516 research outputs found
Model averaging: A shrinkage perspective
Model averaging (MA), a technique for combining estimators from a set of
candidate models, has attracted increasing attention in machine learning and
statistics. In the existing literature, there is an implicit understanding that
MA can be viewed as a form of shrinkage estimation that draws the response
vector towards the subspaces spanned by the candidate models. This paper
explores this perspective by establishing connections between MA and shrinkage
in a linear regression setting with multiple nested models. We first
demonstrate that the optimal MA estimator is the best linear estimator with
monotone non-increasing weights in a Gaussian sequence model. The Mallows MA,
which estimates weights by minimizing the Mallows' , is a variation of the
positive-part Stein estimator. Motivated by these connections, we develop a
novel MA procedure based on a blockwise Stein estimation. Our resulting
Stein-type MA estimator is asymptotically optimal across a broad parameter
space when the variance is known. Numerical results support our theoretical
findings. The connections established in this paper may open up new avenues for
investigating MA from different perspectives. A discussion on some topics for
future research concludes the paper
Iterative quantum state transfer along a chain of nuclear spin qubits
Transferring quantum information between two qubits is a basic requirement
for many applications in quantum communication and quantum information
processing. In the iterative quantum state transfer (IQST) proposed by D.
Burgarth et al. [Phys. Rev. A 75, 062327 (2007)], this is achieved by a static
spin chain and a sequence of gate operations applied only to the receiving end
of the chain. The only requirement on the spin chain is that it transfers a
finite part of the input amplitude to the end of the chain, where the gate
operations accumulate the information. For an appropriate sequence of
evolutions and gate operations, the fidelity of the transfer can asymptotically
approach unity. We demonstrate the principle of operation of this transfer
scheme by implementing it in a nuclear magnetic resonance quantum information
processor.Comment: Version for submission. Comments are welcom
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