WEBVTT 00:01.470 --> 00:06.270 Hello everyone and welcome to our next talk which is mine. 00:06.510 --> 00:23.670 To introduce myself, which is wrong, I did a postdoc in machine learning after getting my PhD in algebraic topology with some of the people who did some of the math behind the concepts in this talk and I've just extended it for this thing. 00:23.670 --> 00:27.750 So that's enough about me. 00:28.070 --> 00:30.810 Let me play my talk back for you. 00:32.490 --> 00:34.530 So, here we go. 00:34.530 --> 00:42.610 I welcome everyone to my talk on calculating concepts very quickly with this library called Google which is based on... I 00:59.530 --> 01:01.730 hear no audio. 01:05.790 --> 01:06.930 Oopsie daisy. 01:28.690 --> 01:31.430 Um, there's no... do you hear audio from the talk? 01:38.900 --> 01:41.260 Okay, well that's the problem I'm trying to... 02:02.030 --> 02:04.050 Uh, sorry about this guys. 02:22.810 --> 02:27.950 Uh, sorry, I don't know what's going on. 03:18.250 --> 03:23.590 Um, I am... I'll apologize. 03:34.220 --> 03:39.140 Key takeaway for this talk is this is a novel way of calculating drift. 03:39.980 --> 03:47.160 Welcome everyone to my talk on calculating concept drift very quickly with this library called Google which is based on cover trees. 03:47.260 --> 03:48.560 My name is Sven Kittel. 03:48.560 --> 03:53.940 I am a senior data scientist at Elastic and my Twitter handle is co-mathematician. 03:54.480 --> 04:01.660 So, the key outline... key takeaway for this talk is this is a novel way of calculating drift. 04:01.660 --> 04:05.970 It's done using a new technique using cover trees. 04:06.800 --> 04:13.600 And because it's so fast, it's log-in time to actually calculate drift for a new sample. 04:13.600 --> 04:19.460 We can use it for on... in new ways that concept drift couldn't have been applied before now. 04:19.660 --> 04:28.360 So, we're going to go over the objective, why we care about concept drift, mathematically how it's done, then a couple results, and then finishing up with next steps. 04:28.860 --> 04:31.180 So, why do we care about data set drifts? 04:31.180 --> 04:33.780 Well, our data drifts. 04:35.300 --> 04:41.040 So, I work with malware and there are new malware families coming out every month. 04:41.040 --> 04:45.300 There are new benign pieces, examples of software coming out every month. 04:45.300 --> 04:52.140 Every time that Adobe patches Photoshop, it changes the pattern slightly and it changes its location slightly in our data set. 04:52.300 --> 05:00.880 Every single time a new piece of malware comes up, it's a new... it changes the way our... the malware data is distributed slightly. 05:01.500 --> 05:11.060 Another problem... well, what those do, basically, which gets into the second problem, they lower the efficacy of our models that we deploy. 05:11.700 --> 05:18.640 So, our models expect data in a sort of the same sort of general location as our training data. 05:18.640 --> 05:29.640 And every time we deploy, we are kind of fixing our model's view of the world at a certain day, and then we're training it and we're testing it on essentially future data. 05:29.760 --> 05:40.800 So, it doesn't have a perspective for the... if it's trained in March, it doesn't have... it might not work very well at the end... data coming in at the end of April. 05:41.800 --> 05:47.280 So, one of the methods for dealing with this is you build a dashboard that basically tracks the error. 05:49.020 --> 05:53.340 And when the error gets too high, you discard the model and go on for a new one. 05:53.340 --> 05:59.940 But the problem is, I don't trust VirusTotalLabels, and I don't think anyone really should trust VirusTotalLabels. 05:59.940 --> 06:06.000 And that's the best way we have because of the sheer volume of data we have to kind of trust VirusTotalLabels. 06:06.220 --> 06:16.660 So, and for other things, I wouldn't trust early labels on data because we have to move very quickly and sometimes with whitelisting and stuff. 06:18.380 --> 06:28.620 And , you know, well, and sometimes we only get like a label when our customer complains and we'd rather get ahead of that and figure out like, hey, where's the drift happening? 06:28.680 --> 06:29.920 What's going on? 06:29.920 --> 06:36.400 And then additionally, aside from the fact that things are just changing all the time, our models are also under attack. 06:36.400 --> 06:50.920 People are trying to bypass them by doing new and weird things to their data, like packing a spam filter and seeing if that works, or like posting a different pattern to see if that works, to see if they can get past like the Facebook spam filter. 06:50.920 --> 06:56.020 They're constantly innovating with a specific goal in mind of bypassing our models. 06:56.540 --> 07:04.300 This may not result be an adversarial example per se from the literature, but it sure kind of acts like that sometimes. 07:04.400 --> 07:08.500 And additionally, we could be under attack via a poisoning system. 07:09.420 --> 07:14.760 Maybe if the detector is fast enough, we can get ahead of those things beforehand. 07:15.640 --> 07:18.040 So here's a trivial example. 