Machine Learning 1: Lesson 5

My personal notes from machine learning class. These notes will continue to be updated and improved as I continue to review the course to “really” understand it. Much appreciation to Jeremy and Rachel who gave me this opportunity to learn.

Lessons: 123456789101112


Video

Review

  • Test sets , training sets, validation sets and OOB

We have a dataset with bunch of rows in it and we’ve got some dependent variable. What is the difference between machine learning and any other kind of work? The difference is that in machine learning, the thing we care about is the generalization accuracy or the generalization error where else, in pretty much in everything else, all we care about is how well we could map to the observations. So this thing about generalization is the key unique piece of machine learning. And if we want to know whether we are doing a good job of machine learning, we need to know whether we are doing a good job of generalizing. If we don’t know that, we know nothing.

Question: By generalizing, do you mean scaling? Being able to scale larger? [1:26] No, I don’t mean scaling at all. Scaling is an important thing in many areas. It’s like okay we’ve got something that works on my computer with 10,000 items, I now need to make it work on 10,000 items per second. So scaling is important but not just for machine learning but for just about everything we put in production. Generalization is where I say okay, here is a model that can predict cats from dogs. I’ve looked at five pictures of cats and five pictures of dogs, and I’ve built a model that is perfect. Then I look at a different set of five cats and dogs, and it gets them all wrong. So in that case, what it learned was not the difference between a cat and a dog, but it learnt what those five exact cats looked like and what those five exact dogs looked like. Or I built a model of predicting grocery sales for a particular product, so for toilet rolls in New Jersey last month, and then I go and put it into production and it scales great (in other words, a great latency, no high CPU load) but it fails to predicting anything other than toilet rolls in New Jersey. It also turns out it only did it well for last month, not the next month. So these are all generalization failures.

The most common way that people check for the ability to generalize is to create a random sample. So they will grab a few rows at random and pull it out into a test set. Then they will build all of their models on the rest of the rows and then when they are finished, they will check that the accuracy they got on the test set (the rest of the rows are called the training set). So at the end of their modeling process, on the training set, they got an accuracy of 99% of predicting cats from dogs, at the very end, they check it against a test set to make sure that the model really does generalize.

Now the problem is, what if it doesn’t? Well, I could go back and change some hyper parameters, do some data augmentation, whatever else trying to create a more generalizable model. And then I’ll go back again after doing all that, and check and it’s still no good. I’ll keep doing this again and again until eventually, after fifty attempts, it does generalize. But does it really generalize? Because maybe all I’ve done is accidentally found this one which happens to work just for that test set because I’ve tried fifty different things. So if I’ve got something which is right coincidentally 5% of the time, they are not very likely to accidentally get a good result. So what we generally do is we put aside a second dataset (validation set). Then everything that’s not in the validation or test is now training. What we do is we train a model, check it against the validation to see if it generalizes, do that a few times. Then when we finally got something we think will generalize successfully based on the validation set (at the end of the project), we check it against the test set.

Question: So basically by making this two layer test set validation set, if it gets one right the other wrong, you are kind of double checking your errors? [5:19] It’s checking that we haven’t overfit to the validation set. So if we are using the validation set again and again, then we could end up not coming up with a generalizable sort of hyper parameters but a set of hyper parameters that just so happened to work on the training set and the validation set. So if we try 50 different models against the validation set and then at the end of all that, we then check that against the test set and it’s still generalized as well, then we are going to say okay that’s good we’ve actually come up with generalizable model. If it doesn’t, then that’s going to say we’ve actually now overfit to the validation set. At that point, you are kind of in trouble. Because you don’t have anything left behind. So the idea is to use effective techniques during the modeling so that doesn’t happen. But if it’s going to happen, you want to find out about it — you need that test set to be there because otherwise when you put it in production and then it turns out that it doesn’t generalize, that would be a really bad outcome. You’ll end up with less people clicking on your ads or selling less of your products, or providing car insurance to very risky vehicles.

Question: So just to make sure, do we need to ever check if the validation set and the test set are coherent or you just keep test set?[6:43] So if you’ve done what I’ve just done here which is to randomly sample, there is no particular reason to check as long as they are big enough. But we will come back to your question in a different context in just moment.

Another trick we’ve learnt for random forest is a way of not needing a validation set [7:10]. And the way we learnt was to use, instead, the OOB score. This idea was to say every time we train a tree in a random forest, there is a bunch of observations that are held out anyway because that’s how we get some of the randomness. So let’s calculate our score for each tree based on those held out samples and therefore the forest by averaging the trees that each row was not part of training. So the OOB score gives us something which is pretty similar to the validation score, but on average it’s a little less good. Why? Because every row is going to be using a subset of the trees to make its prediction, and with less trees, we know we get a less accurate prediction. So that’s a subtle one and if you didn’t get it, have a think during the week until you understand why this is because it’s a really interesting test of your understanding of random forests. Why is OOB score on average less good than your validation score? They are both using random held-out subsets.

Anyway, it’s generally close enough [11:06]. So why have a validation set at all when you are using random forests? If it’s a randomly chosen validation set, it’s not strictly speaking necessary but you’ve got like four levels of things to test — so you could test on the OOB, when that’s working well, you can test on the validation set, and hopefully by the time you check against the test set, there’s going to be no surprises so that’ll be one good reason.

What Kaggle do, the way they do this, is kind of clever. What Kaggle do is they split the test set into two pieces: a public and a private. And they don’t tell you which is which. So you submit your predictions to Kaggle and then a random 30% of those are used to tell you the leaderboard score. But then at the end of the competition, that gets thrown away and they use the other 70% to calculate your real score. So what that’s doing is that you are making sure that you are not continuously using that feedback from the leaderboard to figure out some set of hyper parameters that happens to do well on the public that actually doesn’t generalize. So it’s a great test. This is one of the reasons why it’s good practice to use Kaggle because at the end of a competition, at some point this will happen to you, and you’ll drop a hundred places on the leaderboard the last day of the competition when they use the private test set and say oh okay, that’s what it feels like to overfit and it’s much better to practice and get that sense there than it is to do it in a company where there’s hundreds of millions of dollars on the line.

