1,459 research outputs found
An Estimation and Analysis Framework for the Rasch Model
The Rasch model is widely used for item response analysis in applications
ranging from recommender systems to psychology, education, and finance. While a
number of estimators have been proposed for the Rasch model over the last
decades, the available analytical performance guarantees are mostly asymptotic.
This paper provides a framework that relies on a novel linear minimum
mean-squared error (L-MMSE) estimator which enables an exact, nonasymptotic,
and closed-form analysis of the parameter estimation error under the Rasch
model. The proposed framework provides guidelines on the number of items and
responses required to attain low estimation errors in tests or surveys. We
furthermore demonstrate its efficacy on a number of real-world collaborative
filtering datasets, which reveals that the proposed L-MMSE estimator performs
on par with state-of-the-art nonlinear estimators in terms of predictive
performance.Comment: To be presented at ICML 201
Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations
Climate projections continue to be marred by large uncertainties, which
originate in processes that need to be parameterized, such as clouds,
convection, and ecosystems. But rapid progress is now within reach. New
computational tools and methods from data assimilation and machine learning
make it possible to integrate global observations and local high-resolution
simulations in an Earth system model (ESM) that systematically learns from
both. Here we propose a blueprint for such an ESM. We outline how
parameterization schemes can learn from global observations and targeted
high-resolution simulations, for example, of clouds and convection, through
matching low-order statistics between ESMs, observations, and high-resolution
simulations. We illustrate learning algorithms for ESMs with a simple dynamical
system that shares characteristics of the climate system; and we discuss the
opportunities the proposed framework presents and the challenges that remain to
realize it.Comment: 32 pages, 3 figure
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