Properties of Convex Functions

Today, the company started a discussion class on machine learning. During this period, a student asked: why is the mean square error function of linear regression convex (like this )? I was excited that the conclusion "convex function is also convex function by polynomial combination" is incorrect. It should be that the convex function remains convex under the affic change, that is, x ^ 2 is a convex function, then (A1 * X1 + A2 * X2 +... an * XN) ^ 2 is also a convex function.

 

According to Wikipedia's point of view, the nature of Convex Functions, summed up the following three points: http://zh.wikipedia.org/zh/%E5%87%B8%E5%87%BD%E6%95%B0

• If the sum is a convex number, then the sum is also a convex number.
• If the sum is a convex number and the increment is greater, it is a convex number.
• Convex is not changed under the affine ing: that is, if it is a convex function (), it is also a convex function.
• If it is a convex function number in the content and a convex non-empty set, it is a convex function number in the content.

Ah, today's seminar is really a mess. I will be calm and think clearly before making a speech, so as not to mislead others-of course, the scalpers will not be misled by me, Luo, haha ~

 

Xjs.xjtu@gmail.com

2012-09-13