07:18.680 --> 07:20.460 So we have these two data sets. 07:20.460 --> 07:21.760 One is our training data set. 07:21.760 --> 07:24.540 That's we've got 1, 1, 2, 1, 1. 07:24.540 --> 07:29.500 And so our training data set has 70% 1s, 20% 2s, and 10% 3s. 07:29.900 --> 07:32.140 And this is what we trained on. 07:32.680 --> 07:40.040 Realistically, there's no point in training a machine learning model on a sequence of numbers, but suppose we do. 07:41.080 --> 07:44.220 But then we deploy this model, and we get this other sequence of data. 07:44.220 --> 07:46.380 2, 2, 1, 2, so on, so on. 07:46.520 --> 07:50.440 And when we actually deploy it, we see data coming over the wire. 07:50.440 --> 07:53.420 We have 30% 1s, 60% 2s, and 10% 3s. 07:53.420 --> 07:55.400 So that's a little bit different from our training set. 07:55.400 --> 07:59.480 So the real world is different from our training set. 08:00.000 --> 08:06.240 So in this case, this is a... we can model this distribution very easily because it's a discrete space. 08:06.240 --> 08:09.520 There are only three things that our data could be. 08:09.700 --> 08:14.840 There's only... it isn't continuous like a lot of the stuff we have to deal with in data science. 08:15.040 --> 08:18.100 So we can actually compute the distribution fairly easily. 08:18.100 --> 08:22.980 And this is a pretty good... we can feel confident in our estimate of the distribution. 08:23.180 --> 08:29.800 We have to do some Bayesian statistics to do this properly, which we're not getting into this talk. 08:29.800 --> 08:33.880 But this is basically how it works. 08:34.000 --> 08:48.480 And then once we have like a concept of our training distribution, and our real world distribution, or our test distribution, as I'll be calling it today, we can take the Kublai-Klepch divergence. 08:48.520 --> 08:55.930 So this is a sort of a measure of the distance between this distribution and this distribution. 08:56.200 --> 09:08.260 And it's very easy to calculate on this categorical discrete data because it's just going to be, well, 0.7 times log of 0.7 over 0.3. 09:08.260 --> 09:12.040 So that's the category for 1s over the 1s. 09:12.560 --> 09:15.220 Take the log and then multiply it for the category for 1s. 09:15.220 --> 09:16.700 And that gives you the first term. 09:16.700 --> 09:18.740 Second term is the same thing for 2s. 09:18.740 --> 09:21.140 And the third term is the same thing for 3s. 09:21.240 --> 09:27.480 And then we add those all up and you get the KL divergence between these two distributions is 0.16. 09:28.780 --> 09:30.080 So that's all great. 09:30.080 --> 09:32.540 But the problem is our data looks like this. 09:32.640 --> 09:37.580 And I don't know whether this has any difference. 09:37.580 --> 09:43.000 Are my blue points sampled from the same distribution as my orange points? 09:43.120 --> 09:44.680 I don't know. 09:44.940 --> 09:48.020 It's really hard to tell by just looking at this picture. 09:48.600 --> 09:51.140 And now, in this case, they are. 09:51.140 --> 10:01.640 So my orange points are sampled from a two-dimensional Gaussian, two-dimensional normal distribution, where it's just, it's a nice sphere. 10:01.640 --> 10:06.100 And they're both, the covariance matrix is 1, 1. 10:06.100 --> 10:08.000 And the covariance matrix with blues is 1, 1. 10:08.000 --> 10:09.440 And it gives you this nice distribution. 10:09.440 --> 10:11.120 And it looks okay. 10:11.540 --> 10:15.360 Now, what I'm going to do is I'm going to drift the blues slightly over. 10:15.540 --> 10:17.480 And can you tell, is this correct? 10:17.480 --> 10:21.940 Well, you know, every single time that I put a blue, it's right next to some orange points. 10:21.940 --> 10:24.380 So this looks like it could be from the distribution. 10:25.120 --> 10:26.800 I can't really tell with my eyes. 10:26.800 --> 10:36.700 And one of the techniques we might do is like, oh, well, let me take the k-nearest neighbors and see if the distance from my k-nearest neighbors over time goes up, then I'm out of distribution. 10:36.700 --> 10:40.000 But if you tell here, that's not going to tell you much. 10:40.780 --> 10:43.940 If I go here, well, oh, I've got some outliers here now. 10:43.940 --> 10:46.000 So maybe that will work now. 10:46.060 --> 10:48.080 If I go here, well, this is really distributed. 10:48.080 --> 10:51.300 So this center, the center of this distribution should be around here. 10:51.300 --> 10:53.100 And the center for this distribution is around here. 10:53.100 --> 10:54.760 So that's really drifted. 10:54.760 --> 10:56.780 But you've got some outliers over here. 10:56.780 --> 11:02.460 Now, what happens when there's like millions of orange points and there's only a few hundred blue points? 11:02.460 --> 11:05.440 Well, you might not be able to tell the difference with that in that case. 11:05.860 --> 11:11.080 So, and also like, there's all this, what I've described to you is kind of a feeling. 11:11.080 --> 11:15.780 And to actually get at the math of this thing, I have to like model the distributions that these came from. 11:15.780 --> 11:17.620 And that's quite a hard problem. 11:17.680 --> 11:20.160 And especially in high dimensions. 