15,392 research outputs found
Bayesian Inference in Processing Experimental Data: Principles and Basic Applications
This report introduces general ideas and some basic methods of the Bayesian
probability theory applied to physics measurements. Our aim is to make the
reader familiar, through examples rather than rigorous formalism, with concepts
such as: model comparison (including the automatic Ockham's Razor filter
provided by the Bayesian approach); parametric inference; quantification of the
uncertainty about the value of physical quantities, also taking into account
systematic effects; role of marginalization; posterior characterization;
predictive distributions; hierarchical modelling and hyperparameters; Gaussian
approximation of the posterior and recovery of conventional methods, especially
maximum likelihood and chi-square fits under well defined conditions; conjugate
priors, transformation invariance and maximum entropy motivated priors; Monte
Carlo estimates of expectation, including a short introduction to Markov Chain
Monte Carlo methods.Comment: 40 pages, 2 figures, invited paper for Reports on Progress in Physic
Statistical physics-based reconstruction in compressed sensing
Compressed sensing is triggering a major evolution in signal acquisition. It
consists in sampling a sparse signal at low rate and later using computational
power for its exact reconstruction, so that only the necessary information is
measured. Currently used reconstruction techniques are, however, limited to
acquisition rates larger than the true density of the signal. We design a new
procedure which is able to reconstruct exactly the signal with a number of
measurements that approaches the theoretical limit in the limit of large
systems. It is based on the joint use of three essential ingredients: a
probabilistic approach to signal reconstruction, a message-passing algorithm
adapted from belief propagation, and a careful design of the measurement matrix
inspired from the theory of crystal nucleation. The performance of this new
algorithm is analyzed by statistical physics methods. The obtained improvement
is confirmed by numerical studies of several cases.Comment: 20 pages, 8 figures, 3 tables. Related codes and data are available
at http://aspics.krzakala.or
Towards a Principled Integration of Multi-Camera Re-Identification and Tracking through Optimal Bayes Filters
With the rise of end-to-end learning through deep learning, person detectors
and re-identification (ReID) models have recently become very strong.
Multi-camera multi-target (MCMT) tracking has not fully gone through this
transformation yet. We intend to take another step in this direction by
presenting a theoretically principled way of integrating ReID with tracking
formulated as an optimal Bayes filter. This conveniently side-steps the need
for data-association and opens up a direct path from full images to the core of
the tracker. While the results are still sub-par, we believe that this new,
tight integration opens many interesting research opportunities and leads the
way towards full end-to-end tracking from raw pixels.Comment: First two authors have equal contribution. This is initial work into
a new direction, not a benchmark-beating method. v2 only adds
acknowledgements and fixes a typo in e-mai
Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
Compressed sensing is a signal processing method that acquires data directly
in a compressed form. This allows one to make less measurements than what was
considered necessary to record a signal, enabling faster or more precise
measurement protocols in a wide range of applications. Using an
interdisciplinary approach, we have recently proposed in [arXiv:1109.4424] a
strategy that allows compressed sensing to be performed at acquisition rates
approaching to the theoretical optimal limits. In this paper, we give a more
thorough presentation of our approach, and introduce many new results. We
present the probabilistic approach to reconstruction and discuss its optimality
and robustness. We detail the derivation of the message passing algorithm for
reconstruction and expectation max- imization learning of signal-model
parameters. We further develop the asymptotic analysis of the corresponding
phase diagrams with and without measurement noise, for different distribution
of signals, and discuss the best possible reconstruction performances
regardless of the algorithm. We also present new efficient seeding matrices,
test them on synthetic data and analyze their performance asymptotically.Comment: 42 pages, 37 figures, 3 appendixe
Statistical mechanics of error exponents for error-correcting codes
Error exponents characterize the exponential decay, when increasing message
length, of the probability of error of many error-correcting codes. To tackle
the long standing problem of computing them exactly, we introduce a general,
thermodynamic, formalism that we illustrate with maximum-likelihood decoding of
low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and
the binary symmetric channel (BSC). In this formalism, we apply the cavity
method for large deviations to derive expressions for both the average and
typical error exponents, which differ by the procedure used to select the codes
from specified ensembles. When decreasing the noise intensity, we find that two
phase transitions take place, at two different levels: a glass to ferromagnetic
transition in the space of codewords, and a paramagnetic to glass transition in
the space of codes.Comment: 32 pages, 13 figure
Probabilistic Methodology and Techniques for Artefact Conception and Development
The purpose of this paper is to make a state of the art on probabilistic methodology and techniques for artefact conception and development. It is the 8th deliverable of the BIBA (Bayesian Inspired Brain and Artefacts) project. We first present the incompletness problem as the central difficulty that both living creatures and artefacts have to face: how can they perceive, infer, decide and act efficiently with incomplete and uncertain knowledge?. We then introduce a generic probabilistic formalism called Bayesian Programming. This formalism is then used to review the main probabilistic methodology
and techniques. This review is organized in 3 parts: first the probabilistic models from Bayesian networks to Kalman filters and from sensor fusion to CAD systems, second the inference techniques and finally the learning and model acquisition and comparison methodologies. We conclude with the perspectives of the BIBA project as they rise from this state of the art
Bounds on Information Combining With Quantum Side Information
"Bounds on information combining" are entropic inequalities that determine
how the information (entropy) of a set of random variables can change when
these are combined in certain prescribed ways. Such bounds play an important
role in classical information theory, particularly in coding and Shannon
theory; entropy power inequalities are special instances of them. The arguably
most elementary kind of information combining is the addition of two binary
random variables (a CNOT gate), and the resulting quantities play an important
role in Belief propagation and Polar coding. We investigate this problem in the
setting where quantum side information is available, which has been recognized
as a hard setting for entropy power inequalities.
Our main technical result is a non-trivial, and close to optimal, lower bound
on the combined entropy, which can be seen as an almost optimal "quantum Mrs.
Gerber's Lemma". Our proof uses three main ingredients: (1) a new bound on the
concavity of von Neumann entropy, which is tight in the regime of low pairwise
state fidelities; (2) the quantitative improvement of strong subadditivity due
to Fawzi-Renner, in which we manage to handle the minimization over recovery
maps; (3) recent duality results on classical-quantum-channels due to Renes et
al. We furthermore present conjectures on the optimal lower and upper bounds
under quantum side information, supported by interesting analytical
observations and strong numerical evidence.
We finally apply our bounds to Polar coding for binary-input
classical-quantum channels, and show the following three results: (A) Even
non-stationary channels polarize under the polar transform. (B) The blocklength
required to approach the symmetric capacity scales at most sub-exponentially in
the gap to capacity. (C) Under the aforementioned lower bound conjecture, a
blocklength polynomial in the gap suffices.Comment: 23 pages, 6 figures; v2: small correction
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