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
I think I have been pretty productive on technical tasks lately and the method is (at least to me) interesting. The effect was accidental but I think one can explain it and reproduce it by synthesizing three important observations on human behavior. Continue reading Increase your productivity
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
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Research surveys tend to fall on either end of the spectrum: either they are so high level and cursory in their treatment that they are useful only as a dictionary of terms in the field, or they are so deep and terse that the discussion can only be followed by those already experienced in the field. Ensemble Methods in Data Mining (Seni and Elder, 2010) strikes a good balance between these extremes. This book is an accessible introduction to the theory and practice of ensemble methods in machine learning, with sufficient detail for a novice to begin experimenting right away, and copious references for researchers interested in further details of algorithms and proofs. The treatment focuses on the use of decision trees as base learners (as they are the most common choice), but the principles discussed are applicable with any modeling algorithm. The authors also provide a nice discussion of cross-validation and of the more common regularization techniques.
The heart of the text is the chapter on the Importance Sampling. The authors frame the classic ensemble methods (bagging, boosting, and random forests) as special cases of the Importance Sampling methodology. This not only clarifies the explanations of each approach, but also provides a principled basis for finding improvements to the original algorithms. They have one of the clearest explanations of AdaBoost that I’ve ever read.
A major shortcoming of ensemble methods is the loss of interpretability, when compared to single-model methods such as Decision Trees or Linear Regression. The penultimate chapter is on “Rule Ensembles”: an attempt at a more interpretable ensemble learner. They also discuss measures for variable importance and interaction strength. The last chapter discusses Generalized Degrees of Freedom as an alternative complexity measure and its relationship to potential over-fit.
Overall, I found the book clear and concise, with good attention to practical details. I appreciated the snippets of R code and the references to relevant R packages. One minor nitpick: this book has also been published digitally, presumably with color figures. Because the print version is grayscale, some of the color-coded graphs are now illegible. Usually the major points of the figure are clear from the context in the text; still, the color to grayscale conversion is something for future authors in this series to keep in mind.
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
A “for fun” piece, reposted from mzlabs.com.
I would like to comment on Duncan Jones’ movie “Moon” and compare some elements of “Moon” to earlier science fiction. Continue reading Gerty, a character in Duncan Jones’ “Moon.”
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?