## Stirring the pile efficiently

Warning: This is a technical post, and involves some code, etc.

As I’ve ranted a fair bit on this blog over the last year, a lot of “machine learning” in the industry can be described as “stirring the pile”. Regular readers of this blog will be familiar with this image from XKCD by now:

Basically people simply take datasets and apply all the machine learning techniques they have heard of (implementation is damn easy – scikit learn allows you to implement just about any model in three similar looking lines of code; See my code here to see how similar the implementation is).

So I thought I’ll help these pile-stirrers by giving some hints of what method to use for different kinds of data. I’ve over-simplified stuff, and so assume that:

1. There are two predictor variables X and Y. The predicted variable “Z” is binary.
2. X and Y are each drawn from a standard normal distribution.
3. The predicted variable Z is “clean” – there is a region in the X-Y plane where Z is always “true” and another region where Z is always “false”
4. So the idea is to see which machine learning techniques are good at identifying which kind of geometrical figures.
5. Everything is done “in-sample”. Given the nature of the data, it doesn’t matter if we do it in-sample or out-of-sample.

For those that understand Python (and every pile-stirrer worth his salt is excellent at Python), I’ve put my code in a nice Jupyter Notebook, which can be found here.

So this is what the output looks like. The top row shows the “true values” of Z. Then we have a row for each of the techniques we’ve used, which shows how well these techniques can identify the pattern given in the top row (click on the image for full size).

As you can see, I’ve chosen some common geometrical shapes and seen which methods are good at identifying those. A few pertinent observations:

1. Logistic regression and linear SVM are broadly similar, and both are shit for this kind of dataset. Being linear models, they fail to deal with non-linear patterns
2. SVM with RBF kernel is better, but it fails when there are multiple “true regions” in the dataset. At least it’s good at figuring out some non-linear patterns. However, it can’t figure out the triangle or square – it draws curves around them, instead.
3. Naive Bayesian (I’ve never understood this even though I’m pretty good at Bayesian statistics, but I understand this is a commonly used technique; and I’ve used default parameters so not sure how it is “Bayesian” even) can identify some stuff but does badly when there are disjoint regions where Z is true.
4. Ensemble methods such as Random Forests and Gradient Boosting do rather well on all the given inputs. They do well for both polygons and curves. Elsewhere, Ada Boost mostly does well but trips up on the hyperbola.
5. For some reason, Lasso fails to give an output (in the true spirit of pile-stirring, I didn’t explore why). Ridge is again a regression method and so does badly on this non-linear dataset
6. Neural Networks (Multi Layer Perceptron to be precise) does reasonably well, but can’t figure out the sharp edges of the polygons.
7. Decision trees again do rather well. I’m pleasantly surprised that they pick up and classify the disjoint sets (multi-circle and hyperbola) correctly. Maybe it’s the way scikit learn implements them?

Of course, the datasets that one comes across in real life are never such simple geometrical figures, but I hope that this set can give you some idea on what techniques to use where.

At least I hope that this makes you think about the suitability of different techniques for the data rather than simply applying all the techniques you know and then picking the one that performs best on your given training and test data.

That would count as nothing different from p-hacking, and there’s an XKCD for that as well!

## Duckworth Lewis Book

Yesterday at the local council library, I came across this book called “Duckworth Lewis” written by Frank Duckworth and Tony Lewis (who “invented” the eponymous rain rule). While I’d never heard about the book, given my general interest in sports analytics I picked it up, and duly finished reading it by this morning.

The good thing about the book is that though it’s in some way a collective autobiography of Duckworth and Lewis, they restrict their usual life details to a minimum, and mostly focus on what they are famous for. There are occasions when they go into too much detail describing a trip to either Australia or the West Indies, but it’s easy to filter out such stuff and read the book for the rain rule.

Then again, it isn’t a great book. If you’re not interested in cricket analytics there isn’t that much for you to know from the book. But given that it’s a quick read, it doesn’t hurt so much! Anyway, here are some pertinent observations:

