Reduced Isotonic Regression

Add to your list(s) Download to your calendar using vCal

• Chao Gao (University of Chicago)
• Tuesday 26 June 2018, 09:45-10:30
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact INI IT.

STSW04 - Future challenges in statistical scalability

Consider an $n$-dimensional vector $X$ with mean $\theta^{$. In this talk, we consider $\theta}$ that is both nondecreasing and has a piecewise constant structure. We establish the exact minimax rate of estimating such monotone functions, and thus give a non-trivial answer to an open problem in the shape-constrained analysis literature. The minimax rate involves an interesting iterated logarithmic dependence on the dimension. We then develop a penalized least-squares procedure for estimating $\theta^*$ adaptively. This estimator is shown to achieve the derived minimax rate without the knowledge of the number of pieces in linear time. We further allow the model to be misspecified and derive oracle inequalities with the optimal rates for the proposed estimator. This is a joint work with Fang Han and Cun-hui Zhang.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.