This is like the easiest possible situation where you are able to use a random sample for your validation set [12:55]. Why might I not be able to use a random sample from my validation or possibly fail? My claim is that by using a random validation set, we could get totally the wrong idea about our model. important thing to remember is when you build a model, you always have a systematic error which is that you’re going to use the model at a later time than the time you built it. You’re going to put it into production by which time the world is different to the world that you are in now and even when you’re building the model, you’re using data which is older than today anyway. So there’s some lag between the data that you are building it on and the data that it’s going to actually be used on in real life. And a lot of the time, if not most of the time, that matters.

So if we are predicting who is going to buy toilet paper in New Jersey and it takes us two weeks to put it in production and we did it using data from the last couple of years and by that time, things may look very different. And particularly our validation set, if we randomly sampled it, and it was from a four year period, then the vast majority of the data is going to be over a year old. And it may be that the toilet paper buying habits of folks in New Jersey may have dramatically shifted. Maybe they’ve got a terrible recession there now and they can’t afford a high-quality toilet paper anymore. Or maybe they know their paper making industry has gone through the roof and suddenly they are buying a lot more toilet paper because it’s so cheap. So the world changes and therefore if you use a random sample for your validation set, then you are actually checking how good are you at predicting things that are totally obsolete now? How good are you at predicting things that happened four years ago? That’s not interesting. So what we want to do in practice, anytime there is some temporal piece is to instead say assuming that we’ve ordered it by time, we’ll use the latest portion as our validation set. I suppose, actually do it properly:

That’s our validation set, and that’s our test set. So the rest is our training set and we use that and we try and be able to model that still works on stuff that’s later in time than anything the model was built on. So we are not just testing generalization in some kind of abstract sense but in a very specific time sense which is it generalizes to the future.

Question: As you said, there is some temporal ordering in the data, so in that case, is it wise to take the entire data for training or only a few recent dataset for training [19:07]? Yeah, that is a whole other question. So how do you get the validation set to be good? So I build a random forest on all the training data. It looks good on the training data, it looks good on OOB. And this is actually a really good reason to have OOB. If it looks good on the OOB then it means you are not overfitting in a statistical sense. It’s working well on a random sample. But then it looks bad on the validation set. So what happened? Well, what happened was that you somehow failed to predict the future. You only predicted the past so Suraj had an idea about how we could fix that. Okay, well, maybe we should just train so maybe we shouldn’t use the whole training set. We should try a recent period only. Now on the downside, we are now using less data so we can create less rich models, on the upside, it’s more up-to-date data. And this is something you have to play around with. Most machine learning functions have the ability to provide a weight that is given to each row. So for example, with a random forest, rather than bootstrapping at random, you could have a weight on every row and randomly pick that row with some probability. So we could put probability such that the most recent rows have a higher probability of being selected. That can work really well. It’s something that you have to try and if you don’t have a validation set that represents the future compared to what you are training on, you have no way to know which of your techniques are working.

How do you make the compromise between amount of data vs. recency of data? What I tend to do is when I have this kind of temporal issue, which is probably most of the time, once I have something that’s working well on the validation set, I wouldn’t then go and just use that model on the test set because the test set is much farther in the future compared to the training set. So I would then replicate building that model again but this time I would combine the training and validation sets together and retrain the model. At that point, you’ve got no way to test against a validation set, so you have to make sure you have a reproducible script or notebook that does exactly the same steps in exactly the same ways because if you get something wrong then you’re going to find on the test set that you’ve got a problem. So what I do in practice is I need to know if my validation set is a truly representative of the test set. So what I do is I build five models on the training set, and I try to have them vary in how good I think they are. Then I score my five models on the validation set and then I also score them on the test set. So I’m not cheating since I’m not using any feedback from the test set to change my hyper parameters — I’m only using it for this one thing which is to check my validation set. So I get my five scores from the validation set and test set and then I check that they fall in a line. If they don’t, then you’re not going to get good enough feedback from the validation set. So keep doing that process until you’re getting a line and that can be quite tricky . Trying to create something that’s as similar to the real-world outcome as possible is difficult. And in the real world, the same is true of creating the test set — the test set has to be as close to production as possible. So what’s the actual mix of customers that are going to be using this, how much time is there actually going to be between when you build the model and when you put it in production? How often you are going to be able to refresh the model? These are all the things to think about when you build that test set.

Question: So first you build five models on the training data and if you didn’t get a straight-line relationship, change your validation and test set [24:01]? You can’t really change the test set generally, so this is assuming that the test set is given and you change the validation set. So if you start with a random sample validation set and then it’s all over the place and you realize oh I should have picked the last two months. Then you pick the last two months and it’s still going all over the place and you realize oh I should have picked it so that it’s also from the first of the month to the fifteenth of the month, and keep changing the validation set until you found a set which is indicative of your test set results.

Question: For five models, you start with maybe just random data, average, etc [24:45]? Maybe five not terrible ones but you want some variety and you also particularly want some variety in how well they might generalize through time. So one that was trained on the whole training set, one was trained on the last two weeks, one that was trained on the last six week, one which used lots and lots of columns and might over fit a bit more. So you want to get a sense of if my validation set fails to generalize temporarily, I’d want to see that, if it fails to generalize statistically, I’d want to see that.

