Regularisation and Support Vector Machines

colossalbangΤεχνίτη Νοημοσύνη και Ρομποτική

7 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

94 εμφανίσεις

 
   
  
   
     
 
       
     
   
 

   
         
  
 
   
  
   


 

   

  

   
   
         
  
 
   
  
   
 
       
         
  
             
     
           
          
 
              
          
  
   
         
  
 
   
  
   
  
           

         
          
         
    
   
         
  
 
   
  
   
   
      
  
         
    D
    (, ) ∈  ×{−, }
   
         
  
 
   
  
   
   
         
   

D
( ) = D{(, ): ( ) ￿=  }
     
      
           
          
   
           
         
    
   
         
  
 
   
  
   
    
        

 
           
 = {(

,

),...,(
￿
,
￿
)}
    D

D
(

)         
    
          
          
  ￿
   
         
  
 
   
  
   
    
     δ     
D
(

)   
      ￿ = ￿ (￿,,δ)    
    −δ     
   ￿        


     

D
(

) ≤ ￿ (￿,,δ)
      
           
          
D
￿
{:
D
(

) > ￿ (￿,,δ)} < δ
           
      
   
         
  
 
   
  
   
  
               
    
D
￿
{:
D
(

) > ￿ (￿,,δ)} < δ
          
      
   ￿      
     
D
( ) > ￿    
D
￿
{:   
D
( ) > ￿} ≤ ( −￿)
￿
≤  (−￿￿)
   
         
  
 
   
  
   
   
   | |        
           
| |  (−￿￿)
          

    ￿
D
￿
{:

  
D
( ) > ￿} < | |  (−￿￿)
   
         
  
 
   
  
   
   
           δ  
￿ = ￿ (￿,,δ) =

￿

| |
δ
          
           
         
      
   
         
  
 
   
  
   
   
            
     
D
￿
{:∃ ∈ :

( ) = ,
D
( ) > ￿}
≤  D
 ￿
￿

ˆ
:∃ ∈ :

( ) = ,
ˆ

( ) > ￿￿/
￿
         
￿ > /￿
             ￿
          
           
 
   
         
  
 
   
  
   
   
          
              

        
            
  
−￿￿/
        ￿
  
        ￿     
           
  
 ￿
    ￿  
   
         
  
 
   
  
   
   
           
              
        ￿    
 


(￿) = 
(

,...,
￿
)∈
|{( (

), (

),..., (
￿
)): ∈  }|
    
￿
     
           
 ￿
   
         
  
 
   
  
   
   
     {

,....
￿
}    
{( (

), (

),..., (
￿
)): ∈  } = {−, }
￿
    
   
             
     
￿
  ￿
   
         
  
 
   
  
   
   
           
            
            
  ￿ ≥ 


(￿) ≤
￿
 ￿

￿

          
   
         
  
 
   
  
   
   
            
  
D
￿
{:∃ ∈ :

( ) = ,
D
( ) > ￿} ≤ 
￿
  ￿

￿


−￿￿/
            

D
( ) ≤ ￿ (￿,,δ) =

￿
￿
 
  ￿

+

δ
￿
  ≤ ￿  ￿ > /￿
   
         
  
 
   
  
   
   
         
        
       
            
         
  
         
     
   
         
  
 
   
  
   
   
          
        
            
       
            
           
         
    
   
         
  
 
   
  
   
   
          
          ￿

  
             
      
 
      +      
          
          
    ￿ >  +      
           
   
         
  
 
   
  
   
   
          
    
              
          
      
   
         
  
 
   
  
   
   
         

D
( ) ≤ ￿ (￿,,δ) =
 
￿
+

￿
￿
 
  ￿

+

δ
￿
            
 
   
         
  
 
   
  
   
   
          
          
     
            

 
             
        

       

   
         
  
 
   
  
   
   
    F      
       
     (

,

) ∈  ×{−, }   
    ∈ F   
γ

= 

 (

)
γ

>    
   
         
  
 
   
  
   
   
  

( )        



>      
             F 
      ∈ F
          
       
   
         
  
 
   
  
   
  
  γ        
         
    γ/       
 γ −  F        
 = {

,...,
￿
}           
 ∈ F    ∈   

 ≤ ≤￿
(| (

) − (

)|) < γ
N (F,,γ)    
N (F,￿,γ) = 
 ∈

N (F,,γ)     
   
         
  
 
   
  
   
  
          
D
￿
{:∃ ∈ :

( ) = ,

( ) ≥ γ,
D
( ) > ￿}
≤  D
 ￿
￿

ˆ
:∃ ∈ :

( ) = ,

( ) ≥ γ,
ˆ

( ) > ￿￿/
￿
           
    
≤  | | 
−￿￿/
≤  N (F, ￿,γ/ ) 
−￿￿/
   
         
  
 
   
  
   
  
    

D
( ) ≤ ￿ (￿,,δ,γ) =

￿
￿
 N (F, ￿,γ/ ) +

δ
￿
 ￿ > /￿
     N (F,￿,γ)     
          
           
          
     
   
         
  
 
   
  
   
   
     

,...,
￿
 γ −  F   
   

     
 ∈ {−, }
￿
  

∈ F  


(

) =
￿
≥ 

+γ,

= 
< 

−γ,

= −
     γ     
 γ −      

      γ      
          
        
   
         
  
 
   
  
   
  
           
   

D
( ) ≤

￿
+
￿

￿
￿



,
( )



￿ +

δ
￿
  /￿         
,
( )   /￿
   

( )
         
          
          γ −    
   γ
   
         
  
 
   
  
   
  
    F      
 X         
      (

,

) ∈ X  {−, }
       ∈ F    γ   
 
￿ ((

,

),,γ) = ￿

=  (,γ −

 (

))
   
         
  
 
   
  
   
   
       
        X   γ ∈ 
+

          
  X  {−, }          
     −δ  ￿    
    ∈ L     

D
( ) ≤

￿
￿


+￿￿￿


γ


  ￿

+

δ
￿
 ￿           γ
   
         
  