DAGs can be generated in
deterministic quasi-polynomial time or randomized polylogarithmic time in the
depth. These results portray a doubly-exponential advantage for storing a bit
in DAGs compared to trees, where but layer sizes must grow exponentially
with depth in order to enable broadcasting.Comment: 33 pages, double column format. arXiv admin note: text overlap with
arXiv:1803.0752
Influential Listeners: An Experiment on Persuasion Bias in Social Networks
This paper presents an experimental investigation of persuasion bias, a form of bounded rationality whereby agents communicating through a social network are unable to account for possible repetitions in the information they receive. The results indicate that network structure plays a significant role in determining social influence. However, the most influential agents are not those with more outgoing links, as predicted by the persuasion bias hypothesis, but those with more incoming links. We show that a boundedly rational updating rule that takes into account not only agents' outdegree, but also their indegree, provides a better explanation of the experimental data. In this framework, consensus beliefs tend to be swayed towards the opinions of influential listeners. We then present an effort-weighted updating model as a more general characterization of information aggregation in social networks.
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