| EPSRC Reference: |
EP/H020071/1 |
| Title: |
Kernel methods for approximation and learning theory |
| Principal Investigator: |
Levesley, Professor J |
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| Department: |
Mathematics |
| Organisation: |
University of Leicester |
| Scheme: |
Standard Research |
| Starts: |
06 January 2010 |
Ends: |
05 July 2010 |
Value (£): |
20,059
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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In many different situations we are given information at some unstructured set of points, and asked to deduce something concrete from the data. In approximation theory we tyypically try to develop an algorithm which will recover the information at all points in a certain set, given a finite set of information. We then provide estimates for the error of approximation.We can ask other questions. Given a certain amount of information and a given set of functions, what is the best we can expect to do in terms of error using a linear process (if we approximate a combination of functions we obtain the same approximation as if we had individually approximated each component of the combination, and combine these in the same proportion). Such consideration lies in the field of n-widths, and it clearly of importance to know if any particular algorithm realises the best possible error. Closely related to the notion of n-width is that of entropy, which deals with the number of sets of a certain size it would take to cover a fixed set (for instance, how many circles of radius 1 does it take to cover a circle of radius r).In machine learning we are often interested in the probability of obtaining a good estimate. It maybe that there are a very small number of bad functions in my set, and n-width gives the worst case scenario. The average case might be much better, so an estimate of probability of a reasonable answer is useful information.We intend to investigate these issues when the information we have lies on some sort of smooth manifold, like a sphere. We would like to write a research monograph which will allow people who do not have much experience in this area to get to the stage where they could do research, and in a self-contained way. This will require the collection of theory from a wide range of subjects in mathematics.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.le.ac.uk |