Better call Thomas – Bayes in the Database

This is my third and last post covering my presentations from last week’s Tech Event, and it’s no doubt the craziest one :-).
Again I had the honour to be invited by my colleague Ludovico Caldara to participate in the cool “Oracle Database Lightning Talks” session. Now, there is a connection to Oracle here, but mainly, as you’ll see, it’s about a Reverend in a Casino.

So, imagine one of your customers calls you. They are going to use Oracle Transparent Data Encryption (TDE) in their main production OLTP database. They are in a bit of panic. Will performance get worse? Much worse?

Well, you can help. You perform tests using Swingbench Order Entry benchmark, and soon you can assure them: No problem. The below chart shows average response times for one of the transaction types of Order Entry, using either no encryption or TDE with one of AES-128 or AES-256.
Wait a moment – doesn’t it even look as though response times are even lower with TDE!?

Swingbench Order Entry response times (Customer Registration)

Well, they might be, or they might not be … the Swingbench results include how often a transaction was performed, and the standard deviation … so how about we ask somebody who knows something about statistics?

Cool, but … as you can see, for example, in this xkcd comic, there is no such thing as an average statistician … In short, there’s frequentist statistics and there’s Bayesian, and while there is a whole lot you can say about the respective philosophical backgrounds it mainly boils down to one thing: Bayesians take into account not just the actual data – the sample – but also the prior probability.

This is where the Reverend enters the game . The fundament of Bayesian statistics is Bayes theorem, named after Reverend Thomas Bayes.

Bayes theorem

In short, Bayes Theorem says that the probability of a hypothesis, given my measured data (POSTERIOR), is equal to the the probability of the data, given the hypothesis is correct (LIKELIHOOD), times the prior probability of the hypothesis (PRIOR), divided by the overall probability of the data (EVIDENCE). (The evidence may be neglected if we’re interested in proportionality only, not equality.)

So … why should we care? Well, from what we know how TDE works, it cannot possibly make things faster! In the best case, we’re servicing all requests from the buffer cache and so, do not have to decrypt the data. Then we shouldn’t incur any performance loss. But I cannot imagine how TDE could cause a performance boost.

So we go to our colleague the Bayesian statistian, give him our data and tell him about our prior beliefs.(Prior belief sounds subjective? It is, but prior assumptions are out in the open, to be questioned, discussed and justified.).

Now harmless as Bayes theorem looks, in practice it may be difficult to compute the posterior probability. Fortunately, there is a solution:Markov Chain Monte Carlo (MCMC). MCMC is a method to obtain the parameters of the posterior distribution not by calculating them directly, but by sampling, performing a random walk along the posterior distribution.

We assume our data is gamma distributed, the gamma distribution generally being adequate for response time data (for motivation and background, see chapter 3.5 of Analyzing Computer System Performance with Perl::PDQ by Neil Gunther).
Using R, JAGS (Just Another Gibbs Sampler), and rjags, we (oh, our colleague the statistian I meant, of course) go to work and create a model for the likelihood and the prior.
We have two groups, TDE and “no encryption”. For both, we define a gamma likelihood function, each having its own shape and rate parameters. (Shape and rate parameters can easily be calculated from mean and standard deviation.)

model {
    for ( i in 1:Ntotal ) {
      y[i] ~ dgamma( sh[x[i]] , ra[x[i]] )
    }
    sh[1] <- pow(m[1],2) / pow(sd[1],2)
    sh[2] <- pow(m[2],2) / pow(sd[2],2)
    ra[1]  <- m[1] / pow(sd[1],2)
    ra[2]  <- m[2] / pow(sd[2],2
    [...]

Second, we define prior distributions on the means and standard deviations of the likelihood functions:

    [...]
    m[1] ~ dgamma(priorSha1, priorRa1)
    m[2] ~ dgamma(priorSha2, priorRa2)
    sd[1] ~ dunif(0,100)
    sd[2] ~ dunif(0,100)
  }

As we are convinced that TDE cannot possibly make it run faster, we assume that the means of both likelihood functions are distributed according to prior distributions with the same mean. This mean is calculated from the data, averaging over all response times from both groups. As a consequence, in the above code, priorSha1 = priorSha2 and priorRa1 = priorRa2. On the other hand, we have no prior assumptions about the likelihood functions’ deviations, so we model them as uniformly distributed, choosing noninformative priors.

