Philipp Wacker
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phkwacker.bsky.social
Philipp Wacker
@phkwacker.bsky.social
170 followers 550 following 150 posts
Senior Lecturer in Statistics, University of Canterbury (NZ).
he/him
Bayesian stats, Applied Math, filtering & sampling
pls send me awesome vegan waffle recipes!
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phkwacker.bsky.social
Relevant xkcd. imgs.xkcd.com/comics/thesi...
A woman in front of a seminar room (implied to be the PhD candidate in a defense), yelling "In conclusion, AAAAAAAA!!!" while charging towards her examiners. Subtitled: The best thesis defense is a good thesis offense
August 2, 2025 at 6:44 AM
phkwacker.bsky.social
The last few weeks I have been using our fantastic UC makerspace (with its 3d printers, soldering iron, and tools) to print the OpenFlexure Project Manual Microscope. Kudos to @openflexure.bsky.social for an amazing open source design. Looking forward to looking at pond water and earth critters.
3d-printed microscope in black, gray, and light blue. Shows a power source consisting of 3 AA batteries and badly soldered connections. A hair follicle under magnification. Looks like a black-ish twisted worm with four edges (?)
July 29, 2025 at 7:46 AM
phkwacker.bsky.social
I found more!
u(\cdot) = \cdot^{1-\rho}/(1-\rho), but they used a fancy bold version of \cdot. g \equiv \Gamma^4 - 1^{57}, but 4 is a power, and 57 is a footnote marker crossed out "Agemo" (horse shoe). Looks like a symbol for bad luck
July 17, 2025 at 9:42 PM
phkwacker.bsky.social
Next time I run out of symbols/letters for a paper, I will take my cue from the ridiculous stuff economists seem to be get away with. This is all from a single publication.
(grave) accented beta, boldly generalising the concept of pitch accent from vowels to consonants. A hebrew Dalet, and a strike-out capital, no-serif D. The strike out comes directly after an inline "/", leading to two diagonal lines with very different meaning. I would have given bonus points for combining Dalet with a capital Gamma but it seems the authors chickened out at the last time. vertically flipped capital Omega ("Agemo"?), superscript g word-final version of lower case sigma, multiplied by "normal" lower-case sigma (squared), subscript capital Xi (cursive!)
July 17, 2025 at 2:34 AM
phkwacker.bsky.social
What is the correct metre for the "woof, woof, woof, woof" part of "Who let the dogs out"? This has been on my mind too much recently, so here's my attempt. You're welcome, internet. (or am I wrong?)
four bits of "woof", on ONE-e-and-e-two-e-AND-e-three-e-AND-e-four-E-and-e
June 3, 2025 at 6:14 AM
phkwacker.bsky.social
the sound that you're hearing is global maths research grinding to a halt
May 14, 2025 at 8:01 AM
phkwacker.bsky.social
New dating platform for tradies just dropped
Photo of "Pro-strength Liquid PLUMR clog destroyer gel"
May 13, 2025 at 8:23 PM
phkwacker.bsky.social
One of the most fun things about reading comic books in languages you are trying to learn is that you learn "comic speak", i.e. other languages equivalents of "kaboom" and the like.
A cartoon panel of an old Victorian (?) home with lots of forest and shrubbery in the background. In the sky above the house the words هاهاها، هاهاها hang in the air, transliterating hearty laughter that can be heard outside
April 27, 2025 at 5:06 AM
phkwacker.bsky.social
Finally time for baking over the holidays. Rye/wheat
Two long-ish loaves of bread, dark brown color, with diagonal cuts
April 20, 2025 at 9:50 AM
phkwacker.bsky.social
In fact, let's focus on this part: We should read this as something in the form f(C_1) - f(C_0) - Df(C_0)[C_1-C_0], where f(C) = ln(det(C)) (and C instead of Sigma). I believe this is also due to the connection of KL-divergence to Bregman divergences in general (en.wikipedia.org/wiki/Bregman...).
Just the matrix-dependent quantities: \ln \det \Sigma _{1} - \ln \det \Sigma _{0} - \operatorname {tr} \left(I-\Sigma _{1}^{-1}\Sigma _{0}\right)
March 24, 2025 at 9:52 AM
phkwacker.bsky.social
This makes sense if we rewrite the expression a bit:
A slight rewrite of the KL divergence, pulling apart the logarithmic determinants, and including the constant k as the trace of an identity matrix: {\displaystyle D_{\text{KL}}\left({\mathcal {N}}_{0}\parallel {\mathcal {N}}_{1}\right)={\frac {1}{2}}\left(\ln \det \Sigma _{1} - \ln \det \Sigma _{0} - \operatorname {tr} \left(I-\Sigma _{1}^{-1}\Sigma _{0}\right)+\left(\mu _{1}-\mu _{0}\right)^{\mathsf {T}}\Sigma _{1}^{-1}\left(\mu _{1}-\mu _{0}\right)\right).}
March 24, 2025 at 9:52 AM
phkwacker.bsky.social
Something cool I understood this week: The Kullback-Leibler divergence between two multivariate Gaussian distributions has a closed form solution. The term with the means somehow makes sense: Penalise a covariance-weighted squared distance between the respective means. But all these matrix terms?
