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Distractions and amusements, with a sandwich and coffee.

Here we are now at the middle of the fourth large part of this talk.
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Like music with numbers? Here's a short list of some of my favourite songs that have numbers in their lyrics. Absolutely none of them is about bottles of beer.

1 —
Numbers, Smoke City | This song is entirely composed of references to different numbers. The bonus? It's both in English and Portuguese. I love the way it ends—"*Isn't it beautiful out here?*".

Un

Un

Four

Five

Fifteen

Quinze

Seventeen

Seven

...

Tres

forty nine

Isn't it beautiful out here?

Isn't it beautiful out here?

Isn't it beautiful out here?

2 — 99 luftbaloons, Nena | The numerical classic.

Hast du etwas Zeit für mich

Dann singe ich ein Lied für dich

Von 99 Luftballons

3 — One, Aimee Mann | Beautiful mathematics of relationships using small numbers.

One is the lonliest number that you'll ever do. Two can be as bad as one, it's the lonliest number since the number one.

4 — Angels at My Door, Una | Long sequences of numbers.

58, 56, 54 angels at my door.

63, 62, 61, 60, 59, 58 angels at my gate.

5 — Tricky, Tricky, Royksopp | Number words about the fearful six from Norway.

Six afraid of seven 'cause seven, eight, nine

I'm about to lose it the second time

6 — Pt vs Ys, Yoshinori Sunahara | The first four numbers, in German, are this song's lyrics.

Eins, zwei, drei, vier.

7 —
Der Kommissar, Falco | Unlike the previous song, this one starts with a German count (doesn't get to *vier*, though) and just gets better from there.

Two, three, four

Eins, zwei, drei

Na, es is nix dabei

Na, wenn ich euch erzähl' die G'schicht'

8 — 2wicky, Hooverphonic | The numbers likely reference the Prophet-600 and SH-101 synthesizers.

Prophet 60091.

Before we start you should know that you're not the only one who can hurt me.

SH10151.

This is the serial number of our orbital gun.

SH10151.

You better be sure before you leave me for another one.

9 — Straight to Number One, Touch and Go | Something to listen to after midnight.

Fingers, four, play, three, to number one.

10 — The Beat Experience, Pepe Deluxe | I am reminded of this song at too many academic seminars.

Here we are now, at the middle, of the fourth large part of this talk.

More and more I have the feeling that we are getting nowhere.

Slowly, as the talk goes on, we are getting nowhere.

And that is a pleasure.

It is not irritating where one is.

It is only irritating to think one would like to be somewhere else.

Here we are now, a little bit after the middle, of the fourth large part of this talk.

11 —
Thousand Kisses Deep, Leonard Cohen | A list of songs that doesn't include one by Cohen is not worth reading.
The sentiment of a thousand kisses is as old as lips existed. Catullus wrote to Lesbia *"da mi basia mille, deinde centum, dein mille altera, dein secunda centum, deinde usque altera mille, deinde centum"* [*Give me a thousand kisses, then a hundred, then another thousand, then a second hundred, then yet another thousand, then a hundred.*] Well, you get the idea.

And sometimes when the night is slow,

The wretched and the meek,

We gather up our hearts and go,

A Thousand Kisses Deep.

12 — Six Seven Times, Flunk | Curiously the product here is 42. This song is the answer to life.

You've got it all

Six seven times

You've got it all

Makes me feel so fine

And it's all there is

13 — 7 seconds, Youssou N'Dour | Dreamy references to a short period of time.

7 seconds away. Just as long as I stay. I'll be waiting.

14 — 100 Billion Stars, Lux | Something to relax to while you ponder insignificance.

15 — First Picture, Nikolaj Grandjean | First is the most memorable number.

I remember

The first picture

One million different shadows

Where we've been around the willows

16 — Millions of Millions, Music for a French Elevator | Very desirable. And I can't believe I transcribed the whole thing.

