51 karma · joined March 23, 2011
Instead this process is left to the individual corporations. So, you get mixed results in judging quality, because there is no standardization.
This statement is complete bullshit. The California DMV doesn't have any clear details defining operations of vehicles at this point in time. They only have rules about what is required to test on public roads. This includes 5 million dollar bond, applying for permit, etc...[1]
This statement alone (if correct from the reporter) makes me nervous about the amount of spin going on.
[1] : http://www.dmv.ca.gov/portal/wcm/connect/d48f347b-8815-458e-...
I believe that one of two things will arise when you go to write up a mathematical proof. One, you will be dependent on a statistical test that makes a normal distribution assumption implicitly or explicitly. Two, you will dependent on a bound that only applies in the limit. There is a third possibility, which is the most interesting to me, which is that you are dependent on a period of stationarity in your data, in other words, the distribution you are measuring must be stationary.
The proofs in the MAB papers are not intentionally obtuse or ignoring mainstream statistical ideas. They are written that way to say very explicit things under well defined assumptions. Locking down assumptions and being very precise is what writing down a mathematical proof is all about.
I believe further discussion will not be productive. But, I suggest if you have a proof about A/B testing as it relates to the MAB problem or even if you have a proof about A/B testing in general that drops the normally distributed assumption or tells you exactly when to switch from exploring to exploiting, I suggest you write it up and publish it on arXv.
Thanks for your time.
Second, I believe I am getting hung up on the fact that different arrival times are "weighted" differently. I think you are claiming that the Poisson assumption gives us equal numbers of A and B trials, so we can combined the statistics (counts) and avoid Simpson's paradox. This is fine, but why would you say "different times of arrival are not weighted the same". Does this mean you are somehow weighting periods of heavy traffic down and weighting low traffic up?
So, what happens when trial A becomes less favorable over time or is less favorable for brief periods? This means that the underlying random variable's mean is changing over time. Most statistical bounds cannot handle this situation.
I am not saying that A/B testing is not something we should do in general. I am saying that it is a good heuristic with very few provable properties compared with logarithmic regret MAB algorithms.
I think you said one thing that are at the heart of the issue. We assume that the E[conversion of B] > E[conversion of A] for the entire period sampled.
I think all of the details about Poisson processes are not required if you just assume that each person is drawn IID from the population.
I just don't think you are answering the right questions here.
Let's assume that each person arrives IID from the infinite population. Then, we have a Bernoulli process for each A or B query. A "conversion" results in a 1, a failure results in a 0. Since, these people are arriving IID, we can select a sub-sample which is also IID. We would now like to estimate the parameters for each process and/or compare the two processes. We can do this using t-test. This will give us the statistical significance that the one group had a higher "conversion rate" than the other group. Note: rate does not factor into this problem at all because we assume the participants were IID, so the t-test (used correctly accounting for different number of samples) will tell us which test is larger.
My question is now what happens when the parameters of your queries for A or B change over time. Still under the assumption that E[B] > E[A], it now matters greatly in which order you use your samples.
I think the only reason you brought the Poisson model into the discussion is to weight the more recent samples higher and down weight the earlier samples in your basket of samples. This is a heuristic for considering a fixed interval in which the samples are stationary. It effectively considers a window that slides with the time of arrival.
I am slightly confused and this may demonstrate my ignorance, but I was under the impression that A/B testing worked by allocating two different approach to the users and then scoring the response. This provides a sampling from the population of users as to how effective A or B is. You can then run some statistical test on the averages of the scores for each test to determine which one is the winner.
If what I said is true, these statistical tests almost always assume that the distribution that is being drawn from is stationary. So, the only way things work out is if you have an underlying stationary distribution. Otherwise, your statistical test might indicate the wrong thing.
I freely admit that many of your points are still valid, but I don't see how A/B is a more powerful algorithm that has less assumptions.
But, to be clear, this is a heuristic in A/B testing. If you have a window of time over which you know your distributions are stationary, you should always use a logarithmic regret MAB algorithm because it is theoretically better.
I think the best way to frame this argument is that because the domain does not match the assumptions of MAB, A/B testing has been shown to be robust and easy to modify for non-stationary domains, while logarithmic regret algorithms are somewhat more fragile.
I have some experience with the medical trial literature and specifically bandit algorithms and using cumulative regret verses other statistical measures like PAC frameworks. And regret is most certainly not a Bayesian idea. Instead you are explicitly modeling the cost of each action (providing an A or B test to a user) instead of assuming all costs are equal.
Yes, this is a better approach because it explicitly models the costs associated with the exploration/exploitation dilemma. But, it is not Bayesian.
But, I believe there is a method to the madness. They have so many qualified applicants that they would rather err on the side of caution. They would rather reduce the false-positives even if the number of false-negatives grows. They can afford this luxury. They want the best and they can afford rejecting good candidates.
My favorite way of thinking about this was from Steve Yegge's blog post about the interview process : "Because of the inherently flawed nature of the interviewing process, it's highly likely that someone on the loop will be unimpressed with you, even if you are Alan Turing. Especially if you're Alan Turing, in fact, since it means you obviously don't know C++"