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Distractions and amusements, with a sandwich and coffee.

music + dance + projected visuals
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This section contains various art work based on `\pi`, `\phi` and `e` that I created over the years.

Some of the numerical art reveals interesting and unexpected observations. For example, the sequence 999999 in π at digit 762 called the Feynman Point. Or that if you calculate π to 13,099,586 digits you will find love.

`\pi` day art and `\pi` approximation day art is kept separate.

All of the posters are listed in the posters section. Some also appear in the methods section, where I describe how they were made. Most of the circular art was made with Circos.

Circular and spiral art based on the digits of `\pi`, `\phi` and `e`.

Read about how they were made and browse through the posters.

Some of the art shown here has been featured in a Numberphile video.

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.

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

My illustration of the location of genes in the human genome that are implicated in disease appears in The Objects that Power the Global Economy, a book by Quartz.

We introduce two common ensemble methods: bagging and random forests. Both of these methods repeat a statistical analysis on a bootstrap sample to improve the accuracy of the predictor. Our column shows these methods as applied to Classification and Regression Trees.

For example, we can sample the space of values more finely when using bagging with regression trees because each sample has potentially different boundaries at which the tree splits.

Random forests generate a large number of trees by not only generating bootstrap samples but also randomly choosing which predictor variables are considered at each split in the tree.

Krzywinski, M. & Altman, N. (2017) Points of Significance: Ensemble methods: bagging and random forests. *Nature Methods* **14**:933–934.

Krzywinski, M. & Altman, N. (2017) Points of Significance: Classification and regression trees. *Nature Methods* **14**:757–758.

Decision trees classify data by splitting it along the predictor axes into partitions with homogeneous values of the dependent variable. Unlike logistic or linear regression, CART does not develop a prediction equation. Instead, data are predicted by a series of binary decisions based on the boundaries of the splits. Decision trees are very effective and the resulting rules are readily interpreted.

Trees can be built using different metrics that measure how well the splits divide up the data classes: Gini index, entropy or misclassification error.

When the predictor variable is quantitative and not categorical, regression trees are used. Here, the data are still split but now the predictor variable is estimated by the average within the split boundaries. Tree growth can be controlled using the complexity parameter, a measure of the relative improvement of each new split.

Individual trees can be very sensitive to minor changes in the data and even better prediction can be achieved by exploiting this variability. Using ensemble methods, we can grow multiple trees from the same data.

Krzywinski, M. & Altman, N. (2017) Points of Significance: Classification and regression trees. *Nature Methods* **14**:757–758.

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

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression *Nature Methods* **12**:1103-1104.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. *Nature Methods* **13**:603-604.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Model Selection and Overfitting. *Nature Methods* **13**:703-704.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Regularization. *Nature Methods* **13**:803-804.

The artwork was created in collaboration with my colleagues at the Genome Sciences Center to celebrate the 5 year anniversary of the Personalized Oncogenomics Program (POG).

The Personal Oncogenomics Program (POG) is a collaborative research study including many BC Cancer Agency oncologists, pathologists and other clinicians along with Canada's Michael Smith Genome Sciences Centre with support from BC Cancer Foundation.

The aim of the program is to sequence, analyze and compare the genome of each patient's cancer—the entire DNA and RNA inside tumor cells— in order to understand what is enabling it to identify less toxic and more effective treatment options.