For more and more clients we have been using a nice coding pattern taught to us by Garrett Grolemund in his book Hands-On Programming with R: make a function that returns a list of functions. This turns out to be a classic functional programming techique: use closures to implement objects (terminology we will explain).
It is a pattern we strongly recommend, but with one caveat: it can leak references similar to the manner described in here. Once you work out how to stomp out the reference leaks the “function that returns a list of functions” pattern is really strong.
We will discuss this programming pattern and how to use it effectively. Continue reading Using closures as objects in R
Having worked in finance I am a public fan of the Sharpe ratio. I have written about this here and here.
One thing I have often forgotten (driving some bad analyses) is: the Sharpe ratio isn’t appropriate for models of repeated events that already have linked mean and variance (such as Poisson or Binomial models) or situations where the variance is very small (with respect to the mean or expectation). These are common situations in a number of large scale online advertising problems (such as modeling the response rate to online advertisements or email campaigns).
Photo “eggs in a basket” copyright MicoAssist appropriate CC license
In this note we will quickly explain the problem. Continue reading One place not to use the Sharpe ratio
Recently there has been some controversy over David Mumford’s Nature magazine invited obituary of Alexander Grothendieck being initially rejected on submission (see here and here). At issue was the attempt to explain the mathematical idea of schemes (one of Alexander Grothendieck’s most important contributions) to a non-mathematician audience. Professor Mumford is a mathematician of great stature and his explanation is better than anything I could even attempt. However, in addition to the issues he raises I don’t think he was sensitive enough to what a non-mathematician considers motivation.
I’ll take a quick stab at explaining a very tiny bit of the motivation of schemes. I not sure the kind of chain of analogies argument I am attempting would work in an obituary (or in a short length), so I certainly don’t presume to advise professor Mumford on his obituary of a great mathematician (and person). Continue reading Let’s try to motivate schemes
I have been working through (with some honest appreciation) a recent article comparing many classifiers on many data sets: “Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?” Manuel Fernández-Delgado, Eva Cernadas, Senén Barro, Dinani Amorim; 15(Oct):3133−3181, 2014 (which we will call “the DWN paper” in this note). This paper applies 179 popular classifiers to around 120 data sets (mostly from the UCI Machine Learning Repository). The work looks good and interesting, but we do have one quibble with the data-prep on 8 of the 123 shared data sets. Given the paper is already out (not just in pre-print) I think it is appropriate to comment publicly. Continue reading A comment on preparing data for classifiers
Win-Vector LLC’s Nina Zumel has a great new article on the issue of taste in design and problem solving: Design, Problem Solving, and Good Taste. I think it is a big issue: how can you expect good work if you can’t even discuss how to tell good from bad?
Continue reading Great new post by Win-Vector’s Nina Zumel
Any practicing data scientist is going to eventually have to work with a data stored in a Microsoft
Excel spreadsheet. A lot of analysts use this format, so if you work with others you are going to run into it. We have already written how we don’t recommend using
Excel-like formats to exchange data. But we know if you are going to work with others you are going to have to make accommodations (we even built our own modified version of
Perl script to work around a bug).
But one thing that continues to confound us is how hard it is to read
Excel data correctly. When
Excel exports into
CSV/TSV style formats it uses fairly clever escaping rules about quotes and new-lines. Most
CSV/TSV readers fail to correctly implement these rules and often fail on fields that contain actual quote characters, separators (tab or comma), or new-lines. Another issue is
Excel itself often transforms data without any user verification or control. For example:
Excel routinely turns date-like strings into time since epoch (which it then renders as a date). We recently ran into another uncontrollable
Excel transform: changing the strings “
TRUE” and “
FALSE” into 1 and 0 inside the actual “
.xlsx” file. That is
Excel does not faithfully store the strings “
TRUE” and “
FALSE” even in its native format. Most
Excel users do not know about this, so they certainly are in no position to warn you about it.
This would be a mere annoyance, except it turns out
Libre Office (or at least LibreOffice_4.3.4_MacOS_x86-64) has a severe and silent data mangling bug on this surprising Microsoft boolean type.
We first ran into this in client data (and once the bug triggered it seemed to alter most of the columns), but it turns out the bug is very easy to trigger. In this note we will demonstrate the data representation issue and bug. Continue reading Excel spreadsheets are hard to get right
In most of our data science teaching (including our book Practical Data Science with R) we emphasize the deliberately easy problem of “exchangeable prediction.” We define exchangeable prediction as: given a series of observations with two distinguished classes of variables/observations denoted “x”s (denoting control variables, independent variables, experimental variables, or predictor variables) and “y” (denoting an outcome variable, or dependent variable) then:
- Estimate an approximate functional relation
y ~ f(x).
