203 research outputs found
Mismatched Quantum Filtering and Entropic Information
Quantum filtering is a signal processing technique that estimates the
posterior state of a quantum system under continuous measurements and has
become a standard tool in quantum information processing, with applications in
quantum state preparation, quantum metrology, and quantum control. If the
filter assumes a nominal model that differs from reality, however, the
estimation accuracy is bound to suffer. Here I derive identities that relate
the excess error caused by quantum filter mismatch to the relative entropy
between the true and nominal observation probability measures, with one
identity for Gaussian measurements, such as optical homodyne detection, and
another for Poissonian measurements, such as photon counting. These identities
generalize recent seminal results in classical information theory and provide
new operational meanings to relative entropy, mutual information, and channel
capacity in the context of quantum experiments.Comment: v1: first draft, 8 pages, v2: added introduction and more results on
mutual information and channel capacity, 12 pages, v3: minor updates, v4:
updated the presentatio
Unconstrained Dynamic Regret via Sparse Coding
Motivated by the challenge of nonstationarity in sequential decision making,
we study Online Convex Optimization (OCO) under the coupling of two problem
structures: the domain is unbounded, and the comparator sequence
is arbitrarily time-varying. As no algorithm can guarantee low
regret simultaneously against all comparator sequences, handling this setting
requires moving from minimax optimality to comparator adaptivity. That is,
sensible regret bounds should depend on certain complexity measures of the
comparator relative to one's prior knowledge.
This paper achieves a new type of these adaptive regret bounds via a sparse
coding framework. The complexity of the comparator is measured by its energy
and its sparsity on a user-specified dictionary, which offers considerable
versatility. Equipped with a wavelet dictionary for example, our framework
improves the state-of-the-art bound (Jacobsen & Cutkosky, 2022) by adapting to
both () the magnitude of the comparator average , rather than the maximum ; and ()
the comparator variability , rather than the
uncentered sum . Furthermore, our analysis is simpler due
to decoupling function approximation from regret minimization.Comment: Split the two results from the previous version. Expanded the results
on Haar wavelets. Improved writin
A tutorial introduction to the minimum description length principle
This tutorial provides an overview of and introduction to Rissanen's Minimum
Description Length (MDL) Principle. The first chapter provides a conceptual,
entirely non-technical introduction to the subject. It serves as a basis for
the technical introduction given in the second chapter, in which all the ideas
of the first chapter are made mathematically precise. The main ideas are
discussed in great conceptual and technical detail. This tutorial is an
extended version of the first two chapters of the collection "Advances in
Minimum Description Length: Theory and Application" (edited by P.Grunwald, I.J.
Myung and M. Pitt, to be published by the MIT Press, Spring 2005).Comment: 80 pages 5 figures Report with 2 chapter
Preference Learning
This report documents the program and the outcomes of Dagstuhl Seminar 14101 “Preference Learning”. Preferences have recently received considerable attention in disciplines such as machine learning, knowledge discovery, information retrieval, statistics, social choice theory, multiple criteria decision making, decision under risk and uncertainty, operations research, and others. The motivation for this seminar was to showcase recent progress in these different areas with the goal of working towards a common basis of understanding, which should help to facilitate future synergies
Scenario-based portfolio model for building robust and proactive strategies
In order to address major changes in the operational environment, companies can (i) define scenarios that characterize different alternatives for this environment, (ii) assign probabilities to these scenarios, (iii) evaluate the performance of strategic actions across the scenarios, and (iv) choose those actions that are expected to perform best. In this paper, we develop a portfolio model to support the selection of such strategic actions when the information about scenario probabilities is possibly incomplete and may depend on the selected actions. This model helps build a strategy that is robust in that it performs relatively well in view of all available probability information, and proactive in that it can help steer the future as reflected by the scenarios toward the desired direction. We also report a case study in which the model helped a group of Nordic, globally operating steel and engineering companies build a platform ecosystem strategy that accounts for uncertainties related to markets, politics, and technological development
The minimum description length principle
The pdf file in the repository consists only if the preface, foreword and chapter 1; I am not allowed by the publisher to put the remainder of this book on the web.
If you are a member of the CWI evaluation committee and yu read this: you are of course entitled to access the full book. If you would like to see it, please contact CWI (or, even easier, contact me directly), and we will be happy to give you a copy of the book for free
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