Question: Can you explain a bit more in detail what you mean by change your validation set so it indicates the test set? What does that look like [25:28]? Let’s take the groceries competitions where we are trying to predict the next two weeks of grocery sales. The possible validation set that Terrance and I played with was:

  • Random sample (4 years)
  • Last month of data (July 15–August 15)
  • Last 2 weeks (August 1–15)
  • Same day range one month earlier (July 15–30)

The test set in this competition was the 15th to the 30th of the August. So above were four different validation sets we tried. With random, our results were all over the place. With last month, they were not bad but not great. The last two weeks, there was a couple that didn’t look good but on the whole they were good. The same day range a month earlier, they’ve got a basically perfect line.

Question: What exactly are we comparing it to from the test set [26:58]? I build 5 models, so there might be 1. just predict the average, 2. do some kind of simple group mean of the whole data set, 3. do some group mean over the last month of the data, 4. build a random forests of the whole thing, 5, build random forest from the last three weeks. On each of those, I calculate the validation score. Then I retrain the model on the whole training set and calculate the same thing on the test set. So each of these points now tells me how well did it go on the validation set and how well did it go in the test set. If the validation set is useful, we would say every time the validation score set improves, the test set score should also improve.

Question : When you say “re-train” do you mean re-train the model on training and validation set [27:50]? Yes, so once I’ve got the validation score based on just the training set, then retrain it on the train and validation and check against the test set.

Question: By test set, do you mean submitting it to Kaggle and check the score? If it’s Kaggle, then your test set is Kaggle’s leader board. In the real world, the test set is this third data set you put aside. It’s that third dataset that having it reflect real world production differences is the most important step in a machine learning project. Why is it the most important step? Because if you screw up everything else but you don’t screw up that, you’ll know you screwed up. If you’ve got a good test set, then you’ll know you screwed up because you screwed up something else and you tested it and it didn’t work out, it’s okay. You’re not going to destroy the company. If you screwed up creating the test set, that would be awful. Because then you don’t know if you’ve made a mistake. You try to build a model, you test it on the test set and it looks good. But the test set was not indicative of real-world environment. So you don’t actually know if you are going to destroy the company. Hopefully you’ve got ways to put things into production gradually so you won’t actually destroy the company but you’ll at least destroy your reputation at work. Oh, Jeremy tried to put this thing into production and in the first week the cohort we tried it on, their sales halved and we’re never gonna give Jeremy a machine learning job again. But if Jeremy had used a proper test set then he would have known, uh-oh this is half as good as my validation set said it would be, I’ll keep trying. Now I’m not going to get in any trouble. I was actually like oh, Jeremy is awesome — he identifies ahead of time when there’s going to be a generalization problem.

This is something everybody talks about a little bit in machine learning classes but often it stops at the point where you learned that there is a thing in sklearn called make train_test_split and it returns these things and off you go, or here is the cross-validation function [30:10]. The fact that these things always give you random samples tells you that much if not most of the time, you shouldn’t be using them. The fact that random forest gives you an OOB for free, it’s useful but only tells you that this generalizes in a statistical sense, not in a practical sense.

Cross validation [30:54]

Outside of class, you guys have been talking about a lot which makes me feel somebody’s been over emphasizing the value of this technique. So I’ll explain what cross-validation is and then I explain why you probably shouldn’t be using it most of the time.

Cross validation says let’s not just pull out one validation set, but let’s pull out five, for example. So let’s assume that we’re going to randomly shuffle the data first of all. This is critical.

  1. Randomly shuffle the data.
  2. Split it into five groups
  3. For model №1, we will call the first one the validation set, and the bottom four the training set.
  4. We will train and we will check against the validation and we get some RMSE, R², etc.
  5. We will repeat that five times, and we will take the average of RMSE, R², etc, and that is a cross-validation average accuracy.

What is the benefit of using cross-validation over a standard validation set I talked about before? You can use all of the data. You don’t have to put anything aside. And you get a little benefit as well in that you’ve now got five models that you could ensemble together, each one used 80% of the data. So sometimes that ensemble can be helpful.

What could be some reasons that you wouldn’t use cross-validation? For large dataset, it will take a long time. We have to fit five models rather than one, so time is a key downside. If we are doing deep learning and it takes a day to run, suddenly it takes five days or we need 5 GPUs. What about my earlier issues about validation sets? Our earlier concerns about why random validation sets are a problem are entirely relevant here. These validation sets are random, so if a random validation set is not appropriate for your problem, most likely because, for example, of temporal issues then none of these five validation sets are any good. They are all random. So if you have temporal data like we did before, there’s no way to do cross validation or no good way to do cross validation. You want to have your validation set to be as close to the test set as possible, and you can’t do that by randomly sampling different things. You may well not need to do cross validation because most of the time in the real world, we don’t really have that little data — unless your data is based on some very very expensive labeling process or some experiments that cost a lot to run, etc. But nowadays, data scientists are not very often doing that kind of work. Some are, in which case this is an issue, but most of us aren’t. So we probably don’t need to. If we do do it, it’s going to take a whole a lot of time, then even if we did do it and we took up all that time, it might give us totally the wrong answer because random validation sets are inappropriate for our probblem.

I’m not going to be spending much time on cross validation because I think it’s an interesting tool to have, it’s easy to use (sklearn has a cross validation thing you can use), but it’s not that often that it’s going to be an important part of your toolbox in my opinion. It’ll come up sometimes. So that is validation sets.

Tree interpretation [38:02]

What does tree interpreter do and how does it do it? Let’s start with the output of tree interpreter [38:51]. Here is a single tree:

The root of the tree is before there’s been any split at all. So 10.189 is the average log price of all of the options in our training set. Then if I go Coupler_System ≤ 0.5, then we get an average of 10.345 (the subset of 16815). Off the people with Coupler_System ≤0.5, we then take the subset where Enclosure ≤ 2.0 and average log price there is 9.955. Then the final step is ModelID ≤ 4573.0 and that gives us 10.226.

