Deep Generative Neural Networks

Deep Learning: Deep Generative Neural Networks

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Maximum Likelihood

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**Generative Adversarial Networks**

Generative Adversarial Networks python code

# calculating cost function
import numpy as np
X = [
    [1,2],
    [3,4]
]
X = np.array(X)
X_pred = [
    [5,6],
    [7,8]
]
X_pred = np.array(X_pred)

weight = np.ones(2)*0.5

# define of Discriminator
def Dx(x,a = 0.1,b = 0.2):
    x = np.transpose(x)
    return 1/(1+np.exp(-a*x[0]+b*x[1]+2))

# Calculate the cost
def V(x,x_pred = X_pred ,weight = weight,Dx = Dx):
    # E(ln(D(x)))
    E_lnDx = np.dot(np.log(Dx(X)),weight.transpose())
    # E(ln(1-D(G(x)))),G(x) = X_pred
    E_ln_1_DGx = np.dot(np.log(1-Dx(X_pred)),weight.transpose())
    return E_lnDx + E_ln_1_DGx


print(V(X,X_pred,weight,Dx))

Output

-2.5465207684425333

Continue Python code

from jax import grad
import jax.numpy as jnp
import numpy as np
a = [0.1,0.2]
def Dm_1(a,x = X, b = 0.2):
    temp = 1/(jnp.exp(jnp.dot(jnp.array([-a,b]),jnp.transpose(x)) + 2)+1)
    return temp
    

def Dm_2(a,x = X[0], b = 0.1):
    return 1/(jnp.exp(jnp.dot(jnp.array([-b,a]),jnp.transpose(x)) + 2)+1)


def multi_Dm_1(a,x):
    result = []
    for sample in x:
        temp_func = grad(Dm_1)(a,sample)
        result.append(temp_func)
    return np.array(result)

def multi_Dm_2(a,x):
    result = []
    for sample in x:
        temp_func = grad(Dm_2)(a,sample)
        result.append(temp_func)
    return np.array(result)


print(1/Dx(X)*multi_Dm_1(0.1,X))

Output

[0.90887703 2.77242559]

Continue Python code

# Calculate gradient update
from jax import grad
import jax.numpy as jnp
import numpy as np
X = [
    [1,2],
    [3,4]
]
X = np.array(X)
X_pred = [
    [5,6],
    [7,8]
]
X_pred = np.array(X_pred)
weight = np.ones(2)*0.5

# define learning rate
n = 0.02

a = [0.1,0.2]

def Dm_1(a,x = X, b = 0.2):
    temp = 1/(jnp.exp(jnp.dot(jnp.array([-a,b]),jnp.transpose(x)) + 2)+1)
    return temp
    

def Dm_2(a,x = X[0], b = 0.1):
    return 1/(jnp.exp(jnp.dot(jnp.array([-b,a]),jnp.transpose(x)) + 2)+1)


def multi_Dm_1(a,x):
    result = []
    for sample in x:
        temp_func = grad(Dm_1)(a,sample)
        result.append(temp_func)
    return np.array(result)

def multi_Dm_2(a,x):
    result = []
    for sample in x:
        temp_func = grad(Dm_2)(a,sample)
        result.append(temp_func)
    return np.array(result)

def d_V(x,x_pred = X_pred ,weight = weight,Dx = Dx):
    # d(ln(D(x)))/dm1 + d(ln(1 - D(G(x))))/dm1 = d(ln(D(x))/d(D(x)) * d(D(x))/dm1+ 
    # d(ln(1 - D(G(x))))/d(1 - D(G(x))) * d(1 - D(G(x)))/d(D(G(x))) * d(D(G(x)))/dm1
    d_m1 = 1/Dx(x) * multi_Dm_1(a[0],X) + 1/(1-Dx(x_pred)) * (-1) * multi_Dm_1(a[0],x_pred)
    
    # d(ln(D(x)))/dm2 + d(ln(1 - D(G(x))))/dm2 = d(ln(D(x))/d(D(x)) * d(D(x))/dm2+ 
    # d(ln(1 - D(G(x))))/d(1 - D(G(x))) * d(1 - D(G(x)))/d(D(G(x))) * d(D(G(x)))/dm2
    d_m2 = 1/Dx(x) * multi_Dm_2(a[1],X) + 1/(1-Dx(x_pred)) * (-1) * multi_Dm_2(a[1],x_pred)

    # sum and apply weight
    result = np.dot([d_m1,d_m2],weight)
    return result

update = d_V(X)
a_new = a + n*update
print(a_new)

Output

[0.13001361 0.15280747]

GAN Problems

None-convergence

Diminished gradient