Now we start our sampler. Faites vos jeux … rien ne va plus … and what do we get?

Posterior distribution of means

Here we see the outcome of our random walks, the posterior distributions of means for the two conditions. Clearly, the modes are different. But what to conclude? The means of the two data sets were different too, right?

What we need to look at is the distribution of the difference of both parameters. What we see here is that the 95% highest density interval (HDI) [3] of the posterior distribution of the difference ranges from -0.69 to +1.89, and thus, includes 0. (HDI is a concept similar, but superior to the classical frequentist confidence interval, as it is composed of the 95% values with the highest probability.)

Posterior distribution of difference between means

From this we conclude that statistically, our observed difference of means is not significant – what a shame. Wouldn’t it have been nice if we could speed up our app using TDE 😉

Advertisements

Tune the App, Not the SQL – DBA Sherlock’s Adventures in Hibernate/jOOQ Land

Last weekend at Trivadis Tech Event, in addition to my session on Oracle 12c Client High Availability for Java (Application Continuity, Transaction Guard … choose your degrees of freedom”), I gave a quite different talk called Tune the App, Not the SQL – DBA Sherlock’s Adventures in Hibernate/jOOQ Land”.

In a nutshell, what is it all about? Well, if you’re a DBA, you might sometimes (or often, or seldom – depends on your job ;-)) do what we call “SQL Tuning”. It might look like this: You get a call that the application “is slow”. Fortunately, you’re able to narrow that down quickly, and it’s just “the click on that button” that is slow. Fortunately, too, the application is well instrumented, and getting traces for specific tasks is not a problem. So you get a SQL trace file, run tkprof on it, and obtain the problematic SQLs in order of elapsed time. Then you analyse the “Top SQL”. You may find it should be rewritten, or that it would benefit from an index. Perhaps adding additional data structures might help, such as creating a materialized view. Perhaps you’re unlucky and just an ugly hint will fix it.

So you tell the developers “please rewrite that, like this”, or you create that index. And after, it’s waiting and hoping that performance will improve – noticeably, that is. Because tuning that single statement might – if you’re unlucky – not make that much of a difference.

There is, however, another approach to tuning application performance (always talking about the DB related part of it here, of course), and that has to do with the application logic and not single statements. There is an excellent demonstration of this in Stéphane Faroults very recommendable book “Refactoring SQL applications”, in fact, this is right at the beginning of the book and something that immediately “draws you in” (it was like that for me :-)).

Application logic affects what, when, and how much data is fetched. Of course, there are many aspects to this – for example, it just may not be possible to replace two DB calls by one simply because another service has to be queried in between. Also, there will have to be a tradeoff between performance and readability/maintainability of the code. But often there will be a choice. And you will see in the presentation it is not always that combining two queries into one results in better performance.

In fact, it all depends. So the first conclusion is the ubiquitous “don’t just assume, but test”.

There is another aspect to this, though. While Stéphane Faroult, in his test case, uses plain JDBC, I am using – and comparing, in a way – two commonly used frameworks: Hibernate and jOOQ. (For an “interdisciplinary introduction” to Hibernate, see my talk from previous Tech Event, Object Relational Mapping Tools – let’s talk to each other!. Quite a contrast, jOOQ is a lightweight, elegant wrapper framework providing type safety and near-100% control over the generated SQL.)

Now while for a DBA looking at a raw trace file, it will always be a challenge to “reverse engineer” application logic from the SQL sent to the database (even if plain JDBC or jOOQ are being used), the difficulties rise to a new dimension with Hibernate :-). In the talk, I am showing a DBA – who doesn’t need to be convinced any more about the importance of application logic – trying to make sense of the flow of statements in a trace file: the only information he’s got. And it turns out to be very difficult …

But as he’s not just “some DBA”, but Sherlock, he of course has his informants and doesn’t remain stuck with his DB-only view of the world – which brings me to one of my ceterum censeo’s, which is “DBAs and developers, let’s talk to each other” :-).

The slides are here.