We can then calculate the change in average log price by each additional criteria. We can draw that as what’s called a waterfall plot. Waterfall plots are one of the most useful plots I know about and weirdly enough, there’s nothing in Python to do them. This is one of these things where there’s this disconnect between the world of management consulting and business where everybody uses waterfall plots all the time and academia who have no idea what these things are. Every time you have a starting point and a number of changes and a finishing point, waterfall charts are pretty much always the best way to show it.

With Excel 2016, it’s build-in. You just click insert waterfall chart and there it is. If you want to be a hero, create a waterfall chart package for matplotlib, put it on pip, and everybody will love you for it. These are actually super easy to build. You basically do a stacked column plot where the bottom of this is all white. You can kind of do it but if you can wrap that up, put the points in the right spots and color them nicely, that would be totally awesome. I think you’ve all got the skills to do it, and would be a terrific thing for your portfolio.

In general, they are going from all, then going through each change, then the sum of all of those is going to be equal to the final prediction [43:38]. So if we were just doing a decision tree and someone asks “how come this particular auction’s prediction was this particular price?”, this is how you can answer “because these three things had these three impacts”.

For a random forest, we could do that across all of the trees. So every time we see coupler, we add up that change. Every time we see enclosure, we add up that change, and so on. Then we combine them all together, we get what tree interpreter does. So you could go into the source code for tree interpreter and it’s not at all complex logic. Or you could build it yourself and you can see how it does exactly this.

from treeinterpreter import treeinterpreter as ti
df_train, df_valid = split_vals(df_raw[df_keep.columns], n_trn)
row = X_valid.values[None,0]; row
array([[4364751, 2300944, 665, 172, 1.0, 1999, 3726.0, 3, 3232, 1111, 0, 63, 0, 5, 17, 35, 4, 4, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 19, 29, 3, 2, 1, 0, 0, 0, 0, 0, 2010, 9, 37,
16, 3, 259, False, False, False, False, False, False, 7912, False, False]], dtype=object)
prediction, bias, contributions = ti.predict(m, row)

So when you go treeinterpreter.predict with a random forest model for some specific auction (in this case it’s zero index row), it tells you:

  • prediction: the same as the random forest prediction
  • bias: this is going to be always the same — it’s the average sale price for everybody for each of the random samples in the tree
  • contributions: the total of all the contributions for each time we see that specific column appear in a tree.
prediction[0], bias[0]
(9.1909688098736275, 10.10606580677884)

The last time I made a mistake of not sorting this correctly. so this time np.argsort is a super handy function. It doesn’t actually sort contributions[0], it just tells you where each item would move to if it were sorted. So now by passing idxs to each one of the column, the level, and contribution , I can then print out all those in the right order.

idxs = np.argsort(contributions[0])
[o for o in zip(df_keep.columns[idxs], df_valid.iloc[0][idxs], contributions[0][idxs])]
[('ProductSize', 'Mini', -0.54680742853695008),
('age', 11, -0.12507089451852943),
('fiProductClassDesc',
'Hydraulic Excavator, Track - 3.0 to 4.0 Metric Tons',
-0.11143111128570773),
('fiModelDesc', 'KX1212', -0.065155113754146801),
('fiSecondaryDesc', nan, -0.055237427792181749),
('Enclosure', 'EROPS', -0.050467175593900217),
('fiModelDescriptor', nan, -0.042354676935508852),
('saleElapsed', 7912, -0.019642242073500914),
('saleDay', 16, -0.012812993479652724),
('Tire_Size', nan, -0.0029687660942271598),
('SalesID', 4364751, -0.0010443985823001434),
('saleDayofyear', 259, -0.00086540581130196688),
('Drive_System', nan, 0.0015385818526195915),
('Hydraulics', 'Standard', 0.0022411701338458821),
('state', 'Ohio', 0.0037587658190299409),
('ProductGroupDesc', 'Track Excavators', 0.0067688906745931197),
('ProductGroup', 'TEX', 0.014654732626326661),
('MachineID', 2300944, 0.015578052196894499),
('Hydraulics_Flow', nan, 0.028973749866174004),
('ModelID', 665, 0.038307429579276284),
('Coupler_System', nan, 0.052509808150765114),
('YearMade', 1999, 0.071829996446492878)]

So small piece of industrial equipment meant that it was less expensive. If it was made pretty recently meant that was more expensive, etc. So this is not going to really help you much at all with Kaggle where you just need predictions. But it’s going to help you a lot in a production environment or even pre production. So something which any good manager should do if you say here is a machine learning model I think we should use is they should go away and grab a few example of actual customers or actual auctions and check whether your model looks intuitive. If it says my prediction is that lots of people are going to really enjoy this crappy movie, and it is like “wow, that was a really crappy movie” then they’re going to come back to you and say “explain why your model is telling me that I’m going to like this movie because I hate that movie”. Then you can go back and say well, it’s because you like this movie and because you’re this age range and you’re this gender, and on average actually people like you did like that movie.

Question: What’s the second element of each tuple [47:25]? This is saying for this particular row, ‘ProductSize’ was ‘Mini’, and it was 11 years old, etc. So it’s just feeding back and telling you. Because this is actually what it was:

array([[4364751, 2300944, 665, 172, 1.0, 1999, 3726.0, 3, 3232, 1111, 0, 63, 0, 5, 17, 35, 4, 4, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 19, 29, 3, 2, 1, 0, 0, 0, 0, 0, 2010, 9, 37,
16, 3, 259, False, False, False, False, False, False, 7912, False, False]], dtype=object)

It was these numbers. So I just went back to the original data to actually pull out the descriptive versions of each one.

