Multivariate Density Estimation: An SVM Approach
We formulate density estimation as an inverse operator problem. We then use convergence results of empirical distribution functions to true distribution functions to develop an algorithm for multivariate density estimation. The algorithm is based upon a Support Vector Machine (SVM) approach to solvi...
| Main Authors: | , |
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| Language: | en_US |
| Published: |
2004
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| Online Access: | http://hdl.handle.net/1721.1/7260 |
| _version_ | 1826194910320001024 |
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| author | Mukherjee, Sayan Vapnik, Vladimir |
| author_facet | Mukherjee, Sayan Vapnik, Vladimir |
| author_sort | Mukherjee, Sayan |
| collection | MIT |
| description | We formulate density estimation as an inverse operator problem. We then use convergence results of empirical distribution functions to true distribution functions to develop an algorithm for multivariate density estimation. The algorithm is based upon a Support Vector Machine (SVM) approach to solving inverse operator problems. The algorithm is implemented and tested on simulated data from different distributions and different dimensionalities, gaussians and laplacians in $R^2$ and $R^{12}$. A comparison in performance is made with Gaussian Mixture Models (GMMs). Our algorithm does as well or better than the GMMs for the simulations tested and has the added advantage of being automated with respect to parameters. |
| first_indexed | 2024-09-23T10:03:46Z |
| id | mit-1721.1/7260 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:03:46Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/72602019-04-15T00:40:24Z Multivariate Density Estimation: An SVM Approach Mukherjee, Sayan Vapnik, Vladimir We formulate density estimation as an inverse operator problem. We then use convergence results of empirical distribution functions to true distribution functions to develop an algorithm for multivariate density estimation. The algorithm is based upon a Support Vector Machine (SVM) approach to solving inverse operator problems. The algorithm is implemented and tested on simulated data from different distributions and different dimensionalities, gaussians and laplacians in $R^2$ and $R^{12}$. A comparison in performance is made with Gaussian Mixture Models (GMMs). Our algorithm does as well or better than the GMMs for the simulations tested and has the added advantage of being automated with respect to parameters. 2004-10-20T21:04:30Z 2004-10-20T21:04:30Z 1999-04-01 AIM-1653 CBCL-170 http://hdl.handle.net/1721.1/7260 en_US AIM-1653 CBCL-170 7189923 bytes 15850137 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | Mukherjee, Sayan Vapnik, Vladimir Multivariate Density Estimation: An SVM Approach |
| title | Multivariate Density Estimation: An SVM Approach |
| title_full | Multivariate Density Estimation: An SVM Approach |
| title_fullStr | Multivariate Density Estimation: An SVM Approach |
| title_full_unstemmed | Multivariate Density Estimation: An SVM Approach |
| title_short | Multivariate Density Estimation: An SVM Approach |
| title_sort | multivariate density estimation an svm approach |
| url | http://hdl.handle.net/1721.1/7260 |
| work_keys_str_mv | AT mukherjeesayan multivariatedensityestimationansvmapproach AT vapnikvladimir multivariatedensityestimationansvmapproach |