I did not realize he had developed CTSS. Folks in the AI lab developed ITS which was the "Incompatible Timesharing System" that had a user interface which was a REPL to the debugger (DDT at the time). They gave out 'tourist' accounts for anyone who wanted one and I used mine and met several people that way.
It sounds like he was way ahead of his peers in understanding the privacy aspects of future computers.
Among other things, he was known for Fano's Inequality, which gives a limit for how well you can predict the value of a random variable based on knowledge of a related variable. Apparently this is quite useful in signal processing for communications over a noisy channel, where the signal that you receive is not quite the same as what was sent.
Very useful in statistics too: if you can show that your estimator attains the Fano lower bound rate of convergence then it's optimal--nothing else can possibly beat it (in the minimax sense anyways).
Though I'm not a stats researcher, that sounds very similar to the Cramer Rao bound (a lower limit on the variance of any unbiased estimator, something akin to the Cauchy-Schwartz inequality only for point estimation).
That is good intuition, but note that one of the general drawbacks of Cramer Rao is that it applies for the unbiased case only (technically no, there is a version for the biased case, I have never seen it used though), and that too only well under certain regularity conditions. Indeed, there is a term for estimators where equality is met in CR, they are called "efficient" estimators.
There is significant research effort these days on going beyond unbiasedness and asymptotics, which in many cases has been beaten to death and is "classical", though there are still plenty of questions.
Here is a simple illustration of unbiasedness/going beyond it. Consider n iid (independent and identically distributed) coin flips of coin of P(heads) = p, and based on the observations, we want to estimate p, call the estimate p'. Optimum estimate in the sense of minimax - min (over estimators) max (over p in [0, 1]) E[(p-p')^2] is not the simple maximum likelihood which is the sample average.
Sample average yields a score of (1/4)(1/n), while optimum is (1/4)(1/(sqrt(n)+1)^2), which is slightly lower. It is natural to wonder why people care, typically the motivation is in high dim statistics where there is dependence on the dimension as well. In such a case fine grained characterization of performance sometimes affects the scaling in terms of the target loss amount and dimension, i.e the asymptotics now has at least 2 parameters, sometimes more.
My personal unhappiness with these problem formulations is their lack of robustness to transformations - suppose I now want to estimate p^3 instead of p, the optimum min-max will change in most cases, and definitely does here. Plugging in the sample average and then cubing is far more intuitive, and often works fine even though it is not optimal. There are more extreme examples of this, but that will take the thread too far afield.
If one is interested in the topic of biased estimators, I suggest reading about James-Stein estimators and more generally shrinkage estimators.
> Robert Mario Fano (2008), Scholarpedia, 3(10):6648.
So he was 90 years old when he wrote that. That is really cool, especially in the context of this section of the obituary:
> In many respects, Fano was one of the world’s first open-source advocates. He frequently described computing as a public utility that, like water or electricity, should be accessible to all. His writings in the 1960s often discussed computing’s place in society, and predated today’s debates about the ethical implications of technology.
> “One must consider the security of a system that may hold in its mass memory detailed information on individuals and organizations,” he wrote in a 1966 paper he co-authored with Corbató. “How will access to the utility be controlled? Who will regulate its use?”
In addition to the other contributions listed, we should add the Fano/Adler/Chu E&M series, which was one of the touchstones for an earlier gen of students. RIP
While I do imagine that Robert Fano's name is familiar to many who have studied computer science, the original article title (which I submitted) was a bit more descriptive; the HN moderators changed it.
This was an original conception of information theory, somewhat beat to the press by Shannon, though the two had talked about it (and indeed Shannon cites this in "A Mathematical Theory of Communication").
I have a copy of TR 149, Transmission of Information II, as well, but no scanner anymore.
You do have a scanner - you just don't realize it - your phone. Download any photo to pdf app and photograph the pages with your phone. Or just do photos and then share those.
Many libraries have scanners, or photocopiers which will scan to TIFF or JPEG on a USB stick, or even email / share directly to a specified device or service.
Otherwise, the 63 combined pages are available for the low, low price of $275.
In those days [batch processing] programmers never even
documented their programs, because it was assumed that
nobody else would ever use them. Now, however, time-sharing
had made exchanging software trivial: you just stored one
copy in the public repository and therby effectively gave it
to the world. Immediately people began to document their
programs and to think of them as being usable by others.
They started to build on each other's work.
Another passing in my college lineage. Studied under Glem Langdon (passed a few years back), Huffman (a few years prior to that), I recall Shannon passing.
Glen Langdon and David Huffman I knew from UC Santa Cruz. Shannon and Fano, I only heard stories about. Jorma Rissanen is still alive at the age of 98.
29 comments
[ 3.0 ms ] story [ 37.2 ms ] threadIt sounds like he was way ahead of his peers in understanding the privacy aspects of future computers.
https://en.wikipedia.org/wiki/Fano%27s_inequality
There is significant research effort these days on going beyond unbiasedness and asymptotics, which in many cases has been beaten to death and is "classical", though there are still plenty of questions.
Here is a simple illustration of unbiasedness/going beyond it. Consider n iid (independent and identically distributed) coin flips of coin of P(heads) = p, and based on the observations, we want to estimate p, call the estimate p'. Optimum estimate in the sense of minimax - min (over estimators) max (over p in [0, 1]) E[(p-p')^2] is not the simple maximum likelihood which is the sample average. Sample average yields a score of (1/4)(1/n), while optimum is (1/4)(1/(sqrt(n)+1)^2), which is slightly lower. It is natural to wonder why people care, typically the motivation is in high dim statistics where there is dependence on the dimension as well. In such a case fine grained characterization of performance sometimes affects the scaling in terms of the target loss amount and dimension, i.e the asymptotics now has at least 2 parameters, sometimes more.
My personal unhappiness with these problem formulations is their lack of robustness to transformations - suppose I now want to estimate p^3 instead of p, the optimum min-max will change in most cases, and definitely does here. Plugging in the sample average and then cubing is far more intuitive, and often works fine even though it is not optimal. There are more extreme examples of this, but that will take the thread too far afield.
If one is interested in the topic of biased estimators, I suggest reading about James-Stein estimators and more generally shrinkage estimators.
http://www.scholarpedia.org/article/Fano's_inequality
So he was 90 years old when he wrote that. That is really cool, especially in the context of this section of the obituary:
> In many respects, Fano was one of the world’s first open-source advocates. He frequently described computing as a public utility that, like water or electricity, should be accessible to all. His writings in the 1960s often discussed computing’s place in society, and predated today’s debates about the ethical implications of technology.
> “One must consider the security of a system that may hold in its mass memory detailed information on individuals and organizations,” he wrote in a 1966 paper he co-authored with Corbató. “How will access to the utility be controlled? Who will regulate its use?”
Who?
https://archive.org/details/fano-tr65.7z
This was an original conception of information theory, somewhat beat to the press by Shannon, though the two had talked about it (and indeed Shannon cites this in "A Mathematical Theory of Communication").
I have a copy of TR 149, Transmission of Information II, as well, but no scanner anymore.
How delightfully ironic! ;)
Otherwise, the 63 combined pages are available for the low, low price of $275.
http://www.jnorman.com/cgi-bin/hss/39416
http://www.inspiringquotes.us/quotes/pCID_em9jKLpk
Glen Langdon and David Huffman I knew from UC Santa Cruz. Shannon and Fano, I only heard stories about. Jorma Rissanen is still alive at the age of 98.
Pillars in compression and information theory.
One of my favorite memories of David was how he got grumpy about being best known for that term paper. He had done much more.
(Sorry for side track memory)