Pmf of Poisson Distribution is as follows:

\[f(X=k;\lambda)=\frac{\lambda^k e^{-\lambda}}{k!}\]

Our aim is to derive the the expectation of \(E(X)\) and the variance \(Var(X)\). Given that the formula of expectation: \[

There are many classification algorithm such as Logistic Regression, SVM and Decision Tree etc. Today we’ll talk about Gaussian Discriminant Analysis(GDA) Algorithm, which is not so popular. Actually, Logistic Regression performance better than GDA because it can fit any distributions from exponential family. However, we can learn more knowledge about gaussian distribution from the algorithm which is the most import distribution in statistics. Furthermore, if you want to understand Gaussian Mixture Model or Factor Analysis, GDA is a good start.

In April 9th, 2017, incident occurred in United Airlines where crew of UA beat up a passenger and dragged him out of the plane before which was about to take off attracted attention all around the world. Many would gave out doubt: why a company being so rude to passengers can exist in this world? Actually, UA is going well is just because they have an extremely precise emergency situation procedure which is calculate by compute depending on big-data analysis. Computer can help us make decisions though, it has no emotions, which is effective in most cases, but can not be approved by our human beings. Let’s take a look at how algorithm make a decision: It is a decision tree, which simply represents the procedure of how UA algorithm make the decision. First of all, before taking off, four employees of UA need fly from Chicago to Kentucky. Then the algorithm check if there is any seats left, if so, passengers were safe for the moment. But UA3411 was full, the algorithm began assessing the importance of employees or passengers. Obviously, the algorithm think crew is more important due to business consideration. Then how to choose who should be evicted from the plane. The algorithm was more complicated than the tree I drew, however, Asian or not was one of the criterion. But why? Because Asian are pushovers. The passenger agreed at first, however, when he heard that he had to wait for one day, he realized that he could not treat his patient, then he refused. Then he was beat up and dragged off the plane.

Under some circumstance, we want to compress data to save storage space. For example, when iPhone7 was released, many were trapped in a dilemma: Should I buy a 32G iPhone without enough free space or that of 128G with a lot of storage being wasted? I had been trapped in such dilemma indeed. I still remember that I only had 8G storage totally when I was using my first Android phone. What annoyed me most was my thousands of photos. Well, I confess that I was being always a mad picture taker. I knew that there were some technique which could compress a picture through reducing pixel. However, it is not enough, because, as you know, in some arbitrary position in a picture, we can tell that the picture share the same color. An extreme Example: if we have a pure color picture, what we just need know is the RGB value and the size, then reproducing the picture is done without extra effort. What I was dreaming is done perfectly by Singular Value Decomposition(SVD).

You are sitting in front your sceen, annoyed by a bunch of spam mails. You wonder if there are any appoaches to get rid of so much many offended emails. Last time you doped out a extremely good idea. You set a series of words to identify those emails: every mail invovled by words “coupon” was trown to trash. However, on one hand, there were only about 10% spam including “coupon”, one the other hand, you had trashed two significant emails, due to which, you lost two business valued about two million dollars. The thing was that, your inbox seems being overrun by those spams. Who can rescue you from endless deleting spams everyday?

Deep learning is very popular recently, which is based on Neural Network, an old algorithm that had degraded for years but is resurging right now. We talk about some basic concept about Neural network today, hoping supply a intuitive perspective of it.