So if we sum up all the contributions together, and then add them to the bias, then that would give us the final prediction.

contributions[0].sum()
-0.7383536391949419

This is an almost totally unknown technique and this particular library is almost totally unknown as well. So it’s a great opportunity to show something that a lot of people don’t know. It’s totally critical in my opinion but rarely done.

So this is kind of the end of the random forest interpretation piece and hopefully you’ve now seen enough that when somebody says we can’t use modern machine learning techniques because they are black boxes that aren’t interpretable, you have enough information to say you are full of crap. They are extremely interpretable and the stuff that we’ve just done — trying to do that with a linear model, good luck to you. Even where you can do something similar with a linear model, trying to do it so that is not giving you totally the wrong answer and you had no idea it’s a wrong answer is going to be a real challenge.

Extrapolation [49:23]

The last step we are going to do before we try and build our own random forest is to deal with this tricky issue of extrapolation. So in this case, if we look at the accuracy of our recent trees, we still have a big difference between our validation score and our training score.

Actually, in this case, the difference between the OOB (0.89420) and the validation (0.89319) is actually pretty close. So if there was a big difference, I’d be very worried about whether we’ve dealt with the temporal side of things correctly. Here is the most recent model:

On Kaggle, you need that last decimal place. In real world, I probably stopped here. But quite often you’ll see there’s a big difference between your validation score and your OOB score, and I want to show you how you would deal with that particularly because we know that the OOB score should be a little worse because it’s using less trees so it gives me a sense that we should get to do a little bit better. The way we should be able to do a little bit better is by handling the time component a little bit better.

Here is the problem with random forests when it comes to extrapolation. When you’ve got a dataset that got four years of sales data in it, and you create your tree and it says if it’s in some particular store and some particular item and it is on special, here is the average price. And it actually tells us the average price over the whole training set which could be pretty old. So when you then want to step forward to what is going to be the price next month, it’s never seen next month. Where else with a linear model, it can find a relationship between time and price where even though we only had this much data, when you then go and predict something in the future, it can extrapolate that. But a random forest can’t do that. If you think about it, there is no way for a tree to be able to say well next month, it would be higher still. So there is a few ways to deal with this and we’ll talk about it over the next couple of lessons, but one simple way is just to try to avoid using time variables as predictors if there’s something else we could use that’s going to give us a better or stronger relationship that’s actually going to work in the future [52:19].

So in this case, what I wanted to do was to first of all figure out what’s the difference between our validation set and our training set. If I understand the difference between our validation set and our training set, then that tells me what are the predictors which have a strong temporal component and therefore they may be irrelevant by the time I get to the future time period. So I do something really interesting which is I create a random forest where my dependent variable is “is it in the validation set” (is_valid). I’ve gone back and I’ve got my whole data frame with the training and validation all together and I’ve created a new column called is_valid which I’ve set to one and then for all of the stuff in the training set, I set it to zero. So I’ve got a new column which is just is this in the validation set or not and then I’m going to use that as my dependent variable and build a random forest. This is a random forest not to predict price but predict is this in the validation set or not. So if your variable were not time dependent, then it shouldn’t be possible to figure out if something is in the validation set or not.

df_ext = df_keep.copy()
df_ext['is_valid'] = 1
df_ext.is_valid[:n_trn] = 0
x, y, nas = proc_df(df_ext, 'is_valid')

This is a great trick in Kaggle because they often won’t tell you whether the test set is a random sample or not. So you could put the test set and training set together, create a new column called is_test and see if you can predict it. If you can, you don’t have a random sample which means you have to figure out how to create a validation set from it.

m = RandomForestClassifier(n_estimators=40, min_samples_leaf=3, max_features=0.5, n_jobs=-1, oob_score=True)
m.fit(x, y);
m.oob_score_
0.99998753505765037

In this case, I can see I don’t have a random sample because my validation set can be predicted with a .9999 R².

So then if I look at feature importance, the top thing is SalesID [54:36]. So this is really interesting. It tells us very clearly SalesID is not a random identifier but probably it’s something that’s just set consecutively as time goes on — we just increase the SalesID. saleElapsed was the number of days since the first date in our dataset so not surprisingly that also is a good predictor. Interestingly MachineID — clearly each machine is being labeled with some consecutive identifier as well and then there’s a big drop in importance, so we’ll stop here.

fi = rf_feat_importance(m, x); fi[:10] 

Let’s next grab those top three and we can then have a look at their values both from the training set and in the validation set. [55:22]

feats=['SalesID', 'saleElapsed', 'MachineID']
(X_train[feats]/1000).describe()
(X_valid[feats]/1000).describe()

We can see for example, SalesID on average is 1.8 million in the training set and 5.8 million in the validation set (notice that the value is divided by 1000). So you can confirm they are very different.

So let’s drop them.

x.drop(feats, axis=1, inplace=True)
m = RandomForestClassifier(n_estimators=40, min_samples_leaf=3, max_features=0.5, n_jobs=-1, oob_score=True)
m.fit(x, y);
m.oob_score_
0.9789018385789966

So after I drop them, let’s now see if I can predict whether something is in the validation set. I still can with 0.98 R².

fi = rf_feat_importance(m, x); fi[:10]

Once you remove some things, then other things can come to the front, and it now turns out that not surprisingly age — things that are old are more likely to be in the validation set because earlier on in the training set, they can’t be that old yet. YearMade for the same reason. So then we can try removing those as well — SalesID, saleElapsed, MachineID from the first one, age, YearMade, and saleDayofyear from the second one. They are all time dependent features. I still want them in my random forest if they are important. But if they are not important, then taking them out if there are some other none-time dependent variables that work just as well — that would be better. Because now I am going to have a model that generalizes over time better.

