Ting Qian's Blog

Mobile blogging

2010-09-07T07:42:00.001-04:00

Okay! Now that I have an application on my android phone for blogging, there are no excuse for not updating this blog anymore!

ha...this is funny

2010-03-28T10:36:00.002-04:00

http://astro.berkeley.edu/~mwhite/referee_funny.html

Probability as a Linking Function for Love

2010-02-10T16:13:00.001-05:00

The mainstream thought in current psycholinguistics studies, or almost all computational studies in cognitive science, assumes that probability is an explanatory factor in cognition. Probability, estimated by various methods, can predict learning of word segmentation, speech duration, omission of phonetic details, and so on.

Recently I've become increasingly reluctant to attribute that much explanatory power to probability alone. A probability value is essentially just a point estimate. To make clear what I mean by this, let's consider an example of trigrams. Suppose we have learned in a fictitious world the love story between Romeo and Juliet is planned by God in the following way.

Romeo loves Juliet 3

Romeo loves Jane 2

Juliet loves Romeo 3

Juliet loves Andy 1

Juliet loves Jack 1

The numbers in the second column above indicate how many times the lover has said she loves the person being mentioned as the lovee. And we further assume in this world, nobody lies about romantic feelings, and that a person's affection for another is positively proportional to the number of times she indicated the feeling.

Then, we could ask, what is the probability that Romeo loves Juliet? To answer this question, we can look at the probability of that situation. First, we shall see there are a total of 5 instances of love expressions for Romeo. Second, the number of instances with Juliet is 3. By simple statistics, the reader can easily determine the probability of interest - 3/ 5 = 0.6.

For the probability of "romeo" preceded by "juliet likes", one could similarly find the answer to be 0.6.

So a rare occasion in love stories: Romeo loves Juliet just as much as Juliet loves Romeo. Good, no one gets hurt.

But let's pay a bit closer attention to the scenario. The probabilities of these two events are estimated from two different distributions (in each of which the probabilities of all events sum up to 1). Does 0.6 mean the same thing in both distributions? Or in other words, does an event of probability 0.6 tell you equally as much information in the first distribution as in the second?

No.

Yes?

Well. It is a matter of perspective. However, I am going to argue that saying "no" is better than the other.

Let's look at the problem in terms of information theory. The first distribution has an entropy of 0.97 bits, and the second one has 1.37 bits. The information theory (communication theory) points out entropy is an indicator of choices - higher entropy corresponds to more choices. In other words, Juliet has more choices than Romeo in our hypothetical world. How much more? Juliet has 2.58 choices, and Romeo has only 1.97 choices.

This gets interesting. When Juliet apparently has more choices than Romeo, she loves him just as probably as he loves her. Does this make Juliet's love more valuable?

In a sense, yes. By how much? 0.61 choices, whatever that means.

Now let's look at another quantity. How many choices does each of them have besides the primary one (Juliet for Romeo, and Romeo for Juliet)? For Romeo, there's only one alternative left - Jane, which would have a probability of 1 if Juliet were not in the picture. Thus, the entropy of the alternatives is 0 for Romeo. For Juliet, the entropy of the alternatives is 1 bits.

This is even more interesting. If Romeo does not love Juliet, then he literally has no other choices but Jane, which makes the choice meaningless (choice with one option isn't really a choice). However, if Romeo is not an option for Juliet, she is better off by 1 bits, which are 2 choices.

Juliet is then doing a huge favor to Romeo by loving him with a chance of 60%! Because if they are mutually refusing to be in a relationship, Juliet is in a situation way better than Romeo's.

So, in general, the message to take away from this silly example is, Romeo should feel fortunate if Juliet ends up loving him, because her 60% is more valuable than his 60%.

Ok, seriously.

Updates

2010-01-06T22:28:00.000-05:00

It has been a while since I last updated this blog. But a random narcissist search of my name in google shows this blog has been indexed. Well...that's some motivation for a new post.

The first semester of my PhD life is done, which is relatively enjoyable. However, I am now more inclined to leave academia once I am done with graduate studies. I've always felt that professors are a noble job, and are people who contribute to the society significantly. Yet this contribute is rather indirect. And perhaps due to this indirect influence, many research projects are conducted with no specific intention of making social impact. I am rather dissatisfied with that.

