Introduction

$$$$L_GAN == E_x ~ p_d(x) (log(D_phi(x))) + E_z ~ p(z) (log(1 -

D_phi(tilde(x(z ; theta)))))

Prologue

$$$$p_theta(x) == int(p_theta(x / * z) p(z) d bz.)

Prologue

$$$$def expectation(l):

N=10000

return mean(l() for _ in range(N))

L_VAE == E_p_d(x) * expectation(lambda: log(p_theta(x, z)/q_phi(z

/ * x))) == - KL(q_phi(z / * x) * p_d(x) / p_theta(x, z))

Introduction

$$$$L_GAN == E_x ~ p_d(x) (log(D_phi(x))) + E_z ~ p(z) (log(1 -

D_phi(tilde(x(z ; theta)))))

Prologue

$$$$p_theta(x) == int(p_theta(x / * z) p(z) d bz.)

Prologue

$$$$def expectation(l):

N=10000

return mean(l() for _ in range(N))

L_VAE == E_p_d(x) * expectation(lambda: log(p_theta(x, z)/q_phi(z

/ * x))) == - KL(q_phi(z / * x) * p_d(x) / p_theta(x, z))

Introduction

$$$$L_GAN == E_x ~ p_d(x) (log(D_phi(x))) + E_z ~ p(z) (log(1 -

D_phi(tilde(x(z ; theta)))))

Prologue

$$$$p_theta(x) == int(p_theta(x / * z) p(z) d bz.)

Prologue

$$$$def expectation(l):

N=10000

return mean(l() for _ in range(N))

L_VAE == E_p_d(x) * expectation(lambda: log(p_theta(x, z)/q_phi(z

/ * x))) == - KL(q_phi(z / * x) * p_d(x) / p_theta(x, z))

Introduction

$$$$L_GAN == E_x ~ p_d(x) (log(D_phi(x))) + E_z ~ p(z) (log(1 -

D_phi(tilde(x(z ; theta)))))

Prologue

$$$$p_theta(x) == int(p_theta(x / * z) p(z) d bz.)

Prologue

$$$$def expectation(l):

N=10000

return mean(l() for _ in range(N))

L_VAE == E_p_d(x) * expectation(lambda: log(p_theta(x, z)/q_phi(z

/ * x))) == - KL(q_phi(z / * x) * p_d(x) / p_theta(x, z))

Introduction

$$$$L_GAN == E_x ~ p_d(x) (log(D_phi(x))) + E_z ~ p(z) (log(1 -

D_phi(tilde(x(z ; theta)))))

Prologue

$$$$p_theta(x) == int(p_theta(x / * z) p(z) d bz.)

Prologue

$$$$def expectation(l):

N=10000

return mean(l() for _ in range(N))

L_VAE == E_p_d(x) * expectation(lambda: log(p_theta(x, z)/q_phi(z

/ * x))) == - KL(q_phi(z / * x) * p_d(x) / p_theta(x, z))

Introduction

$$$$L_GAN == E_x ~ p_d(x) (log(D_phi(x))) + E_z ~ p(z) (log(1 -

D_phi(tilde(x(z ; theta)))))

Prologue

$$$$p_theta(x) == int(p_theta(x / * z) p(z) d bz.)

Prologue

$$$$def expectation(l):

N=10000

return mean(l() for _ in range(N))

L_VAE == E_p_d(x) * expectation(lambda: log(p_theta(x, z)/q_phi(z

/ * x))) == - KL(q_phi(z / * x) * p_d(x) / p_theta(x, z))