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Feb 24, 2012

### Some definitions in detection and estimation theory

A message passes through a `noisy channel’ and is then observed as a variable z. Based on the observation made, we need to ‘decide’ or ‘detect’ which message was sent. In particular, consider two detections d1 = {z | z belongs to Z1 } and d2 = {z | z belongs to Z2 } and two messages m1 and m2.

Such a setting has a prototypical example application: the radar problem. Here m1 is the message that no object is present and m2 is the message that an object is present and z is the radar observation made. We give conditional probabilities popular names:
P(d2|m1) is sometimes called false alarm probability.
P(d1|m2) is called miss probability.
P(d2|m2) is called detection probability.
The randomness is in the noise which gets added in the channel or while measuring. That is, z is a random variable.
Hence, detecting d2 when m1 is true, is a detection that an object is present, when in fact, no object is present, i.e., a false alarm.

In terms of statistical ‘decision’ theory, on the other hand:
P(d2|m1) is called level of significance.
P(d2|m2) is called power of the test.
Equate m1 to the null hypothesis (no change has occurred) and m2 as the alternative (soem change has occurred). The power of the test describes the probability of announcing a change, when in fact, one has occurred. The level of significance represents the probability of incorrectly announcing a change. For a good ‘decision’, one would like to make the power as large as possible and the level of significance as small as possible. Neyman-Pearson criterion can help maximize power subject to significance bounded above by alpha. Parameter alpha is user determined, typically using Receiver Operating Characteristic (ROC) curves.

Note that these detection or decision problems are different from (yes-no/feasible-infeasible) decision problems in optimization and complexity theory.

Reference: Mesa and Cohn 1978, Detection and Estimation theory.

Jan 13, 2012

### Understanding your data is important

Hello Everyone!

It is January again. There seem to be a lot of IAP activities going on: from dancing to cooking to physics to sports. One interesting event which me and my friend have been going to is about data processing and visualization using python. The class is being organized by Adam and Eugene from CSAIL (Computer Science and AI Laboratory), both of whom are grad researchers in databases and systems. Needless to say, I am greatly benefitting from the class! Up till now, we learned how to understand data by visualizing it using various graphing tools (never underestimate histograms, scatter plots etc), set forth hypotheses and then reject/not-reject these hypotheses using suitable tests (classical statistics). We also learned how to clean data, especially when it is textual so as to improve our own subsequent analyses.

The importance of amassing such useful tools for applied mathematicians and model engineers cannot be understated. A recent poll on the kdnuggets website shows that people think ‘big data’ and data analytics are two important developments in related industries. But while using such tools in practice, I feel one must tread large scale data in a delicate way. The reason is because of the following: There might be a lot of domain wisdom involved with related activities like data preprocessing, making hypotheses, making subsequent data collection and so on which can make or break the entire analysis process. This not only applies to the easily available web data but also to engineering and natural science datasets which have also exploded rapidly thanks to better systems and high quality/faster measurements (e.g., images sent by satellites, surveillance footage, data from physical experiments like those at CERN etc). There are quite a few small companies which have come up around the web data industry which exclusively maintain and sell datasets. I wonder which areas (that un till now haven’t seen data deluge) could immensely benefit from aggressive large scale data analysis?

Dec 21, 2011

### Risk Taking Behavior

Hello there!

After a long hiatus, something compelled me to post this morning. Two disconnected events which exemplify the modeling challenges in engineering systems as a whole just became too pertinent to me that I didn’t want to let them go unregistered. The challenge in particular, involves modeling a specific aspect of human response or action: is she risk taking or is she risk-averse?

Risk-averse behavioral assumption is quite common in fields which are a few hops away from the social sciences: for example, adversarial modeling of nature are assumed quite natural in sub-fields of AI like online learning and reinforcement learning (aka approx. dynamic programming). The sub-field of robust optimization (in the field of math programming) also talks about deciding on a solution which withstands all sorts of ‘adversarial’ uncertainty of nature.

Lets focus on humans as they sometimes (maybe even all the time) need to take decisions when using an engineered system. Are they risk averse? Are they seeking to make a decision pitted against worst case adversarial behavior of nature? The answer seems to be both yes and no. Sometimes humans seem to be risk-averse and sometimes they are not. For example, when one wants to invest in stocks and such, one wants to pick stocks which can give a good return even in the ‘most’ adversarial scenario. Would one want to potentially pick stocks which can give a higher return with a small probability but lower return otherwise?

In a recent talk on the origin of behavior by an EECS Faculty (Andrew Lo, who is also in the Business School), he gave a simple live example where the audience was asked if they would go for a riskier option or a risk-averse one, and surprisingly, the audience choose a riskier option (I’ll skip the details here). But there is a more immediate real example. Immediate in the sense that you can see it with your own eyes all the time. Consider the system of traffic intersections. People tend to cross at intersections even when it is not safe to cross. This happens with a high probability around the time when everyone is either getting into their offices or leaving. Aren’t people undervaluing the risk involved with being hit by a motor vehicle? Aren’t they jeopardizing themselves and other people? The same goes with people who bike. They seem to take arbitrary turns at intersections when their fellow motorized traffic is patiently waiting for the go signal. Aren’t they risk taking?

Of course, modeling humans accurately is a very complicated task. But at least knowing their risk-seeking behavior can help the mechanism designer (the road authority for example) design a better game.