set_rf_samples(50000)
feats=['SalesID', 'saleElapsed', 'MachineID', 'age', 'YearMade', 'saleDayofyear']
X_train, X_valid = split_vals(df_keep, n_trn)
m = RandomForestRegressor(n_estimators=40, min_samples_leaf=3,
max_features=0.5, n_jobs=-1, oob_score=True)
m.fit(X_train, y_train)
print_score(m)
[0.21136509778791376, 0.2493668921196425, 0.90909393040946562, 0.88894821098056087, 0.89255408392415925]

So here, I’m just going to go through each one of those features and drop each one, one at a time, retrain a new random forest, and print out the score [57:19]. Before we do any of that, our score was 0.88 for validation, 0.89 for OOB. And you can see below, when I remove SalesID, my score goes up. This is what we were hoping for. We’ve removed a time dependent variable, there were other variables that could find similar relationships without the time dependency. So removing it caused our validation to go up. Now OOB didn’t go up, because this is genuinely statistically a useful predictor, but it’s a time dependent one and we have a time dependent validation set. So this is really subtle but it can be really important. It’s trying to find the things that gives you a generalizable-across-time prediction and here is how you can see it.

for f in feats:
df_subs = df_keep.drop(f, axis=1)
X_train, X_valid = split_vals(df_subs, n_trn)
m = RandomForestRegressor(n_estimators=40, min_samples_leaf=3,
max_features=0.5, n_jobs=-1, oob_score=True)
m.fit(X_train, y_train)
print(f)
print_score(m)
SalesID
[0.20918653475938534, 0.2459966629213187, 0.9053273181678706, 0.89192968797265737, 0.89245205174299469]
saleElapsed
[0.2194124612957369, 0.2546442621643524, 0.90358104739129086, 0.8841980790762114, 0.88681881032219145]
MachineID
[0.206612984511148, 0.24446409479358033, 0.90312476862123559, 0.89327205732490311, 0.89501553584754967]
age
[0.21317740718919814, 0.2471719147150774, 0.90260198977488226, 0.89089460707372525, 0.89185129799503315]
YearMade
[0.21305398932040326, 0.2534570148977216, 0.90555219348567462, 0.88527538596974953, 0.89158854973045432]
saleDayofyear
[0.21320711524847227, 0.24629839782893828, 0.90881970943169987, 0.89166441133215968, 0.89272793857941679]

We should remove SalesID for sure, but saleElapsed didn’t get better, so we don’t want. MachineID did get better — 0.888 to 0.893 so it’s actually quite a bit better. age got a bit better. YearMade got worse, saleDayofyear got a bit better.

reset_rf_samples()

So now we can say, let’s get rid of the three where we know that getting rid of it actually made it better. And as a result, we are now up to .915! So we got rid of three time dependent things and now as expected our validation is better than our OOB.

df_subs = df_keep.drop(['SalesID', 'MachineID', 'saleDayofyear'], 
axis=1)
X_train, X_valid = split_vals(df_subs, n_trn)
m = RandomForestRegressor(n_estimators=40, min_samples_leaf=3,
max_features=0.5, n_jobs=-1, oob_score=True)
m.fit(X_train, y_train)
print_score(m)
[0.1418970082803121, 0.21779153679471935, 0.96040441863389681, 0.91529091848161925, 0.90918594039522138]

So that was a super successful approach there, and now we can check the feature importance.

plot_fi(rf_feat_importance(m, X_train));
np.save('tmp/subs_cols.npy', np.array(df_subs.columns))

Let’s go ahead and say alright, that was pretty darn good. Let’s now leave it for a while so give it 160 trees, let it chew on it, and see how that goes.

Our final model!

m = RandomForestRegressor(n_estimators=160, max_features=0.5, 
n_jobs=-1, oob_score=True)
%time m.fit(X_train, y_train)
print_score(m)
CPU times: user 6min 3s, sys: 2.75 s, total: 6min 6s
Wall time: 16.7 s
[0.08104912951128229, 0.2109679613161783, 0.9865755186304942, 0.92051576728916762, 0.9143700001430598]

As you can see, we did all of our interpretation, all of our fine-tuning basically with smaller models/subsets and at the end, we run the whole thing. And it actually still only took 16 seconds and so we’ve now got an RMSE of 0.21. Now we can check that against Kaggle. Unfortunately, this is an older competition and we are not allowed to enter anymore to see how we would have gone. So the best we can do is check whether it looks like we could have done well based on their validation set so it should be in the right area. Based on that, we would have come first.

I think this is an interesting series of steps. So you can go through the same series of steps in your Kaggle projects and more importantly, your real-world projects. One of the challenges is once you leave this learning environment, suddenly you are surrounded by people who never have enough time, they always want you to be in a hurry, they’re always telling you do this and then do that. You need to find the time to step away and go back because this is a genuine real-world modeling process you can use. And it gives, when I said gives world-class results, I mean it. The guy who won this, Leustagos, sadly he passed away but he is the top Kaggle competitor of all time. He won I believe dozens of competitions so if we can get a score even within cooee of him, then we are doing really well.

Clarification [1:01:31]: The change in R² between these two is not just due to the fact that we removed these three predictors. We also went reset_rf_samples() . So to actually see the impact of just removing, we need to compare it to the final step earlier.

So it’s actually compared to 0.907 validation. So removing those three things took us from 0.907 to 0.915. In the end, of course, what matters is our final model but just to clarify.

Writing Random Forest from scratch! [1:02:31]

Notebook

My original plan here was to do it in real time and then as I started to do it, I realized that would have been boring, so instead, we might do more of a walk through the code together.

