119,162 research outputs found
Pairwise MRF Calibration by Perturbation of the Bethe Reference Point
We investigate different ways of generating approximate solutions to the
pairwise Markov random field (MRF) selection problem. We focus mainly on the
inverse Ising problem, but discuss also the somewhat related inverse Gaussian
problem because both types of MRF are suitable for inference tasks with the
belief propagation algorithm (BP) under certain conditions. Our approach
consists in to take a Bethe mean-field solution obtained with a maximum
spanning tree (MST) of pairwise mutual information, referred to as the
\emph{Bethe reference point}, for further perturbation procedures. We consider
three different ways following this idea: in the first one, we select and
calibrate iteratively the optimal links to be added starting from the Bethe
reference point; the second one is based on the observation that the natural
gradient can be computed analytically at the Bethe point; in the third one,
assuming no local field and using low temperature expansion we develop a dual
loop joint model based on a well chosen fundamental cycle basis. We indeed
identify a subclass of planar models, which we refer to as \emph{Bethe-dual
graph models}, having possibly many loops, but characterized by a singly
connected dual factor graph, for which the partition function and the linear
response can be computed exactly in respectively O(N) and operations,
thanks to a dual weight propagation (DWP) message passing procedure that we set
up. When restricted to this subclass of models, the inverse Ising problem being
convex, becomes tractable at any temperature. Experimental tests on various
datasets with refined or regularization procedures indicate that
these approaches may be competitive and useful alternatives to existing ones.Comment: 54 pages, 8 figure. section 5 and refs added in V
Adaptive weight estimator for quantum error correction
Quantum error correction of a surface code or repetition code requires the
pairwise matching of error events in a space-time graph of qubit measurements,
such that the total weight of the matching is minimized. The input weights
follow from a physical model of the error processes that affect the qubits.
This approach becomes problematic if the system has sources of error that
change over time. Here we show how the weights can be determined from the
measured data in the absence of an error model. The resulting adaptive decoder
performs well in a time-dependent environment, provided that the characteristic
time scale of the variations is greater than , with the duration of one error-correction cycle and
the typical error probability per qubit in one cycle.Comment: 5 pages, 4 figure
The Complexity Of The NP-Class
This paper presents a novel and straight formulation, and gives a complete
insight towards the understanding of the complexity of the problems of the so
called NP-Class. In particular, this paper focuses in the Searching of the
Optimal Geometrical Structures and the Travelling Salesman Problems. The main
results are the polynomial reduction procedure and the solution to the Noted
Conjecture of the NP-Class
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