xgboost and Small Numbers of Subtrees

John Mount covers an interesting issue you can run into when using xgboost:

While reading Dr. Nina Zumel’s excellent note on bias in common ensemble methods, I ran the examples to see the effects she described (and I think it is very important that she is establishing the issue, prior to discussing mitigation).
In doing that I ran into one more avoidable but strange issue in using xgboost: when run for a small number of rounds it at first appears that xgboost doesn’t get the unconditional average or grand average right (let alone the conditional averages Nina was working with)!

It’s not something you’ll hit very often, but if you’re trying xgboost against a small enough data set with few enough rounds, it is something to keep in mind.

Reinforcement Learning with R

Holger von Jouanne-Diedrich takes us through concepts in reinforcement learning:

At the core this can be stated as the problem a gambler has who wants to play a one-armed bandit: if there are several machines with different winning probabilities (a so-called multi-armed bandit problem) the question the gambler faces is: which machine to play? He could “exploit” one machine or “explore” different machines. So what is the best strategy given a limited amount of time… and money?

There are two extreme cases: no exploration, i.e. playing only one randomly chosen bandit, or no exploitation, i.e. playing all bandits randomly – so obviously we need some middle ground between those two extremes. We have to start with one randomly chosen bandit, try different ones after that and compare the results. So in the simplest case the first variable e=0.1 is the probability rate with which to switch to a random bandit – or to stick with the best bandit found so far.

Click through for various cases and a pathfinding example in R. H/T R-Bloggers

Biases in Tree-Based Models

Nina Zumel looks at tree-based ensembling models like random forest and gradient boost and shows that they can be biased:

In our previous article , we showed that generalized linear models are unbiased, or calibrated: they preserve the conditional expectations and rollups of the training data. A calibrated model is important in many applications, particularly when financial data is involved.

However, when making predictions on individuals, a biased model may be preferable; biased models may be more accurate, or make predictions with lower relative error than an unbiased model. For example, tree-based ensemble models tend to be highly accurate, and are often the modeling approach of choice for many machine learning applications. In this note, we will show that tree-based models are biased, or uncalibrated. This means they may not always represent the best bias/variance trade-off.

Read on for an example.

Comparing Poisson Regression to Regressing Against Logs

Nina Zumel compares a pair of methods for performing regression when income is the dependent variable:

Regressing against the log of the outcome will not be calibrated; however it has the advantage that the resulting model will have lower relative error than a Poisson regression against income. Minimizing relative error is appropriate in situations when differences are naturally expressed in percentages rather than in absolute amounts. Again, this is common when financial data is involved: raises in salary tend to be in terms of percentage of income, not in absolute dollar increments.

Unfortunately, a full discussion of the differences between Poisson regression and regressing against log amounts was outside of the scope of our book, so we will discuss it in this note.

This is an interesting post with a great teaser for the next post in the series.

tidylo: Calculating Log Odds in R

Julia Silge announces a new package, tidylo:

The package contains examples in the README and vignette, but let’s walk though another, different example here. This weighted log odds approach is useful for text analysis, but not only for text analysis. In the weeks since we’ve had this package up and running, I’ve found myself reaching for it in multiple situations, both text and not, in my real-life day job. For this example, let’s look at the same data as my last post, names given to children in the US.

Which names were most common in the 1950s, 1960s, 1970s, and 1980?

This package looks like it’s worth checking out if you deal with frequency-based problems.

Random Forest on Small Numbers of Observations

Neil Saunders takes us through an interesting problem:

A recent question on Stack Overflow [r] asked why a random forest model was not working as expected. The questioner was working with data from an experiment in which yeast was grown under conditions where (a) the growth rate could be controlled and (b) one of 6 nutrients was limited. Their dataset consisted of 6 rows – one per nutrient – and several thousand columns, with values representing the activity (expression) of yeast genes. Could the expression values be used to predict the limiting nutrient?

The random forest was not working as expected: not one of the nutrients was correctly classified. I pointed out that with only one case for each outcome, this was to be expected – as the random forest algorithm samples a proportion of the rows, no correct predictions are likely in this case. As sometimes happens the question was promptly deleted, which was unfortunate as we could have further explored the problem.

Neil decided to explore the problem further regardless and came to some interesting conclusions.

Lasso and Ridge Regression in Python

Kristian Larsen shows off a few regression techniques using Python:

Variables with a regression coefficient equal to zero after the shrinkage process are excluded from the model. Variables with non-zero regression coefficients variables are most strongly associated with the response variable. Therefore, when you conduct a regression model it can be helpful to do a lasso regression in order to predict how many variables your model should contain. This secures that your model is not overly complex and prevents the model from over-fitting which can result in a biased and inefficient model.

Read on for demonstrations.

Using Cohen’s D for Experiments

Nina Zumel takes us through Cohen’s D, a useful tool for determining effect sizes in experiments:

Cohen’s d is a measure of effect size for the difference of two means that takes the variance of the population into account. It’s defined as
d = | μ1 – μ2 | / σpooled
where σpooled is the pooled standard deviation over both cohorts.

Read the whole thing.

Sales Predictions with Pandas

Megan Quinn shows how you can use Pandas and linear regression to predict sales figures:

Pandas is an open-source Python package that provides users with high-performing and flexible data structures. These structures are designed to make analyzing relational or labeled data both easy and intuitive. Pandas is one of the most popular and quintessential tools leveraged by data scientists when developing a machine learning model. The most crucial step in the machine learning process is not simply fitting a model to a given data set. Most of the model development process takes place in the pre-processing and data exploration phase. An accurate model requires good predictors and, in order to acquire them, the user must understand the raw data. Through Pandas’ numerous data wrangling and analysis tools, this important step can easily be achieved. The goal of this blog is to highlight some of the central and most commonly used tools in Pandas while illustrating their significance in model development. The data set used for this demo consists of a supermarket chain’s sales across multiple stores in a variety of cities. The sales data is broken down by items within the stores. The goal is to predict a certain item’s sale.

Click through for an example of the process, including data cleansing and feature extraction, data analysis, and modeling.

Linear Regression Assumptions

Stephanie Glen has a chart which explains the four key assumptions behind when Ordinary Least Squares is the Best Linear Unbiased Estimator:

If any of the main assumptions of linear regression are violated, any results or forecasts that you glean from your data will be extremely biased, inefficient or misleading. Navigating all of the different assumptions and recommendations to identify the assumption can be overwhelming (for example, normality has more than half a dozen options for testing).

Violating one of the assumptions isn’t the end of the world, though it can make understanding the model and generating accurate predictions harder.

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