MURAL - Maynooth University Research Archive Library



    Bounds on inference


    Calmon, Flavio P. and Varia, Mayank and Medard, Muriel and Christiansen, Mark M. and Duffy, Ken R. and Tessaro, Stefano (2013) Bounds on inference. Working Paper. arXiv.org.

    [img]
    Preview
    Download (187kB) | Preview


    Share your research

    Twitter Facebook LinkedIn GooglePlus Email more...



    Add this article to your Mendeley library


    Abstract

    Lower bounds for the average probability of error of estimating a hidden variable X given an observation of a correlated random variable Y , and Fano’s inequality in particular, play a central role in information theory. In this paper, we present a lower bound for the average estimation error based on the marginal distribution of X and the principal inertias of the joint distribution matrix of X and Y . Furthermore, we discuss an information measure based on the sum of the largest principal inertias, called k-correlation, which generalizes maximal correlation. We show that k-correlation satisfies the Data Processing Inequality and is convex in the conditional distribution of Y given X. Finally, we investigate how to answer a fundamental question in inference and privacy: given an observation Y , can we estimate a function f(X) of the hidden random variable X with an average error below a certain threshold? We provide a general method for answering this question using an approach based on rate-distortion theory.

    Item Type: Monograph (Working Paper)
    Additional Information: Paper given at the 51st Allerton Conference on Communication, Control, and Computing (2013). This work is sponsored by the Intelligence Advanced Research Projects Activity under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions and recommendations are those of the authors and are not necessarily endorsed by the United States Government. M.C. and K.D. are supported by Science Foundation Ireland Grant No. 11/PI/1177.
    Keywords: Bounds; inference; information theory; rate-distortion theory;
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 5982
    Identification Number: arXiv:1310.1512
    Depositing User: Dr Ken Duffy
    Date Deposited: 24 Mar 2015 17:02
    Publisher: arXiv.org
    Refereed: Yes
    Funders: Intelligence Advanced Research Projects Activity, Science Foundation Ireland (SFI)
    URI:
      Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

      Repository Staff Only(login required)

      View Item Item control page

      Downloads

      Downloads per month over past year

      Origin of downloads