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Archive for the ‘Tutorials’ Category

Automatic bias correction doesn’t fix omitted variable bias

July 8th, 2014 1 comment

Page 94 of Gelman, Carlin, Stern, Dunson, Vehtari, Rubin “Bayesian Data Analysis” 3rd Edition (which we will call BDA3) provides a great example of what happens when common broad frequentist bias criticisms are over-applied to predictions from ordinary linear regression: the predictions appear to fall apart. BDA3 goes on to exhibit what might be considered the kind of automatic/mechanical fix responding to such criticisms would entail (producing a bias corrected predictor), and rightly shows these adjusted predictions are far worse than the original ordinary linear regression predictions. BDA3 makes a number of interesting points and is worth studying closely. We work their example in a bit more detail for emphasis. Read more…

Frequentist inference only seems easy

July 1st, 2014 3 comments

Two of the most common methods of statistical inference are frequentism and Bayesianism (see Bayesian and Frequentist Approaches: Ask the Right Question for some good discussion). In both cases we are attempting to perform reliable inference of unknown quantities from related observations. And in both cases inference is made possible by introducing and reasoning over well-behaved distributions of values.

As a first example, consider the problem of trying to estimate the speed of light from a series of experiments.

In this situation the frequentist method quietly does some heavy philosophical lifting before you even start work. Under the frequentist interpretation since the speed of light is thought to have a single value it does not make sense to model it as having a prior distribution of possible values over any non-trivial range. To get the ability to infer, frequentist philosophy considers the act of measurement repeatable and introduces very subtle concepts such as confidence intervals. The frequentist statement that a series of experiments places the speed of light in vacuum at 300,000,000 meters a second plus or minus 1,000,000 meters a second with 95% confidence does not mean there is a 95% chance that the actual speed of light is in the interval 299,000,000 to 301,000,000 (the common incorrect recollection of what a confidence interval is). It means if the procedure that generated the interval were repeated on new data, then 95% of the time the speed of light would be in the interval produced: which may not be the interval we are looking at right now. Frequentist procedures are typically easy on the practitioner (all of the heavy philosophic work has already been done) and result in simple procedures and calculations (through years of optimization of practice).

Bayesian procedures on the other hand are philosophically much simpler, but require much more from the user (production and acceptance of priors). The Bayesian philosophy is: given a generative model, a complete prior distribution (detailed probabilities of the unknown value posited before looking at the current experimental data) of the quantity to be estimated, and observations: then inference is just a matter of calculating the complete posterior distribution of the quantity to be estimated (by correct application of Bayes’ Law). Supply a bad model or bad prior beliefs on possible values of the speed of light and you get bad results (and it is your fault, not the methodology’s fault). The Bayesian method seems to ask more, but you have to remember it is trying to supply more (complete posterior distribution, versus subjunctive confidence intervals).

In this article we are going to work a simple (but important) problem where (for once) the Bayesian calculations are in fact easier than the frequentist ones. Read more…

R minitip: don’t use data.matrix when you mean model.matrix

June 10th, 2014 No comments

A quick R mini-tip: don’t use data.matrix when you mean model.matrix. If you do so you may lose (without noticing) a lot of your model’s explanatory power (due to poor encoding). Read more…

R style tip: prefer functions that return data frames

June 6th, 2014 3 comments

While following up on Nina Zumel’s excellent Trimming the Fat from glm() Models in R I got to thinking about code style in R. And I realized: you can make your code much prettier by designing more of your functions to return data.frames. That may seem needlessly heavy-weight, but it has a lot of down-stream advantages. Read more…

Trimming the Fat from glm() Models in R

May 30th, 2014 10 comments

One of the attractive aspects of logistic regression models (and linear models in general) is their compactness: the size of the model grows in the number of coefficients, not in the size of the training data. With R, though, glm models are not so concise; we noticed this to our dismay when we tried to automate fitting a moderate number of models (about 500 models, with on the order of 50 coefficients) to data sets of moderate size (several tens of thousands of rows). A workspace save of the models alone was in the tens of gigabytes! How is this possible? We decided to find out.

