750 research outputs found
Quantum estimation via minimum Kullback entropy principle
We address quantum estimation in situations where one has at disposal data
from the measurement of an incomplete set of observables and some a priori
information on the state itself. By expressing the a priori information in
terms of a bias toward a given state the problem may be faced by minimizing the
quantum relative entropy (Kullback entropy) with the constraint of reproducing
the data. We exploit the resulting minimum Kullback entropy principle for the
estimation of a quantum state from the measurement of a single observable,
either from the sole mean value or from the complete probability distribution,
and apply it as a tool for the estimation of weak Hamiltonian processes. Qubit
and harmonic oscillator systems are analyzed in some details.Comment: 7 pages, slightly revised version, no figure
A Quantitative Occam's Razor
This paper derives an objective Bayesian "prior" based on considerations of
entropy/information. By this means, it produces a quantitative measure of
goodness of fit (the "H-statistic") that balances higher likelihood against the
number of fitting parameters employed. The method is intended for
phenomenological applications where the underlying theory is uncertain or
unknown.
For example, it can help decide whether the large angle anomalies in the CMB
data should be taken seriously.
I am therefore posting it now, even though it was published before the arxiv
existed.Comment: plainTeX, 16 pages, no figures. Most current version is available at
http://www.physics.syr.edu/~sorkin/some.papers/ (or wherever my home-page may
be
Fairness-Aware Ranking in Search & Recommendation Systems with Application to LinkedIn Talent Search
We present a framework for quantifying and mitigating algorithmic bias in
mechanisms designed for ranking individuals, typically used as part of
web-scale search and recommendation systems. We first propose complementary
measures to quantify bias with respect to protected attributes such as gender
and age. We then present algorithms for computing fairness-aware re-ranking of
results. For a given search or recommendation task, our algorithms seek to
achieve a desired distribution of top ranked results with respect to one or
more protected attributes. We show that such a framework can be tailored to
achieve fairness criteria such as equality of opportunity and demographic
parity depending on the choice of the desired distribution. We evaluate the
proposed algorithms via extensive simulations over different parameter choices,
and study the effect of fairness-aware ranking on both bias and utility
measures. We finally present the online A/B testing results from applying our
framework towards representative ranking in LinkedIn Talent Search, and discuss
the lessons learned in practice. Our approach resulted in tremendous
improvement in the fairness metrics (nearly three fold increase in the number
of search queries with representative results) without affecting the business
metrics, which paved the way for deployment to 100% of LinkedIn Recruiter users
worldwide. Ours is the first large-scale deployed framework for ensuring
fairness in the hiring domain, with the potential positive impact for more than
630M LinkedIn members.Comment: This paper has been accepted for publication at ACM KDD 201
Effective rate equations for the over-damped motion in fluctuating potentials
We discuss physical and mathematical aspects of the over-damped motion of a
Brownian particle in fluctuating potentials. It is shown that such a system can
be described quantitatively by fluctuating rates if the potential fluctuations
are slow compared to relaxation within the minima of the potential, and if the
position of the minima does not fluctuate. Effective rates can be calculated;
they describe the long-time dynamics of the system. Furthermore, we show the
existence of a stationary solution of the Fokker-Planck equation that describes
the motion within the fluctuating potential under some general conditions. We
also show that a stationary solution of the rate equations with fluctuating
rates exists.Comment: 18 pages, 2 figures, standard LaTeX2
Probability density of determinants of random matrices
In this brief paper the probability density of a random real, complex and
quaternion determinant is rederived using singular values. The behaviour of
suitably rescaled random determinants is studied in the limit of infinite order
of the matrices
Information Theory based on Non-additive Information Content
We generalize the Shannon's information theory in a nonadditive way by
focusing on the source coding theorem. The nonadditive information content we
adopted is consistent with the concept of the form invariance structure of the
nonextensive entropy. Some general properties of the nonadditive information
entropy are studied, in addition, the relation between the nonadditivity
and the codeword length is pointed out.Comment: 9 pages, no figures, RevTex, accepted for publication in Phys. Rev.
E(an error in proof of theorem 1 was corrected, typos corrected
Some Objects Are More Equal Than Others: Measuring and Predicting Importance
We observe that everyday images contain dozens of objects, and that humans, in describing these images, give different priority to these objects. We argue that a goal of visual recognition is, therefore, not only to detect and classify objects but also to associate with each a level of priority which we call 'importance'. We propose a definition of importance and show how this may be estimated reliably from data harvested from human observers. We conclude by showing that a first-order estimate of importance may be computed from a number of simple image region measurements and does not require access to image meaning
Statistical distinguishability between unitary operations
The problem of distinguishing two unitary transformations, or quantum gates,
is analyzed and a function reflecting their statistical distinguishability is
found. Given two unitary operations, and , it is proved that there
always exists a finite number such that and are perfectly distinguishable, although they were not in the single-copy
case. This result can be extended to any finite set of unitary transformations.
Finally, a fidelity for one-qubit gates, which satisfies many useful properties
from the point of view of quantum information theory, is presented.Comment: 6 pages, REVTEX. The perfect distinguishability result is extended to
any finite set of gate
Quantifying Self-Organization with Optimal Predictors
Despite broad interest in self-organizing systems, there are few
quantitative, experimentally-applicable criteria for self-organization. The
existing criteria all give counter-intuitive results for important cases. In
this Letter, we propose a new criterion, namely an internally-generated
increase in the statistical complexity, the amount of information required for
optimal prediction of the system's dynamics. We precisely define this
complexity for spatially-extended dynamical systems, using the probabilistic
ideas of mutual information and minimal sufficient statistics. This leads to a
general method for predicting such systems, and a simple algorithm for
estimating statistical complexity. The results of applying this algorithm to a
class of models of excitable media (cyclic cellular automata) strongly support
our proposal.Comment: Four pages, two color figure
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