1. Duckworth and Lewis didn’t get paid much for their method. They managed to get the ICC to accept their method sometime in the mid 90s, but it wasn’t until the early 2000s, by when Lewis had become a business school professor, that they managed to strike a financial deal with ICC. Even when they did, they make it sound like they didn’t make much money off it.
2. The method came about when Duckworth quickly put together something for a statistics conference he was organising, where another speaker who was supposed to speak about cricket pulled out at the last minute. Lewis later came across the paper, and then got one of his undergrad students to do a project about it. The two men subsequently collaborated
3. It’s amazing (not in a positive way) the kind of data that went into the method. Until the early 2000s, the only dataset that was used to calibrate the method was what was put together by Lewis’s undergrad. And this was mostly English County games, played over 40, 55 and 60 overs. Even after that, the frequency of updation with new data (which reflects new playing styles and strategies) is rather low.
4. The system doesn’t seem to have been particularly well software engineered – it was initially simply coded up by Duckworth, and until as late as 2007 it ran on the DOS operating system. It was only in 2008 or so, when Steven Stern joined the team (now the method is called DLS to include his name), that a windows version was introduced.
5. There is very little discussion of alternate methods, and though there is a chapter about it, Duckworth and Lewis are rather dismissive about them. For example, another popular method is by this guy called V Jayadevan from Thrissur. Here is some excellent analysis by Srinivas Bhogle where he compares the two methods. Duckworth and Lewis spend a couple of pages listing a couple of scenarios where Jayadevan’s method doesn’t work, and then spends a paragraph disparaging Bhogle for his support of the VJD method.
6. This was the biggest takeaway from the book for me – the Duckworth Lewis method doesn’t equalise probabilities of victory of the two teams before and after the rain interruption. Instead, the method equalises the margin of victory between the teams before and after the break. So let’s say a team was 10 runs behind the DL “par score” when it rains. When the game restarts, the target is set such that the team is still 10 runs behind the par score! They make an attempt to explain why this is superior to equalising probabilities of winning  but don’t go too far with it.
7. The adoption of Duckworth Lewis seems like a fairly random event. Following the World Cup 1992 debacle (when South Africa’s target went from 22 off 13 to 22 off 1 ball after a rain break), there was a demand for new rain rules. Duckworth and Lewis somehow managed to explain their method to the ECB secretary. And since it was superior to everything that was there then, it simply got adopted. And then it became incumbent, and became hard to dislodge!
8. There is no mention in the book about the inherent unfairness of the DL method (in that it can be unfair to some playing styles).

Ok this is already turning out to be a long post, but one final takeaway is that there’s a fair amount of randomness in sports analytics, and you shouldn’t get into it if your only potential customer is a national sporting body. In that sense, developments such as the IPL are good for sports analytics!

## Ratings revisited

Sometimes I get a bit narcissistic, and check how my book is doing. I log on to the seller portal to see how many copies have been sold. I go to the Amazon page and see what are the other books that people who have bought my book are buying (on the US store it’s Ray Dalio’s Principles, as of now. On the UK and India stores, Sidin’s Bombay Fever is the beer to my book’s diapers).

And then I check if there are new reviews of my book. When friends write them, they notify me, so it’s easy to track. What I discover when I visit my Amazon page are the reviews written by people I don’t know. And so far, most of them have been good.

So today was one of those narcissistic days, and I was initially a bit disappointed to see a new four-star review. I started wondering what this person found wrong with my book. And then I read through the review and found it to be wholly positive.

A quick conversation with the wife followed, and she pointed out that this reviewer perhaps reserves five stars for the exceptional. And then my mind went back to this topic that I’d blogged about way back in 2015 – about rating systems.

The “4.8” score that Amazon gives as an average of all the ratings on my book so far is a rather crude measure – since one reviewer’s 4* rating might differ significantly from another reviewer’s.

For example, my “default rating” for a book might be 5/5, with 4/5 reserved for books I don’t like and 3/5 for atrocious books. On the other hand, you might use the “full scale” and use 3/5 as your average rating, giving 4 for books you really like and very rarely giving a 5.

By simply taking an arithmetic average of ratings, it is possible to overstate the quality of a product that has for whatever reason been rated mostly by people with high default ratings (such a correlation is plausible). Similarly a low average rating for a product might mask the fact that it was rated by people who inherently give low ratings.

As I argue in the penultimate chapter of my book (or maybe the chapter before that – it’s been a while since I finished it), one way that platforms foster transactions is by increasing information flow between the buyer and the seller (this is one thing I’ve gotten good at – plugging my book’s name in random sentences), and one way to do this is by sharing reviews and ratings.

From this perspective, for a platform’s judgment on a product or seller (usually it’s the seller, but for products such as AirBnb, information about buyers also matters) to be credible, it is important that they be aggregated in the right manner.

One way to do this is to use some kind of a Z-score (relative to other ratings that the rater has given) and then come up with a normalised rating. But then this needs to be readjusted for the quality of the other items that this rater has rated. So you can think of some kind of a Singular Value Decomposition you can perform on ratings to find out the “true value” of a product (ok this is an achievement – using a linear algebra reference given how badly I suck in the topic).

I mean – it need not be THAT complicated, but the basic point is that it is important that platforms aggregate ratings in the right manner in order to convey accurate information about counterparties.

So after much deliberation and procrastination, I’ve finally started a newsletter. I call it “the art of data science” and the title should be self-explanatory. It’s pure unbridled opinion (the kind of which usually goes on this blog), except that I only write about one topic there.

I intend to have three sections and then a “chart of the edition” (note how cleverly I’ve named this section to avoid giving much away on the frequency of the newsletter!). This edition, though, I ended up putting too much harikathe, so I restricted to two sections before the chart.

I intend to talk a bit each edition about some philosophical part of dealing with data (this section got a miss this time), a bit on data analysis methods (I went a bit meta on this this time) and a little bit on programming languages (which I used for bitching a bit).

And that I plan to put a “chart of the edition” means I need to read newspapers a lot more, since you are much more likely to find gems (in either direction) there than elsewhere. For the first edition, I picked off a good graph I’d seen on Twitter, and it’s about Hull City!

