Deep Mukhopadhyay, Ph.D.

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What's The Point of Doing Fundamental Science?

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What’s the point of doing fundamental science? Nima Arkani-Hamed presented his own fascinating perspective in a recent public lecture at Cornell, which everybody should listen. These are some of my top picks:

What does it require to do fundamental science?

Nima: Doing fundamental science necessitates working on hard problems for very long periods of time and it is not obvious how to go about attacking a problem that seems impossible to solve and might take decades to make progress on….You don’t sit around and read in a book “how you go about solving an impossibly hard problem.” You need a small group of people who have actually done it and you learn from them by osmosis. The people who work on these things are driven by a cause that is bigger than themselves and to earn it they have to work their asses off.

How can we make funding possible for this kind of people?

Nima: If you are somehow gotten into doing fundamental science with the idea that it is some sort of safe nice things to do with your life, you are crazy, you are wrong. It’s not safe, it’s risky. You are risking the most important thing you have, your life and your time to pursue things. So it’s a big risk, you should know it….if it pays out you will get all the joys and any other kind of more practical reward you get out it will be similarly bigger.

Should you work on more ambitious slightly crazier ideas or the things that most other people are working on?

Nima: There is no clean answer to this question. But it’s true that if you go a little bit further to the other people and something works, even a little bit, poof, you are lifted out of the masses and you will have a wonderful academic life after that. In academics, the greatest thing can happen is that a crazy idea actually ending up being somewhat right.

How do you approach solving problems? 

Nima:  Don’t be a monkey who is only interested in the calculation. Zoom in (detailed calculations) and zoom out (the grand vision that draws you in) constantly when solving any problem. They not orthogonal to each other, but they are not the same either. They are the two different ends of one beast that is known as a scientist.

What is the number one thing that the current academic system needs?

Nima: The number one thing that academics need is utter and complete freedom to do anything the hell they want. Freedom, freedom, freedom the most important commodity in any academic pursuit.

Is there any systemic thing that can be done to ensure the rapid development of fundamental science research? 

Nima: I think we could be doing a lot better on increasing the number of weird people that we actually have in academics. We need many many more of them. So actually, what I personally want to fight for: is enlarging the group of strange people that we allow into our mix. I find too much of a certain kind of homogeneity.

Two sides of Theoretical Data Science: Analysis and Synthesis

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Theory of [Efficient] Computing: A branch of Theoretical Computer Science that deals with how quickly one can solve (compute) a given algorithm.  The critical task is to analyze algorithms carefully based on their performance characteristics to make it computationally efficient.

Theory of Unified Algorithms: An emerging branch of Theoretical Statistics that deals with how efficiently one can represent a large class of diverse algorithms using a single unified semantics. The critical task is to put together different “mini-algorithms” into a coherent master algorithm.

For overall development of Data Science, we need both ANALYSIS + SYNTHESIS. However, it is also important to bear in mind the distinction between the two.

The "Science" and "Management" of Data Analysis

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Hierarchy and branches of Statistical Science

The phrases “Science” and “Management” of data analysis were introduced by Manny Parzen (2001) while discussing Leo Breiman’s Paper on “Statistical Modeling: The Two Cultures,” where he pointed out: “Management seeks profit, practical answers (predictions) useful for decision making in the short run. Science seeks truth, fundamental knowledge about nature which provides understanding and control in the long run.” Management = Algorithm, prediction and inference is undoubtedly the most useful and “sexy” part of Statistics. Over the past two decades, there have been tremendous advancements made in this front, leading to a growing number of literature and excellent textbooks like Hastie, Tibshirani, and Friedman (2009) and more recently Efron and Hastie (2016). Nevertheless, we surely all agree that algorithms do not arise in a vacuum and our job as a Statistical scientist should be better than just finding another “gut” algorithm. It has long been observed that elegant statistical learning methods can be often derived from something more fundamental. This forces us to think about the guiding principles for designing (wholesale) algorithms. The “Science” of data analysis = Algorithm discovery engine (Algorithm of Algorithms). Finding such a consistent framework of Statistical Science (from which one might be able to systematically derive a wide range of working algorithms) promises to not be trivial. Above all, I strongly believe the time has come to switch our focus from “management” to the heart of the matter: how can we create an inclusive and coherent framework of data analysis (to accelerate the innovation of new versatile algorithms)–“A place for everything, and everything in its place”– encoding the fundamental laws of numbers. In this (difficult yet rewarding) journey, we have to remind ourselves constantly the enlightening piece of advice from Murray Gell-Mann (2005): “We have to get rid of the idea that careful study of a problem in some NARROW range of issues is the only kind of work to be taken seriously, while INTEGRATIVE thinking is relegated to cocktail party conversation”  ]]>

Confirmatory Culture: Time To Reform or Conform?

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THEORY

Culture 1: Algorithm + Theory: the role of theory is to justify or confirm. Culture 2: Theory + Algorithm: From confirmatory to constructive theory, explaining the statistical origin of the algorithm(s)–an explanation of where they came from. Culture 2 views “Algorithms” as the derived product, not the fundamental starting point [this point of view separates statistical science from machine learning].

PRACTICE 

Culture 1: Science + Data: Job of a Statistician is to confirm scientific guesses. Thus, happily play in everyone’s backyard as a confirmatist. Culture 2: Data + Science: Exploratory nonparametric attitude. Plays in the front-yard as the key player in order to guide scientists to ask the “right question”.

TEACHING 

Culture 1: It proceeds in the following sequences: for (i in 1:B) { Teach Algorithm-i; Teach Inference-i; Teach Computation-i } By construction, it requires extensive bookkeeping and memorization of a long list of disconnected algorithms. Culture 2: The pedagogical efforts emphasize the underlying fundamental principles and statistical logic whose consequences are algorithms. This “short-cut” approach substantially accelerates the learning by making it less mechanical and intimidating. Should we continue to conform to the confirmatory culture or It’s time to reform? The choice is ours and the consequences are ours as well.]]>

Data Scientist and Data Mechanic

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Netflix competition. As the datasets are getting BIG and COMPLEX, the most difficult challenge for Statistical Scientist is to figure out “Where is the information hidden.”  It’s an interactive process of investigation rather than a passive application of algorithms and calculating error rates. Two critical skills:  (1)  “look at the data”, which is missing in the mechanical push the button culture; and (2)  learn “how to question the data”, rather than only answering a specific question.  They allow data scientists to discover the unexpected in addition to the usual verification of the expected. This begs the question whether

  • the Data Science training curriculum should look like a long manual of specialized methods and (series of cookbook) algorithms;
  • or, should train students (and industry professionals) in the Scientific Data Exploration (Sci-Dx) — A systematic and pragmatic approach to data modeling addressing the “Monkey and banana problem” [Pigeon’s approach] for practitioners. [I believe Wolfgang Kohler‘s “insight learning” idea can guide us to  develop such a curriculum.]
The first path will produce DataRobots, not Data Scientists. The later goal looks out of reach unless we figure out how to design the “LEGO Bricks” of Statistical Science (fundamental building blocks of Statistical learning), which help to understand disparate Statistical procedures from a common perspective (thus reduces the size of the manual) and can be appropriately combined to build versatile data products brick by brick.    ]]>