218 research outputs found
Unsupervised Learning via Total Correlation Explanation
Learning by children and animals occurs effortlessly and largely without
obvious supervision. Successes in automating supervised learning have not
translated to the more ambiguous realm of unsupervised learning where goals and
labels are not provided. Barlow (1961) suggested that the signal that brains
leverage for unsupervised learning is dependence, or redundancy, in the sensory
environment. Dependence can be characterized using the information-theoretic
multivariate mutual information measure called total correlation. The principle
of Total Cor-relation Ex-planation (CorEx) is to learn representations of data
that "explain" as much dependence in the data as possible. We review some
manifestations of this principle along with successes in unsupervised learning
problems across diverse domains including human behavior, biology, and
language.Comment: Invited contribution for IJCAI 2017 Early Career Spotlight. 5 pages,
1 figur
Relaxed uncertainty relations and information processing
We consider a range of "theories" that violate the uncertainty relation for
anti-commuting observables derived in [JMP, 49, 062105 (2008)]. We first show
that Tsirelson's bound for the CHSH inequality can be derived from this
uncertainty relation, and that relaxing this relation allows for non-local
correlations that are stronger than what can be obtained in quantum mechanics.
We continue to construct a hierarchy of related non-signaling theories, and
show that on one hand they admit superstrong random access encodings and
exponential savings for a particular communication problem, while on the other
hand it becomes much harder in these theories to learn a state. We show that
the existence of these effects stems from the absence of certain constraints on
the expectation values of commuting measurements from our non-signaling
theories that are present in quantum theory.Comment: 33 pages, 1 figure. v2: improved notation, to appear in QI
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