Variance and variability

Today, Léo presented on the mathematical principles behind a Principal Component Analysis (PCA). It was a great refresher for myself, and amazing to give students a clear picture of what this technique does and why we use it so much for dimensionality reduction. Also, Léo prompted a discussion about why variance and variability are so important in understanding the world with these images of Mona Lisa (La Joconde), one of which is Mona Lisa with her Cat (its name is Zarathustra). I loved it! He explained that in terms of information theory,  variation is where the information resides. Information comes from comparison (of the two paintings), and this information is what makes the “message” important (there is a cat in Mona Lisa’s arms). This whole discussion about variance, comparison and variability is really in line with the major aim of the entire field of population genetics (my field !!), a field “that deals with genetic differences within and between populations, and is a part of evolutionary biology “, as formulated by Wikipedia. This is probably one reason why PCA is so widely used in analysis of biological data. Also, please note that deep learning methods can generate tons of art work with cats!

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