Loss functions for classification: Difference between revisions

Revision as of 15:47, 26 July 2019

Revision as of 18:50, 26 July 2019

Line 60:

!<math>C(\eta)</math>

!<math>f^{-1}(v)</math>

!<math>f(\eta)</math>

|-

|Exponential

Line 65 ⟶ 66:

|<math>2\sqrt{\eta(1-\eta)}</math>

|<math>\frac{e^{2v}}{1+e^{2v}}</math>

|<math>\frac{1}{2}\log(\frac{\eta}{1-\eta})</math>

|-

|Logistic

Line 70 ⟶ 72:

|<math>\frac{1}{\ln(2)}[-\eta\ln(\eta)-(1-\eta)\ln(1-\eta)]</math>

|<math>\frac{e^v}{1+e^v}</math>

|<math>\log(\frac{\eta}{1-\eta})</math>

|-

|Square

Line 75 ⟶ 78:

|<math>4\eta(1-\eta)</math>

|<math>\frac{1}{2}(v+1)</math>

|<math>2\eta-1</math>

|-

|Savage

Line 80 ⟶ 84:

|<math>\eta(1-\eta)</math>

|<math>\frac{e^v}{1+e^v}</math>

|<math>\log(\frac{\eta}{1-\eta})</math>

|-

|Tangent

Line 85 ⟶ 90:

|<math>4\eta(1-\eta)</math>

|<math>\arctan(v)+\frac{1}{2}</math>

|<math>\tan(\eta-\frac{1}{2})</math>

|}<br />

== Square loss ==