- Apply that relation to new instances where
x is known and
y is not yet known.
An example of this would be to use measured characteristics of online shoppers to predict if they will purchase in the next month. Data more than a month old gives us a training set where both
y are known. Newer shoppers give us examples where only
x is currently known and it would presumably be of some value to estimate
y or estimate the probability of different
y values. The problem is philosophically “easy” in the sense we are not attempting inference (estimating unknown parameters that are not later exposed to us) and we are not extrapolating (making predictions about situations that are out of the range of our training data). All we are doing is essentially generalizing memorization: if somebody who shares characteristics of recent buyers shows up, predict they are likely to buy. We repeat: we are not forecasting or “predicting the future” as we are not modeling how many high-value prospects will show up, just assigning scores to the prospects that do show up.
The reliability of such a scheme rests on the concept of exchangeability. If the future individuals we are asked to score are exchangeable with those we had access to during model construction then we expect to be able to make useful predictions. How we construct the model (and how to ensure we indeed find a good one) is the core of machine learning. We can bring in any big name machine learning method (deep learning, support vector machines, random forests, decision trees, regression, nearest neighbors, conditional random fields, and so-on) but the legitimacy of the technique pretty much stands on some variation of the idea of exchangeability.
One effect antithetical to exchangeability is “concept drift.” Concept drift is when the meanings and distributions of variables or relations between variables changes over time. Concept drift is a killer: if the relations available to you during training are thought not to hold during later application then you should not expect to build a useful model. This one of the hard lessons that statistics tries so hard to quantify and teach.
We know that you should always prefer fixing your experimental design over trying a mechanical correction (which can go wrong). And there are no doubt “name brand” procedures for dealing with concept drift. However, data science and machine learning practitioners are at heart tinkerers. We ask: can we (to a limited extent) attempt to directly correct for concept drift? This article demonstrates a simple correction applied to a deliberately simple artificial example.
Image: Wikipedia: Elgin watchmaker
Continue reading Can we try to make an adjustment?
Continuing our series of reading out loud from a single page of a statistics book we look at page 224 of the 1972 Dover edition of Leonard J. Savage’s “The Foundations of Statistics.” On this page we are treated to an example attributed to Leo A. Goodman in 1953 that illustrates how for normally distributed data the maximum likelihood, unbiased, and minimum variance estimators of variance are in fact typically three different values. So in the spirit of gamesmanship you always have at least two reasons to call anybody else’s estimator incorrect. Continue reading Bias/variance tradeoff as gamesmanship
What is the Gauss-Markov theorem?
From “The Cambridge Dictionary of Statistics” B. S. Everitt, 2nd Edition:
A theorem that proves that if the error terms in a multiple regression have the same variance and are uncorrelated, then the estimators of the parameters in the model produced by least squares estimation are better (in the sense of having lower dispersion about the mean) than any other unbiased linear estimator.
This is pretty much considered the “big boy” reason least squares fitting can be considered a good implementation of linear regression.
Suppose you are building a model of the form:
y(i) = B . x(i) + e(i)
B is a vector (to be inferred),
i is an index that runs over the available data (say
x(i) is a per-example vector of features, and
y(i) is the scalar quantity to be modeled. Only
y(i) are observed. The
e(i) term is the un-modeled component of
y(i) and you typically hope that the
e(i) can be thought of unknowable effects, individual variation, ignorable errors, residuals, or noise. How weak/strong assumptions you put on the
e(i) (and other quantities) depends on what you know, what you are trying to do, and which theorems you need to meet the pre-conditions of. The Gauss-Markov theorem assures a good estimate of
B under weak assumptions.
How to interpret the theorem
The point of the Gauss-Markov theorem is that we can find conditions ensuring a good fit without requiring detailed distributional assumptions about the
e(i) and without distributional assumptions about the
x(i). However, if you are using Bayesian methods or generative models for predictions you may want to use additional stronger conditions (perhaps even normality of errors and even distributional assumptions on the
We are going to read through the Wikipedia statement of the Gauss-Markov theorem in detail.
Continue reading Reading the Gauss-Markov theorem
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. Continue reading Automatic bias correction doesn’t fix omitted variable bias