CIF: Small: Statistical Inference via Convex Optimization
CIF: Small: Statistical Inference via Convex Optimization
批准号:
1523768
负责人:
Arkadi Nemirovski
金额:
$46.01万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
2015
资助国家:
美国
项目状态:
已结题
起止时间:
2015-08-01 至 2019-07-31
中文摘要
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英文摘要
In a variety of applications in modern science and technology, there is a strong need in accurate statistical inferences from massive sets of high-dimensional data. To meet this need, it is a must to develop novel methods combining provably (nearly) optimal statistical performance with computational efficiency and scalability. The project aims at designing innovative Convex Optimization based inference techniques meeting the above requirements and utilizing these techniques in important applications (Positron Emission Tomography, Nanoscale Fluorescent Microscopy, Quantum Statistics,...). Challenges to be addressed combined with clear "applied appeal" make the project a good training ground for Ph.D. students. Project?s outcomes could make a valuable contribution to the computational tools of "Big Data."The approach is based on designing statistical tests with near-optimal risk for multiple composite hypotheses in a class of statistical models where observation is: (a) affine image of unknown vector ("signal") corrupted by Gaussian noise; (b) random vector with independent Poisson entries, the underlying parameters being affine functions of the signal; (c) random variable taking finitely many values with probabilities affinely depending on the signal; (d) direct products of models (a) - (c). While restrictive with respect to the allowed models, the approach is highly permissive with respect to the number and the structure of the hypotheses. The proposed efficiently computable and scalable tests and their risks stem from optimal solutions to explicit convex programs, and can be used as building blocks in more complicated inferential problems. The research agenda includes the design of sequential tests and dynamical tests; change point detection; estimating functionals of a signal; "sparsity-oriented" testing/estimation; applications to Poisson Imaging, Active Learning, and Quantum Statistics.
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Collaborative Research: Modeling and Control of Magnetic Chemotherapy
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批准号:1262063
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财政年份:2013
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负责人:Arkadi Nemirovski
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依托单位:
Design of Efficient Saddle Point Algorithms for Large-scale/Complex Geometry Convex Optimization
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批准号:1232623
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资助金额:$45.0万
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依托单位:
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财政年份:2006
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负责人:Arkadi Nemirovski
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依托单位:
国内基金
海外基金
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