Text Normalization With Spark

Engineers at Treselle Systems have put together a two-part series on text normalization using Apache Spark.  First, they walk through normalizing the text:

We have used Spark shared variable “broadcast” to achieve distributed caching. Broadcast variables are useful when large datasets need to be cached in executors. “stopwords_en.txt” is not a large dataset but we have used in our use case to make use of that feature.

What are Broadcast Variables?
Broadcast variables in Apache Spark is a mechanism for sharing variables across executors that are meant to be read-only. Without broadcast variables, these variables would be shipped to each executor for every transformation and action, which can cause network overhead. However, with broadcast variables, they are shipped once to all executors and are cached for future reference.

From there, they dig into details on what the Spark engine did and why we see what we do:

Note: Stage 2 has both reduceByKey() and sortByKey() operations and as indicated in job summary “saveAsTextFile()” action triggered Job 2. Do you have any guess whether Stage 2 will be further divided into other stages in Job 2? The answer is: yes Job 2 DAG: This job is triggered due to saveAsTextFile() action operation. The job DAG clearly indicates the list of operations used before the saveAsTextFile() operations.Stage 2 in Job 1 is further divided into another stage as Stage 2. In Stage 2 has both reduceByKey() and sortByKey() operations and both operations can shuffle the data so that Stage 2 in Job 1 is broken down into Stage 4 and Stage 5 in Job 2. There are three stages in this job. But, Stage 3 is skipped. The answer for the skipped stage is provided below “What does “Skipped Stages” mean in Spark?” section.

There’s some good information here if you want to become more familiar with how Spark works.

Measuring Correlation In SQL

Phil Factor shows how to calculate Kendall’s Tau and Spearman’s Rho in SQL:

Kendall’s Tau rank correlation is a handy way of determining how correlated two variables are, and whether this is more than chance. If you just want a measure of the correlation then you don’t have to assume very much about the distribution of the variables. Kendall’s Tau is popular with calculating correlations with non-parametric data. Spearman’s Rho is possibly more popular for the purpose, but Kendall’s tau has a distribution with better statistical properties (the sample estimate is close to a population variance) so confidence levels are more reliable, but in general, Kendall’s tau and Spearman’s rank correlation coefficient are very similar. The obvious difference between them is that, for the standard method of calculation,  Spearman’s Rank correlation required ranked data as input, whereas the algorithm to calculate Kendall’s Tau does this for you.  Kendall’s Tau consumes any non-parametric data with equal relish.

Kendall’s Tau is easy to calculate on paper, and makes intuitive sense. It deals with the probabilities of observing the agreeable (concordant) and non-agreeable (discordant) pairs of rankings. All observations are paired with each of the others, A concordant pair is one whose members of one observation are both larger than their respective members of the other paired observation, whereas discordant pairs have numbers that differ in opposite directions. Kendall’s Tau-b takes tied rankings into account.

I appreciate Phil putting this series together.  I’d probably stick with R, but it’s good to have options.

Probabilistic Record Linking In Spark

Tom Lous builds a solution to link similar companies together by address:

Recently a colleague asked me to help her with a data problem, that seemed very straightforward at a glance.
She had purchased a small set of data from the chamber of commerce (Kamer van Koophandel: KvK) that contained roughly 50k small sized companies (5–20FTE), which can be hard to find online.
She noticed that many of those companies share the same address, which makes sense, because a lot of those companies tend to cluster in business complexes.

Read on for the solution.  Like many data problems, it turns out to be a lot more complicated than you’d think at first glance.

Understanding Boosted Trees

Maria Jesus Alonso explains decision trees and their subsequent improvements:

Bagging (or Bootsrap Aggregating), the second prediction technique brought to the BigML Dashboard and API, uses a collection of trees (rather than a single one), each tree built with a different random subset of the original dataset for each model in the ensemble. Specifically, BigML defaults to a sampling rate of 100% (with replacement) for each model. This means some of the original instances will be repeated and others will be left out. Bagging performs well when a dataset has many noisy features and only one or two are relevant. In those cases, Bagging will be the best option.

Random Decision Forests extend the Bagging technique by only considering a random subset of the input fields at each split of the tree. By adding randomness in this process, Random Decision Forests help avoid overfitting. When there are many useful fields in your dataset, Random Decision Forests are a strong choice.

Click through for how boosted trees change this model a bit.

