文章1: NICE: NON-LINEAR INDEPENDENT COMPONENTS ESTIMATION
文章2：Real-valued Non-Volume Preserving （RealNVP）
文章3：Glow: Generative Flow with Invertible 1x1 Convolutions
NICE
Learning goals : to find a transformation H = F (X) , so that the distribution of each component after conversion is independent of
We assume h and x dimensions are the same , and f is reversible , then we have
Also, we want to f the Jacobian matrix and f -1 easier calculation. If it can be operated, then we can sample directly to the p- the X- (the X-) ,
The f key insight is that the design of the x split into two parts (x1, X2) , and then converted to (y1, y2) ,
m may be an arbitrary function (ie, a ReLU MLP). notes, the determinant of the Jacobian matrix is a unit matrix , and is very easy to count the inverse function of the number,
Of course, we can define a more general framework ,, additive staggered coupling structure. And there may be conversion layer by layer, the kind of flow feeling.
We can define the maximum likelihood function:
P H (H) : prior distribution, may be pre-defined, for example, if an isotropic Gaussian distribution. H each component are independent , we can write,
RealNVP
Split approach:
s and t are scale and translation, function, R & lt D -> R & lt D-D ,
Jacobia corresponding matrix,
The PS : Because our process and the inverse function calculation Jacobia matrix, are not directed to the inverse function of s and t, s and t can be so arbitrarily complex, IE, neural network.
Glow
There are many models, continued. . .