102,188 research outputs found
Equitability, mutual information, and the maximal information coefficient
Reshef et al. recently proposed a new statistical measure, the "maximal
information coefficient" (MIC), for quantifying arbitrary dependencies between
pairs of stochastic quantities. MIC is based on mutual information, a
fundamental quantity in information theory that is widely understood to serve
this need. MIC, however, is not an estimate of mutual information. Indeed, it
was claimed that MIC possesses a desirable mathematical property called
"equitability" that mutual information lacks. This was not proven; instead it
was argued solely through the analysis of simulated data. Here we show that
this claim, in fact, is incorrect. First we offer mathematical proof that no
(non-trivial) dependence measure satisfies the definition of equitability
proposed by Reshef et al.. We then propose a self-consistent and more general
definition of equitability that follows naturally from the Data Processing
Inequality. Mutual information satisfies this new definition of equitability
while MIC does not. Finally, we show that the simulation evidence offered by
Reshef et al. was artifactual. We conclude that estimating mutual information
is not only practical for many real-world applications, but also provides a
natural solution to the problem of quantifying associations in large data sets
Estimating mutual information and multi--information in large networks
We address the practical problems of estimating the information relations
that characterize large networks. Building on methods developed for analysis of
the neural code, we show that reliable estimates of mutual information can be
obtained with manageable computational effort. The same methods allow
estimation of higher order, multi--information terms. These ideas are
illustrated by analyses of gene expression, financial markets, and consumer
preferences. In each case, information theoretic measures correlate with
independent, intuitive measures of the underlying structures in the system
Yet another puzzle? the relation between price and performance in the mutual fund industry
Gruber (1996) drew attention to the puzzle that investors buy actively-managed funds even though, on average, they underperform index funds. We uncover another puzzling fact about the market for actively-managed equity mutual funds: funds with worse before-fee performance charge higher fees. We then conduct a series of robustness checks and find that the apparently anomalous fee-performance relation survives all of them. Finally, we show that this relation may be explained as the outcome of strategic fee setting by mutual funds in the presence of investors with different degrees of sensitivity to performance
Understanding confounding effects in linguistic coordination: an information-theoretic approach
We suggest an information-theoretic approach for measuring stylistic
coordination in dialogues. The proposed measure has a simple predictive
interpretation and can account for various confounding factors through proper
conditioning. We revisit some of the previous studies that reported strong
signatures of stylistic accommodation, and find that a significant part of the
observed coordination can be attributed to a simple confounding effect - length
coordination. Specifically, longer utterances tend to be followed by longer
responses, which gives rise to spurious correlations in the other stylistic
features. We propose a test to distinguish correlations in length due to
contextual factors (topic of conversation, user verbosity, etc.) and
turn-by-turn coordination. We also suggest a test to identify whether stylistic
coordination persists even after accounting for length coordination and
contextual factors
Early life conditions and financial risk–taking in older age
Using life-history survey data from eleven European countries, we investigate whether childhood conditions, such as socioeconomic status, cognitive abilities and health problems influence portfolio choice and risk attitudes later in life. After controlling for the corresponding conditions in adulthood, we find that superior cognitive skills in childhood (especially mathematical abilities) are positively associated with stock and mutual fund ownership. Childhood socioeconomic status, as indicated by the number of rooms and by having at least some books in the house during childhood, is also positively associated with the ownership of stocks, mutual funds and individual retirement accounts, as well as with the willingness to take financial risks. On the other hand, less risky assets like bonds are not affected by early childhood conditions. We find only weak effects of childhood health problems on portfolio choice in adulthood. Finally, favorable childhood conditions affect the transition in and out of risky asset ownership, both by making divesting less likely and by facilitating investing (i.e., transitioning from non-ownership to ownership)
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