Formula for KL divergence between two Gaussians N_0 and N_1 {\displaystyle D_{\text{KL}}\left({\mathcal {N}}_{0}\parallel {\mathcal {N}}_{1}\right)={\frac {1}{2}}\left(\operatorname {tr} \left(\Sigma _{1}^{-1}\Sigma _{0}\right)-k+\left(\mu _{1}-\mu _{0}\right)^{\mathsf {T}}\Sigma _{1}^{-1}\left(\mu _{1}-\mu _{0}\right)+\ln \left({\frac {\det \Sigma _{1}}{\det \Sigma _{0}}}\right)\right).}
March 24, 2025 at 9:52 AM
phkwacker.bsky.social
Ah, very interesting! Look at this: This is the output of $Y_i Y_i^\top$ $Y_i {Y_i}^\top$ (note the brackets)
PDF LaTeX output of $Y_i Y_i^\top$ $Y_i {Y_i}^\top$. First version has wrong alignment of i, second one is correct.
March 23, 2025 at 11:11 PM
phkwacker.bsky.social
What's happening with the indices here? Why are they not aligned?
PDF LaTeX output of $Y_i Y_i^\top$. The heights of the two indices i are not aligned.
March 23, 2025 at 10:06 PM
phkwacker.bsky.social
Ominous. (Seen in Sydney)
A scary looking storm drain(?) with a placque above it which says "The detention control pit shall be regularly inspected and cleaned"
March 13, 2025 at 9:15 AM
phkwacker.bsky.social
Same energy
German FDP politicians giving a press conference with lighting weirdly place below and to the left of them, casting pronounced shadows in their faces Little boy holding a flashlight under his face to look creepy
February 24, 2025 at 7:11 AM
phkwacker.bsky.social
I (think I) finally figured out a Venn diagram for all these pesky set systems: sigma algebra, lambda-system, algebra, monotone class, pi-system!
A Venn diagram of five properties: sigma-algebra, algebra, lambda -system, monotone class, and pi-system
February 6, 2025 at 9:53 AM
phkwacker.bsky.social
Don't look back, you'll trip over Michael Caine!
Book cover. Title: dont look back, you'll trip over, by Michael Caine
December 27, 2024 at 7:55 PM
phkwacker.bsky.social
More farm animal math!
A cosine function on top of a cow, setting up a pun parallel to "elf on a shelf".
December 18, 2024 at 10:58 PM
phkwacker.bsky.social
Bonus image
More belly-mouth cats
December 18, 2024 at 6:39 AM
phkwacker.bsky.social
I can't get over how these cats are drawn. Pure nightmare fuel
Children's book with two drawn cats. Cats look normal with the exception that their mouths are somehow in the middle of their belly.
December 18, 2024 at 6:39 AM
phkwacker.bsky.social
Apparently, math conferences go like this: It's raining, everyone sits/stands in a puddle while some dude tries to convince everyone that pi=3.14, to the confusion of everyone, while notes taken dissolve in the puddle, letters and numbers floating away.
It's raining, 2 men and one woman sit in a puddle while some dude tries to convince everyone that pi=3.14, to the confusion of everyone, while notes taken dissolve in the puddle, letters and numbers floating away.
December 13, 2024 at 10:09 PM
phkwacker.bsky.social
Summarising: The three different models have different bias-variance decompositions. The constant model has considerable bias (red point cloud not centered around ground truth), but it has low variance (small spread). Order 5 has minimal bias, but high variance. Quadratic seems good compromise.
Constant models: Considerable bias, low variance. Polynomial order 5: Low bias, high variance. Quadratic polynomial somewhere in the middle.
November 18, 2024 at 12:03 AM
phkwacker.bsky.social
And this is for 1000 independent models of polynomials, order 5.
Ensemble of order-5 polynomial regression lines, showing a very wide spread of predictions around a ground truth (blue cross)
November 18, 2024 at 12:03 AM
phkwacker.bsky.social
Here the same thing for 1000 independent "quadratic" models of type f(x) = b0 + b1*x+ b2*x^2.
Ensemble of quadratic regression lines, showing a spread of predictions as a red point cloud around a ground truth (blue cross)
November 18, 2024 at 12:03 AM