The Anvil

A place to hammer out ideas

All I Overfitting for Overfitting is Overfitting

November 23, 2021

A couple of weeks ago I used Forecast Forge to build a forecast for the number of pageviews of the “All I Want for Christmas is You” wikipedia page in the run-up to Christmas.

pageviews for the “All I Want For Christmas is You” wikipedia page will peak on 24th December close to 30k

This forecast “looks” good - it has the peak roughly when we’d expect it and the magnitude is comparable with previous years. It passes the smell test, but I am still concerned about whether it predicts the size of the peak correctly. As you can see from the chart, the peak in 2019 was way higher than any of the preceeding years and getting this right is the most important part of my prediction. How can we tell in advance what kind of peak there is going to be?

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Forecasting for Paid Media

November 16, 2021

PPC and Google Ads is where I first started in my career so it has a special place in my heart. I have a million ideas on how forecasting and Forecast Forge can help in this industry and they are all logjammed up in my head waiting for me to write “The Ultimate Guide to PPC Forecasting” or something like that.

You could say I’m having some supply chain issues with keeping the blog posts flowing so I thought I’d just get something out there with some of my thoughts even if it isn’t everything.

Using Daily Spend as a Regressor Column

When thinking about which factors inflience paid channels one of the most important and most obvious ones is the amount of money you spend! Spend more money, get more clicks/conversions/revenue etc. How much more is an important question which I’ll get to later.

Without data on how much was spent any machine learning algorithm will struggle to tell the difference between changes in budget and other factors (e.g. seasonality, growth in the market etc.). Was June a big month because conversion rates are higher in June or is it just that the budget was a lot higher?

In Forecast Forge you need to specify the values for any regressor columns into the future in order to make a forecast. This is easier with paid media budgets than it is with something like the weather because people generally have a budget plan for the year ahead which can be a good starting point.

Transform the Data

You can think of a very simple model of paid media performance as being something like this:

output = media spend * other stuff

  • output is whatever metric you are interested in; normally revenue, conversions or clicks
  • media spend is the amount of money you spent
  • other stuff is everything else from cost per clicks to conversion rates and the seasonalities in all these things
  • media spend and other stuff are multiplied together because if either one of them is zero then output needs to be zero

One of the good things about machine learning is that we can give is a vague model like this and it can fill in a lot of the details for us. The big idea here is that you can train the Forecast Forge algorithm on historical output and media spend data so that it will learn all the important patterns in the other stuff.

Things like the long term trend in CPA are part of other stuff

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All I Want for Christmas is You

November 9, 2021

Every year someone notices Google Trends rising for “All I Want for Christmas is You”. It signals the start of the Christmas period for some. How high will it get this year?

Rather than forecast the Google Trend (complicated because the whole scale will be redone if Christmas 2021 is bigger than previous years) let’s look at the amount of traffic to the All I Want for Christmas is You wikipedia page. This data is freely available from Toolforge

Given this data from 2015 up until yesterday what will the pageviews forecast look like for this year?

Running the most basic Forecast Forge forecast looks like this:

There are a few good things here; the algorithm has clearly learned that something big happens in December and it isn’t doing anything too crazy like predicting negative values. But, it seems to me, that the algorithm is massively underestimating the scale of the “All I Want for Christmas is You”-mania that is likely to happen in 2021.

The above statement is partially me making a judgement call (I think it is possible but unlikely that the wikipedia page will see the lowest levels of traffic since 2015) ad partially me knowing that the default Forecast Forge algorithm will struggle to fit seasonalities as extreme as we see in the training data.

This kind of thing is a tradeoff that all machine learning approaches will have to make somewhere; the flexibility required to fit extreme seasonality like this would also allow the algorithm to overfit in other situations where there is random noise. Unfortunately I can’t just make a few easy tweaks behind the scenes to Forecast Forge and have it magically work for this forecast and all the others. So I’m going to have to get creative to improve things.

The first thing to do is to look at the chart and try to figure out what kind of seasonal pattern there is.

To me, it looks like there is two parts to it:

  1. A triangular “sawtooth” or sharksfin part that rises in a straigtish line starting roughly at the start of November (in green on the above chart)
  2. An extra massive spike on top of that a few days before Christmas

You can add regressor columns to help fit both of these patterns as long as the pattern is the same every year; to me, this looks fairly close to the truth for the sawtooth section, but less so for the extra spike.

You can easily add a sawtooth regressor by having an ascending count of days since November 1st. The count resets back to zero after December 25th and then starts again on November 1st the next year. The machine learning then makes sure that the slope of the sawtooth in the forecast is the best fit for the training data.

This looks much more like it! Now let’s add another regressor for the big spike. This is a bit more of a judgement call; I’ve added it just for December 24th and 25th but you could spread it out across more days. You could even do a “final week” sawtooth if that was a better fit for the data (the end result would be two sawtooths stacked on top of each other).

The forecast with this method is quite similar to with just the sawtooth but the extra regressor column allows for a slightly higher peak:

There is a bit more work that could be done here; Maria re-released her Merry Christmas album in 2019 which is probably why that year is so high and in 2020 she was in an Apple TV Christmas special. As far as I can figure out this will not be happening in 2021 although she has released a new collaboration with Khalid on November 5th.

