10,362 research outputs found
The Consistency dimension and distribution-dependent learning from queries
We prove a new combinatorial characterization of polynomial
learnability from equivalence queries, and state some of its
consequences relating the learnability of a class with the
learnability via equivalence and membership queries of its
subclasses obtained by restricting the instance space.
Then we propose and study two models of query learning in which there
is a probability distribution on the instance space, both as an
application of the tools developed from the combinatorial
characterization and as models of independent interest.Postprint (published version
Counterexample-Guided Data Augmentation
We present a novel framework for augmenting data sets for machine learning
based on counterexamples. Counterexamples are misclassified examples that have
important properties for retraining and improving the model. Key components of
our framework include a counterexample generator, which produces data items
that are misclassified by the model and error tables, a novel data structure
that stores information pertaining to misclassifications. Error tables can be
used to explain the model's vulnerabilities and are used to efficiently
generate counterexamples for augmentation. We show the efficacy of the proposed
framework by comparing it to classical augmentation techniques on a case study
of object detection in autonomous driving based on deep neural networks
The LU-LC conjecture is false
The LU-LC conjecture is an important open problem concerning the structure of
entanglement of states described in the stabilizer formalism. It states that
two local unitary equivalent stabilizer states are also local Clifford
equivalent. If this conjecture were true, the local equivalence of stabilizer
states would be extremely easy to characterize. Unfortunately, however, based
on the recent progress made by Gross and Van den Nest, we find that the
conjecture is false.Comment: Added a new part explaining how the counterexamples are foun
On The Positive Definiteness of Polarity Coincidence Correlation Coefficient Matrix
Polarity coincidence correlator (PCC), when used to estimate the covariance
matrix on an element-by-element basis, may not yield a positive semi-definite
(PSD) estimate. Devlin et al. [1], claimed that element-wise PCC is not
guaranteed to be PSD in dimensions p>3 for real signals. However, no
justification or proof was available on this issue. In this letter, it is
proved that for real signals with p<=3 and for complex signals with p<=2, a PSD
estimate is guaranteed. Counterexamples are presented for higher dimensions
which yield invalid covariance estimates.Comment: IEEE Signal Processing Letters, Volume 15, pp. 73-76, 200
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