October 2005


Someone should really do some rigorous distribution testing on the shuffle feature. I have a sneaking suspicion it’s not really uniform over the songs in the machine.

1. Foxy Lady (Jimi Hendrix)
2. Minimum Wage (They Might Be Giants)
3. Das Lied vom Kelch (Eisler/Brecht, perf. by Gisela May)
4. Everything Hits At Once (Spoon)
5. Line Up (Lennie Tristano)
6. Mach Doch (Fischmob)
7. Acetate Prophets (Jurassic 5)
8. The Deforme (Beatniks)
9. Sham Gayi Raat Aai, from Shri 420 (Lata Mangeshkar)
10. Bagatellen for String Quartet (Anton Webern)
11. Living Life [w/Rec Center] (Prefuse 73)
12. Po Lazuras (some chain gang from the O Brother Where Art Thou soundtrack)
13. No Compassion (Talking Heads)
14. Bag’s Groove (Thelonious Monk)
15. A Tisket A Tasket (Ella Fitzgerald)
16. Chramer Gip Die Varwe Mir, from Carmina Burana (Carl Orff)
17. Come Rain or Come Shine (Billie Holiday)
18. Everything Is Catching On Fire (They Might Be Giants)
19. Como Dos Extranos (Roberto Goyeneche)
20. Daughters of The Lonesome Isle (John Cage)
21. Fugue in A minor, BWV865 (J.S. Bach, perf. Glenn Gould)
22. Montparnasse (Francis Poulenc, perf. Stutzmann and Södergren)

In trying to figure out if this problem I’m working on has been addressed by the statistics community, I found myself forming Google queries on “semiparametric Gaussian estimation.” The problem I’m looking at is the following. Suppose X(t) is an iid Gaussian vector. I get to observe Y(t) = A(t) X(t) + W(t) where W(t) is an iid Gaussian vector of noise and A(t) is a matrix-valued random variables taking values in a finite set, iid across time. I want to form a minimum mean-squared error (MMSE) estimate of X(t) from Y(t). If A(t) is known at all times t then this is easy since I can make a linear estimator for each value that A(t) can take. Instead, I’ll make the crazy assumption that the estimator has to be linear and designed off-line (i.e. not data dependent), and that the distribution p(A) is not known. What’s the best estimator and worst-case error?

In my searching the web, however, I turned up some crazy things on long memory parameters in nonstationary time series. I also came across the term kriging, which looked like a typo for something. Instead, it really means Gaussian process regression — yet another instance of jargon standing in the way of understanding. Unfortunately, I don’t think it’s quite what I want. Back to the ol’ search engine…

1. Crush With Eyeliner (REM)
2. Domino Theories Part I (Don Byron)
3. Critic Intro (They Might Be Giants)
4. Craisons in the Snole (Fischmob)
5. Lay, Lady, Lay (Bob Dylan)
6. Polka Dots and Moonbeams (Cassandra Wilson)
7. New Years Eve in A Haunted House (Raymond Scott)
8. Straight, No Chaser (Thelonious Monk)
9. Polly’s Lied, from The Seven Deadly Sins (Kurt Weill)
10. W.O.E. Is Me (Jurassic 5)
11. Rollend in schaumenden Wellen, from Die Schöpfung (Franz Josef Haydn)
12. Body And Soul (Frank Sinatra)
13. O Mistress Mine (Ralph Vaughan Williams)
14. Freundselig ist das Wort, from Cantata no. 2, op. 31 (Anton Webern)
15. Wax The Nip (Aphex Twin)
16. Nouvelles Adventures : Agitato Molto (György Ligeti)
17. Nicolas From Prison, from Saint Nicolas (Benjamin Britten)
18. Dreidel Song (Don Byron)
19. I’ll Wait and Pray [alt. take] (John Coltrane)
20. Big Time (Medeski, Martin & Wood)

A short observation before I head off to rehearsal, apropos to my previous post: in acting classes we are taught that you cannot phrase your objective in terms of a negative. That is, you cannot say that in this scene “I don’t want to do X.” That’s not actable — you can’t concretely do things to not do something. You have to instead phrase it like “I want to do Y.”

The argument against SSM could be phrased like “we want to preserve marriage for heterosexuals.” But that would make them seem like bigots. Instead, they try to phrase it like “we don’t want the meaning of marriage (= baby-making) to change.” But that’s not an actable objective, so all the arguments amount to sidling around confronting the real objective.

UPDATE : Upon browsing the Volokh commentariat, they don’t seem to buy her
“arguments” either.

