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Optimization Process
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3Optimization Process's Shortform
5y
7
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Histograms are to CDFs as calibration plots are to...
Optimization Process1mo10

It sounds like you're assuming you have access to some "true" probability for each event; do I misunderstand? How would I determine the "true" probability of e.g. Harris winning the 2028 US presidency? Is it 0/1 depending on the ultimate outcome?

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Histograms are to CDFs as calibration plots are to...
Optimization Process1mo10

(Hmm. Come to think of it, if the y-axis were in logits, the error bars might be ill-defined, since "all the predictions come true" would correspond to +inf logits.)

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Histograms are to CDFs as calibration plots are to...
Optimization Process1mo20

Ah-- I took every prediction with p<0.50 and flipped 'em, so that every prediction had p>=0.50, since I liked the suggestion "to represent the symmetry of predicting likely things will happen vs unlikely things won't."

Thanks for the close attention!

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Histograms are to CDFs as calibration plots are to...
Optimization Process1mo60

I like the idea, but with n>100 points a histogram seems better, and for few points it's hard to draw conclusions. e.g., I can't work out an interpretation of the stdev lines that I find helpful.

Nyeeeh, I see your point. I'm a sucker for mathematical elegance, and maybe in this case the emphasis is on "sucker."

I'd make the starting point p=0.5, and use logits for the x-axis; that's a more natural representation of probability to me. Optionally reflect p<0.5 about the y-axis to represent the symmetry of predicting likely things will happen vs unlikely things won't.

(same predictions from my last graph, but reflected, and logitified)

Hmm. This unflattering illuminates a deficiency of the "cumsum(prob - actual)" plot: in this plot, most of the rise happens in the 2-7dB range, not because that's where the predictor is most overconfident, but because that's where most of the predictions are. A problem that a normal calibration plot wouldn't share!

 

(A somewhat sloppy normal calibration plot for those predictions:

Perhaps the y-axis should be be in logits too; but I wasn't willing to figure out how to twiddle the error bars and deal with buckets where all/none of the predictions came true.)

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Histograms are to CDFs as calibration plots are to...
Optimization Process1mo40

Random numbers! Code for the last figures.

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Escape from Alderaan I
Optimization Process5mo90

That all of physics was perfectly beautiful and symmetric except for hyperspace, artificial gravity, shields and a few weapon types.

Oh, this is genius. I love this.

Reply1
The quantum red pill or: They lied to you, we live in the (density) matrix
Optimization Process6mo10

Ahhh! Yes, this is very helpful! Thanks for the explanation.

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The quantum red pill or: They lied to you, we live in the (density) matrix
Optimization Process6mo*20

Question: if I'm considering an isolated system (~= "the entire universe"), you say that I can swap between state-vector-format and matrix-format via

|ϕ⟩↔ρ=|ϕ⟩⟨ϕ|

. But later, you say...

If HS is uncoupled to its environment (e.g. we are studying a carefully vacuum-isolated system), then we still have to replace the old state vector picture |ϕ⟩∈H by a (possibly rank >1) density matrix ρ∈OpH...

But if ρ:=|ϕ⟩⟨ϕ|, how could it ever be rank>1?

(Perhaps more generally: what does it mean when a state is represented as a rank>1 density matrix? Or: given that the space of possible ρs is much larger than the space of possible |ϕ⟩s, there are sometimes (always?) multiple ρs that correspond to some particular |ϕ⟩; what's the significance of choosing one versus another to represent your system's state?)

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Quantum without complication
Optimization Process6mo10

That is... a very interesting and attractive way of looking at it. I'll chew on your longer post and respond there!

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Magnitudes: Let's Comprehend the Incomprehensible!
Optimization Process7mo50

I have an Anki deck in which I've half-heartedly accumulated important quantities. Here are mine! (I keep them all as log10(value in kilogram/meter/second/dollar/whatever seems natural), to make multiplication easy.)

QuantityValue
Electron mass-30
Electron charge-18.8
Gravitational constant-10.2
Reduced Planck constant-34
Black body radiation peak wavelength-2.5
Mass of the earth24.8
Moon-Earth distance8.6
Earth-sun distance11.2
log10( 1 )0
log10( 2 )0.3
log10( 3 )0.5
log10( 4 )0.6
log10( 5 )0.7
log10( 6 )0.8
log10( 7 )0.85
log10( 8 )0.9
log10( 9 )0.95
Boltzmann constant-22.9
1 amu-26.8
1 mi3.2
1 in-1.6
Earth radius6.8
1 ft-0.5
1 lb-0.3
world population10
US federal budget 202312.8
SWE wage (per sec)-1.4
Seattle min wage (per sec) 2024-2.3
1 hr3.6
1 work year6.9
1 year7.5
federal min wage (per sec)-2.7
1 acre3.6
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35Histograms are to CDFs as calibration plots are to...
1mo
9
30Quantum without complication
6mo
2
29Why are there no interesting (1D, 2-state) quantum cellular automata?
Q
7mo
Q
13
18If I ran the zoo
2y
1
10Two children's stories
2y
1
17How can I help inflammation-based nerve damage be temporary?
Q
2y
Q
4
72Who are some prominent reasonable people who are confident that AI won't kill everyone?
Q
3y
Q
54
6Is there an equivalent of the CDF for grading predictions?
Q
3y
Q
5
23Book summary: Selfish Reasons to Have More Kids
4y
10
54Mildly against COVID risk budgets
4y
15
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