Relative error distributions, without the heavy tail theatrics

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Nina Zumel prepared an excellent article on the consequences of working with relative error distributed quantities (such as wealth, income, sales, and many more) called “Living in A Lognormal World.” The article emphasizes that if you are dealing with such quantities you are already seeing effects of relative error distributions (so it isn’t an exotic idea you bring to analysis, it is a likely fact about the world that comes at you). The article is a good example of how to plot and reason about such situations.

I am just going to add a few additional references (mostly from Nina) and some more discussion on log-normal distributions versus Zipf-style distributions or Pareto distributions. Continue reading Relative error distributions, without the heavy tail theatrics

Variables can synergize, even in a linear model

Posted on Categories Statistics, TutorialsTags , , , , 5 Comments on Variables can synergize, even in a linear model

Introduction

Suppose we have the task of predicting an outcome y given a number of variables v1,..,vk. We often want to “prune variables” or build models with fewer than all the variables. This can be to speed up modeling, decrease the cost of producing future data, improve robustness, improve explain-ability, even reduce over-fit, and improve the quality of the resulting model.

For some informative discussion on such issues please see the following:

In this article we are going to deliberately (and artificially) find and test one of the limits of the technique. We recommend simple variable pruning, but also think it is important to be aware of its limits.

Continue reading Variables can synergize, even in a linear model

Variable pruning is NP hard

Posted on Categories Computer Science, math programming, Statistics, TutorialsTags , , , 2 Comments on Variable pruning is NP hard

I am working on some practical articles on variable selection, especially in the context of step-wise linear regression and logistic regression. One thing I noticed while preparing some examples is that summaries such as model quality (especially out of sample quality) and variable significances are not quite as simple as one would hope (they in fact lack a lot of the monotone structure or submodular structure that would make things easy).

That being said we have a lot of powerful and effective heuristics to discuss in upcoming articles. I am going to leave such positive results for my later articles and here concentrate on an instructive technical negative result: picking a good subset of variables is theoretically quite hard. Continue reading Variable pruning is NP hard

My criticism of R numeric summary

Posted on Categories Rants, Statistics, TutorialsTags , 8 Comments on My criticism of R numeric summary

My criticism of R‘s numeric summary() method is: it is unfaithful to numeric arguments (due to bad default behavior) and frankly it should be considered unreliable. It is likely the way it is for historic and compatibility reasons, but in my opinion it does not currently represent a desirable set of tradeoffs. summary() likely represents good work by high-ability researchers, and the sharp edges are due to historically necessary trade-offs.


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The Big Lebowski, 1998.

Please read on for some context and my criticism.

Edit 8/25/2016: Martin Maechler generously committed a fix! Assuming this works out in testing it looks like we could see an improvement on this core function in April 2017. I really want to say “thank you” to Martin Maechler and the rest of the team for not only this, for all the things they do, and for putting up with me.

Continue reading My criticism of R numeric summary

The Win-Vector parallel computing in R series

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With our recent publication of “Can you nest parallel operations in R?” we now have a nice series of “how to speed up statistical computations in R” that moves from application, to larger/cloud application, and then to details.

For your convenience here they are in order:

  1. A gentle introduction to parallel computing in R
  2. Running R jobs quickly on many machines
  3. Can you nest parallel operations in R?

Please check it out, and please do Tweet/share these tutorials.

Can you nest parallel operations in R?

Posted on Categories Programming, TutorialsTags , , , 2 Comments on Can you nest parallel operations in R?

Parallel programming is a technique to decrease how long a task takes by performing more parts of it at the same time (using additional resources). When we teach parallel programming in R we start with the basic use of parallel (please see here for example). This is, in our opinion, a necessary step before getting into clever notation and wrapping such as doParallel and foreach. Only then do the students have a sufficiently explicit interface to frame important questions about the semantics of parallel computing. Beginners really need a solid mental model of what services are really being provided by their tools and to test edge cases early.

One question that comes up over and over again is “can you nest parLapply?”

The answer is “no.” This is in fact an advanced topic, but it is one of the things that pops up when you start worrying about parallel programming. Please read on for what that is the right answer and how to work around that (simulate a “yes”).

I don’t think the above question is usually given sufficient consideration (nesting parallel operations can in fact make a lot of sense). You can’t directly nest parLapply, but that is a different issue than can one invent a work-around. For example: a “yes” answer (really meaning there are work-arounds) can be found here. Again this is a different question than “is there a way to nest foreach loops” (which is possible through the nesting operator %.% which presumably handles working around nesting issues in parLapply).

Continue reading Can you nest parallel operations in R?

On accuracy

Posted on Categories Administrativia, Statistics, Statistics To English Translation, TutorialsTags , Leave a comment on On accuracy

In our last article on the algebra of classifier measures we encouraged readers to work through Nina Zumel’s original “Statistics to English Translation” series. This series has become slightly harder to find as we have use the original category designation “statistics to English translation” for additional work.

To make things easier here are links to the original three articles which work through scores, significance, and includes a glossery.

A lot of what Nina is presenting can be summed up in the diagram below (also by her). If in the diagram the first row is truth (say red disks are infected) which classifier is the better initial screen for infection? Should you prefer the model 1 80% accurate row or the model 2 70% accurate row? This example helps break dependence on “accuracy as the only true measure” and promote discussion of additional measures.


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y-aware scaling in context

Posted on Categories Exciting Techniques, Practical Data Science, Pragmatic Data Science, Pragmatic Machine Learning, Statistics, TutorialsTags , , ,

Nina Zumel introduced y-aware scaling in her recent article Principal Components Regression, Pt. 2: Y-Aware Methods. I really encourage you to read the article and add the technique to your repertoire. The method combines well with other methods and can drive better predictive modeling results.

From feedback I am not sure everybody noticed that in addition to being easy and effective, the method is actually novel (we haven’t yet found an academic reference to it or seen it already in use after visiting numerous clients). Likely it has been applied before (as it is a simple method), but it is not currently considered a standard method (something we would like to change).

In this note I’ll discuss some of the context of y-aware scaling. Continue reading y-aware scaling in context

Why you should read Nina Zumel’s 3 part series on principal components analysis and regression

Posted on Categories Administrativia, Exciting Techniques, Expository Writing, Statistics, TutorialsTags , , ,

Short form:

Win-Vector LLC’s Dr. Nina Zumel has a three part series on Principal Components Regression that we think is well worth your time.

  • Part 1: the proper preparation of data (including scaling) and use of principal components analysis (particularly for supervised learning or regression).
  • Part 2: the introduction of y-aware scaling to direct the principal components analysis to preserve variation correlated with the outcome we are trying to predict.
  • Part 3: how to pick the number of components to retain for analysis.

Continue reading Why you should read Nina Zumel’s 3 part series on principal components analysis and regression

Using geom_step

Posted on Categories TutorialsTags , , , , 4 Comments on Using geom_step

geom_step is an interesting geom supplied by the R package ggplot2. It is an appropriate rendering option for financial market data and we will show how and why to use it in this article.

Continue reading Using geom_step