It's Not Mathemagic

It's Not Mathemagic

The mathematics doesn't have to be simple. But when an important decision depends on it, the reasoning shouldn't have to be a secret.

I've been working with statistical models for a long time.

Some fairly straightforward.

Some, considerably more complex.

And occasionally, some that required me to dig out a textbook and get reacquainted the ins-and-outs of something I’d forgotten.

But here's something I've never quite understood.

Why do some software companies seem so reluctant to explain the mathematics behind their products?

I mean...

It's… just… math.

You know… “statistics.”

What are they hiding?

The Great and Powerful Algorithm

A few years ago – maybe 2018 or 2019 – I was evaluating a new AI/ML capability offered by a software provider we were already using.

Artificial Intelligence.

Machine Learning.

Some pretty exciting stuff.

A lot of it over-hyped.

And most of it way over-priced.

This new capability was supposed to “radically improve” our lead and pipeline scoring.

Naturally, a colleague and I had some questions.

What exactly was this thing doing?

What methodology was it using?

What assumptions were being made?

Our account executive did his best explain the machinery, but we were asking questions that went beyond the sales presentation.

Fair enough.

So he arranged a meeting with one of their product engineers.

You know… someone who could explain what was happening behind the curtain.

And when we finally to take a peek…

Ordinary least squares.

Essentially, they were using OLS to predict a binary outcome.

Now, that's not automatically wrong.

There are circumstances where a linear probability model can be useful.

But there are also statistical considerations that come with using that approach.

And as we dug further into the details, we discovered some additional methodological hand-waving that could compromise the reliability of the results.

My colleague and I recognized the problems.

The product engineer didn't appear to.

Great…

We'd come expecting something pretty sophisticated and advanced.

Instead, we'd found some pretty basic stuff being applied in ways that weren’t totally kosher.

We passed on the upgrade.

Pay no attention...

Remember The Wizard of Oz?

The smoke.

The flames.

The booming voice.

The enormous floating head.

And then Toto pulls back the curtain.

“Pay no attention to that man behind the curtain.”

Yep.

Nothing to see here.

Keep moving along.

I've occasionally had that same feeling when evaluating platforms that employ analytics.

Enter a few numbers.

Click a button.

Out comes a result.

Voilà!

The Great and Powerful Algorithm has spoken.

How did it arrive at that result?

What assumptions were made?

What happens if those assumptions aren't true?

Well...

That's the special sauce.

And to be fair, not everyone selling an analytical product needs to understand every equation under the hood,

But somebody has to.

And when a customer (or prospective customer) asks reasonable questions about the methodology, there ought to be reasonable answers.

It's probably not really special sauce

Here's what makes this especially puzzling to me.

I've used statistical software like SAS, EViews, and LIMDEP for decades.

These applications perform some extraordinarily sophisticated mathematics.

Ordinary least squares.

Maximum likelihood estimation.

Time-series models.

Panel estimation.

All sorts of things that can make your head hurt if you haven't spent much time with them.

But if I want to understand how those methods work, I can find detailed documentation.

The equations.

The estimation procedures.

The assumptions.

The statistical properties.

Sometimes I understand everything I'm reading.

Sometimes I have to work at it.

And sometimes...

Well, there are people out there who are a lot smarter than I am.

But the information is there.

Nobody is asking me to believe in mathemagic.

And SAS and EViews haven't become less valuable because they explain their methods.

Quite the opposite.

Their value isn't that they invented ordinary least squares or maximum likelihood estimation.

It's that they've made established mathematical methods accessible, reliable, computationally practical, and useful.

They don't need to pretend the mathematics is magic.

Open Box. Not Black Box.

Now, I'm not suggesting software companies need to publish their proprietary source code.

That's an entirely different deal.

Open Box doesn't mean Open Source.

But if an application produces an analytical result that might influence an important decision, I think we ought to be able to understand how that result was produced.

What methodology was used?

Why was it appropriate?

What assumptions does it depend upon?

What are its limitations?

What does (and doesn’t) the result actually establish?

I'm not suggesting that every user be inundated with a wall of equations every time they open an application.

That would be ridiculous.

Good design should make sophisticated tools accessible to people who don't necessarily understand all the underlying mathematics.

But accessibility shouldn't come at the expense of transparency.

You shouldn't have to understand every equation to use a tool.

But you should be able to examine the equations when you need to.

And perhaps more importantly, you should be able to scrutinize the reasoning.

Because showing me the math doesn't prove it's the right math.

Showing me the assumptions doesn't prove they're reasonable.

And showing me the calculations doesn't establish that we're answering the question we actually needed answered.

But at least it gives us an opportunity to find out.

The hard part isn't always the math

There's something else I've come to appreciate over the years.

The mathematics is often the relatively straightforward part.

But not always.

Some of it is extraordinarily difficult.

Often however the real challenge in applied analytics lies in everything surrounding the equations.

Understanding the business problem.

Asking the right question(s).

Selecting an appropriate method.

Recognizing the assumptions.

Understanding the limitations.

And interpreting what the results actually mean (and don’t).

You can execute a mathematical procedure perfectly and still arrive at a conclusion that isn't supported by the evidence.

And making the procedure more sophisticated doesn't necessarily improve the situation.

Sometimes it just makes the problem harder to recognize.

Math can't fix a bad question.

And sophisticated math can't rescue an inappropriate methodology.

That's why I want to know what's happening behind the curtain.

Not because I expect to find something wrong.

Because I want to understand what makes the answer worth trusting.

For lack of a conclusion...

I don't expect everyone to understand the mathematics behind every analytical tool they use.

I certainly don't.

But when we're relying on mathematics to support an important decision, somebody ought to understand what's happening.

And the rest of us ought to be able to ask.

What did you calculate?

Why?

What assumptions did you make?

And what would change your conclusion?

If the answers are complicated, that's okay.

I'll get another cup of coffee.

Maybe dig out a textbook.

But please...

Don't tell me to pay no attention to the man behind the curtain.

It's not mathemagic.

It's math.

Show me.