As many R users know (but often forget), a glm model object carries a copy of its training data by default. You can use the settings y=FALSE and model=FALSE to turn this off.

set.seed(2325235)


# Set up a synthetic classification problem of a given size
# and two variables: one numeric, one categorical
# (two levels).
synthFrame = function(nrows) {
   d = data.frame(xN=rnorm(nrows),
      xC=sample(c('a','b'),size=nrows,replace=TRUE))
   d$y = (d$xN + ifelse(d$xC=='a',0.2,-0.2) + rnorm(nrows))>0.5
   d
}


# first show that model=F and y=F help reduce model size

dTrain = synthFrame(1000)
model1 = glm(y~xN+xC,data=dTrain,family=binomial(link='logit'))
model2 = glm(y~xN+xC,data=dTrain,family=binomial(link='logit'),
             y=FALSE)
model3 = glm(y~xN+xC,data=dTrain,family=binomial(link='logit'),
              y=FALSE, model=FALSE)

#
# Estimate the object's size as the size of its serialization
#
length(serialize(model1, NULL))
# [1] 225251
length(serialize(model2, NULL))
# [1] 206341
length(serialize(model3, NULL))
# [1] 189562

dTest = synthFrame(100)
p1 = predict(model1, newdata=dTest, type='response')
p2 = predict(model2, newdata=dTest, type='response')
p3 = predict(model3, newdata=dTest, type='response')
sum(abs(p1-p2))
# [1] 0
sum(abs(p1-p3))
# [1] 0

Read more…

A clear picture of power and significance in A/B tests

May 3rd, 2014 2 comments

A/B tests are one of the simplest reliable experimental designs.

Controlled experiments embody the best scientific design for establishing a causal relationship between changes and their influence on user-observable behavior.

“Practical guide to controlled experiments on the web: listen to your customers not to the HIPPO” Ron Kohavi, Randal M Henne, and Dan Sommerfield, Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, 2007 pp. 959-967.

The ideas is to test a variation (called “treatment” or “B”) in parallel with continuing to test a baseline (called “control” or “A”) to see if the variation drives a desired effect (increase in revenue, cure of disease, and so on). By running both tests at the same time it is hoped that any confounding or omitted factors are nearly evenly distributed between the two groups and therefore not spoiling results. This is a much safer system of testing than retrospective studies (where we look for features from data already collected).

Interestingly enough the multi-armed bandit alternative to A/B testing (a procedure that introduces online control) is one of the simplest non-trivial Markov decision processes. However, we will limit ourselves to traditional A/B testing for the remainder of this note. Read more…

You don’t need to understand pointers to program using R

April 1st, 2014 9 comments

R is a statistical analysis package based on writing short scripts or programs (versus being based on GUIs like spreadsheets or directed workflow editors). I say “writing short scripts” because R’s programming language (itself called S) is a bit of an oddity that you really wouldn’t be using except it gives you access to superior analytics data structures (R’s data.frame and treatment of missing values) and deep ready to go statistical libraries. For longer pure programming tasks you are better off using something else (be it Python, Ruby, Java, C++, Javascript, Go, ML, Julia, or something else). However, the S language has one feature that makes it pleasant to learn (despite any warts): it can be initially used and taught without having the worry about the semantics of references or pointers. Read more…

Can a classifier that never says “yes” be useful?

March 8th, 2014 2 comments

Many data science projects and presentations are needlessly derailed by not having set shared business relevant quantitative expectations early on (for some advice see Setting expectations in data science projects). One of the most common issues is the common layman expectation of “perfect prediction” from classification projects. It is important to set expectations correctly so your partners know what you are actually working towards and do not consider late choices of criteria disappointments or “venue shopping.” Read more…

Bad Bayes: an example of why you need hold-out testing

February 1st, 2014 3 comments

We demonstrate a dataset that causes many good machine learning algorithms to horribly overfit.

The example is designed to imitate a common situation found in predictive analytic natural language processing. In this type of application you are often building a model using many rare text features. The rare text features are often nearly unique k-grams and the model can be anything from Naive Bayes to conditional random fields. This sort of modeling situation exposes the modeler to a lot of training bias. You can get models that look good on training data even though they have no actual value on new data (very poor generalization performance). In this sort of situation you are very vulnerable to having fit mere noise.

Often there is a feeling if a model is doing really well on training data then must be some way to bound generalization error and at least get useful performance on new test and production data. This is, of course, false as we will demonstrate by building deliberately useless features that allow various models to perform well on training data. What is actually happening is you are working through variations of worthless models that only appear to be good on training data due to overfitting. And the more “tweaking, tuning, and fixing” you try only appears to improve things because as you peek at your test-data (which you really should have held some out until the entire end of project for final acceptance) your test data is becoming less exchangeable with future new data and more exchangeable with your training data (and thus less helpful in detecting overfit).

Any researcher that does not have proper per-feature significance checks or hold-out testing procedures will be fooled into promoting faulty models. Read more…

Use standard deviation (not mad about MAD)

January 19th, 2014 14 comments

Nassim Nicholas Taleb recently wrote an article advocating the abandonment of the use of standard deviation and advocating the use of mean absolute deviation. Mean absolute deviation is indeed an interesting and useful measure- but there is a reason that standard deviation is important even if you do not like it: it prefers models that get totals and averages correct. Absolute deviation measures do not prefer such models. So while MAD may be great for reporting, it can be a problem when used to optimize models. Read more…