Implementing random forest algorithm is actually quite tricky not because the code is tricky [1:05:03]. Generally speaking, most random forest algorithms are pretty conceptually easy. Generally speaking, academic papers and books have a knack of making them look difficult, but they are not difficult conceptually. What’s difficult is getting all the details right and knowing when you’re right. In other words, we need a good way of doing testing. So if we are going to reimplement something that already exists, like say we want to create a random forest in some different framework, different language, different operating system, I would always start with something that does exist. So in this case, we’re just going to do it as learning exercise, writing a random forest in Python, so for testing, I’m going to compare it to an existing random forest implementation.

That’s critical. Anytime you are doing anything involving non-trivial amounts of code in machine learning, knowing whether you’ve got it right or wrong is the hardest bit. I always assume that I’ve screwed everything up at every step, and so I’m thinking okay assuming that I screwed it up, how do I figure out that I screwed it up. Then much to my surprise from time to time, I actually get something right and then I can move on. But most of the time, I get it wrong, so unfortunately with machine learning, there’s a lot of ways you can get things wrong that don’t give you an error. They just make your result slightly less good and so that’s what you you want to pick up.

%load_ext autoreload
%autoreload 2
%matplotlib inline

from fastai.imports import *
from fastai.structured import *
from sklearn.ensemble import RandomForestRegressor,
RandomForestClassifier
from IPython.display import display
from sklearn import metrics

So given that I want to compare it to an existing implementation, I’m going to use our existing dataset, our existing validation set, and then to simplify things, I’m just going to use two columns to start with [1:06:44]. So let’s go ahead and start writing a random forest.

PATH = "data/bulldozers/"

df_raw = pd.read_feather('tmp/bulldozers-raw')
df_trn, y_trn, nas = proc_df(df_raw, 'SalePrice')
def split_vals(a,n): return a[:n], a[n:]
n_valid = 12000
n_trn = len(df_trn)-n_valid
X_train, X_valid = split_vals(df_trn, n_trn)
y_train, y_valid = split_vals(y_trn, n_trn)
raw_train, raw_valid = split_vals(df_raw, n_trn)
x_sub = X_train[['YearMade', 'MachineHoursCurrentMeter']]

My way of writing nearly all code is top-down just like my teaching. So by top-down, I start by assuming that everything I want already exists. In other words, the first thing I want to do, I’m going to call this a tree ensemble. To create a random forest, the first question I have is what do I need to pass in. What do I need to initialize my random forest. I’m going to need:

  • x: some independent variables
  • y: some dependent variable
  • n_trees: pick how many trees I want
  • sample_sz: I’m going to use the sample size parameter from the start here, so how big you want each sample to be
  • min_leaf: then maybe some optional parameter of what’s the smallest leaf size.
class TreeEnsemble():
def __init__(self, x, y, n_trees, sample_sz, min_leaf=5):
np.random.seed(42)
self.x,self.y,self.sample_sz,self.min_leaf =
x,y,sample_sz,min_leaf
self.trees = [self.create_tree() for i in range(n_trees)]

def create_tree(self):
rnd_idxs = np.random.permutation(len(self.y))
[:self.sample_sz]
return DecisionTree(self.x.iloc[rnd_idxs], self.y[rnd_idxs],
min_leaf=self.min_leaf)

def predict(self, x):
return np.mean([t.predict(x) for t in self.trees], axis=0)

For testing, it’s nice to use a constant random seed, so we’ll get the same result each time. So np.random.seed(42) is how you set a random seed. Maybe it’s worth mentioning for those of you who aren’t familiar with it, random number generators on computers aren’t random at all. They are actually called pseudo random number generators and what they do is given some initial starting point (in this case 42), a pseudo random number generator is a mathematical function that generates a deterministic (always the same) sequence of numbers such that those numbers are designed to be:

  • as uncorrelated with the pervious number as possible
  • as unpredictable as possible
  • as uncorrelated as possible with something with a different random seed (so the second number in the sequence starting with 42 should be very different to the second number starting with 41)

And generally, they involve using big prime numbers, taking mods, and stuff like that. It’s an interesting area of math. If you want real random numbers, the only way to do that is you can actually buy hardware called a hardware random number generator that’ll have inside them like a little bit of some radioactive substance and something that detects how many things it’s spitting out or there’ll be some hardware thing.

Question: Is current system time a valid random number generation [1:09:25]? So that would be maybe for a random seed (the thing we start the function with). One of the really interesting area is in your computer, if you don’t set the random seed, what is it set to. Quite often, people use the current time for security — obviously we use a lot of random number stuff for security, like if you are generating an SSH key, it needs to be random. It turns out people can figure out roughly when you created a key. They could look at oh, id_rsa has a timestamp and they could try all the different nanoseconds starting points for a random number generator around that timestamp and figure out your key. So in practice, a lot of high randomness requiring applications actually have a step that say “please move your mouse and type random stuff at the keyboard for a while” and so it gets you to be a source of “entropy”. Other approach is they’ll look at the hash of some of your log files or stuff like that. It’s a really really fun area.

In our case, our purpose actually is to remove randomness [1:10:48]. So we are saying okay, generate a series of pseudo random numbers starting with 42, so it always should be the same.

If you haven’t done much stuff in Python OO, this is basically standard idiom at least I write it this way, most people don’t, but if you pass in five things that you are going to want to keep inside this object, then you basically have to say self.x = x, etc. We can assign to a tuple from a tuple.

This is my way of coding. Most people thing this is horrible, but I prefer to be able to see everything at once and so I know in my code anytime I see something that looks like this, it’s always all of the stuff in the method being set. If I did it a different way, then half of the code now come off the bottom of the page and you can’t see it.

So that was the first thing I thought about — to create a random forest what information do you need. Then I’m going to need to store that information inside my object, and then I need to create some trees. A random forest is something that has some trees. So I basically figured to use list comprehension to create a list of trees. How many trees do we have? We got n_trees trees. That’s what we asked for. range(n_trees) gives me the numbers from 0 up to n_trees — 1. So if I create a list comprehension that loops through that range calling create_tree each time, I now have n_trees trees.

