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Expressing the amount of sequence in the human genome in terms of the number of printed pages has been done before. At the Broad Institute, all of the human reference genome is printed in bound volumes.

At our sequencing facility, we sequence about 1 terabases per day. This is equivalent to 167 diploid human genomes (167 × 6 gigabases). The sequencing is done using a pool of 13 Illumina HiSeq 2500 sequencers, of which about 50% are sequencing at any given time.

This sequencing is *extremely* fast.

To understand just how fast this is, consider *printing* this amount of sequence using a modern office laser printer. Let's pick the HP P3015n which costs about $400—a cheap and fast network printer. It can print at about 40 pages per minute.

If we print the sequence at 6pt Courier using 0.25" margins, each 8.5" × 11" page will accomodate 18,126 bases. I chose this font size because it's reasonably legible. To print 1 terabases we need `10^12 / 18126 = 55.2` million pages.

If we print continuously at 40 pages per minute, we need `10^12 / (18126*40*1440) = 957.8` days.

If we had 958 printers working around the clock, we could print everything we sequence and not fall behind. This does not account for time required to replenish toner or paper.

It costs us about $12,000 to sequence a terabase in reagents. If we do it on a cost-recovery basis, it is about twice that, to include labor and storage. Let's say $25,000 per terabase.

Coincidentally, this is about $150 per 1× coverage of a diploid human genome. The cost of sequencing a single genome would be significantly higher because of overhead. To overcome gaps in coverage and to be sensitive to alleles in heterogenous samples, sequencing should be done to 30× or more. For example, we sequence cancer genomes at over 100×. For theory and review see Aspects of coverage in medical DNA sequencing by Wendl *et al.* and Sequencing depth and coverage: key considerations in genomic analyses by Sims *et al.*. (Thanks to Nicolas Robine for pointing out that redundant coverage should be mentioned here).

Printing is 44× more expensive than sequencing, per base: 25 n$ vs 1.1 μ$.

I should mention that the cost of analyzing the sequenced genome should be considered—this step is always the much more expensive one. In The $1,000 genome, the $100,000 analysis? Mardis asks "*If our efforts to improve the human reference sequence quality, variation, and annotation are successful, how do we avoid the pitfall of having cheap human genome resequencing but complex and expensive manual analysis to make clinical sense out of the data?*"

The cost of a single printed page (toner, power, etc) is about $0.02–0.05, depending on the printer. Let's be generous and say it's $0.02. To print 55.2 million pages would cost us $1.1M. This is about 44 times as expensive as sequencing.

Think about this. It's 44× more expensive to merely print a letter on a page than it is to determine it from the DNA of a cell. In other words, to go from the physical molecule to a bit state on a disk is much cheaper than from a bit state on a disk to a representation of the letter on a page.

Per base, our sequencing costs `$25000/10^12 = $25*10^-9`, or 25 nanodollars. At $0.02 and 18,126 bp per page, printing costs `0.02/18126 = $1.1*10^-6` or 1.1 microdollars.

If at this point you're thinking that printing isn't practical, the fact that the pages would weigh 248,000 kg and stack to 5.5 km should cinch the argument.

The capital cost of sequencing is, of course, much higher. The printers themselves would cost about $400,000 to purchase. The 6 sequencers, on the other hand, cost about $3,600,000.

We sequence at a rate close to the average internet bandwidth available to the public.

At 3.86 Mb/s, we could download a terabase of compressed sequence in a day, assuming the sequence can be compressed by a factor of 3. This level of compression is reasonable—the current human assembly is 938 Mb zipped).

In other words, you would have to be downloading essentially continuously to keep up with our sequencing.

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.