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Category: Data Science

Diamond: Solving Generalized Linear Models Using Python

Published 2017-08-11 by Kevin Feasel

Tim Sweester and Aaron Bradley announce Diamond, a Python library which solves certain kinds of generalized linear models.  In a two-part series, they explain more.  Part 1 covers the mathematical principles behind it:

Many computational problems in data science and statistics can be cast as convex problems. There are many advantages to doing so:

  • Convex problems have a unique global solution, i.e. there is one best answer
  • There are well-known, efficient, and reliable algorithms for finding it

One ubiquitous example of a convex problem in data science is finding the coefficients of an L2L2-regularized logistic regression model using maximum likelihood. In this post, we’ll talk about some basic algorithms for convex optimization, and discuss our attempts to make them scale up to the size of our models. Unlike many applications, the “scale” challenge we faced was not the number of observations, but the number of features in our datasets. First, let’s review the model we want to fit.

Part 2 looks at one interesting use case:

In this example, GLMMs allow you to pool information across different brands, while still learning individual effects for each brand. It breaks the problem into sets of fixed and random effects. The fixed effects are similar to what you would find in a traditional logistic regression model, while the random effects allow the regression relationship to vary for each brand. One of the advantages of GLMMs is that they learn how different brands are from each other. Brands that are very similar to the overall average will have small random effect estimates. Because of the regularization of these models, brands with few observations will also have small random effect estimates, and be treated more like the overall average. In contrast, for brands that are very different from the average, with lots of data to support that, GLMMs will learn large random effect estimates.

Check it out.  Part 2 also contains a link to the GitHub repo if you want to try it on your own.

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Understanding K-Means Clustering

Published 2017-08-10 by Kevin Feasel

Chaitanya Sagar has a good explanation of the assumptions k-means clustering makes:

Why do we assume in the first place? The answer is that making assumptions helps simplify problems and simplified problems can then be solved accurately. To divide your dataset into clusters, one must define the criteria of a cluster and those make the assumptions for the technique. K-Means clustering method considers two assumptions regarding the clusters – first that the clusters are spherical and second that the clusters are of similar size. Spherical assumption helps in separating the clusters when the algorithm works on the data and forms clusters. If this assumption is violated, the clusters formed may not be what one expects. On the other hand, assumption over the size of clusters helps in deciding the boundaries of the cluster. This assumption helps in calculating the number of data points each cluster should have. This assumption also gives an advantage. Clusters in K-means are defined by taking the mean of all the data points in the cluster. With this assumption, one can start with the centers of clusters anywhere. Keeping the starting points of the clusters anywhere will still make the algorithm converge with the same final clusters as keeping the centers as far apart as possible.

Read on as Chaitanya shows several examples; the polar coordinate transformation was quite interesting.  H/T R-Bloggers

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Forecasting Versus Predicting

Published 2017-08-09 by Kevin Feasel

Rob Collie explains that there are two different concepts which use similar names:

Once you’ve digested the illustration at the top of this article, yeah, you’ve kind already got it.

  • Forecasting is when we anticipate the behavior of “Lots” of people (customers, typically) on “Long” timelines.
  • Predictive Analytics anticipate the behavior of One person (again, typically a customer) on a “Short” timeline.

So…  Macro versus Micro.

But let’s delve just a little bit deeper, in order to “cement” the concepts.

There’s a very useful distinction here and Rob does well to flesh out the details.  I highly recommend this if you’re curious about micro- versus macro-level predictions.

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Deep Learning Isn’t The End-All Be-All Solution

Published 2017-08-08 by Kevin Feasel

Pablo Cordero explains that deep learning solutions are not the best choice in all cases:

The second preconception I hear the most is the hype. Many yet-to-be practitioners expect deep nets to give them a mythical performance boost just because it worked in other fields. Others are inspired by impressive work in modeling and manipulating images, music, and language – three data types close to any human heart – and rush headfirst into the field by trying to train the latest GAN architecture. The hype is real in many ways. Deep learning has become an undeniable force in machine learning and an important tool in the arsenal of any data modeler. Its popularity has brought forth essential frameworks such as tensorflow and pytorch that are incredibly useful even outside deep learning. Its underdog to superstar origin story has inspired researchers to revisit other previously obscure methods like evolutionary strategies and reinforcement learning. But it’s not a panacea by any means. Aside from lunch considerations, deep learning models can be very nuanced and require careful and sometimes very expensive hyperparameter searches, tuning, and testing (much more on this later in the post). Besides, there are many cases where using deep learning just doesn’t make sense from a practical perspective and simpler models work much better.

It’s a very interesting article, pointing out that deep learning solutions work better than expected on smaller data sizes, but there are areas where it’s preferable to choose something else.