To write that, I didn’t have to think at all. That’s all obvious. So I’ve delayed the thinking to the point where it’s like well wait, we don’t have something to create a tree. Okay, no worries. But let’s pretend we did. If we did, we’ve now created a random forest. we’d still need to do a few things on top of that. For example, once we have it we need a predict function. Okay, let’s write a predict function. How do you predict in a random forest? For a particular row (or rows), go through each tree, calculate its prediction. So here is a list comprehension that is calculating the prediction for every tree for x. I don’t know if x is one row or multiple rows, it doesn’t matter as long as tree.predict works on it. And once you’ve got a list of things, a cool thing to know is you can pass numpy.mean a regular non numpy list and it will take the mean — you just need to tell it axis=0 means average across the lists. So this is going to return the average of .predict() for each tree.

I find list comprehensions allow me to write the code in the way the brain works [1:14:24]. You could take the words and translate them into this code, or you could take this code and translate them into words. So when I write code, I want it to be as much like that as possible. I want it to be readable and so hopefully you’ll find when you look at the fast.ai code trying to understand how Jeremy did x, I try to write things in a way that you can read it and turn it into English in your head.

We’ve nearly finished writing our random forest, haven’t we [1:15:29]? All we need to do now is write create_tree. We will construct a decision tree (i.e. non-random tree) from a random sample of the data. So again, we’ve delayed any actual thought process here. We’ve basically said ok, we could pick some random IDs. This is a good trick to know. If you call np.random.permutation passing in an int, it’ll give you back a randomly shuffled sequence from zero to that int. So if you grab the first :n items of that, that’s now a random subsample. So this is not doing bootstrapping (i.e. we are not doing sampling with replacement) here which I think is fine. For my random forest, I’m deciding that it’s going to be something where we do subsampling not bootstrapping.

np.random.permutation(len(self.y))[:self.sample_sz]

So here is a good line of code to know how to write because it comes up all the time. I find in machine learning, most algorithms I use are somewhat random and so often I need some kind of random sample.

Personally I prefer this over bootstrapping because I feel like most of the time, we have more data than we want to put in a tree at once [1:18:54]. Back when Breiman created random forest, it was 1999 and was a very different world. We now have too much data. So what people tend to do is fire-up a spark cluster and they will run it on hundreds of machines when it makes no sense because if they had just used a subsample each time, they could have done it on one machine. The overhead of spark is a huge amount of I/O overhead. If you do something on a single machine, it can often be hundreds of times faster because you don’t have this I/O overhead and it also tends to be easier to write the algorithms, easier to visualize, cheaper and so forth. So I almost always avoid distributed computing and I have my whole life. Even 25 years ago when I was starting in machine learning, I still didn’t use clusters because I always feel like whatever I could do with a cluster now, I could do with a single machine in five years time. So why not focus on always being as good as possible with a single machine. That would be more interactive and iterative.

So again, we delayed thinking to the point where we have to write decision tree [1:20:26]. So hopefully you get an idea that this top-down approach, the goal is going to be that we’re going to keep delaying thinking so long that eventually we’ve somehow written the whole thing without actually having to think. Notice that you never have to design anything. You just say, what if somebody already gave me the exact API I needed, how would I use it? Then to implement the next stage, what would be the exact API I would need to implement that? You keep going down until eventually you notice oh, that already exists.

This assumes we’ve got a class called DecisionTree , so we’re going to have to create that [1:21:13]. We know what we’re going to have to pass it because we just passed it. So we are passing in random sample of x’s and y’s. We know that a decision tree is going to contain decision trees which themselves contain decision trees. So as we go down the decision tree, there’s going to be some subset of the original data that we’ve kind of got so I’m going to pass in the indexes of the data that we’re actually going to use here. So initially, it’s the entire random sample. And we also pass down the min_leaf size. So everything that we got for constructing the random forest, we’ll pass down to the decision tree except, of course, num_tree which is irrelevant for the decision tree.

class DecisionTree():
def __init__(self, x, y, idxs=None, min_leaf=5):
if idxs is None: idxs=np.arange(len(y))
self.x,self.y,self.idxs,self.min_leaf = x,y,idxs,min_leaf
self.n,self.c = len(idxs), x.shape[1]
self.val = np.mean(y[idxs])
self.score = float('inf')
self.find_varsplit()

# This just does one decision; we'll make it recursive later
def find_varsplit(self):
for i in range(self.c): self.find_better_split(i)

# We'll write this later!
def find_better_split(self, var_idx): pass

@property
def split_name(self): return self.x.columns[self.var_idx]

@property
def split_col(self):
return self.x.values[self.idxs,self.var_idx]
   @property
def is_leaf(self): return self.score == float('inf')

def __repr__(self):
s = f'n: {self.n}; val:{self.val}'
if not self.is_leaf:
s += f'; score:{self.score}; split:{self.split}; var:{self.split_name}'
return s
  • self.n: how many rows we have in this tree (the number of indexes we’ve given)
  • self.c: how many columns we have (how ever many columns there are in the independent variables)
  • self.val: For this tree, what’s its prediction. Prediction of this tree is the mean of our dependent variable for those indexes. When we talk about indexes, we are not talking about the random sampling to create the tree. We’re assuming this tree now has some random sample. Inside decision tree, the whole random sampling thing is gone. That was done by the random forest. So at this point, we are building something that is just a plain old decision tree. It’s not in any way a random sampling anything. So indexes is literally which subset of the data have we got to so far in this tree.

A quick Object Oriented Programming primer[1:24:50]

I’ll skip this but here is the funny bit about self:

You can call it anything you like. If you call it anything other than “self”, everybody will hate you and you’re a bad person. [1:29:24]

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