39,818 research outputs found
Shaded Tangles for the Design and Verification of Quantum Programs (Extended Abstract)
We give a scheme for interpreting shaded tangles as quantum programs, with
the property that isotopic tangles yield equivalent programs. We analyze many
known quantum programs in this way -- including entanglement manipulation and
error correction -- and in each case present a fully-topological formal
verification, yielding in several cases substantial new insight into how the
program works. We also use our methods to identify several new or generalized
procedures.Comment: In Proceedings QPL 2017, arXiv:1802.0973
On the accuracy of language trees
Historical linguistics aims at inferring the most likely language
phylogenetic tree starting from information concerning the evolutionary
relatedness of languages. The available information are typically lists of
homologous (lexical, phonological, syntactic) features or characters for many
different languages.
From this perspective the reconstruction of language trees is an example of
inverse problems: starting from present, incomplete and often noisy,
information, one aims at inferring the most likely past evolutionary history. A
fundamental issue in inverse problems is the evaluation of the inference made.
A standard way of dealing with this question is to generate data with
artificial models in order to have full access to the evolutionary process one
is going to infer. This procedure presents an intrinsic limitation: when
dealing with real data sets, one typically does not know which model of
evolution is the most suitable for them. A possible way out is to compare
algorithmic inference with expert classifications. This is the point of view we
take here by conducting a thorough survey of the accuracy of reconstruction
methods as compared with the Ethnologue expert classifications. We focus in
particular on state-of-the-art distance-based methods for phylogeny
reconstruction using worldwide linguistic databases.
In order to assess the accuracy of the inferred trees we introduce and
characterize two generalizations of standard definitions of distances between
trees. Based on these scores we quantify the relative performances of the
distance-based algorithms considered. Further we quantify how the completeness
and the coverage of the available databases affect the accuracy of the
reconstruction. Finally we draw some conclusions about where the accuracy of
the reconstructions in historical linguistics stands and about the leading
directions to improve it.Comment: 36 pages, 14 figure
"Influence Sketching": Finding Influential Samples In Large-Scale Regressions
There is an especially strong need in modern large-scale data analysis to
prioritize samples for manual inspection. For example, the inspection could
target important mislabeled samples or key vulnerabilities exploitable by an
adversarial attack. In order to solve the "needle in the haystack" problem of
which samples to inspect, we develop a new scalable version of Cook's distance,
a classical statistical technique for identifying samples which unusually
strongly impact the fit of a regression model (and its downstream predictions).
In order to scale this technique up to very large and high-dimensional
datasets, we introduce a new algorithm which we call "influence sketching."
Influence sketching embeds random projections within the influence computation;
in particular, the influence score is calculated using the randomly projected
pseudo-dataset from the post-convergence Generalized Linear Model (GLM). We
validate that influence sketching can reliably and successfully discover
influential samples by applying the technique to a malware detection dataset of
over 2 million executable files, each represented with almost 100,000 features.
For example, we find that randomly deleting approximately 10% of training
samples reduces predictive accuracy only slightly from 99.47% to 99.45%,
whereas deleting the same number of samples with high influence sketch scores
reduces predictive accuracy all the way down to 90.24%. Moreover, we find that
influential samples are especially likely to be mislabeled. In the case study,
we manually inspect the most influential samples, and find that influence
sketching pointed us to new, previously unidentified pieces of malware.Comment: fixed additional typo
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