Anyway, enough of this meta-harikathe. You can read the first edition of the newsletter here. In case you want to get it in your inbox each week/fortnight/whenever I decide to write it, then subscribe here!

And put feedback (by email, not comments here) on what you think of the newsletter!

## High dimension and low dimension data science

I’ve observed that there are two broad approaches that people take to getting information out of data. One approach is to simply throw a kitchen sink full of analytical techniques at the data. Without really trying to understand what the data looks like, and what the relationships may be, the analyst simply uses one method after another to try and get insight from the data. Along the way, a “model” will get built.

The other approach (which I’m partial to) involves understanding each variable, and relationship between variables as a first step to getting insight from the data. Here, too, a model might get built, but it will be conditional on the analyst’s view on what kind of a model might suit the data after looking at the data.

Considering that both these approaches are used by large numbers of analysts, it is highly likely that both are legitimate. Then what explains the fact that some analysts use one approach, and others use another? Having thought about it for a long time, I have a hypothesis – it depends on the kind of data being analysed. More precisely, it has to do with the dimensionality of the data.

The first approach (which one might classify as “machine learning”) works well when the data is of high dimensions – where the number of predictors that can be used for predictors is really large, of the order of thousands or larger. For example, even a seemingly low-resolution 32 by 32 pixel image, looked at as a data point, has 1024 dimensions (colour of the image at each of the 1024 pixels is a different dimension).

Moreover, in such situations, it is likely that the signal in the data doesn’t come from one, or, two, or a handful of predictors. In high dimension data science, the signal usually comes from complex interplay of data along various dimensions. And this kind of search is not something humans are fit for – it is best that the machines are left to “learn” the model by themselves, and so you get machine learning.

On the other hand, when the dimensionality of the dataset is low, it is possible (and “easy”) for an analyst to look at the interplay of factors in detail, and understand the data before going on to build the model. Doing so can help the analyst identify patterns in the data that may not be that apparent to a machine, and it is also likely that in such datasets, the signal  lies with data along a small number of dimensions, where relatively simple manipulation will suffice. The low dimensionality also means that complex machine learning techniques are unlikely to contribute much in such cases.

As you might expect, from an organisational perspective, the solution is quite simple – to deploy high-dimension data scientists on high-dimension problems, and likewise with low-dimension data scientists. Since this distinction between high-dimension and low-dimension data scientists isn’t very well known, it’s quite possible that the scientists might be made to work on a problem of dimensionality that is outside of their comfort zone.

So when you have low dimensional data scientists faced with a large number of dimensions of data, you will see them use brute force to try and find signals in bivariate relationships in the data – an approach that will never work since the signal lies in a more complex interplay of dimensions.

On the other hand, when you put high dimension data scientists on a low dimension problem, you will either see them missing out on associations that a human could easily find but a machine might find hard to find, or they might unnecessarily “reduce the problem to a known problem” by generating and importing large amounts of data in order to turn it into a high dimension problem!

PS: I wanted to tweet this today but forgot. Basically, you use logistic regression when you think the signal is an “or” of conditions on some of the underlying variables. On the other hand, if you think the signal is more likely to be an “and” condition of certain conditions, then you should use decision trees!

## When a two-by-two ruins a scatterplot

The BBC has some very good analysis of the Brexit vote (how long back was that?), using voting data at the local authority level, and correlating it with factors such as ethnicity and educational attainment.

In terms of educational attainment, there is a really nice chart, that shows the proportion of voters who voted to leave against the proportion of population in the ward with at least a bachelor’s degree. One look at the graph tells you that the correlation is rather strong:

‘Source: http://www.bbc.com/news/uk-politics-38762034And then there is the two-by-two that is superimposed on this – with regions being marked off in pink and grey. The idea of the two-by-two must have been to illustrate the correlation – to show that education is negatively correlated with the “leave” vote.

But what do we see here? A majority of the points lie in the bottom left pink region, suggesting that wards with lower proportion of graduates were less likely to leave. And this is entirely the wrong message for the graph to send.

The two-by-two would have been useful had the points in the graph been neatly divided into clusters that could be arranged in a grid. Here, though, what the scatter plot shows is a nice negatively correlated linear relationship. And by putting those pink and grey boxes, the illustration is taking attention away from that relationship.

Instead, I’d simply put the scatter plot as it is, and maybe add the line of best fit, to emphasise the negative correlation. If I want to be extra geeky, I might also write down the $R^2$ next to the line, to show the extent of correlation!

## Medium stats

So Medium sends me this email:

Congratulations! You are among the top 10% of readers and writers on Medium this year. As a small thank you, we’ve put together some highlights from your 2016.

Now, I hardly use Medium. I’ve maybe written one post there (a long time ago) and read only a little bit (blogs I really like I’ve put on RSS and read on Feedly). So when Medium tells me that I, who considers myself a light user, is “in the top 10%”, they’re really giving away the fact that the quality of usage on their site is pretty bad.

Sometimes it’s bloody easy to see through flattery! People need to be more careful on what the stats they’re putting out really convey!