14,403 research outputs found
The Limitations of Using School League Tables to Inform School Choice
In England, so-called ‘league tables’ based upon examination results and test scores are published annually, ostensibly to inform parental choice of secondary schools. A crucial limitation of these tables is that the most recent published information is based on the current performance of a cohort of pupils who entered secondary schools several years earlier, whereas for choosing a school it is the future performance of the current cohort that is of interest. We show that there is substantial uncertainty in predicting such future performance and that incorporating this uncertainty leads to a situation where only a handful of schools’ future performances can be separated from both the overall mean and from one another with an acceptable degree of precision. This suggests that school league tables, including value-added ones, have very little to offer as guides to school choice.Examination results, Institutional comparisons, League tables, Multilevel modelling, Performance indicators, Ranking, School choice, School effectiveness, Value-added
The sign rule and beyond: Boundary effects, flexibility, and noise correlations in neural population codes
Over repeat presentations of the same stimulus, sensory neurons show variable
responses. This "noise" is typically correlated between pairs of cells, and a
question with rich history in neuroscience is how these noise correlations
impact the population's ability to encode the stimulus. Here, we consider a
very general setting for population coding, investigating how information
varies as a function of noise correlations, with all other aspects of the
problem - neural tuning curves, etc. - held fixed. This work yields unifying
insights into the role of noise correlations. These are summarized in the form
of theorems, and illustrated with numerical examples involving neurons with
diverse tuning curves. Our main contributions are as follows.
(1) We generalize previous results to prove a sign rule (SR) - if noise
correlations between pairs of neurons have opposite signs vs. their signal
correlations, then coding performance will improve compared to the independent
case. This holds for three different metrics of coding performance, and for
arbitrary tuning curves and levels of heterogeneity. This generality is true
for our other results as well.
(2) As also pointed out in the literature, the SR does not provide a
necessary condition for good coding. We show that a diverse set of correlation
structures can improve coding. Many of these violate the SR, as do
experimentally observed correlations. There is structure to this diversity: we
prove that the optimal correlation structures must lie on boundaries of the
possible set of noise correlations.
(3) We provide a novel set of necessary and sufficient conditions, under
which the coding performance (in the presence of noise) will be as good as it
would be if there were no noise present at all.Comment: 41 pages, 5 figure
Speeding up Permutation Testing in Neuroimaging
Multiple hypothesis testing is a significant problem in nearly all
neuroimaging studies. In order to correct for this phenomena, we require a
reliable estimate of the Family-Wise Error Rate (FWER). The well known
Bonferroni correction method, while simple to implement, is quite conservative,
and can substantially under-power a study because it ignores dependencies
between test statistics. Permutation testing, on the other hand, is an exact,
non-parametric method of estimating the FWER for a given -threshold,
but for acceptably low thresholds the computational burden can be prohibitive.
In this paper, we show that permutation testing in fact amounts to populating
the columns of a very large matrix . By analyzing the spectrum of this
matrix, under certain conditions, we see that has a low-rank plus a
low-variance residual decomposition which makes it suitable for highly
sub--sampled --- on the order of --- matrix completion methods. Based
on this observation, we propose a novel permutation testing methodology which
offers a large speedup, without sacrificing the fidelity of the estimated FWER.
Our evaluations on four different neuroimaging datasets show that a
computational speedup factor of roughly can be achieved while
recovering the FWER distribution up to very high accuracy. Further, we show
that the estimated -threshold is also recovered faithfully, and is
stable.Comment: NIPS 1
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