Not sure about bad labels, but semi-supervised learning is the term for training on data with a lot of missing labels. Essentially the algorithm makes predictions on the unlabeled data and uses its highest confidence predictions as additional training data. Generative models can also "dream up" entirely new training examples. There is a risk of amplifying the confidence in bad predictions, but it works well overall (better than using only the labeled portion of the data).

> Is there any statistical/mathematical tool to completely eradicate or greatly diminish the effects of bad labeling

Yes, it's called statistics and probability theory.

> Yes it's called statistics and probability theory.

My understanding of statistics is:

- I can halve the % insanity by adding another 100% of good labels.

- If I want to reduce the insanity of labels to 1/33th of ~33% I need to add another 3200% of good labels.

- If I want to reduce the insanity to 0% I need to balance the bad labels with an infinite amount of good labels.

Is there anything I'm missing entirely except probability theory? Is probability theory the answer or is there something else?

You don't reach 0%, that's a straw man. The goal is better than human, and the 35,000+ vehicle-related fatalities that happen in the U.S. each year.

There's a disconnect here.

People who talk about the danger of humans driving cars always seem to talk about the raw numbers, because humans drive cars a lot and the raw numbers are rather large.

But when we talk about automated driving, it's in percentages, because it's not being done on the same scale.

So to compare apples to apples, you'd have to convert the number of fatalities to an accuracy percentage. Have you considered trying? There is certainly more than one way to do it, but it would greatly contribute to the discussion if you made some attempt.

> you'd have to convert the number of fatalities to an accuracy percentage

Telsa's early results for their very limited "self-driving" technology has shown a huge reduction in accidents for any given period of time the vehicles are on the road.

That seems like it incorporates a lot of assumptions. I think it's best to slow down and realize that comparisons don't mean much if you're comparing the wrong things. The first step is to determine the first thing that you are comparing and exactly what it is. Then you can move on to the other half and determine whether it is appropriate.

Humans are much safer than people on average, when driving in conditions suitable for Autopilot.

> Humans are much safer than people on average

This makes zero sense and isn't how "average" works. For the same 1000 hours on the road, a Tesla car with Autopilot will have fewer accidents than a car driven for 1000 hours by humans. This changes as driving conditions get worse, and humans outperform Autopilot.

Deleting half a sentence and saying it doesn't make sense?

The way "average" works is that you average over something - a population or set. It is very important to be clear about what that something is and whether it's appropriate.

Why do you believe that Autopilot outperforms humans in comparable conditions? If this is based on Tesla marketing, I'm extremely prejudiced against them, and assume out of hand that they simply aren't making the right comparison and don't care. However, if you think that is incorrect, you could elaborate on why you have the opinion you do.

The average of something cannot be more than the average of... itself. Thus, "Humans are much safer than people on average" is nonsensical.

> Why do you believe that Autopilot outperforms humans in comparable conditions?

Because they have the data that proves it?

> I'm extremely prejudiced against them

And I've chosen to take them at face value with a grain of salt, and to believe that for the data they've collected from the hundreds of thousands of Tesla's with millions of hours of data using Autopilot, it's fair to say they have a large enough sample to draw conclusions about the safety of their cars vs. any incident rates from pretty much any other distribution.

"Thus, "Humans are much safer than people on average" is nonsensical."

Does it make more sense as "Humans, when driving in conditions suitable for Autopilot, are much safer than people on average"?

"I've chosen to take them at face value with a grain of salt, and to believe that for the data they've collected from the hundreds of thousands of Tesla's with millions of hours of data using Autopilot, it's fair to say they have a large enough sample to draw conclusions about the safety of their cars vs. any incident rates from pretty much any other distribution"

You seem to be saying that if you have a lot of data it doesn't matter what you compare it to. That seems wrong to me. Also, I don't have this data, and you are not bothering to help me find it.

> Humans, when driving in conditions suitable for Autopilot, are much safer than people on average

The immaterial distinction between "humans" and "people" still makes that sentence confusing. I take it that you mean "driving a mile (either as human or autopilot) is safer in conditions that are good for autopilot than driving a mile in average conditions"? Or more directly, isn't your question really "are the conditions the same for the averaged human drivers and the averaged autopilots"?.

"isn't your question really "are the conditions the same for the averaged human drivers and the averaged autopilots"?"

My implication is that I severely doubt the conditions are the same, when somebody touts a comparison, and I would need clear and convincing evidence otherwise to change my mind. As well as strong evidence of good intent and trustworthiness by the source of the information.

It's not just about being intentionally deceitful, but about the fact that it's hard to do the right comparison, so people feel justified in giving up on it.

"Our secret telemetry dataset gives us reason to believe that the cars produced by us are not safe."

Would a statement like this be a surprise for you?

Only because you made it up to spread FUD. Good job.

It's hard to reach 0% bad labels because:

1. You can't have an infinite amount of good labels 2. Humans are in charge of labeling too.

The question is if you can reliably overcome the number of bad labels in your training set, so that 33% of bad labels equates to <33% "insanity" in the system.

Your understanding is wrong for anything nonlinear. The whole reason machine learning is useful is because it is nonlinear.

How nonlinear are we talking? My understanding is probably closer to the truth than to the opposite of the truth. I'm looking for an estimate of how far from the truth I am.

How would a system reliably discredit missing labels while still learning from good labels? The simplest solution would be that system is able to spot the bad/missing labels itself with some certainty, but that seems like a catch 22.

That's correct. I know what goes in and what comes out, not what happens in the middle. How does ~33% insanity in become < ~33% insanity out?

Edit: Parent was edited, was previously (paraphrased)

> I'm guessing you have no technical understanding of how this works

How does making up something ridiculous like "33% insanity" give you anything that's resembles a subject that we can discuss? Hyperbole in, hyperbole out.

I'm 33% insane myself. I believe that's part of what makes me human.

We have a lot more than the gut feeling you're assuming: https://arxiv.org/abs/1611.03530

Maybe we could use deep learning? Oh, wait...