Propensity score matching

I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player

In many experimental designs, we need to keep in mind the possibility of confounding variables, which may give rise to bias in the estimate of the treatment effect.

▲ Nature Methods Points of Significance column: Propensity score matching. (read)

If the control and experimental groups aren't matched (or, roughly, similar enough), this bias can arise.

Sometimes this can be dealt with by randomizing, which on average can balance this effect out. When randomization is not possible, propensity score matching is an excellent strategy to match control and experimental groups.

Kurz, C.F., Krzywinski, M. & Altman, N. (2024) Points of significance: Propensity score matching. Nat. Methods 21:1770–1772.

Nasa to send our human genome discs to the Moon

We'd like to say a ‘cosmic hello’: mathematics, culture, palaeontology, art and science, and ... human genomes.

▲ SANCTUARY PROJECT | A cosmic hello of art, science, and genomes. (details)

▲ SANCTUARY PROJECT | Benoit Faiveley, founder of the Sanctuary project gives the Sanctuary disc a visual check at CEA LeQ Grenoble (image: Vincent Thomas). (details)

▲ SANCTUARY PROJECT | Sanctuary team examines the Life disc at INRIA Paris Saclay (image: Benedict Redgrove) (details)

Comparing classifier performance with baselines

All animals are equal, but some animals are more equal than others. —George Orwell

This month, we will illustrate the importance of establishing a baseline performance level.

Baselines are typically generated independently for each dataset using very simple models. Their role is to set the minimum level of acceptable performance and help with comparing relative improvements in performance of other models.

▲ Nature Methods Points of Significance column: Comparing classifier performance with baselines. (read)

Unfortunately, baselines are often overlooked and, in the presence of a class imbalance, must be established with care.

Megahed, F.M, Chen, Y-J., Jones-Farmer, A., Rigdon, S.E., Krzywinski, M. & Altman, N. (2024) Points of significance: Comparing classifier performance with baselines. Nat. Methods 21:546–548.

Happy 2024 π Day—
sunflowers ho!

Celebrate π Day (March 14th) and dig into the digit garden. Let's grow something.

▲ 2024 π DAY | A garden of 1,000 digits of π. (details)

How Analyzing Cosmic Nothing Might Explain Everything

Huge empty areas of the universe called voids could help solve the greatest mysteries in the cosmos.

My graphic accompanying How Analyzing Cosmic Nothing Might Explain Everything in the January 2024 issue of Scientific American depicts the entire Universe in a two-page spread — full of nothing.

▲ How Analyzing Cosmic Nothing Might Explain Everything. Text by Michael Lemonick (editor), art direction by Jen Christiansen (Senior Graphics Editor), source: SDSS

The graphic uses the latest data from SDSS 12 and is an update to my Superclusters and Voids poster.

Michael Lemonick (editor) explains on the graphic:

“Regions of relatively empty space called cosmic voids are everywhere in the universe, and scientists believe studying their size, shape and spread across the cosmos could help them understand dark matter, dark energy and other big mysteries.

To use voids in this way, astronomers must map these regions in detail—a project that is just beginning.

Shown here are voids discovered by the Sloan Digital Sky Survey (SDSS), along with a selection of 16 previously named voids. Scientists expect voids to be evenly distributed throughout space—the lack of voids in some regions on the globe simply reflects SDSS’s sky coverage.”

voids

Sofia Contarini, Alice Pisani, Nico Hamaus, Federico Marulli Lauro Moscardini & Marco Baldi (2023) Cosmological Constraints from the BOSS DR12 Void Size Function Astrophysical Journal 953:46.

Nico Hamaus, Alice Pisani, Jin-Ah Choi, Guilhem Lavaux, Benjamin D. Wandelt & Jochen Weller (2020) Journal of Cosmology and Astroparticle Physics 2020:023.

Sloan Digital Sky Survey Data Release 12

constellation figures

Alan MacRobert (Sky & Telescope), Paulina Rowicka/Martin Krzywinski (revisions & Microscopium)

stars

Hoffleit & Warren Jr. (1991) The Bright Star Catalog, 5th Revised Edition (Preliminary Version).

cosmology

H₀ = 67.4 km/(Mpc·s), Ω_m = 0.315, Ω_v = 0.685. Planck collaboration Planck 2018 results. VI. Cosmological parameters (2018).

Error in predictor variables

It is the mark of an educated mind to rest satisfied with the degree of precision that the nature of the subject admits and not to seek exactness where only an approximation is possible. —Aristotle

In regression, the predictors are (typically) assumed to have known values that are measured without error.

Practically, however, predictors are often measured with error. This has a profound (but predictable) effect on the estimates of relationships among variables – the so-called “error in variables” problem.

▲ Nature Methods Points of Significance column: Error in predictor variables. (read)

Error in measuring the predictors is often ignored. In this column, we discuss when ignoring this error is harmless and when it can lead to large bias that can leads us to miss important effects.

Altman, N. & Krzywinski, M. (2024) Points of significance: Error in predictor variables. Nat. Methods 21:4–6.

Background reading

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nat. Methods 12:999–1000.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nat. Methods 13:541–542 (2016).

Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nat. Methods 16:451–452.

Convolutional neural networks

Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry. – Richard Feynman

Following up on our Neural network primer column, this month we explore a different kind of network architecture: a convolutional network.

The convolutional network replaces the hidden layer of a fully connected network (FCN) with one or more filters (a kind of neuron that looks at the input within a narrow window).

▲ Nature Methods Points of Significance column: Convolutional neural networks. (read)

Even through convolutional networks have far fewer neurons that an FCN, they can perform substantially better for certain kinds of problems, such as sequence motif detection.

Derry, A., Krzywinski, M & Altman, N. (2023) Points of significance: Convolutional neural networks. Nature Methods 20:1269–1270.

Background reading

Derry, A., Krzywinski, M. & Altman, N. (2023) Points of significance: Neural network primer. Nature Methods 20:165–167.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nature Methods 13:541–542.

Neural network primer

Nature is often hidden, sometimes overcome, seldom extinguished. —Francis Bacon

In the first of a series of columns about neural networks, we introduce them with an intuitive approach that draws from our discussion about logistic regression.

▲ Nature Methods Points of Significance column: Neural network primer. (read)

Simple neural networks are just a chain of linear regressions. And, although neural network models can get very complicated, their essence can be understood in terms of relatively basic principles.

We show how neural network components (neurons) can be arranged in the network and discuss the ideas of hidden layers. Using a simple data set we show how even a 3-neuron neural network can already model relatively complicated data patterns.

Derry, A., Krzywinski, M & Altman, N. (2023) Points of significance: Neural network primer. Nature Methods 20:165–167.

Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nature Methods 13:541–542.