Aug 17, 2011

### Opinion dynamics

I just went to a MSRNE theory talk today. The speaker was Dr. Ozdaglar from the LIDS. She has taught the course 6 grad class ‘game theory and applications’ last year. In the context of this talk she, along with her collaborators, has worked on answering the following broad question: Given a network topology (graph) and rules-of-thumb on how interactions (exchange of belief or state) take place between the nodes (equivalently, agents or people), is it possible to reason about the nodes converging to a consensus? What if some nodes are prominent in the way they exchange beliefs with their neighbors? What is the effect of the randomness we are assuming in the dynamics? Is there (any) learning?

The way I have described the questions here, they will seem vague/non-informative. But one can make precise what all the keywords mean. She has used tools from the theory of markov chains, probability, perturbation analysis etc. The work seems interesting because (as she says) it connects to aspects of game theory, marketing, understanding influential agents in a real society etc.
Dr. Sudan and others in the audience asked very interesting questions. Incidentally I had heard a previous version of the talk but couldn’t understand much. But hearing this again, I could connect more dots.

Aug 10, 2011

### Oded and Scott

[microblog]

I recently came upon an interesting observation by a Professor of Computer Science: It talks about the dominance of competition and the relative weighing between conceptual message and the technical difficulty of a piece of work, as seen in top theory conferences in CS. Here is the link.

Scott Aaronson, a professor affiliated with CSAIL has posted a new survey called “Why Philosophers Should Care About Computational Complexity”… I haven’t looked at it beyond the abstract at the moment, but it seems interesting (see link).

Aug 05, 2011

### Brush with TCS

TCS:Theoretical Computer Science

In the past few days, I had the opportunity to listen to some very exciting TCS research op the topics of list decoding, coding theory, complexity theory and pseudo-randomness. I was not expecting such a brush though. The workshop had a theme related to sparsity and dimensionality reduction too, which was a bit close to what interested me then. So I signed up for the workshop and well, thanks to it, I can connect a few more dots in computer science and electrical engineering research than before. To be honest, my prior encounter with coding (both channel and source) were only in the electrical engineering domain. The latest refresher being Prof. Medard’s 6.450 (which doesn’t actually go into error-correcting codes). But through the workshop, I came to realize that coding theory connects well with complexity theory and pseudo-randomness (expanders, extractors and so on). Related to this, Prof. Sudan’s course on the topic seems to be very popular.
I think I should brush up with algorithms to understand what is happening in the TCS area.

Apr 10, 2011

### A possible evolution of forums and textual discussion on the web

I came across a few ‘apps’ (I don’t use this terminology) on a popular video hosting site youtube about making movies without knowing anything about character animation.

My thesis is this: These apps allow one to pretty much flush out their blog posts in a video format. But then, with one character and text-to-speech rendition of a blog post might be a bit boring, especially if it is in the area of science.
But think about discussions between N parties in a traditional forum (mathoverflow, stackexchange) or even the very latest media: twitter and facebook. They involve textual communication. If the textual communication is on a topic of substance or even relating to matters of education (for example, science and math concepts), I think it will be cool to animate it and flush out a video.

I made a very short video defining a quantity used in learning theory.

Mar 31, 2011

### Reviewing a paper in the 21st century

How about having a video-conferencing with the referees and the author? The author then presents his work and explains all questions that the referees might have.

This saves everyone time. Reinforces faith in the author that his work is actually being processed.

Note that this will work only when the reviewing process in completely transparent. If not, other bells and whistles need to be added.

Maybe a speech-to-text software will transcribe the event too for future purposes (in addition to recording). The recording can then be viewed by everyone (even half a century later). As a side effect, this might make going physically to conferences redundant.

Sep 19, 2010

### An atypical researcher skill

One of the things school (grad or undergrad) doesn’t teach in an overtly formal way is self promotion. But then, the culture of the hostel, class or research group you were a part of might have taught you a trick or two about positioning yourself well and having an audience. I don’t think students think too much about this, other than when they write their resumes for interns or jobs. But that is only one small way with a limited audience.

I am just listing a couple of ways which come to my mind, how people go about branding themselves (a bit specific to researchers I suppose). (technical) Blogs. A great way to promote your research and get an audience. Some of the top science blogs attract world renowned researchers. A good homepage listing all your publications, talks, conferences, collaborations, your future calendar, research interests is pretty much a given these days. I can imagine people recording their talk presentations themselves, posting them on video-sharing sites and linking them to their web pages. This can create, as a (by?)product, wealth of technical information for people world over (research-y OCW success story?). A lot of the scientific talks as well as lot of instructional videos for math and science for high school videos are already on the web.

Today’s researcher should probably augment herself/himself with good sales and marketing skills to push forward their neat ideas to reality. It is also critical for career too. I think there are a few studies and more serious blogs out there that address this issue. Do let me know if you have any insight to add!

Feb 24, 2010

### Activities for Grad Students 1

The past 3-4 weeks have been pretty interesting, not just because the school and the courses are picking up speed and marching into the spring semester but also because there have been a lot of community building activities lately. Even before the semester started, the GSA hosted an ice skating social at the Johnson ice rink of the Z center late January. Then there was this colourful social mixer on the theme of Mardi Gras which a lot of grad students attended. The spring Intramurals are starting this March and the GSA’s athletic chair is buoyant about people signing up in good numbers for various events. Also, Prof. Oppenheim’s Graduate Mentoring Seminar (GMS) is going in full ‘magical’ swing!

On the academic front, there were a couple of very informative sessions organized by the academics committee of the GSA on the Research and Technical Qualifying Exams (RQE and TQE) of our department. A lot of research seminars are going on in full swing in most of the conference/class rooms around buildings 36 and 32. For example, the most recent LIDS seminar about Principle Component Analysis (PCA) had a standing room attendance in 32-141!

Finally, there is a nice one day conference coming up in March called the Multicultural Conference which I am very excited about.