135,921 research outputs found
No stratification without representation
Sortition is an alternative approach to democracy, in which representatives are not elected but randomly selected from the population. Most electoral democracies fail to accurately represent even a handful of protected groups. By contrast, sortition guarantees that every subset of the population will in expectation fill their fair share of the available positions. This fairness property remains satisfied when the sample is stratified based on known features. Moreover, stratification can greatly reduce the variance in the number of positions filled by any unknown group, as long as this group correlates with the strata. Our main result is that stratification cannot increase this variance by more than a negligible factor, even in the presence of indivisibilities and rounding. When the unknown group is unevenly spread across strata, we give a guarantee on the reduction in variance with respect to uniform sampling. We also contextualize stratification and uniform sampling in the space of fair sampling algorithms. Finally, we apply our insights to an empirical case study.Accepted manuscrip
Stratification Trees for Adaptive Randomization in Randomized Controlled Trials
This paper proposes an adaptive randomization procedure for two-stage
randomized controlled trials. The method uses data from a first-wave experiment
in order to determine how to stratify in a second wave of the experiment, where
the objective is to minimize the variance of an estimator for the average
treatment effect (ATE). We consider selection from a class of stratified
randomization procedures which we call stratification trees: these are
procedures whose strata can be represented as decision trees, with differing
treatment assignment probabilities across strata. By using the first wave to
estimate a stratification tree, we simultaneously select which covariates to
use for stratification, how to stratify over these covariates, as well as the
assignment probabilities within these strata. Our main result shows that using
this randomization procedure with an appropriate estimator results in an
asymptotic variance which is minimal in the class of stratification trees.
Moreover, the results we present are able to accommodate a large class of
assignment mechanisms within strata, including stratified block randomization.
In a simulation study, we find that our method, paired with an appropriate
cross-validation procedure ,can improve on ad-hoc choices of stratification. We
conclude by applying our method to the study in Karlan and Wood (2017), where
we estimate stratification trees using the first wave of their experiment
ABJM amplitudes and the positive orthogonal grassmannian
A remarkable connection between perturbative scattering amplitudes of
four-dimensional planar SYM, and the stratification of the positive
grassmannian, was revealed in the seminal work of Arkani-Hamed et. al. Similar
extension for three-dimensional ABJM theory was proposed. Here we establish a
direct connection between planar scattering amplitudes of ABJM theory, and
singularities there of, to the stratification of the positive orthogonal
grassmannian. In particular, scattering processes are constructed through
on-shell diagrams, which are simply iterative gluing of the fundamental
four-point amplitude. Each diagram is then equivalent to the merging of
fundamental OG_2 orthogonal grassmannian to form a larger OG_k, where 2k is the
number of external particles. The invariant information that is encoded in each
diagram is precisely this stratification. This information can be easily read
off via permutation paths of the on-shell diagram, which also can be used to
derive a canonical representation of OG_k that manifests the vanishing of
consecutive minors as the singularity of all on-shell diagrams. Quite
remarkably, for the BCFW recursion representation of the tree-level amplitudes,
the on-shell diagram manifests the presence of all physical factorization
poles, as well as the cancellation of the spurious poles. After analytically
continuing the orthogonal grassmannian to split signature, we reveal that each
on-shell diagram in fact resides in the positive cell of the orthogonal
grassmannian, where all minors are positive. In this language, the amplitudes
of ABJM theory is simply an integral of a product of dlog forms, over the
positive orthogonal grassmannian.Comment: 52 pages: v2, typos corrected, published version in JHE
Cohomology of U(2,1) representation varieties of surface groups
In this paper we use the Morse theory of the Yang-Mills-Higgs functional on
the singular space of Higgs bundles on Riemann surfaces to compute the
equivariant cohomology of the space of semistable U(2,1) and SU(2,1) Higgs
bundles with fixed Toledo invariant. In the non-coprime case this gives new
results about the topology of the U(2,1) and SU(2,1) character varieties of
surface groups. The main results are a calculation of the equivariant Poincare
polynomials, a Kirwan surjectivity theorem in the non-fixed determinant case,
and a description of the action of the Torelli group on the equivariant
cohomology of the character variety. This builds on earlier work for stable
pairs and rank 2 Higgs bundles.Comment: 34 page
Generalized Team Draft Interleaving
Interleaving is an online evaluation method that compares
two ranking functions by mixing their results and interpret-
ing the users' click feedback. An important property of
an interleaving method is its sensitivity, i.e. the ability to
obtain reliable comparison outcomes with few user interac-
tions. Several methods have been proposed so far to im-
prove interleaving sensitivity, which can be roughly divided
into two areas: (a) methods that optimize the credit assign-
ment function (how the click feedback is interpreted), and
(b) methods that achieve higher sensitivity by controlling
the interleaving policy (how often a particular interleaved
result page is shown).
In this paper, we propose an interleaving framework that
generalizes the previously studied interleaving methods in
two aspects. First, it achieves a higher sensitivity by per-
forming a joint data-driven optimization of the credit as-
signment function and the interleaving policy. Second, we
formulate the framework to be general w.r.t. the search do-
main where the interleaving experiment is deployed, so that
it can be applied in domains with grid-based presentation,
such as image search. In order to simplify the optimization,
we additionally introduce a stratifed estimate of the exper-
iment outcome. This stratifcation is also useful on its own,
as it reduces the variance of the outcome and thus increases
the interleaving sensitivity.
We perform an extensive experimental study using large-
scale document and image search datasets obtained from
a commercial search engine. The experiments show that
our proposed framework achieves marked improvements in
sensitivity over efective baselines on both datasets
Initial Draft of a Possible Declarative Semantics for the Language
This article introduces a preliminary declarative semantics for a subset of the language Xcerpt (so-called
grouping-stratifiable programs) in form of a classical (Tarski style) model theory, adapted to the specific
requirements of Xcerpt’s constructs (e.g. the various aspects of incompleteness in query terms, grouping
constructs in rule heads, etc.). Most importantly, the model theory uses term simulation as a replacement
for term equality to handle incomplete term specifications, and an extended notion of substitutions in
order to properly convey the semantics of grouping constructs. Based upon this model theory, a fixpoint
semantics is also described, leading to a first notion of forward chaining evaluation of Xcerpt program
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