8,331 research outputs found
Approximating Likelihood Ratios with Calibrated Discriminative Classifiers
In many fields of science, generalized likelihood ratio tests are established
tools for statistical inference. At the same time, it has become increasingly
common that a simulator (or generative model) is used to describe complex
processes that tie parameters of an underlying theory and measurement
apparatus to high-dimensional observations .
However, simulator often do not provide a way to evaluate the likelihood
function for a given observation , which motivates a new class of
likelihood-free inference algorithms. In this paper, we show that likelihood
ratios are invariant under a specific class of dimensionality reduction maps
. As a direct consequence, we show that
discriminative classifiers can be used to approximate the generalized
likelihood ratio statistic when only a generative model for the data is
available. This leads to a new machine learning-based approach to
likelihood-free inference that is complementary to Approximate Bayesian
Computation, and which does not require a prior on the model parameters.
Experimental results on artificial problems with known exact likelihoods
illustrate the potential of the proposed method.Comment: 35 pages, 5 figure
Testing quantum mechanics: a statistical approach
As experiments continue to push the quantum-classical boundary using
increasingly complex dynamical systems, the interpretation of experimental data
becomes more and more challenging: when the observations are noisy, indirect,
and limited, how can we be sure that we are observing quantum behavior? This
tutorial highlights some of the difficulties in such experimental tests of
quantum mechanics, using optomechanics as the central example, and discusses
how the issues can be resolved using techniques from statistics and insights
from quantum information theory.Comment: v1: 2 pages; v2: invited tutorial for Quantum Measurements and
Quantum Metrology, substantial expansion of v1, 19 pages; v3: accepted; v4:
corrected some errors, publishe
The Emergence of Gravitational Wave Science: 100 Years of Development of Mathematical Theory, Detectors, Numerical Algorithms, and Data Analysis Tools
On September 14, 2015, the newly upgraded Laser Interferometer
Gravitational-wave Observatory (LIGO) recorded a loud gravitational-wave (GW)
signal, emitted a billion light-years away by a coalescing binary of two
stellar-mass black holes. The detection was announced in February 2016, in time
for the hundredth anniversary of Einstein's prediction of GWs within the theory
of general relativity (GR). The signal represents the first direct detection of
GWs, the first observation of a black-hole binary, and the first test of GR in
its strong-field, high-velocity, nonlinear regime. In the remainder of its
first observing run, LIGO observed two more signals from black-hole binaries,
one moderately loud, another at the boundary of statistical significance. The
detections mark the end of a decades-long quest, and the beginning of GW
astronomy: finally, we are able to probe the unseen, electromagnetically dark
Universe by listening to it. In this article, we present a short historical
overview of GW science: this young discipline combines GR, arguably the
crowning achievement of classical physics, with record-setting, ultra-low-noise
laser interferometry, and with some of the most powerful developments in the
theory of differential geometry, partial differential equations,
high-performance computation, numerical analysis, signal processing,
statistical inference, and data science. Our emphasis is on the synergy between
these disciplines, and how mathematics, broadly understood, has historically
played, and continues to play, a crucial role in the development of GW science.
We focus on black holes, which are very pure mathematical solutions of
Einstein's gravitational-field equations that are nevertheless realized in
Nature, and that provided the first observed signals.Comment: 41 pages, 5 figures. To appear in Bulletin of the American
Mathematical Societ
Maximal adaptive-decision speedups in quantum-state readout
The average time required for high-fidelity readout of quantum states can
be significantly reduced via a real-time adaptive decision rule. An adaptive
decision rule stops the readout as soon as a desired level of confidence has
been achieved, as opposed to setting a fixed readout time . The
performance of the adaptive decision is characterized by the "adaptive-decision
speedup," . In this work, we reformulate this readout problem in terms
of the first-passage time of a particle undergoing stochastic motion. This
formalism allows us to theoretically establish the maximum achievable
adaptive-decision speedups for several physical two-state readout
implementations. We show that for two common readout schemes (the Gaussian
latching readout and a readout relying on state-dependent decay), the speedup
is bounded by and , respectively, in the limit of high single-shot
readout fidelity. We experimentally study the achievable speedup in a
real-world scenario by applying the adaptive decision rule to a readout of the
nitrogen-vacancy-center (NV-center) charge state. We find a speedup of with our experimental parameters. In addition, we propose a simple readout
scheme for which the speedup can, in principle, be increased without bound as
the fidelity is increased. Our results should lead to immediate improvements in
nanoscale magnetometry based on spin-to-charge conversion of the NV-center
spin, and provide a theoretical framework for further optimization of the
bandwidth of quantum measurements.Comment: 18 pages, 11 figures. This version is close to the published versio
Quantum Tomography
This is the draft version of a review paper which is going to appear in
"Advances in Imaging and Electron Physics"Comment: To appear in "Advances in Imaging and Electron Physics". Some figs
with low resolutio
Quantum metrology with nonclassical states of atomic ensembles
Quantum technologies exploit entanglement to revolutionize computing,
measurements, and communications. This has stimulated the research in different
areas of physics to engineer and manipulate fragile many-particle entangled
states. Progress has been particularly rapid for atoms. Thanks to the large and
tunable nonlinearities and the well developed techniques for trapping,
controlling and counting, many groundbreaking experiments have demonstrated the
generation of entangled states of trapped ions, cold and ultracold gases of
neutral atoms. Moreover, atoms can couple strongly to external forces and light
fields, which makes them ideal for ultra-precise sensing and time keeping. All
these factors call for generating non-classical atomic states designed for
phase estimation in atomic clocks and atom interferometers, exploiting
many-body entanglement to increase the sensitivity of precision measurements.
The goal of this article is to review and illustrate the theory and the
experiments with atomic ensembles that have demonstrated many-particle
entanglement and quantum-enhanced metrology.Comment: 76 pages, 40 figures, 1 table, 603 references. Some figures bitmapped
at 300 dpi to reduce file siz
PeX 1. Multi-spectral expansion of residual speckles for planet detection
The detection of exoplanets in coronographic images is severely limited by
residual starlight speckles. Dedicated post-processing can drastically reduce
this "stellar leakage" and thereby increase the faintness of detectable
exoplanets. Based on a multi-spectral series expansion of the diffraction
pattern, we derive a multi-mode model of the residuals which can be exploited
to estimate and thus remove the residual speckles in multi-spectral
coronographic images. Compared to other multi-spectral processing methods, our
model is physically grounded and is suitable for use in an (optimal) inverse
approach. We demonstrate the ability of our model to correctly estimate the
speckles in simulated data and demonstrate that very high contrasts can be
achieved. We further apply our method to removing speckles from a real data
cube obtained with the SPHERE IFS instrument.Comment: accepted for publication in MNRAS on 25th of August 2017, 17 pages,
15 figure
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