很早以前学运筹学的时候学过动态规划。最近看题目的时候看到这个名字，借助zhihu上的一篇文章，重新温习一下。

总结了一些网上的资料，比较深度搜索，回溯法和递归，以及怎么用来解决问题。

Modification of the previous question.

Useful links from stackoverflow to solve the errors when pickle for multiprocessing

Got some random walk questions from my friend. We may see lots of similar questions in stochastic process. Here is the question.

An interesting question from my friend. We may see lots of similar questions in stochastic process. Here is one question.

This is an real question with a sample data from internet. We want to predict the defaults from the imbalanced data(default rate is about 0.08%). All the variables are hidden so we need to explore the variables attributes to find some realtion. Also it is imbalanced so we need to apply some sampling methods to balance the data.

continue to introduction some basic knowledge of numpy.

The previous blog shows how to build a neural network manualy from scratch in numpy with matrix/vector multiply and add. Although there are many packages can do this easily and quickly with a few lines of scripts, it is still a good idea to understand the logic behind the packages. This part is from a good blog which use an example predicitng the words in the sentence to explain how to build RNN manually. RNN is a little more complicated than the neural network in the previous blog because the current time status and ourput in RNN will depends on the status in the previous time. So the Backpropagation part will be more complicated. I try to give the details in mathematic formula about how to get the gradients recursively in the partial derivatives.