16,111 research outputs found
Bethe Projections for Non-Local Inference
Many inference problems in structured prediction are naturally solved by
augmenting a tractable dependency structure with complex, non-local auxiliary
objectives. This includes the mean field family of variational inference
algorithms, soft- or hard-constrained inference using Lagrangian relaxation or
linear programming, collective graphical models, and forms of semi-supervised
learning such as posterior regularization. We present a method to
discriminatively learn broad families of inference objectives, capturing
powerful non-local statistics of the latent variables, while maintaining
tractable and provably fast inference using non-Euclidean projected gradient
descent with a distance-generating function given by the Bethe entropy. We
demonstrate the performance and flexibility of our method by (1) extracting
structured citations from research papers by learning soft global constraints,
(2) achieving state-of-the-art results on a widely-used handwriting recognition
task using a novel learned non-convex inference procedure, and (3) providing a
fast and highly scalable algorithm for the challenging problem of inference in
a collective graphical model applied to bird migration.Comment: minor bug fix to appendix. appeared in UAI 201
Numerical methods for a Kohn-Sham density functional model based on optimal transport
In this paper, we study numerical discretizations to solve density functional
models in the "strictly correlated electrons" (SCE) framework. Unlike previous
studies our work is not restricted to radially symmetric densities. In the SCE
framework, the exchange-correlation functional encodes the effects of the
strong correlation regime by minimizing the pairwise Coulomb repulsion,
resulting in an optimal transport problem. We give a mathematical derivation of
the self-consistent Kohn-Sham-SCE equations, construct an efficient numerical
discretization for this type of problem for N = 2 electrons, and apply it to
the H2 molecule in its dissociating limit. Moreover, we prove that the SCE
density functional model is correct for the H2 molecule in its dissociating
limit.Comment: 22 pages, 6 figure
Integrated risk/cost planning models for the US Air Traffic system
A prototype network planning model for the U.S. Air Traffic control system is described. The model encompasses the dual objectives of managing collision risks and transportation costs where traffic flows can be related to these objectives. The underlying structure is a network graph with nonseparable convex costs; the model is solved efficiently by capitalizing on its intrinsic characteristics. Two specialized algorithms for solving the resulting problems are described: (1) truncated Newton, and (2) simplicial decomposition. The feasibility of the approach is demonstrated using data collected from a control center in the Midwest. Computational results with different computer systems are presented, including a vector supercomputer (CRAY-XMP). The risk/cost model has two primary uses: (1) as a strategic planning tool using aggregate flight information, and (2) as an integrated operational system for forecasting congestion and monitoring (controlling) flow throughout the U.S. In the latter case, access to a supercomputer is required due to the model's enormous size
Shadow Prices in PMP and Consequences for Calibration and Estimation of Programming Models
Demand and Price Analysis,
Sampling, Intervention, Prediction, Aggregation: A Generalized Framework for Model-Agnostic Interpretations
Model-agnostic interpretation techniques allow us to explain the behavior of
any predictive model. Due to different notations and terminology, it is
difficult to see how they are related. A unified view on these methods has been
missing. We present the generalized SIPA (sampling, intervention, prediction,
aggregation) framework of work stages for model-agnostic interpretations and
demonstrate how several prominent methods for feature effects can be embedded
into the proposed framework. Furthermore, we extend the framework to feature
importance computations by pointing out how variance-based and
performance-based importance measures are based on the same work stages. The
SIPA framework reduces the diverse set of model-agnostic techniques to a single
methodology and establishes a common terminology to discuss them in future
work
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