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import tensorflow as tf

import numpy as np

def read$\_$parse$\_$a$9$a$()$:

labels $=[]$

data $=[]$

with open$("$a$9$a$.$txt$")$ as f: #ijcnn$1.$txt$,$ a$9$a$.$txt

for line in f:

xs $=$ line.split$("")$

h $=[0\mathrm{.}0]*123$

for s in xs$[1$:$]$:

s $=$ s$.$strip$()$

if len$($s$)==0$:

continue

$($k$,$v$)=$ s$.$split$("$:$")$

h$[$int$($k$)-1]=$ float$($v$)$

data.append$($h$)$

if xs$[0]=="+1"$:

labels.append$(1)$

else:

labels.append$(0)$

return $($data$,$ labels$)$

def prediction$($w$,$ data$)$:

return $1/(1+$np$.$exp$(-$np$.$dot$($w$,$data.transpose$())))$

#computes the average logloss for given prediction

def logloss$($pred$,$ labels$)$:

Li$=-(($labels$*$np$.$log$($pred$))+((1-$labels$)*$np$.$log$(1-$pred$)))$

return sum$($Li$)/$len$($pred$)$

def gradient$($n$,$ w$,$ data, labels$)$:

return $1/$ n $*$ np$.$dot$($data$.$transpose$(),($prediction$($w$,$data$)-$ labels$))$

n$=123$ #number of features

features, labels $=$ read$\_$parse$\_$a$9$a$()$

features$=$np$.$array$($features$)$

labels $=$ np$.$array$($labels$)$

B$=$np$.$eye$($n$)$ #use either identity or compute Hessian in first step for BFGS

w$=$np$.$zeros$($n$)$ #initialize weight vector

predictions$=$prediction$($w$,$features$)$

loss$=$logloss$($predictions$,$labels$)$

grad$=$gradient$($n$,$w$,$features,labels$)$

print$("$Initial gradient shape:", grad.shape$)$

Initial gradient shape: $(123,)$

def wolfe$($w$,$ p$,$ data, labels, grad$\_$f$=$gradient, loss$\_$f$=$logloss$,$ pred$\_$f$=$prediction, alpha$=1\mathrm{.}0,$ c$1=0\mathrm{.}001,$ c$2=0\mathrm{.}9)$:

grad$\_$w$=$grad$\_$f$($len$($w$),$ w$,$ data, labels$)$

for i in range$(1000)$:

if loss$\_$f$($pred$\_$f$($w$+$alpha$*$p$,$ data$),$ labels$)>$ logloss$($pred$\_$f$($w$,$ data$),$ labels$)+$c$1*$alpha$*$np$.$dot$($grad$\_$w$,$ p$)$:

alpha $*=0\mathrm{.}5$

elif np$.$dot$($grad$\_$f$($len$($w$),$ w$+$alpha$*$p$,$ data, labels$),$ p$)<$ c$2*$ np$.$dot$($grad$\_$w$,$ p$)$:

alpha $*=2\mathrm{.}1$

elif i $>999$:

raise Exception$("$wolfe doesn't finish"$)$

else:

break

return alpha

def dfp$($w$\_0,$ B$\_0,$ data, labels, pred$\_$f$=$prediction, grad$\_$f$=$gradient, loss$\_$f$=$logloss$,$ max$\_$iter$=100,$ tol$=0\mathrm{.}0001)$:

w $=$ w$\_0$

B$\_$inv $=$ np$.$linalg.inv$($B$\_0)$ # We only compute the inverse at initialization

grad$\_$w $=$ grad$\_$f$($len$($w$),$ w$,$ data, labels$)$

$$

for i in range$($max$\_$iter$)$:

# Step $1$:

p $=-$np$.$dot$($B$\_$inv, grad$\_$w$)$ # Use np$.$dot instead of np$.$outer

# Step $2$:

alpha $=$ wolfe$($w$,$ p$,$ data, labels$)$

# Step $3$:

s $=$ alpha $*$ p

w$\_$new $=$ w $+$ s

grad$\_$new $=$ grad$\_$f$($len$($w$),$ w$\_$new, data, labels$)$

# Step $4$:

if np$.$linalg.norm$($grad$\_$new $-$ grad$\_$w$)<$ tol:

break

y $=$ grad$\_$new $-$ grad$\_$w

grad$\_$w $=$ grad$\_$new

sy $=$ np$.$dot$($s$,$ y$)$

$$

# Step $5($DFP Update$)$:

Bs $=$ np$.$dot$($B$\_$inv, s$)$

B$\_$inv $=$ B$\_$inv $+$ np$.$outer$($s$,$ s$)/$ np$.$dot$($s$,$ y$)-$ np$.$outer$($Bs$,$ Bs$)/$ np$.$dot$($s$,$ Bs$)$

$$

# Step $6($print$)$:

predictions $=$ pred$\_$f$($w$,$ data$)$

loss $=$ loss$\_$f$($predictions$,$ labels$)$

print$("$iter:$",$ i$,"$ loss:", loss$)$

$$

w $=$ w$\_$new

return w

$$

n $=123$

print$("$DFP$")$

dfp$($np$.$zeros$($n$),$ np$.$eye$($n$),$ features, labels$)$

DFP

iter: $0$ loss: $0\mathrm{.}693147180560079$

iter: $1$ loss: $0\mathrm{.}5292530545167842$

iter: $2$ loss: nan

iter: $3$ loss: $3\mathrm{.}5410760939547634$

iter: $4$ loss: nan

iter: $5$ loss: $5\mathrm{.}358308161688495$

C:$\backslash$Users$\backslash$Mirka$\backslash$AppData$\backslash$Local$\backslash$Temp$\backslash$ipykernel$\_13004\backslash 605386739.$py:$3$: RuntimeWarning: divide by zero encountered in log

Li$=-(($labels$*$np$.$log$($pred$))+((1-$labels$)*$np$.$log$(1-$pred$)))$

C:$\backslash$Users$\backslash$Mirka$\backslash$AppData$\backslash$Local$\backslash$Temp$\backslash$ipykernel$\_13004\backslash 605386739.$py:$3$: RuntimeWarning: invalid value encountered in multiply

Li$=-(($labels$*$np$.$log$($pred$))+((1-$labels$)*$np$.$log$(1-$pred$)))$

iter: $6$ loss: nan

iter: $7$ loss: nan

iter: $8$ loss: nan

iter: $9$ loss: nan

iter: $10$ loss: inf

iter: $11$ loss: nan

iter: $12$ loss: nan

iter: $13$ loss: inf

iter: $14$ loss: nan

iter: $15$ loss: $7\mathrm{.}391548466851556$

iter: $16$ loss: nan

iter: $17$ loss: nan

iter: $18$ loss: $7\mathrm{.}219118683233256$

iter: $19$ loss: nan

iter: $20$ loss: $1\mathrm{.}9819447503890504$

iter: $21$ loss: nan

iter: $22$ loss: $2\mathrm{.}435944655812197$

iter: $23$ loss: $1\mathrm{.}6211073060149195$

iter: $24$ loss: $1\mathrm{.}281807059361977$

iter: $25$ loss: $1\mathrm{.}0287540152733297$

iter: $26$ loss: $0\mathrm{.}7616105043704977$

iter: $27$ loss: $0\mathrm{.}7157585926858517$

iter: $28$ loss: