333,258 research outputs found
Heterogeneous Change Point Inference
We propose HSMUCE (heterogeneous simultaneous multiscale change-point
estimator) for the detection of multiple change-points of the signal in a
heterogeneous gaussian regression model. A piecewise constant function is
estimated by minimizing the number of change-points over the acceptance region
of a multiscale test which locally adapts to changes in the variance. The
multiscale test is a combination of local likelihood ratio tests which are
properly calibrated by scale dependent critical values in order to keep a
global nominal level alpha, even for finite samples. We show that HSMUCE
controls the error of over- and underestimation of the number of change-points.
To this end, new deviation bounds for F-type statistics are derived. Moreover,
we obtain confidence sets for the whole signal. All results are non-asymptotic
and uniform over a large class of heterogeneous change-point models. HSMUCE is
fast to compute, achieves the optimal detection rate and estimates the number
of change-points at almost optimal accuracy for vanishing signals, while still
being robust. We compare HSMUCE with several state of the art methods in
simulations and analyse current recordings of a transmembrane protein in the
bacterial outer membrane with pronounced heterogeneity for its states. An
R-package is available online
Dynamical selection of Nash equilibria using Experience Weighted Attraction Learning: emergence of heterogeneous mixed equilibria
We study the distribution of strategies in a large game that models how
agents choose among different double auction markets. We classify the possible
mean field Nash equilibria, which include potentially segregated states where
an agent population can split into subpopulations adopting different
strategies. As the game is aggregative, the actual equilibrium strategy
distributions remain undetermined, however. We therefore compare with the
results of Experience-Weighted Attraction (EWA) learning, which at long times
leads to Nash equilibria in the appropriate limits of large intensity of
choice, low noise (long agent memory) and perfect imputation of missing scores
(fictitious play). The learning dynamics breaks the indeterminacy of the Nash
equilibria. Non-trivially, depending on how the relevant limits are taken, more
than one type of equilibrium can be selected. These include the standard
homogeneous mixed and heterogeneous pure states, but also \emph{heterogeneous
mixed} states where different agents play different strategies that are not all
pure. The analysis of the EWA learning involves Fokker-Planck modeling combined
with large deviation methods. The theoretical results are confirmed by
multi-agent simulations.Comment: 35 pages, 16 figure
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The Impact of Dual Credit as a School District Policy on Secondary and Postsecondary Student Outcomes
This study estimates the effects of dual credit on outcomes that trace a student’s journey from high school to undergraduate and graduate degree completion. Dual credit is a model program that allows high school students to enroll in college-level courses and simultaneously earn high school and college credit. This study investigates the potential for improving the design of dual-credit programs by exploring heterogeneous effects by program attributes. The study investigates if dual credit effects vary across course subjects. For a limited set of outcomes, the study investigates heterogeneous effects by the instructor’s highest degree earned, instruction mode, and location of instruction. Using panel data with school district fixed effects, this study finds that increases in the share of students earning dual credit are associated with increases in high school graduation; increases in university application, admission, and enrollment; shortened time to degree completion; and increases in degree completion. Districts that increase their average dual credit earned improve outcomes with each increase. Furthermore, dual credit courses produce larger increases in bachelor’s degree completion rates as compared to AP. Finally, evidence suggests that schools can most greatly amplify dual credit effects by prioritizing certain subjects.Ray Marshall Center for the Study of Human Resource
Bandwidth selection for kernel estimation in mixed multi-dimensional spaces
Kernel estimation techniques, such as mean shift, suffer from one major
drawback: the kernel bandwidth selection. The bandwidth can be fixed for all
the data set or can vary at each points. Automatic bandwidth selection becomes
a real challenge in case of multidimensional heterogeneous features. This paper
presents a solution to this problem. It is an extension of \cite{Comaniciu03a}
which was based on the fundamental property of normal distributions regarding
the bias of the normalized density gradient. The selection is done iteratively
for each type of features, by looking for the stability of local bandwidth
estimates across a predefined range of bandwidths. A pseudo balloon mean shift
filtering and partitioning are introduced. The validity of the method is
demonstrated in the context of color image segmentation based on a
5-dimensional space
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