My Predictions

Here is the output from the spreadsheet:

Date Prediction Lower Upper
2021-11-09 2701.5888 933.3499 4348.9477
2021-11-10 2682.6904 854.7259 4306.5129
2021-11-11 2242.9998 589.6002 3947.8674
2021-11-12 2789.1958 1155.4217 4406.2187
2021-11-13 2884.0697 1233.5695 4521.535
2021-11-14 2840.468 1175.7148 4467.9262
2021-11-15 2773.708 1131.5298 4453.812
2021-11-16 2905.6589 1245.4681 4539.7813
2021-11-17 2884.595 1224.1054 4577.9736
2021-11-18 2884.4741 1289.0322 4562.5815
2021-11-19 3054.9337 1390.5864 4709.1608
2021-11-20 3217.4772 1612.2704 4874.9197
2021-11-21 3265.6522 1632.845 4960.8326
2021-11-22 3314.3094 1619.6743 4993.7539
2021-11-23 3584.3009 1864.77 5178.3117
2021-11-24 3722.3373 2156.4043 5292.8001
2021-11-25 4384.6715 2814.9402 6022.6639
2021-11-26 4265.1745 2614.3949 5941.3971
2021-11-27 4635.4638 3060.204 6283.3784
2021-11-28 4901.2347 3226.3424 6635.7226
2021-11-29 5173.5339 3503.3519 6708.9453
2021-11-30 5669.1416 4109.9755 7399.4489
2021-12-01 6030.5107 4343.4766 7548.4478
2021-12-02 6425.1478 4789.5011 8058.7572
2021-12-03 6995.7313 5283.9031 8609.2387
2021-12-04 7556.4337 5908.5305 9160.5009
2021-12-05 7993.2462 6302.7588 9727.1532
2021-12-06 8413.3941 6848.6404 10127.1566
2021-12-07 9030.1956 7443.3617 10697.0961
2021-12-08 9483.0803 7868.2572 11107.7753
2021-12-09 9937.0423 8334.207 11471.425
2021-12-10 10532.8194 8867.4962 12239.714
2021-12-11 11083.2638 9405.8618 12767.5931
2021-12-12 11473.7037 9793.7552 13088.434
2021-12-13 11811.3794 10179.6077 13573.654
2021-12-14 12310.3101 10745.9551 13821.3437
2021-12-15 12611.304 10898.2507 14210.6269
2021-12-16 12881.3891 11313.0435 14636.3938
2021-12-17 13263.9547 11621.3222 14995.5465
2021-12-18 13575.0713 11911.9019 15199.5681
2021-12-19 13703.7888 12058.1878 15352.9095
2021-12-20 13761.4983 12084.2751 15449.1159
2021-12-21 13966.7143 12321.3525 15731.7209
2021-12-22 13964.9939 12298.5484 15571.1297
2021-12-23 13928.2702 12310.1036 15504.8029
2021-12-24 30545.7591 28752.9632 32184.656
2021-12-25 27777.4519 26100.9902 29496.8692
2021-12-26 5774.8394 4123.2926 7438.3634
2021-12-27 5413.7454 3782.4206 6990.3051
2021-12-28 5219.4467 3666.0143 6968.5325
2021-12-29 4841.2889 3146.788 6405.508
2021-12-30 4454.5088 2644.2621 6213.2783
2021-12-31 4691.3097 2973.0348 6339.3716

A quick, easier to check prediction; pageviews for the “All I Want For Christmas is You” wikipedia page will peak on 24th December close to 30k. I will check in again with how this is looking nearer the time and also show you some other forecasting methods.

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Tips for reducing the width of the predictive interval

October 7, 2021

In my last post I talk about how you can use a forecast to measure the impact of a some kind of change (e.g. Google rewriting your title tags in the SERP). One of the main difficulties you might find with this is that the width of the predictive interval is too wide to conclude that a change has had a positive/negative effect with XX% probability.

In this case there we expect there to be a positive difference overall, but we cannot be 95% certain that there has been a positive change

What do you do if your best guess is that the test has a positive outcome but you aren’t 95% sure? Will Critchlow has written about this kind of issue which they sometimes see at Search Pilot. Will has a set of recommendations they use in this situation based around the mantra “we’re doing business, not science” which is an important rule to remember (unless you are a scientist!).

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Measuring the impact of Google's Title Rewrite Change

September 29, 2021


On 24th August 2021 Google announced a change in how page title’s would be displayed in search results. The new system means that Google’s machine learning systems will more often display a custom page title in the links on a search engine results page; before there was less rewriting being done and the contents of the <title> tag was more likely to be used.

Barry Schwartz has written a good summary of the ins and outs of this over at Search Engine Land.

As with any algorithm change, Google are saying that this improves results overall but there are some people for whom the new titles seem to be performing significantly worse.

If something is a lot worse or better than it was previously then you don’t need fancy statistics to be able to see that.

If whatever you are looking at has the same impact as the Moderna covid vaccine then plotting the right chart should be more than enough to convince anyone

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