When I saw that gay marriage opponent Maggie Gallagher was going to be guest-blogging at Volokh, I thought that it would be a good opportunity to sharpen the rhetorical knives to take her argument apart. Unfortunately, life intervened, leaving me with no time, and besides, the folks at Crooked Timber do a much more entertaining evisceration.

However, her last post is really a piece of work. It becomes transparent that her argument comes from the same ideological roots as those against mixed-race marriages (miscegenenation could come back in vogue!), and that for all her attempts to put opposition to SSM (single-sex marriage — her acronym) on a firm rhetorical footing, it just comes down to a desire to put herself and those who believe the way she does on top of the socio-ethical pyramid. For all her protestations, she is deeply and ideologically homophobic.

Her basic argument is that marriage fundamentally exists to make babies and provide babies with a mother and a father. SSM is about providing a seal of approval on what is essentially an intimate and sexual contract between two people, and so confuses marriage (= making babies) with something else (= loving, intimacy). This, she disingenuously argues, is why people should be uncomfortable about SSM. She excuses gay-haters by saying that they can be perfectly ethically sound if they oppose it for her reasons, but then neatly characterizes those on the other side as arguing that the institution of marriage is obsolete. It’s a stupid argument — she wants to define the debate as being about her definitions and her issues, and so casts those on the other side as diametrically opposed to her in a sort of dialectical battle royale.

SSM, she claims, would make baby-making marriage into “as at best a private understanding and most likely a discouraged, discriminatory understanding of marriage.” Where this “most likely” comes from, who can tell? Perhaps the same place that the “yellow peril” comes from. Her next bit of grandstanding is priceless:

I have most of human history on my side. You have your personal moral conviction that only hate explains why people object.

This is my one big message for SSM advocates: don’t minimize what you are proposing. Take responsibility for it.

What a canard! Turning this around, I could make the following argument — I have the deep belief that people of different skin colors were never meant to be married. Marriage is about perpetuating society, and societies are primarily single-race. Indeed, much research has showed that the vast majority of successful societies have been single-race. To me, marriage is about making babies in single-race households, because babies need a mother and a father that are the same skin color. I have the weight of human history on my side. I don’t want to mix the races because it will “most likely lead to a discouraged, discriminated form of marriage,” according to my definition of marriage. Now those of you who think I’m a bigot, please take the time to understand how your demands for mixed-race marriage hurt me.

In this debate, her argument boils down to this — demaning SSM hurts some people’s feelings, so don’t be so strident. You’re asking her to give up the top position on the totem pole, and that’s asking a lot. Also, if you get SSM, you’re going to make all our social problems worse. If you let gay people get married, then you’re just going to make more deadbeat dads. Because those dads will suddenly think “hey, marriage isn’t about babies, so I’m out of here.” It’s not even an argument that’s very rooted in the psychology of fathers who abandon their families.

I’m not going to get into the fact that this whole argument is framed around the “marriage tames those feral sex-crazed men” meme that permeates her argument, or the “let’s go back to the golden era of the 1850′s” cast of it. She also believes that “humanity comes in two halves, male and female, who are called to join together in love, not only as a private satisfaction, but in order to make the future actually happen.” We can call this the argument from mysticism. She kind of constructs arguments like Aristotle constructs his natural history. Or Plato constructs the Republic. The first is wrong, and the second is definitely not a place where anyone would want to live.

The big news in the Bay Area is that a mother threw her three children into the Bay. She is a schitzophrenic who heard voices, and was living with her children in a shelter.

Naturally we will be treated to same media handwringing about how serious mental illness is and why care not cash will force people like this woman to take her medication. “Is it appropriate to use insanity as a defence if you know you’re insane and should be taking your medicine?” people will ask. Some will opine on the need for reforms in the penal code, and others will wax lyrical about how horrific crimes like these are a sign of social order breaking down.

An interesting perspective can also be found at Angry Black Bitch (via Allie). Nobody will address the endemic problems with the health care system in the US, let alone the mental health care system. Many people have the same attitude towards mental health as they do towards disability, or caring for an extremely elderly relative. They just don’t realize how hard it is, and can’t fathom or refuse to fathom how those people who need help end up cut loose from their families or support net.

Come to think of it, the problem is two-edged. On the one hand, they blame the families of the mentally ill for not taking care of them. But then when this mentally ill person does something bad, they want to blame the person. It’s far easier to blame people than institutions, I guess.

