On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions
In this paper, we bound the generalization error of a class of Radial Basis Function networks, for certain well defined function learning tasks, in terms of the number of parameters and number of examples. We show that the total generalization error is partly due to the insufficient representa...
| Main Authors: | , |
|---|---|
| Language: | en_US |
| Published: |
2004
|
| Online Access: | http://hdl.handle.net/1721.1/6624 |
| _version_ | 1826203846885507072 |
|---|---|
| author | Niyogi, Partha Girosi, Federico |
| author_facet | Niyogi, Partha Girosi, Federico |
| author_sort | Niyogi, Partha |
| collection | MIT |
| description | In this paper, we bound the generalization error of a class of Radial Basis Function networks, for certain well defined function learning tasks, in terms of the number of parameters and number of examples. We show that the total generalization error is partly due to the insufficient representational capacity of the network (because of its finite size) and partly due to insufficient information about the target function (because of finite number of samples). We make several observations about generalization error which are valid irrespective of the approximation scheme. Our result also sheds light on ways to choose an appropriate network architecture for a particular problem. |
| first_indexed | 2024-09-23T12:44:33Z |
| id | mit-1721.1/6624 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:44:33Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/66242019-04-12T08:31:40Z On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions Niyogi, Partha Girosi, Federico In this paper, we bound the generalization error of a class of Radial Basis Function networks, for certain well defined function learning tasks, in terms of the number of parameters and number of examples. We show that the total generalization error is partly due to the insufficient representational capacity of the network (because of its finite size) and partly due to insufficient information about the target function (because of finite number of samples). We make several observations about generalization error which are valid irrespective of the approximation scheme. Our result also sheds light on ways to choose an appropriate network architecture for a particular problem. 2004-10-08T20:34:39Z 2004-10-08T20:34:39Z 1994-02-01 AIM-1467 http://hdl.handle.net/1721.1/6624 en_US AIM-1467 261921 bytes 1092393 bytes application/octet-stream application/pdf application/octet-stream application/pdf |
| spellingShingle | Niyogi, Partha Girosi, Federico On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions |
| title | On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions |
| title_full | On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions |
| title_fullStr | On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions |
| title_full_unstemmed | On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions |
| title_short | On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions |
| title_sort | on the relationship between generalization error hypothesis complexity and sample complexity for radial basis functions |
| url | http://hdl.handle.net/1721.1/6624 |
| work_keys_str_mv | AT niyogipartha ontherelationshipbetweengeneralizationerrorhypothesiscomplexityandsamplecomplexityforradialbasisfunctions AT girosifederico ontherelationshipbetweengeneralizationerrorhypothesiscomplexityandsamplecomplexityforradialbasisfunctions |