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Probability Density FunctionDefinition (Probability Density Function): For a continuous r.v. $X$ with CDF $F$, the probability density function (PDF) of $X$ is the derivative $f$ of the $F$ P(a\leq... Continue reading...

$x$: Data we already have $z$: Data we want to generate $\theta_g$: parameter for Generator $\theta_d$: parameter for D $G$: Generator $D$: Discriminator target is training $G$ to minimize \matho... Continue reading...

ExpectationDefinition (Expectation of R.V.) E(X) = \sum_{x}\underbrace{x}_{value} \underbrace{P(X=x)}_{PMF\ at\ x}Theorem (Monotonicity): $X$ and $Y$ are r.v.s. such that $X>Y$ with probability... Continue reading...

Nerual StyleThere are two aspect for a image, one is the content of the image, which can be descriped as elements or object in the image, another is the style of the image, it might be abstract, an... Continue reading...

There are some notation occationals Definition (Discrete Random Variable) A variable $X$ is discrete if there is a finite list of value $a_1,a_2,…,a_n$ that $P(X=a_j) = 1$, $P(X=x)>0$ is the sup... Continue reading...

Defination of Conditonal ProbabilityDefination Two events $A$ and $B$, with $P(B)>0$, the conditional probability of $A$ given $B$ , denoted by $P(A|B)$, is defined as : P(A|B)=\frac{P(AB)}{P(B... Continue reading...

Introduction to RPCAThe data we collect usually have the low rank property, but the property will vanished when the data is collected causing the noisy, but we can still decomposite the matrix int... Continue reading...

r.v.s.: random variable sequence i.i.d: individual identical distribution w.p.: with probability PMF (Probability Mass Function) $P(X=x)$ CDF (Cumulative Distribution Function) $P(X \leq x)$ PDF (P... Continue reading...