@techreport{TD:100358,
	att_abstract={{Consider the set of all sequences of  outcomes, each taking one
    of  values, that satisfy a number of linear constraints. If
     is fixed while  increases, most sequences that satisfy
    the constraints result in frequency vectors whose entropy approaches that
    of the maximum entropy vector satisfying the constraints. This well-known
    ``entropy concentration'' phenomenon underlies the maximum entropy
    method.

    Existing proofs of the concentration phenomenon are based on limits or
    asymptotics and unrealistically assume that constraints hold precisely,
    supporting maximum entropy inference more in principle than in practice.
    We present, for the first time,  non-asymptotic, explicit lower bounds
    on  for a number of variants of the concentration result to hold
    to any prescribed accuracies, with the constraints holding up to any
    specified tolerance, taking into account the fact that allocations of
    discrete units can satisfy constraints only approximately. Again unlike
    earlier results, we measure concentration not by deviation from the
    maximum entropy value, but by the > and
     distances >from the maximum entropy-achieving
    frequency vector. One of our results holds independently of the alphabet
    size  and is based on a novel proof technique using the
    multidimensional Berry-Esseen theorem. We illustrate and compare our
    results using various detailed examples.}},
	att_authors={ko2952},
	att_categories={C_CCF.6, C_CCF.8, C_CCF.3},
	att_copyright={{IEEE}},
	att_copyright_notice={{}},
	att_donotupload={true},
	att_private={false},
	att_projects={},
	att_tags={maximum entropy,  concentration,  bounds,  linear constraints,  tolerances},
	att_techdoc={true},
	att_techdoc_key={TD:100358},
	att_url={},
	author={Kostas Oikonomou and Peter D. Grunwald, CWI},
	institution={{IEEE Transactions on Information Theory}},
	month={March},
	title={{Explicit Bounds for Entropy Concentration under Linear Constraints}},
	year=2016,
}