Maximum A Posterior (MAP) Rule

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1. Main Idea

The right decision should be comparing the probability of the scenario after getting the information. Mathematically, this probability is denoted by p(\omega_{1}) and  p(\omega_{2}). They are called a posterior probability. It means the probability of a class \omega_{i} after knowing the data value x in a particular scenario. Therefore, the right decision is:

Decide \omega_{k} :  if p(\omega_{k}|x) > p(\omega_{i}|x)

Or more general: \omega_{k}=argmax_{\omega _{i}} [p(\omega_{i}|x)]

From the equations above, once we decide class \omega based on the observed value x, the probability that you make a correct decision is hence p(\omega_{k}|x). Therefore, the probability that making a wrong decision or error is

p(e_{k}|x) =1- p(\omega_{k}|x)

In this sense, the decision rule is optimal in the sense of minimizing thee probability of the decision error. This decision rule is called the maximum a posterior (MAP) rule.

\omega_{k}=argmax_{\omega _{i}} [p(\omega_{i}|x)]

\omega_{k}=argmin_{\omega _{i}} [p(e_{i}|x)],

which minimizes the probability of the decision error.

 

2. For c possible classes situation.

 \sum_{i=1}^{c}p(\omega_{i}|x)=1

This is fundamental but very useful.

\sum_{i=1, not k}^{c}p(\omega_{i}|x)=1

So, to compute  p(\omega_{k}|x), we can just add the probability of wrongly classifying to other classes.  By using the formula of computing joint probability.

p(x,\omega_{i})=p(x)p(\omega_{i}|x)=p(\omega_{i})p(x|\omega_{i})

This equation is known as Bayesian formula.

 

 

 

Answers to Review Questions Chapter 2 (C++ Primer Plus)

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1. What are the modules of C++ program called?

They are called functions.

2. What does the following preprocessor directive do?   #include <iostream>

It causes the contents of the iostream file to be substituted for this directive before final compilation.

3. What does the following statement do? using namespace std;

It makes definitions made in the std namespace available to a program.

4.What statement would you use to print the phrase “hello, world” and then start a new line?

cout << “Hello, world\n”;

5. What would you use to create an integer variable with the name cheeses?

int cheeses;

6. What statement would you use to read a value from keyboard input into the variable cheeses?

cin >> cheeses;

7. What statement would you use to assign the value 32 to the variable cheeses?

cheese =32;

8. What statement would you use to print “We have X varieties of cheeses,” where the current value of the cheeses variable replaces X?

cout << “We have “ << cheeses  <<” varieties of cheese\n”;

9. What do the following function prototypes tell you about the functions?

int froop (double t);
void rattle(int n);
int prune(void);

10. When do you not have to use the keyword return when you define a function?

When the function has the return type  void.

HE JIAWEI

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Short Biography:

Since September 2013, I have been a Master by research student working with Professon Ma Kaikuang in Nanyang Technological University (NTU).

I received the Bachelor Degree on Electrical Engineering(2009-2013) in Zhejiang University, Hangzhou, China.
I am interested in the following areas:

  • Computer Vision
  • Machine Learning
  • Pattern Recognition

Publications

coming soon, hopefully this section will grow longer and longer

Projects

  • Hand gesture recognition system 2013-2014

Acted as a main programmer and system builder in this program. This program is under Prof. Ma Kaikuang`s supervision. About to publish one to two papers about the new technique used in the program lately.

  • SUPCON Education Fund for Innovation 2012-2013(national level)

Acted as team leader in SUPCON education fund for innovation (2012-2013) project, came up with a type of smart home system based on the Internet of things. Designed electric circuit and remote control system. Used Kinect as sensor for the first time in smart home system. The system connects basic electrical equipment together with zigbee technique.

  • Provincial Sci. & Tech. Innovations Program 2012-2013

Acted as a main programmer in the Provincial Sci. & Tech. Innovations Program(2012-2013). Focused on wearable portable elderly health monitoring system. The system is used to monitor health indicators such as pulse and heart rate and transport the signals to cellphones or other equipment automatically.

  • Student Research Training Program 2011-2012

Acted as a key team member in Zhejiang University SRTP(2011-2012), Developed a solution on the use of the wheel rotation to provide electricity for electric equipment, such as music player or cellphone. Collected data on the habit of riding, designed electrical circus and made a real model of the innovative design.

  • Motion Control Techniques Course 2012

Made a remote control smart toy car based on Bluetooth technology. Designed the whole system including ARM & android programming, Bluetooth module connection and Interactive interface. The toy car can react exactly to the operation of the cellphone software.

AWARDS

  •  eMEGA scholarship from college of EEE, NTU for three semesters
  • Excellent prize in the 2012 Allen-Bradley Automation System Application Contest
  • Excellent Prize in the 2012 SUPCON Robot Competition (rank 23 out of all teams)

PATTERNS

  •  “Smart six-feet robot which is applied to clean the tube of central air condition”     Filed 2013.
  •  “Smart Inflatable Multifunctional Chair”  Filed 2013
  •  “Elderly health monitoring vest based on wearable sensors”  Filed 2013

Selected Graduate Courses

  • Machine Learning
  • Image analysis and Pattern recognition
  • Machine vision
  • Advanced digital signal processing

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