Using OLS To Fit Rational Functions

Srini Kumar and Bob Horton show how to use the lm function to fit functions using the Pade Approximation:

Now we have a form that lm can work with. We just need to specify a set of inputs that are powers of x (as in a traditional polynomial fit), and a set of inputs that are y times powers of x. This may seem like a strange thing to do, because we are making a model where we would need to know the value of y in order to predict y. But the trick here is that we will not try to use the fitted model to predict anything; we will just take the coefficients out and rearrange them in a function. The fit_pade function below takes a dataframe with x and y values, fits an lm model, and returns a function of x that uses the coefficents from the model to predict y:

The lm function does more than just fit straight lines.

The Central Limit Theorem

Mala Mahadevan explains the Central Limit Theorem with an example:

The central limit theorem states that the sampling distribution of the mean of any independent,random variable will be normal or nearly normal, if the sample size is large enough. How large is “large enough”? The answer depends on two factors.

  • Requirements for accuracy. The more closely the sampling distribution needs to resemble a normal distribution, the more sample points will be required.
  • The shape of the underlying population. The more closely the original population resembles a normal distribution, the fewer sample points will be required. (from stattrek.com).

The main use of the sampling distribution is to verify the accuracy of many statistics and population they were based upon.

Read on for an example and to see how to calculate this in T-SQL.

Linear Support Vector Machines

Ananda Das explains how linear Support Vector Machines work in classifying spam messages:

Linear SVM assumes that the two classes are linearly separable that is a hyper-plane can separate out the two classes and the data points from the two classes do not get mixed up. Of course this is not an ideal assumption and how we will discuss it later how linear SVM works out the case of non-linear separability. But for a reader with some experience here I pose a question which is like this Linear SVM creates a discriminant function but so does LDA. Yet, both are different classifiers. Why ? (Hint: LDA is based on Bayes Theorem while Linear SVM is based on the concept of margin. In case of LDA, one has to make an assumption on the distribution of the data per class. For a newbie, please ignore the question. We will discuss this point in details in some other post.)

This is a pretty math-heavy post, so get your coffee first. h/t R-Bloggers.

Introduction To Probability

Mala Mahadevan covers some basics of probability:

Probability is an important statistical and mathematical concept to understand. In simple terms – probability refers to the chances of possible outcome of an event occurring within the domain of multiple outcomes. Probability is indicated by a whole number – with 0 meaning that the outcome has no chance of occurring and 1 meaning that the outcome is certain to happen. So it is mathematically represented as P(event) = (# of outcomes in event / total # of outcomes). In addition to understanding this simple thing, we will also look at a basic example of conditional probability and independent events.

It’s a good intro to a critical topic in statistics.  If I would add one thing to this, it would be to state that probability is always conditional upon something.  It’s fair to write something as P(Event) understanding that it’s a shortcut, but in reality, it’s always P(Event | Conditions), where Conditions is the set of assumptions we made in collecting this sample.

Time Series Errors

Alex Smolyanskaya explains some common errors when doing time series analysis:

Non-zero model error indicates that our model is missing explanatory features. In practice, we don’t expect to get rid of all model error—there will be some error in the forecast from unavoidable natural variation. Natural variation should reflect all the stuff we will probably never capture with our model, like measurement error, unpredictable external market forces, and so on. The distribution of error should be close to normal and, ideally, have a small mean. We get evidence that an important explanatory variable is missing from the model when we find that the model error doesn’t look like simple natural variation—if the distribution of errors skews one way or another, there are more outliers than expected, or if the mean is unpleasantly large. When this happens we should try to identify and correct any missing or incorrect model features.

It’s an interesting article, especially the bit about cross-validation, which is a perfectly acceptable technique in non-time series models.

Building A Python Project Template

Henk Griffioen shows how to create a standardized project in Python, focusing on data science scenarios:

Project structures often organically grow to suit people’s needs, leading to different project structures within a team. You can consider yourself lucky if at some point in time you find, or someone in your team finds, a obscure blog post with a somewhat sane structure and enforces it in your team.

Many years ago I stumbled upon ProjectTemplate for R. Since then I’ve tried to get people to use a good project structure. More recently DrivenData (what’s in a name?) released their more generic Cookiecutter Data Science.

The main philosophies of those projects are:

  • A consistent and well-organized structure allows people to collaborate more easily.

  • Your analyses should be reproducible and your structure should enable that.

  • A projects starts from raw data that should never be edited; consider raw data immutable and only edit derived sources.

This is a set of prescriptions and focuses on the phase before the project actually kicks off.

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