PyData Seattle 2015

Cam Davidson-Pilon

# Who am I?

Cam Davidson-Pilon

- Lead on the Data Team at Shopify

- Open source contributer

- Author of Bayesian Methods for Hackers

(in print soon!)

Ottawa

Ottawa

Ottawa?

# Case Study 1

We needed to predict mail return rates based on census data.

Sample Data (simplified):

Well I'm predicting the rate, so I build that:

Don't need margin of errors...

...then do "data science"

Outcome: failure

What went wrong? At the time, ¯\_(ツ)_/¯

(highly, highly recommended!)

\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}}
$\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}}$
\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}}
$\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}}$

"The std. deviation of the sample mean is equal to the std. deviation of the population over square-root n"

What I learned

1. Sample sizes are so important when dealing with aggregate level data.
2. It was only an issue because the sample sizes were different, too.
3. Use the Margin of Error, don't ignore it - it's there for a reason.
4. I got burned so bad here, I became a Bayesian soon after.

# Case Study 2

A intra-day time series of S&P, Dow, Nasdaq and FTSE (UK index)

Suppose you are interested in doing some day trading. Your target: UK stocks.

Futures on the FTSE in particular.

Post Backtesting Results

Push to Production - investing really money

What happened?

Data Leakage happened

What I learned

1. Your backtesting / cross validation will always be equal or overly optimistic - plan for that.
2. Understand where your data comes from, from start to finish.

# Case Study 3

What I learned

1. When developing statistical software that already exists in the wild, write tests against the output of that software.
2. Be responsible for your software:

# Case Study 4

It was my first A/B test at Shopify...

Control group: 4%

Experiment group: 5%

Bayesian A/B testing told me there was a significant statistical difference between the groups...

Upper management wanted to know the relative increase...

(5% - 4%) / 4% = 25%

No.

We forgot sample size again.

What I learned

1. Don't naively compute stats on top of stats - this only compounds the uncertainty.
2. Better to underestimate than overestimate
3. Visualizing uncertainty is a the role of a statistician.

# Machine Learning counter examples

Sparse-ing the solution naively

Coefficients after linear regression*:

*Assume data has been normalized too, i.e. mean 0 and standard deviation 1

Decide to drop a variable:

Suppose this is the true model...

Okay, out regression got the coefficients right, but...

So actually, together, these variables have very little contribution to Y!

Solution:

Any form of regularization will solve this. For example, using ridge regression with with even the slightest penalizer gives:

PCA before Regression

PCA is great at many things, but it can actually significantly hurt regression if used as a preprocessing step. How?

Suppose we wish to regress Y onto X and W. The true model of Y is Y = X - W. We don't know this yet.

Suppose further there is a positive correlation between X and W, say 0.5.

Apply PCA to [X W], we get a new matrix:

[ \frac{1}{\sqrt{2}}X + \frac{1}{\sqrt{2}}W, \frac{1}{\sqrt{2}}X - \frac{1}{\sqrt{2}}W ]
$[ \frac{1}{\sqrt{2}}X + \frac{1}{\sqrt{2}}W, \frac{1}{\sqrt{2}}X - \frac{1}{\sqrt{2}}W ]$
[ \frac{1}{\sqrt{2}}X + \frac{1}{\sqrt{2}}W, \frac{1}{\sqrt{2}}X - \frac{1}{\sqrt{2}}W ]
$[ \frac{1}{\sqrt{2}}X + \frac{1}{\sqrt{2}}W, \frac{1}{\sqrt{2}}X - \frac{1}{\sqrt{2}}W ]$

Textbook analysis tells you to drop the second dimension from this new PCA.

[ \frac{1}{\sqrt{2}}X + \frac{1}{\sqrt{2}}W]
$[ \frac{1}{\sqrt{2}}X + \frac{1}{\sqrt{2}}W]$

So now we are regressing Y onto:

i.e., find values to fit the model:

Y = \alpha + \beta(X + W)
$Y = \alpha + \beta(X + W)$

But there are no good values for these unknowns!

Quick IPython Demo

Solution:

Don't use naive PCA before regression, you are losing information - try something like supervised PCA, or just don't do it.

Thanks for listening :)

@cmrn_dp