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Explaining Singular Value Decomposition

Published 2017-08-03 by Kevin Feasel

Tim Bock explains how Singular Value Decomposition works:

The table above is a matrix of numbers. I am going to call it Z. The singular value decomposition is computed using the svd function. The following code computes the singular value decomposition of the matrix Z, and assigns it to a new object called SVD, which contains one vector, d, and two matrices, u and v. The vector, d, contains the singular values. The first matrix, u, contains the left singular vectors, and vcontains the right singular vectors. The left singular vectors represent the rows of the input table, and the right singular vectors represent their columns.

Tim includes R scripts to follow along, and for this topic I definitely recommend following along.

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Scaling Out Random Forest

Published 2017-08-01 by Kevin Feasel

Denis C. Bauer, et al, explain VariantSpark RF, a random forest algorithm designed for huge numbers of variables:

VariantSpark RF starts by randomly assigning subsets of the data to Spark Executors for decision tree building (Fig 1). It then calculates the best split over all nodes and trees simultaneously. This implementation avoids communication bottlenecks between Spark Driver and Executors as information exchange is minimal, allowing it to build large numbers of trees efficiently. This surveys the solution space appropriately to cater for millions of features and thousands of samples.

Furthermore, VariantSpark RF has memory efficient representation of genomics data, optimized communication patterns and computation batching. It also provides efficient implementation of Out-Of-Bag (OOB) error, which substantially simplifies parameter tuning over the computationally more costly alternative of cross-validation.

We implemented VariantSpark RF in scala as it is the most performant interface languages to Apache Spark. Also, new updates to Spark and the interacting APIs will be deployed in scala first, which has been important when working on top of a fast evolving framework.

Give it a read.  Thankfully, I exhibit few of the traits of the degenerative disease known as Hipsterism.

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Reducing Dimensionality

Published 2017-08-01 by Kevin Feasel

Antoine Guillot explains some of the basic concepts of variable reduction in a data analysis:

Each of these people can be represented as points in a 3 Dimensional space. With a gross approximation, each people is in a 50*50*200 (cm) cube. If we use a resolution of 1cm and three color channels, then can be represented by 1,000,000 variables.
On the other hand, the shadow is only in 2 dimensions and in black and white, so each shadow only needs 50*200=10,000 variables.
The number of variables was divided by 100 ! And if your goal is to detect human vs cat, or even men vs women, the data from the shadow may be enough.

Read on for intuitive discussions of techniques like principal component analysis and linear discriminant analysis.  H/T R-Bloggers

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Random Forests In R

Published 2017-07-25 by Kevin Feasel

Anish Sing Walia explains the basics of random forests and provides sample code in R:

Random Forests are similar to a famous Ensemble technique called Bagging but have a different tweak in it. In Random Forests the idea is to decorrelate the several trees which are generated on the different bootstrapped samples from training Data.And then we simply reduce the Variance in the Trees by averaging them.
Averaging the Trees helps us to reduce the variance and also improve the Perfomance of Decision Trees on Test Set and eventually avoid Overfitting.

The idea is to build lots of Trees in such a way to make the Correlation between the Trees smaller.

Random forests frequently give a good answer to classification problems, enough so as to make them a nice starting point.

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Neural Networks From Scratch

Published 2017-07-19 by Kevin Feasel

Ilia Karmanov explains neural nets and shows how to build one in R:

Hence, my motivation for this post is two-fold:

  1. Understanding (by writing from scratch) the leaky abstractions behind neural-networks dramatically shifted my focus to elements whose importance I initially overlooked. If my model is not learning I have a better idea of what to address rather than blindly wasting time switching optimisers (or even frameworks).
  2. A deep-neural-network (DNN), once taken apart into lego blocks, is no longer a black-box that is inaccessible to other disciplines outside of AI. It’s a combination of many topics that are very familiar to most people with a basic knowledge of statistics. I believe they need to cover very little (just the glue that holds the blocks together) to get an insight into a whole new realm.

Starting from a linear regression we will work through the maths and the code all the way to a deep-neural-network (DNN) in the accompanying R-notebooks. Hopefully to show that very little is actually new information.

This is pretty detailed.  Karmanov mentions Andrej Karpathy, whose Hacker’s guide to Neural Networks is also a must-read on the topic.

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Using bsts In R

Published 2017-07-12 by Kevin Feasel

Steven L. Scott explains what the bsts package does:

Time series data appear in a surprising number of applications, ranging from business, to the physical and social sciences, to health, medicine, and engineering. Forecasting (e.g. next month’s sales) is common in problems involving time series data, but explanatory models (e.g. finding drivers of sales) are also important. Time series data are having something of a moment in the tech blogs right now, with Facebook announcing their “Prophet” system for time series forecasting (Taylor and Letham 2017), and Google posting about its forecasting system in this blog (Tassone and Rohani 2017).

This post summarizes the bsts R package, a tool for fitting Bayesian structural time series models. These are a widely useful class of time series models, known in various literatures as “structural time series,” “state space models,” “Kalman filter models,” and “dynamic linear models,” among others. Though the models need not be fit using Bayesian methods, they have a Bayesian flavor and the bsts package was built to use Bayesian posterior sampling.

If you’re looking for time series models, this looks like a good one.

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