3,577 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
An exploration of two infinite families of snarks
Thesis (M.S.) University of Alaska Fairbanks, 2019In this paper, we generalize a single example of a snark that admits a drawing with even rotational symmetry into two infinite families using a voltage graph construction techniques derived from cyclic Pseudo-Loupekine snarks. We expose an enforced chirality in coloring the underlying 5-pole that generated the known example, and use this fact to show that the infinite families are in fact snarks. We explore the construction of these families in terms of the blowup construction. We show that a graph in either family with rotational symmetry of order m has automorphism group of order m2m⁺¹. The oddness of graphs in both families is determined exactly, and shown to increase linearly with the order of rotational symmetry.Chapter 1: Introduction -- 1.1 General Graph Theory -- Chapter 2: Introduction to Snarks -- 2.1 History -- 2.2 Motivation -- 2.3 Loupekine Snarks and k-poles -- 2.4 Conditions on Triviality -- Chapter 3: The Construction of Two Families of Snarks -- 3.1 Voltage Graphs and Lifts -- 3.2 The Family of Snarks, Fm -- 3.3 A Second Family of Snarks, Rm -- Chapter 4: Results -- 4.1 Proof that the graphs Fm and Rm are Snarks -- 4.2 Interpreting Fm and Rm as Blowup Graphs -- 4.3 Automorphism Group -- 4.4 Oddness -- Chapter 5: Conclusions and Open Questions -- References
Food Environment, Food Store Access, Consumer Behavior, and Diet
Food Environment, Food Deserts, Obesity, Consumer Behavior, Diet, Food Consumption/Nutrition/Food Safety, I18, R50,
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
Efficient Estimation of Mutual Information for Strongly Dependent Variables
We demonstrate that a popular class of nonparametric mutual information (MI)
estimators based on k-nearest-neighbor graphs requires number of samples that
scales exponentially with the true MI. Consequently, accurate estimation of MI
between two strongly dependent variables is possible only for prohibitively
large sample size. This important yet overlooked shortcoming of the existing
estimators is due to their implicit reliance on local uniformity of the
underlying joint distribution. We introduce a new estimator that is robust to
local non-uniformity, works well with limited data, and is able to capture
relationship strengths over many orders of magnitude. We demonstrate the
superior performance of the proposed estimator on both synthetic and real-world
data.Comment: 13 pages, to appear in International Conference on Artificial
Intelligence and Statistics (AISTATS) 201
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