In this article we will discuss the machine learning method called “decision trees”, moving quickly over the usual “how decision trees work” and spending time on “why decision trees work.” We will write from a computational learning theory perspective, and hope this helps make both decision trees and computational learning theory more comprehensible. The goal of this article is to set up terminology so we can state in one or two sentences why decision trees tend to work well in practice.
[Reader’s Note. Some of our articles are applied and some of our articles are more theoretical. The following article is more theoretical, and requires fairly formal notation to even work through. However, it should be of interest as it touches on some of the fine points of cross-validation that are quite hard to perceive or discuss without the notational framework. We thought about including some “simplifying explanatory diagrams” but so many entities are being introduced and manipulated by the processes we are describing we found equation notation to be in fact cleaner than the diagrams we attempted and rejected.]
Please consider either of the following common predictive modeling tasks:
- Picking hyper-parameters, fitting a model, and then evaluating the model.
- Variable preparation/pruning, fitting a model, and then evaluating the model.
In each case you are building a pipeline where “y-aware” (or outcome aware) choices and transformations made at each stage affect later stages. This can introduce undesirable nested model bias and over-fitting.
Our current standard advice to avoid nested model bias is either:
- Split your data into 3 or more disjoint pieces, such as separate variable preparation/pruning, model fitting, and model evaluation.
- Reserve a test-set for evaluation and use “simulated out of sample data” or “cross-frame”/“cross simulation” techniques to simulate dividing data among the first two model construction stages.
The first practice is simple and computationally efficient, but statistically inefficient. This may not matter if you have a lot of data, as in “big data”. The second procedure is more statistically efficient, but is also more complicated and has some computational cost. For convenience the cross simulation method is supplied as a ready to go procedure in our
R data cleaning and preparation package
What would it look like if we insisted on using cross simulation or simulated out of sample techniques for all three (or more) stages? Please read on to find out.
Hyperbole and a Half copyright Allie Brosh (use allowed in some situations with attribution)
Consider the problem of “parametric programming” in R. That is: simply writing correct code before knowing some details, such as the names of the columns your procedure will have to be applied to in the future. Our latest version of
replyr::let makes such programming easier.
Archie’s Mechanics #2 (1954) copyright Archie Publications
(edit: great news! CRAN just accepted our
replyr 0.2.0 fix release!)
Please read on for examples comparing standard notations and
replyr::let. Continue reading Comparative examples using replyr::let
One thing I teach is: when evaluating the performance of regression models you should not use correlation as your score.
This is because correlation tells you if a re-scaling of your result is useful, but you want to know if the result in your hand is in fact useful. For example: the Mars Climate Orbiter software issued thrust commands in pound-seconds units to an engine expecting the commands to be in newton-seconds units. The two quantities are related by a constant ratio of 1.4881639, and therefore anything measured in pound-seconds units will have a correlation of 1.0 with the same measurement in newton-seconds units. However, one is not the other and the difference is why the Mars Climate Orbiter “encountered Mars at a lower than anticipated altitude and disintegrated due to atmospheric stresses.”
The need for a convenient direct F-test without accidentally triggering the implicit re-scaling that is associated with calculating a correlation is one of the reasons we supply the sigr R library. However, even then things can become confusing.
Please read on for a nasty little example. Continue reading Be careful evaluating model predictions
A quick demo of RStudio’s R Notebooks shown by John Mount (of Win-Vector LLC, a statistics, data science, and algorithms consulting and training firm).
It looks like some of the new in-line display behavior is back-ported to R Markdown and some of the difference is the delayed running and different level of interactivity in the HTML document. This makes it a bit hard to call out which RStudio’s improvements are “R notebooks” versus “R markdown”, but it means there is a lot of new functionality available. I’ve updated the video to reflect the subtlty (unfortunately on YouTube that means a new URL as you can’t replace videos).
And some just in case decelerations/clarifications/reminders: this video is not from RStudio (the company), and Rstudio client (the software) is a user interface that is separate from the R analysis system itself.
Nina Zumel recently announced upcoming speaking appearances. I want to promote the upcoming sessions at ODSC West 2016 (11:15am-1:00pm on Friday November 4th, or 3:00pm-4:30pm on Saturday November 5th) and invite executives, managers, and other data science consumers to attend. We assume most of the Win-Vector blog audience is made of practitioners (who we hope are already planning to attend), so we are asking you our technical readers to help promote this talk to a broader audience of executives and managers.
Our messages is: if you have to manage data science projects, you need to know how to evaluate results.
In these talks we will lay out how data science results should be examined and evaluated. If you can’t make ODSC (or do attend and like what you see), please reach out to us and we can arrange to present an appropriate targeted summarized version to your executive team. Continue reading Data science for executives and managers
I (Nina Zumel) will be speaking at the Women who Code Silicon Valley meetup on Thursday, October 27.
The talk is called Improving Prediction using Nested Models and Simulated Out-of-Sample Data.
In this talk I will discuss nested predictive models. These are models that predict an outcome or dependent variable (called y) using additional submodels that have also been built with knowledge of y. Practical applications of nested models include “the wisdom of crowds”, prediction markets, variable re-encoding, ensemble learning, stacked learning, and superlearners.
Nested models can improve prediction performance relative to single models, but they introduce a number of undesirable biases and operational issues, and when they are improperly used, are statistically unsound. However modern practitioners have made effective, correct use of these techniques. In my talk I will give concrete examples of nested models, how they can fail, and how to fix failures. The solutions we will discuss include advanced data partitioning, simulated out-of-sample data, and ideas from differential privacy. The theme of the talk is that with proper techniques, these powerful methods can be safely used.
John Mount and I will also be giving a workshop called A Unified View of Model Evaluation at ODSC West 2016 on November 4 (the premium workshop sessions), and November 5 (the general workshop sessions).
We will present a unified framework for predictive model construction and evaluation. Using this perspective we will work through crucial issues from classical statistical methodology, large data treatment, variable selection, ensemble methods, and all the way through stacking/super-learning. We will present R code demonstrating principled techniques for preparing data, scoring models, estimating model reliability, and producing decisive visualizations. In this workshop we will share example data, methods, graphics, and code.
I’m looking forward to these talks, and I hope some of you will be able to attend.
I’ve been thinking a bit on statistical tests, their absence, abuse, and limits. I think much of the current “scientific replication crisis” stems from the fallacy that “failing to fail” is the same as success (in addition to the forces of bad luck, limited research budgets, statistical naiveté, sloppiness, pride, greed and other human qualities found even in researchers). Please read on for my current thinking. Continue reading The unfortunate one-sided logic of empirical hypothesis testing