5.50 million dollars, 2.6775 and very desirable 8 million dollars 5.6 million and 2.4 million 3.4 million and 2.9 million 1.2 would've amounted to 4 million 1.2 million 19.4 million 6.6 million 5.275 million 1.2 million 3-and-a-half million dollars 6.453 million 8 million 5.050 million 1.4 million close to a million dollars 933.5 million 3.8 million 5 million dollars 2-and-a-half million 600 million dollars can you shut the door? 3-and-a-half million dollars 2.5 million .050 million 572,750 thousand 5.050 million 3.8 million 3 million 150 thousand 8 million 419.5 million

17 — Love Potion #9, The Searchers | I started kissing everythying in sight.

It smelled like turpentine, it looked like Indian ink

I held my nose, I closed my eyes, I took a drink.

18 — 93 Million Miles, Luan Santana feat. John Kip | A little sticky, a little sweet but it makes up for the fact that much of it is in Portuguese.

But the absence of the light is a necessary part.

Inference creates a mathematical model of the datageneration process to formalize understanding or test a hypothesis about how the system behaves. Prediction aims at forecasting unobserved outcomes or future behavior. Typically we want to do both and know how biological processes work and what will happen next. Inference and ML are complementary in pointing us to biologically meaningful conclusions.

Statistics asks us to choose a model that incorporates our knowledge of the system, and ML requires us to choose a predictive algorithm by relying on its empirical capabilities. Justification for an inference model typically rests on whether we feel it adequately captures the essence of the system. The choice of pattern-learning algorithms often depends on measures of past performance in similar scenarios.

Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Statistics vs machine learning. Nature Methods 15:233–234.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: supervised methods. Nature Methods 15:5–6.

Celebrate `\pi` Day (March 14th) and go to brand new places. Together with Jake Lever, this year we shrink the world and play with road maps.

Streets are seamlessly streets from across the world. Finally, a halva shop on the same block!

Intriguing and personal patterns of urban development for each city appear in the Boonies, Burbs and Boutiques series.

No color—just lines. Lines from Marrakesh, Prague, Istanbul, Nice and other destinations for the mind and the heart.

The art is featured in the Pi City on the Scientific American SA Visual blog.

Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day and 2017 `\pi` Day.

We examine two very common supervised machine learning methods: linear support vector machines (SVM) and k-nearest neighbors (kNN).

SVM is often less computationally demanding than kNN and is easier to interpret, but it can identify only a limited set of patterns. On the other hand, kNN can find very complex patterns, but its output is more challenging to interpret.

We illustrate SVM using a data set in which points fall into two categories, which are separated in SVM by a straight line "margin". SVM can be tuned using a parameter that influences the width and location of the margin, permitting points to fall within the margin or on the wrong side of the margin. We then show how kNN relaxes explicit boundary definitions, such as the straight line in SVM, and how kNN too can be tuned to create more robust classification.

Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Machine learning: a primer. Nature Methods 15:5–6.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

In a Nature graphics blog article, I present my process behind designing the stark black-and-white Nature 10 cover.

Nature 10, 18 December 2017

In this primer, we focus on essential ML principles— a modeling strategy to let the data speak for themselves, to the extent possible.

The benefits of ML arise from its use of a large number of tuning parameters or weights, which control the algorithm’s complexity and are estimated from the data using numerical optimization. Often ML algorithms are motivated by heuristics such as models of interacting neurons or natural evolution—even if the underlying mechanism of the biological system being studied is substantially different. The utility of ML algorithms is typically assessed empirically by how well extracted patterns generalize to new observations.

We present a data scenario in which we fit to a model with 5 predictors using polynomials and show what to expect from ML when noise and sample size vary. We also demonstrate the consequences of excluding an important predictor or including a spurious one.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

Just in time for the season, I've simulated a snow-pile of snowflakes based on the Gravner-Griffeath model.

The work is described as a wintertime tale in In Silico Flurries: Computing a world of snow and co-authored with Jake Lever in the Scientific American SA Blog.

Gravner, J. & Griffeath, D. (2007) Modeling Snow Crystal Growth II: A mesoscopic lattice map with plausible dynamics.