2,128 research outputs found
On the Bayes-optimality of F-measure maximizers
The F-measure, which has originally been introduced in information retrieval,
is nowadays routinely used as a performance metric for problems such as binary
classification, multi-label classification, and structured output prediction.
Optimizing this measure is a statistically and computationally challenging
problem, since no closed-form solution exists. Adopting a decision-theoretic
perspective, this article provides a formal and experimental analysis of
different approaches for maximizing the F-measure. We start with a Bayes-risk
analysis of related loss functions, such as Hamming loss and subset zero-one
loss, showing that optimizing such losses as a surrogate of the F-measure leads
to a high worst-case regret. Subsequently, we perform a similar type of
analysis for F-measure maximizing algorithms, showing that such algorithms are
approximate, while relying on additional assumptions regarding the statistical
distribution of the binary response variables. Furthermore, we present a new
algorithm which is not only computationally efficient but also Bayes-optimal,
regardless of the underlying distribution. To this end, the algorithm requires
only a quadratic (with respect to the number of binary responses) number of
parameters of the joint distribution. We illustrate the practical performance
of all analyzed methods by means of experiments with multi-label classification
problems
T-Duality, and the K-Theoretic Partition Function of TypeIIA Superstring Theory
We study the partition function of type IIA string theory on 10-manifolds of
the form T^2 x X where X is 8-dimensional, compact, and spin. We pay particular
attention to the effects of the topological phases in the supergravity action
implied by the K-theoretic formulation of RR fields, and we use these to check
the T-duality invariance of the partition function. We find that the partition
function is only T-duality invariant when we take into account the T-duality
anomalies in the RR sector, the fermionic path integral (including 4-fermi
interaction terms), and 1-loop corrections including worldsheet instantons. We
comment on applications of our computation to speculations about the role of
the Romans mass in M-theory. We also discuss some issues which arise when one
attempts to extend these considerations to checking the full U-duality
invariance of the theory.Comment: 73 pages, harvmac, b-mod
Heights of one- and two-sided congruence lattices of semigroups
The height of a poset is the supremum of the cardinalities of chains in
. The exact formula for the height of the subgroup lattice of the symmetric
group is known, as is an accurate asymptotic formula for the
height of the subsemigroup lattice of the full transformation monoid
. Motivated by the related question of determining the heights
of the lattices of left- and right congruences of , we develop a
general method for computing the heights of lattices of both one- and two-sided
congruences for semigroups. We apply this theory to obtain exact height
formulae for several monoids of transformations, matrices and partitions,
including: the full transformation monoid , the partial
transformation monoid , the symmetric inverse monoid
, the monoid of order-preserving transformations
, the full matrix monoid , the partition
monoid , the Brauer monoid and the
Temperley-Lieb monoid
A methodology for producing reliable software, volume 1
An investigation into the areas having an impact on producing reliable software including automated verification tools, software modeling, testing techniques, structured programming, and management techniques is presented. This final report contains the results of this investigation, analysis of each technique, and the definition of a methodology for producing reliable software
On the Bayes-optimality of F-measure maximizers
The F-measure, which has originally been introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction. Optimizing this measure is a statistically and computationally challenging problem, since no closed-form solution exists. Adopting a decision-theoretic perspective, this article provides a formal and experimental analysis of different approaches for maximizing the F-measure. We start with a Bayes-risk analysis of related loss functions, such as Hamming loss and subset zero-one loss, showing that optimizing such losses as a surrogate of the F-measure leads to a high worst-case regret. Subsequently, we perform a similar type of analysis for F-measure maximizing algorithms, showing that such algorithms are approximate, while relying on additional assumptions regarding the statistical distribution of the binary response variables. Furthermore, we present a new algorithm which is not only computationally efficient but also Bayes-optimal, regardless of the underlying distribution. To this end, the algorithm requires only a quadratic (with respect to the number of binary responses) number of parameters of the joint distribution. We illustrate the practical performance of all analyzed methods by means of experiments with multi-label classification problems
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