76,869 research outputs found
Faithfulness and learning hypergraphs from discrete distributions
The concepts of faithfulness and strong-faithfulness are important for
statistical learning of graphical models. Graphs are not sufficient for
describing the association structure of a discrete distribution. Hypergraphs
representing hierarchical log-linear models are considered instead, and the
concept of parametric (strong-) faithfulness with respect to a hypergraph is
introduced. Strong-faithfulness ensures the existence of uniformly consistent
parameter estimators and enables building uniformly consistent procedures for a
hypergraph search. The strength of association in a discrete distribution can
be quantified with various measures, leading to different concepts of
strong-faithfulness. Lower and upper bounds for the proportions of
distributions that do not satisfy strong-faithfulness are computed for
different parameterizations and measures of association.Comment: 23 pages, 6 figure
Geometry of the faithfulness assumption in causal inference
Many algorithms for inferring causality rely heavily on the faithfulness
assumption. The main justification for imposing this assumption is that the set
of unfaithful distributions has Lebesgue measure zero, since it can be seen as
a collection of hypersurfaces in a hypercube. However, due to sampling error
the faithfulness condition alone is not sufficient for statistical estimation,
and strong-faithfulness has been proposed and assumed to achieve uniform or
high-dimensional consistency. In contrast to the plain faithfulness assumption,
the set of distributions that is not strong-faithful has nonzero Lebesgue
measure and in fact, can be surprisingly large as we show in this paper. We
study the strong-faithfulness condition from a geometric and combinatorial
point of view and give upper and lower bounds on the Lebesgue measure of
strong-faithful distributions for various classes of directed acyclic graphs.
Our results imply fundamental limitations for the PC-algorithm and potentially
also for other algorithms based on partial correlation testing in the Gaussian
case.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1080 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Norm estimates and asymptotic faithfulness of the quantum representations of the mapping class groups
We give a direct proof for the asymptotic faithfulness of the quantum
representations of the mapping class groups using peak sections in Kodaira
embedding. We give also estimates on the norm of the parallell transport of the
projective connection on the Verlinde bundle. The faithfulness has been proved
earlier in [1] using Toeplitz operators of compact K\"ahler manifolds and in
[10] using skein theory.Comment: Geometriae Dedicata (online), 10 pages, minor change
Towards Faithful Neural Table-to-Text Generation with Content-Matching Constraints
Text generation from a knowledge base aims to translate knowledge triples to
natural language descriptions. Most existing methods ignore the faithfulness
between a generated text description and the original table, leading to
generated information that goes beyond the content of the table. In this paper,
for the first time, we propose a novel Transformer-based generation framework
to achieve the goal. The core techniques in our method to enforce faithfulness
include a new table-text optimal-transport matching loss and a table-text
embedding similarity loss based on the Transformer model. Furthermore, to
evaluate faithfulness, we propose a new automatic metric specialized to the
table-to-text generation problem. We also provide detailed analysis on each
component of our model in our experiments. Automatic and human evaluations show
that our framework can significantly outperform state-of-the-art by a large
margin.Comment: Accepted at ACL202
Faithfulness of free product states
It is proved that the free product state, in the reduced free product of
C*-algebras, is faithful if the initial states are faithful
Imprinting a complete information about a quantum channel on its output state
We introduce a novel property of bipartite quantum states, which we call
"faithfulness", and we say that a state is faithful when acting with a channel
on one of the two quantum systems, the output state carries a complete
information about the channel. The concept of faithfulness can also be extended
to sets of states, when the output states patched together carry a complete
imprinting of the channel.Comment: revtex4, 4 pages, submitted to PR
Enriching the Symphony of Gravitational Waves from Binary Black Holes by Tuning Higher Harmonics
For the first time, we construct an inspiral-merger-ringdown waveform model
within the effective-one-body formalism for spinning, nonprecessing binary
black holes that includes gravitational modes beyond the dominant mode, specifically . Our multipolar
waveform model incorporates recent (resummed) post-Newtonian results for the
inspiral and information from 157 numerical-relativity simulations, and 13
waveforms from black-hole perturbation theory for the (plunge-)merger and
ringdown. We quantify the improved accuracy including higher-order modes by
computing the faithfulness of the waveform model against the
numerical-relativity waveforms used to construct the model. We define the
faithfulness as the match maximized over time, phase of arrival,
gravitational-wave polarization and sky position of the waveform model, and
averaged over binary orientation, gravitational-wave polarization and sky
position of the numerical-relativity waveform. When the waveform model contains
only the mode, we find that the averaged faithfulness to
numerical-relativity waveforms containing all modes with 5 ranges
from to for binaries with total mass (using
the Advanced LIGO's design noise curve). By contrast, when the
modes are also included in the model, the
faithfulness improves to for all but four configurations in the
numerical-relativity catalog, for which the faithfulness is greater than
. Using our results, we also develop also a (stand-alone) waveform
model for the merger-ringdown signal, calibrated to numerical-relativity
waveforms, which can be used to measure multiple quasi-normal modes. The
multipolar waveform model can be extended to include spin-precession, and will
be employed in upcoming observing runs of Advanced LIGO and Virgo.Comment: 28 page
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