类似涉及到条件概率的问题可以用Eikosograms直观的理解。关于Eikosograms可以参考http://sas.uwaterloo.ca/~rwoldfor/papers/venn/eikosograms/paperpdf.pdf。我们学概率的时候常常使用文氏图,但是文氏图有时候会比较misleading,比如 disjoint 的事件和 independent 的事件文氏图并不容易区分。


在一个Eikosogram中,region表示一个事件,region的面积表示此事件发生的概率。比如上面的图中有三个随机变量:A,B和C。这三个随机变量均包含0,1两个outcome (扩展到多个outcome也直接)。条件概率自然的可以用面积比表示(方框的总面积为1)。比如定义

C= 0: shaded region;

C=1:un-shaded region。


Pr( C=1 | A = 0, B = 0 ) / Pr( C=0 | A = 0, B = 0 )  = Area of T1 / Area of (S1).

基于这个定义,independence有很直观的表示。比如 S1 和 S3 的“水位”相同则表示 B 和 C 在 A=0 的条件下独立。同样的,S2 和 S4 的“水位”相同表示B 和 C 在 A=1(即A-complement) 的条件下独立。那么B 和 C 是否是 unconditionally independent 呢?这个时候我们只需要把第1列和第2列合并,第3列和第4列合并,然后看等效的“水位”是否相同即可

Area(  S1 + S2 ) / Area( T1 + T2 )  ?= Area(  S3 + S4 ) / Area( T3 + T4 )




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Do not believe those who try to persuade you that composition is only a cold exercise of the intellect. The only music capable of moving and touching us is that which flows from the depths of a composer’s soul when he is stirred by inspiration. There is no doubt that even the greatest musical geniuses have sometimes worked without inspiration. This guest does not always respond to the first invitation. We must always work, and a self-respecting artist must not fold his hands on the pretext that he is not in the mood. If we wait for the mood, without endeavouring to meet it half-way, we easily become indolent and apathetic. We must be patient, and believe that inspiration will come to those who can master their disinclination.

A few days ago I told you I was working every day without any real inspiration. Had I given way to my disinclination, undoubtedly I should have drifted into a long period of idleness. But my patience and faith did not fail me, and to-day I felt that inexplicable glow of inspiration of which I told you; thanks to which I know beforehand that whatever I write to-day will have power to make an impression, and to touch the hearts of those who hear it. I hope you will not think I am indulging in self-laudation, if I tell you that I very seldom suffer from this disinclination to work. I believe the reason for this is that I am naturally patient. I have learnt to master myself, and I am glad I have not followed in the steps of some of my Russian colleagues, who have no self-confidence and are so impatient that at the least difficulty they are ready to throw up the sponge. This is why, in spite of great gifts, they accomplish so little, and that in an amateur way.

Inspiration and work ethic — they ride right next to each other…. Not every day you’re gonna wake up and the clouds are gonna part and rays from heaven are gonna come down and you’re gonna write a song from it. Sometimes, you just get in there and just force yourself to work, and maybe something good will come out.

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“怕什么真理无穷 进一寸有一寸的欢喜”

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New Year Resolution,虽然迟了一个月。


  • NOMA,OAMP coding,小梁,志鹏,许师兄,PT分析
  • 至少与Arian合作一篇文章,实在不行就PT分析这个工作


  • ESL podcast继续听,每天读新闻
  • Optimization,duality,KKT这些搞到烂熟,computational statistics课认真上
  • Follow一些优化领域的热点,比如Goldfarb在UCLA的几个slides,stochastic optimization,tensor等等;读一些arXiv上optimization的文章,找到一个自己以后做PI时可以从事的方向

3. 继续postdoc,如果晓东没有funding,备选??

4. 养成写东西的习惯,be a creator rather than a consumer

  • 每个月在这里记录一次,越多越好
  • 学的知识多做note;比如对optimization基础知识的总结
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