The important reason why everyone should feel good about themselves

2009-12-08T16:03:00.000-05:00

here is the reason:

http://www.scientificamerican.com/article.cfm?id=the-psychology-of-social

Bayesian Calculator

2009-12-08T15:50:00.002-05:00

Aha! I've been looking for this kind of stuff for a long time. Glad someone made it:

http://psych.fullerton.edu/mbirnbaum/bayes/BayesCalc.htm

Infinity in Python

2009-12-03T22:28:00.001-05:00

There are only two constants in the Python math module: pi and e. However, it is often useful to have positive and negative infinities as well. After a bit googling, there is a rather interesting way to get these values:

For positive infinity, just do:

float('inf')

For negative infinity, guess what -- float('-inf')

Somehow I find it very amusing.

Aluminum Foil for Burritos

2009-10-31T23:05:00.000-04:00

The three happiest things in life are: sleeping, eating, and urinating. Having said that, I want to point out that Mexican-food-wise, Chipotle is my favorite restaurant. I sincerely love their chicken burritos, perfect for either lunch or dinner.

Today is Halloween. Although I've never it officially advertised, Chipotle is said to give a free burrito to whoever dresses like one. I went to Chipotle this evening to enjoy my burrito, and to see how others attempt to get a free burrito. To my amazement, most people just put some aluminum foil around arms or heads! That costume is too cheap!

But it was fun anway. =)

TA Preferences

2009-10-31T14:14:00.000-04:00

It's always easier to bitch about this world than to adulate it. Nevertheless, I'll try.

The most rewarding part about being a TA is leading the workshop session (see previous post). During the workshop, I got to know students in person. And once such face-to-face interaction emerges, those students are no longer of only statistical significance.

(For the ideas on statistical significance and individual significance, Steven Landsburg wrote a very good chapter in his book "More Sex is Safer Sex". You might want to read it.)

One student came to my office hour once and seemingly got a very satisfying response to her question. She came again. This kind of "returning customer" illustrates a simple trust that has been built between me and students -- that Ting explains problems well and that students recognize my work. The same with my workshop. I've noticed it is almost the same group of people that will come to my workshop session. And once a new member joins, she stays.

I have been against excessive use of complicated language in either learning or teaching. It annoys me that some people, for reasons that we all probably know, are particular fond of showing off knowledge in convoluted manners. When I explain problems to students, I always try to use the simplest language and a straight-forward logic to illustrate the problem. Learning is not just about acquiring a technical language, but more importantly, the correct way of thinking.

TA Bias/Preference

2009-10-23T20:19:00.000-04:00

This year I have been assigned to be one of the two TAs (teaching assistant) for a statistics course offered by our department (http://www.bcs.rochester.edu). I am responsible for grading students' homework, exams, and offering a workshop session, where students can come and ask questions about homework problems. Additionally, I need to prepare keys to homework and/or exams every other week (rotating with the other TA).

This is the first time that I've been a TA. And as with all first-time experiences, I've become overly sensitive to all the interesting observations. Of all encounters with students, both enjoyable and annoying, one rule seems to be true: students have clear preferences/biases towards me, and that's probably due to the fact that I am an international student.

Students never turn homework into my mailbox. The mailboxes are ordered by last names in our department. And my last name, QIAN, looks strikingly weird since it breaks one important spelling/phonological rule of English -- Q is usually followed by U. Students may remember that my first name is Ting. But it may appear difficult to locate my mailbox by remembering my last name.

Relatively few students come to my workshop session. This is also interesting. I suppose there are two reasons: a practical one, and one, again, due to my non-American background. First, my workshop session is at 8pm in the evening, which might be party time for some people. Second, it is very natural for students to try to avoid non-American TAs, since bad accents do affect the quality of teaching. I personally have such preferences when I was an undergrad.

Students tend to argue with me, insisting that his/her answer is only "saying the same thing" as the correct key. Interestingly, some students assume that I can be easily fooled around by trying to confuse me verbally. The basic strategy is to 1) extract keywords from the key (which I prepared), 2) re-order the keywords and plug them into a sentence using a different structure, 3) show that this sentence is (almost) the same as his/her answer and asks for points back. On such occasions, I respond as follows: 1) your answer is mathematically equivalent to: (blablabla), and 2) the key is mathematically equivalent to: (yadayadayada). Bla is not yada. Therefore, you are still wrong.

In next blog, I'll write about the preferences.