The important criterion for a graph is not simply how fast we can see a result; rather it is whether through the use of the graph we can see something that would have been harder to see otherwise or that could not have been seen at all.
— William Cleveland, The Elements of Graphing Data, Chapter 2
In this article, I will discuss some graphs that I find extremely useful in my day-to-day work as a data scientist. While all of them are helpful (to me) for statistical visualization during the analysis process, not all of them will necessarily be useful for presentation of final results, especially to non-technical audiences.
I tend to follow Cleveland’s philosophy, quoted above; these graphs show me — and hopefully you — aspects of data and models that I might not otherwise see. Some of them, however, are non-standard, and tend to require explanation. My purpose here is to share with our readers some ideas for graphical analysis that are either useful to you directly, or will give you some ideas of your own.
Continue reading My Favorite Graphs
We share our admiration for a set of results called “locality sensitive hashing” by demonstrating a greatly simplified example that exhibits the spirit of the techniques. Continue reading An Appreciation of Locality Sensitive Hashing
We give a simple explanation of the interrelated machine learning techniques called kernel methods and support vector machines. We hope to characterize and de-mystify some of the properties of these methods. To do this we work some examples and draw a few analogies. The familiar no matter how wonderful is not perceived as mystical. Continue reading Kernel Methods and Support Vector Machines de-Mystified
Nina Zumel recently gave a very clear explanation of logistic regression ( The Simpler Derivation of Logistic Regression ). In particular she called out the central role of log-odds ratios and demonstrated how the “deviance” (that mysterious
quantity reported by fitting packages) is both a term in “the pseudo-R^2” (so directly measures goodness of fit) and is the quantity that is actually optimized during the fitting procedure. One great point of the writeup was how simple everything is once you start thinking in terms of derivatives (and that it isn’t so much the functional form of the sigmoid that is special but its relation to its own derivative that is special).
We adapt these presentation ideas to make explicit the well known equivalence of logistic regression and maximum entropy models. Continue reading The equivalence of logistic regression and maximum entropy models
Logistic regression is one of the most popular ways to fit models for categorical data, especially for binary response data. It is the most important (and probably most used) member of a class of models called generalized linear models. Unlike linear regression, logistic regression can directly predict probabilities (values that are restricted to the (0,1) interval); furthermore, those probabilities are well-calibrated when compared to the probabilities predicted by some other classifiers, such as Naive Bayes. Logistic regression preserves the marginal probabilities of the training data. The coefficients of the model also provide some hint of the relative importance of each input variable.
While you don’t have to know how to derive logistic regression or how to implement it in order to use it, the details of its derivation give important insights into interpreting and troubleshooting the resulting models. Unfortunately, most derivations (like the ones in [Agresti, 1990] or [Hastie, et.al, 2009]) are too terse for easy comprehension. Here, we give a derivation that is less terse (and less general than Agresti’s), and we’ll take the time to point out some details and useful facts that sometimes get lost in the discussion. Continue reading The Simpler Derivation of Logistic Regression
Programmers should definitely know how to use R. I don’t mean they should switch from their current language to R, but they should think of R as a handy tool during development. Continue reading Programmers Should Know R
One of the recurring frustrations in data analytics is that your data is never in the right shape. Worst case: you are not aware of this and every step you attempt is more expensive, less reliable and less informative than you would want. Best case: you notice this and have the tools to reshape your data.
There is no final “right shape.” In fact even your data is never right. You will always be called to re-do your analysis (new variables, new data, corrections) so you should always understand you are on your “penultimate analysis” (always one more to come). This is why we insist on using general methods and scripted techniques, as these methods are much much easier to reliably reapply on new data than GUI/WYSWYG techniques.
In this article we will work a small example and call out some R tools that make reshaping your data much easier. The idea is to think in terms of “relational algebra” (like SQL) and transform your data towards your tools (and not to attempt to adapt your tools towards the data in an ad-hoc manner). Continue reading Your Data is Never the Right Shape
With the well deserved popularity of A/B testing computer scientists are finally becoming practicing statisticians. One part of experiment design that has always been particularly hard to teach is how to pick the size of your sample. The two points that are hard to communicate are that:
- The required sample size is essentially independent of the total population size.
- The required sample size depends strongly on the strength of the effect you are trying to measure.
These things are only hard to explain because the literature is overly technical (too many buzzwords and too many irrelevant concerns) and these misapprehensions can’t be relieved unless you spend some time addressing the legitimate underlying concerns they are standing in for. As usual explanation requires common ground (moving to shared assumptions) not mere technical bullying.
We will try to work through these assumptions and then discuss proper sample size. Continue reading What is a large enough random sample?
This is a tutorial on how to try out a new package in R. The summary is: expect errors, search out errors and don’t start with the built in examples or real data.
Suppose you want to try out a novel statistical technique? A good fraction of the time R is your best bet for a first trial. Take as an example general additive models (“Generalized Additive Models,” Trevor J Hastie, Robert Tibshirani, Statistical Science (1986) vol. 1 (3) pp. 297-318); R has a package named “gam” written by Trevor Hastie himself. But, like most R packages, trying the package from the supplied documentation brings in unfamiliar data and concerns. It is best to start small and quickly test if the package itself is suitable to your needs. We give a quick outline of how to learn such a package and quickly find out if the package is for you.
Continue reading The cranky guide to trying R packages
We discuss a “medium scale data” technique that we call “SQL Screwdriver.”
Previously we discussed some of the issues of large scale data analytics. A lot of the work done at the MapReduce scale is necessarily limited to mere aggregation and report generation. But what of medium scale? That is data too large to perform all steps in your favorite tool (R, Excel or something else) but small enough that you are expected to produce sophisticated models, decisions and analysis. At this scale, if properly prepared, you don’t need large scale tools and their limitations. With extra preparation you can continue to use your preferred tools. We call this the realm of medium scale data and discuss a preparation tool style we call “screwdriver” (as opposed to larger hammers).
We stand the “no SQL” movement on its head and discuss the beneficial use of SQL without a server (as opposed to their vision of a key-value store without SQL). Database servers can be a nuisance- but that is not enough reason to give up the power of relational query languages.
Continue reading SQL Screwdriver