Tag: dimensionalityreduction

Calibrating algorithmic predictions with logistic regression

Calibrating algorithmic predictions with logistic regression

I found this interesting blog by Guilherme Duarte Marmerola where he shows how the predictions of algorithmic models (such as gradient boosted machines, or random forests) can be calibrated by stacking a logistic regression model on top of it: by using the predicted leaves of the algorithmic model as features / inputs in a subsequent logistic model.

When working with ML models such as GBMs, RFs, SVMs or kNNs (any one that is not a logistic regression) we can observe a pattern that is intriguing: the probabilities that the model outputs do not correspond to the real fraction of positives we see in real life.

Guilherme’s in his blog post

This is visible in the predictions of the light gradient boosted machine (LGBM) Guilherme trained: its predictions range only between ~ 0.45 and ~ 0.55. In contrast, the actual fraction of positive observations in those groups is much lower or higher (ranging from ~ 0.10 to ~0.85).

Motivated by sklearn’s topic Probability Calibration and the paper Practical Lessons from Predicting Clicks on Ads at Facebook, Guilherme continues to show how the output probabilities of a tree-based model can be calibrated, while simultenously improving its accuracy.

I highly recommend you look at Guilherme’s code to see for yourself what’s happening behind the scenes, but basically it’s this:

  • Train an algorithmic model (e.g., GBM) using your regular features (data)
  • Retrieve the probabilities GBM predicts
  • Retrieve the leaves (end-nodes) in which the GBM sorts the observations
  • Turn the array of leaves into a matrix of (one-hot-encoded) features, showing for each observation which leave it ended up in (1) and which not (many 0’s)
  • Basically, until now, you have used the GBM to reduce the original features to a new, one-hot-encoded matrix of binary features
  • Now you can use that matrix of new features as input for a logistic regression model predicting your target (Y) variable
  • Apparently, those logistic regression predictions will show a greater spread of probabilities with the same or better accuracy

Here’s a visual depiction from Guilherme’s blog, with the original GBM predictions on the X-axis, and the new logistic predictions on the Y-axis.

As you can see, you retain roughly the same ordering, but the logistic regression probabilities spread is much larger.

Now according to Guilherme and the Facebook paper he refers to, the accuracy of the logistic predictions should not be less than those of the original algorithmic method.

Much better. The calibration plot of lgbm+lr is much closer to the ideal. Now, when the model tells us that the probability of success is 60%, we can actually be much more confident that this is the true fraction of success! Let us now try this with the ET model.

Guilherme in https://gdmarmerola.github.io/probability-calibration/

In his blog, Guilherme shows the same process visually for an Extremely Randomized Trees model, so I highly recommend you read the original article. Also, you can find the complete code on his GitHub.

t-SNE, the Ultimate Drum Machine and more

t-SNE, the Ultimate Drum Machine and more

This blog explains t-Distributed Stochastic Neighbor Embedding (t-SNE) by a story of programmers joining forces with musicians to create the ultimate drum machine (if you are here just for the fun, you may start playing right away).

Kyle McDonald, Manny Tan, and Yotam Mann experienced difficulties in pinpointing to what extent sounds are similar (ding, dong) and others are not (ding, beep) and they wanted to examine how we, humans, determine and experience this similarity among sounds. They teamed up with some friends at Google’s Creative Lab and the London Philharmonia to realize what they have named “the Infinite Drum Machine” turning the most random set of sounds into a musical instrument.

Drum Machine.png

The project team wanted to include as many different sounds as they could, but had less appetite to compare, contrast and arrange all sounds into musical accords themselves. Instead, they imagined that a computer could perform such a laborious task. To determine the similarities among their dataset of sounds – which literally includes a thousand different sounds from the ngaaarh of a photocopier to the zing of an anvil – they used a fairly novel unsupervised machine learning technique called t-Distributed Stochastic Neighbor Embedding, or t-SNE in short (t-SNE Wiki; developer: Laurens van der Maaten). t-SNE specializes in dimensionality reduction for visualization purposes as it transforms highly-dimensional data into a two- or three-dimensional space. For a rapid introduction to highly-dimensional data and t-SNE by some smart Googlers, please watch the video below.

As the video explains, t-SNE maps complex data to a two- or three-dimensional space and was therefore really useful to compare and group similar sounds. Sounds are super highly-dimensional as they are essentially a very elaborate sequence of waves, each with a pitch, a duration, a frequency, a bass, an overall length, etcetera (clearly I am no musician). You would need a lot of information to describe a specific sound accurately. The project team compared sound to fingerprints, as there is an immense amount of data in a single padamtss.

t-SNE takes into account all this information of a sound and compares all sounds in the dataset. Next, it creates 2 or 3 new dimensions and assigns each sound values on these new dimensions in such a way that sounds which were previously similar (on the highly-dimensional data) are also similar on the new 2 – 3 dimensions. You could say that t-SNE summarizes (most of) the information that was stored in the previous complex data. This is what dimensionality reduction techniques do: they reduce the number of dimensions you need to describe data (sufficiently). Fortunately, techniques such as t-SNE are unsupervised, meaning that the project team did not have to tag or describe the sounds in their dataset manually but could just let the computer do the heavy lifting.

The result of this project is fantastic and righteously bears the name of Infinite Drum Machine (click to play)!  You can use the two-dimensional map to explore similar sounds and you can even make beats using the sequencing tool. The below video summarizes the creation process.

Amazed by this application, I wanted to know how t-SNE is being used in other projects. I have found a tremendous amount of applications that demonstrate how to implement t-SNE in Python, R, and even JS whereas the method also seems popular in academia.

Luke Metz argues implementation in Python is fairly easy and Analytics Vidhya and a visualized blog by O’Reilly back this claim. Superstar Andrej Karpathy has an interactive t-SNE demo which allows you to compare the similarity among top Twitter users using t-SNE (I think in JavaScript). A Kaggle user and Data Science Heroes have demonstrated how to apply t-SNE in R and have compared the method to other unsupervised methods, for instance to PCA.

indico_features_img_callout_small-1024x973[1].jpg
Clusters of similar cats/dogs in Luke Metz’ application of t-SNE.
Cho et al., 2014 have used t-SNE in their natural language processing projects as it allows for an easy examination of the similarity among words and phrases. Mnih and colleagues (2015) have used t-SNE to examine how neural networks were playing video games.

t-SNE video games
Two-dimensional t-SNE visualization of the hidden layer activity of neural network playing Space Invaders (Mnih et al., 2015)

On a final note, while acknowledging its potential, this blog warns for the inaccuracies in t-SNE due to the aesthetical adjustments it often seems to make. They have some lovely interactive visualizations to back up their claim. They conclude that it’s incredible flexibility allows t-SNE to find structure where other methods cannot. Unfortunately, this makes it tricky to interpret t-SNE results as the algorithm makes all sorts of untransparent adjustments to tidy its visualizations and make the complex information fit on just 2-3 dimensions.