In our previous note, we discussed some problems that can arise when using standard principal components analysis (specifically, principal components regression) to model the relationship between independent (x) and dependent (y) variables. In this note, we present some dimensionality reduction techniques that alleviate some of those problems, in particular what we call Y-Aware Principal Components Analysis, or Y-Aware PCA. We will use our variable treatment package vtreat in the examples we show in this note, but you can easily implement the approach independently of vtreat.
We have been recently working on and presenting on nested modeling issues. These are situations where the output of one trained machine learning model is part of the input of a later model or procedure. I am now of the opinion that correct treatment of nested models is one of the biggest opportunities for improvement in data science practice. Nested models can be more powerful than non-nested, but are easy to get wrong.
One of the trickier tasks in clustering is determining the appropriate number of clusters. Domain-specific knowledge is always best, when you have it, but there are a number of heuristics for getting at the likely number of clusters in your data. We cover a few of them in Chapter 8 (available as a free sample chapter) of our book Practical Data Science with R.
We also came upon another cool approach, in the mixtools package for mixture model analysis. As with clustering, if you want to fit a mixture model (say, a mixture of gaussians) to your data, it helps to know how many components are in your mixture. The boot.comp function estimates the number of components (let’s call it k) by incrementally testing the hypothesis that there are k+1 components against the null hypothesis that there are k components, via parametric bootstrap.
You can use a similar idea to estimate the number of clusters in a clustering problem, if you make a few assumptions about the shape of the clusters. This approach is only heuristic, and more ad-hoc in the clustering situation than it is in mixture modeling. Still, it’s another approach to add to your toolkit, and estimating the number of clusters via a variety of different heuristics isn’t a bad idea.
A great number of readers reacted very positively to Nina Zumel‘s article Using PostgreSQL in R: A quick how-to. Part of the reason is she described an incredibly powerful data science pattern: using a formerly expensive permanent system infrastructure as a simple transient tool.
In her case the tools were the data manipulation grammars SQL (Structured Query Language) and dplyr. It happened to be the case that in both cases the implementation was supplied by a backing database system (PostgreSQL), but the database was not the center of attention for very long.
In this note we will concentrate on SQL (which itself can be used to implement dplyr operators, and is available on even Hadoop scaled systems such as Hive). Our point can be summarized as: SQL isn’t the price of admission to a server, a server is the fee paid to use SQL. We will try to reduce the fee and show how to containerize PostgreSQL on Microsoft Windows (as was already done for us on Apple OSX).
The Smashing Pumpkins “Bullet with Butterfly Wings” (start 2 minutes 6s)
“Despite all my rage I am still just a rat in a cage!”
The reason we care is: by making the computer work harder (perform many calculations simultaneously) we wait less time for our experiments and can run more experiments. This is especially important when doing data science (as we often do using the R analysis platform) as we often need to repeat variations of large analyses to learn things, infer parameters, and estimate model stability.
Typically to get the computer to work a harder the analyst, programmer, or library designer must themselves work a bit hard to arrange calculations in a parallel friendly manner. In the best circumstances somebody has already done this for you:
Good parallel libraries, such as the multi-threaded BLAS/LAPACK libraries included in Revolution R Open (RRO, now Microsoft R Open) (see here).
Parallelization abstraction frameworks such as Thrust/Rth (see here).
Using R application libraries that dealt with parallelism on their own (examples include gbm, boot and our own vtreat). (Some of these libraries do not attempt parallel operation until you specify a parallel execution environment.)
In addition to having a task ready to “parallelize” you need a facility willing to work on it in a parallel manner. Examples include:
Your own machine. Even a laptop computer usually now has four our more cores. Potentially running four times faster, or equivalently waiting only one fourth the time, is big.
Graphics processing units (GPUs). Many machines have a one or more powerful graphics cards already installed. For some numerical task these cards are 10 to 100 times faster than the basic Central Processing Unit (CPU) you normally use for computation (see here).
We’ve just finished off a series of articles on some recent research results applying differential privacy to improve machine learning. Some of these results are pretty technical, so we thought it was worth working through concrete examples. And some of the original results are locked behind academic journal paywalls, so we’ve tried to touch on the highlights of the papers, and to play around with variations of our own.
A Simpler Explanation of Differential Privacy: Quick explanation of epsilon-differential privacy, and an introduction to an algorithm for safely reusing holdout data, recently published in Science (Cynthia Dwork, Vitaly Feldman, Moritz Hardt, Toniann Pitassi, Omer Reingold, Aaron Roth, “The reusable holdout: Preserving validity in adaptive data analysis”, Science, vol 349, no. 6248, pp. 636-638, August 2015).
Note that Cynthia Dwork is one of the inventors of differential privacy, originally used in the analysis of sensitive information.
Using differential privacy to reuse training data: Specifically, how differential privacy helps you build efficient encodings of categorical variables with many levels from your training data without introducing undue bias into downstream modeling.
Nina and I were noodling with some variations of differentially private machine learning, and think we have found a variation of a standard practice that is actually fairly efficient in establishing differential privacy a privacy condition (but, as commenters pointed out- not differential privacy).
One of the things I like about R is: because it is not used for systems programming you can expect to install your own current version of R without interference from some system version of R that is deliberately being held back at some older version (for reasons of script compatibility). R is conveniently distributed as a single package (with automated install of additional libraries).
Want to do some data analysis? Install R, load your data, and go. You don’t expect to spend hours on system administration just to get back to your task.
Python, being a popular general purpose language does not have this advantage, but thanks to Anaconda from Continuum Analytics you can skip (or at least delegate) a lot of the system environment imposed pain. With Anaconda trying out Python packages (Jupyter, scikit-learn, pandas, numpy, sympy, cvxopt, bokeh, and more) becomes safe and pleasant. Continue reading Thumbs up for Anaconda