3 Tbsp soy sauce
2 Tbsp mirin
1 Tbsp lemon juice
1 Tbsp ground ginger
1 tsp sambal paste
2 tsp sesame oil

Slice tofu into 1/4″ thick slices. Make enough to cover tofu and let sit at least 1 hour (best if overnight). Pan fry in a light oil (grapeseed works) until each side seals. Use in sandwiches, etc.

Verdict : marinating for a long time makes the tofu weak and so plan your slice thickness accordingly. Next time I will add garlic and change the lemon juice to lime. Putting in more sambal could help too, or maybe just raw chilies (for that fresh bite). Tofu definitely needs saltiness — citrus doesn’t really penetrate it very well.

I came across some references to “Bernstein’s trick” in some papers I was reading, but had to do a little digging to find out what it really meant. Suppose you have independent and identically distributed random variables Xi for i = 1, 2, … n, taking values in [-1, 1], and with E[Xi] = 0. Our goal is to bound

Pr[ (1/n) ∑ Xi > a ] .

The Bernstein trick is to multiply both sides by a dummy variable t and exponentiate both sides:

Pr[ (1/n) ∑ Xi > a ] = Pr[ exp(t ∑ Xi) > exp(a n t) ] ,

Now we use the Markov inequality on the random variable exp(t ∑ X_i):

Pr[ exp(t ∑ Xi) > exp(a n t) ] ≤ exp(- a n t) E[ exp(t ∑ Xi) ],

Now we can leverage the fact that the X_i‘s are independent:

exp(- a n t) E[ exp(t ∑ Xi) ] = exp(- a n t) E[ exp(tX) ]n,

where X has the same distribution as Xi. Then we can expand exp(tX) as a Taylor series:

exp(- a n t) E[ exp(tX) ]n = exp(- a n t) E[ 1 + t X + (1/2!) (t X)2 + ... ] .

We now leverage the fact that X is in the interval [-1,1] and that E[X] = 0 to bound the sum of the higher-order terms in the Taylor series:

exp(- a n t) E[ 1 + t X + (1/2!) (t X)2 + ... ] ≤ exp(- a n t) exp(b k t2) .

For some constant b, which you can pick based on how much you know about the distribution of X.

Now the more probability-savvy may say “wait a minute, E[ exp(tX) ] is just the moment generating function mX(t), so isn’t this just a fancy Chernoff bound? The answer is basically yes, but the term “Chernoff bound” is used for a lot of related bounds. The one I’m most familiar with requires you to know the moment generating function E[ exp(tX) ]:

P( exp(t X) > exp(a t) ) ≤ exp(-a t) mX(t) .

Since this holds for all t, you differentiate with respect to t and find the minimum to get the tightest bound.

The main difference in these two Chernoff-style bounds is the lack of knowledge needed to apply the former to sums of iid random variables. Of course, you can get all of these bounds from large deviations theory or concentration inequalities, but sometimes a rough trick is all you need to get a sufficiently fast exponential decay so that you can move on to the next step.

Note : updated with nicer characters, thanks to Erin.

[1] Ahlswede, R. “Elimination of Correlation in Random Codes for Arbitrarily Varying Channels,” Zeitschr. Wahr. und Verw. Geb. V.44, 1978, pp. 159–175.
[2] Wigderson, A. and Xiao, D. “A Randomness-Efficient Sampler for Matrix-valued Functions and Applications.” FOCS 2005.
[3] Gallager, R. Discrete Stochastic Processes, Boston : Kluwer, 1996.

In going through Google hits for my name I came across this reference to the ExploraVision contest that I did in high school. It seems so long ago, those trips to the Viscount Den for huge Pepsi’s, pulling all-nighters to get AfterEffects to correctly composite our video, having play performances and going immediately afterwards to NCSA to work… Looking back on it, we were completely insane. But I think that experience helped break previous attitudes I had about how days and work should be structured, and how much you can really do in one day if you put your mind to it.

It is pretty cool that we’re in the Congressional record though…

Harold Pinter won the Nobel Prize for Literature this year. It coincides nicely with a BBC radio programme of his more recent plays, including the harrowing Mountain Language.

Pinter presents a wonderful challenge to actors and directors alike. How can we make this play fresh and surprising? The biggest mistake is to think that because the text is so spare that it is somehow more malleable than other plays. What’s great about directing or acting in a Pinter scene is that when you’re doing it wrong, you can tell. It becomes boring, confusing, or too obvious very quickly. It makes you pay attention to details.

It’s interesting to see how Pinter dramatizes meanace and state oppression in an overt yet disguised way, versus Caryl Churchill’s more oblique approach in her (somewhat) recent play Far Away.

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