
| Symbol                 | Description                                  | First Referenced   |
|------------------------|----------------------------------------------|--------------------|
| X                      | Input Space                                  | 155                |
| Y                      | Output Space                                 | 155                |
| P                      | Distribution on X  Y (learning task)                                              | 155                |
| l                      | Loss function                                | 155                |
| H                      | Hypothesis Space                             | 155                |
| h                      | Hypothesis                                   | 155                |
| erP (h)                | Error of hypothesis h on distribution P      | 156                |
| z                      | Training set                                 | 156                |
| A                      | Learning Algorithm                           | 156                |
| ^erz (h)               | Empirical error of h on training set z       | 156                |
| P                      | Set of all learning tasks P                  | 157                |
| Q                      | Distribution over learning tasks             | 157                |
| H                      | Family of hypothesis spaces                  | 157                |
| erQ(H)                 | Loss of hypothesis space H on environment Q  | 158                |
| z                      | (n; m)-sample                                | 158                |
| ^erz(H)                | Empirical loss of H on z                     | 158                |
| A                      | Bias learning algorithm                      | 159                |
| hl                     | Function induced by h and l                  | 159                |
| Hl                     | Set of hl                                    | 159                |
| (h1; : : : ; hn)l      | Average of h1;l ; : : : ; hn;l               | 159                |
| hl                     | Same as(h1; : : : ; hn)l                     | 159                |
| l                      | Set of (h1; : : : ; hn)l                     | 159                |
| Hn l                   | Set of Hn l                                  | 159                |
| H n H                        | Function on probability distributions        | 160                |
| H                         | Set of H                                              | 160                |
| dP                     | Pseudo-metric on Hn l                        | 160                |
| dQ                     | Pseudo-metric on H                                               | 160                |
| ; dQ)                  | Covering number of H                                               | 160                |
| N ("; H  )                        | Capacity of H                                               | 160                |
| C("; H  ; dP)                        | Covering number of H n l                     | 160                |
| N ("; H n l C("; H n ) | Capacity of H n l                            | 160                |
| l                      |                                              |                    |
| h                      | Sequence of n hypotheses (h1; : : : ; hn)    | 163                |
| P                      | Sequence of n distributions (P1; : : : ; Pn) | 163                |
| erP(h)                 | Average loss of h on P                       | 164                |
| ^erz(h)                | Average loss of h on z                       | 164                |
| F                      | Set of feature maps                          | 166                |
| G                      | Output class composed with feature maps f    | 166                |
| G Æ f                  | Hypothesis space associated with f           | 166                |
| Gl                     | Loss function class associated with G        | 166                |
| N ("; Gl ; dP )        | Covering number of Gl                        | 166                |
| C ("; Gl )             | Capacity of Gl                               | 166                |
| d[P;Gl℄(f ; f 0 )      | Pseudo-metric on feature maps f ; f 0        | 166                |
| N ("; F; d[P;Gl ℄)     | Covering number of F                         | 166                |
