1. Sequential Model

1.1 Conditional Probability

$$P(\bold x)=P(x_1)P(x_2|x_1)P(x_3|x_1,x_2)…P(x_t|x_1,x_2,…,x_{t-1})$$

1.2 Autoregressive Model

For ever-known model, we call it AR Model.

$$p(x_t|x_1,x_2,…,x_{t-1})=p(x_t|f(x_1,x_2,…,x_{t-1}))$$

1.3 Markov Model

By Markov Hypothesis, the current state is determined by previous$$\tau$$ points.

$$p(x_t|x_1,x_2,…,x_{t-1})=p(x_t|x_{t-\tau},…,x_{t-1})=p(x_t|f(x_{t-\tau},…,x_{t-1}))$$

1.4 Latent Model 潜变量模型

we use a variable to represent the inner states (RNN is one of the Latent Model)

$$h_t=f(x_1,…,x_{t-1})$$

$$x_t=p(x_t|h_t)$$

QA…