11:20.160 --> 11:22.280 So things get kind of complicated. 11:22.280 --> 11:26.500 So the solution to this that I came up with is to use a cover tree. 11:26.520 --> 11:29.160 Now, why do I want to use a cover tree? 11:29.640 --> 11:36.200 So the cover tree, basically, the key takeaway for cover trees is it's a k-nearest neighbors data structure. 11:36.200 --> 11:37.320 There are many like it. 11:37.320 --> 11:49.700 There's kd trees, there's b trees, there's kd trees, you know, there's k-means trees, a whole bunch. 11:50.140 --> 12:03.820 And, well, the cover tree has this wonderful thing where in 2016, Mario Maggiorni and Wenjing Lau proved that it can arbitrarily well approximate the underlying distribution of the data. 12:04.560 --> 12:10.520 There's some caveats to that statement, and mathematically, it will probably, to properly statement, will take it, take the whole page. 12:10.520 --> 12:18.860 But basically, the whole concept of their proof is for a nice data set, and to know what a nice data set is, you need to know what a low dimensional manifold is. 12:19.360 --> 12:21.600 And you have to have enough data from that. 12:22.000 --> 12:33.260 But for a nice data set, which most of our data sets are pretty nice, sort of, kind of, a cover tree will arbitrarily well approximate the underlying distribution of the data. 12:34.460 --> 12:39.160 There's some caveats, and you can go read their paper if you want on exactly what that means. 12:39.160 --> 12:52.500 But for us, what this means is, if I use a cover tree to build a model of my data for k-nearest neighbors, I can take k-nearest neighbors, or I can just fiddle around with the properties of the cover tree to, like, get information about my data set. 12:53.420 --> 13:01.560 So, I can tell things like the local dimensionality, I can tell things like how things glue together, and I can tell, like, sort of, the shape of my data fairly well. 13:01.560 --> 13:02.980 I can tell clusters and things. 13:02.980 --> 13:05.600 I can infer what clusters are. 13:05.680 --> 13:08.780 Let's go build a very simple cover tree in two-dimensional data. 13:08.820 --> 13:17.900 So, here's a, you know, infinity sign, a bow tie, whatever you want to call it, and I start my cover tree by picking a point at random and then building a sphere. 13:18.080 --> 13:21.340 You know, in this case, it's a circle that covers everything. 13:21.340 --> 13:22.740 So, this is the start. 13:22.740 --> 13:24.540 And now, this doesn't help me that much. 13:24.540 --> 13:38.880 I haven't split up my data geometrically to, like, divide and conquer the k-nearest neighbors structure, because the naive way would take a linear time, big O of n, but we want to divide and conquer, so it takes log of n. 13:38.880 --> 13:40.120 So, here's what I do. 13:40.120 --> 13:43.640 I shrink my sphere down, add another one, and I cover it again. 13:43.760 --> 13:48.480 You can kind of tell that this object is longer than it is wide. 13:48.500 --> 13:53.460 It's kind of, if you really squint, it's kind of a one-dimensional thing in this direction. 13:55.100 --> 13:56.080 So, that's great. 13:56.080 --> 14:08.020 But now, if I go, okay, well, I'm going to split it up further, so really divide and conquer, and I, so I've got these two nodes, and they're both children of the previous node on the previous slide, and I'm going to build their children. 14:08.260 --> 14:10.220 So, here's their children. 14:10.880 --> 14:23.580 So, I divide and conquer their stuff, and I can kind of tell that each of their children have four, and if I, if you squint a little bit, it's kind of square-shaped in this dimension. 14:23.740 --> 14:27.360 At the scale, the top scale, it was too blurry. 14:27.360 --> 14:28.500 I could only see a line here. 14:28.500 --> 14:41.360 At the scale, I can kind of see that it's up in, it's got a nice shape, square shape, and so there's four children, and the reason, you know, that that dimensionality is relevant to the number of children you have. 14:41.540 --> 14:57.980 And then I can go further, and you know, it's got some more, it's kind of split up nicely, and I've got like a one-dimensional object here again, because all these children are kind of one-dimensional-ish, and I can split up some more, and you can see that it's kind of conforming to your data nicely, 14:57.980 --> 15:03.480 and at every single step of the way, I can make some inferences about what the shape of my data is. 15:03.480 --> 15:06.380 They're very cheap, because it's basically counting. 15:06.980 --> 15:10.140 So how do we build a probability distribution? 15:10.200 --> 15:31.460 So on slide two, we built a very simple probability distribution, where I had a discrete space, and now I've got a tree, and essentially, when I have a tree, at every single node, I can either go left, or right, or down, or you know, in this case, my number of children I have is variable, 15:31.460 --> 15:35.320 but I will be at a parent node, and I have to go to one of its children. 15:35.320 --> 15:41.620 So I always have discrete choices, a discrete choice of where to go. 15:42.320 --> 15:43.800 So how does that apply? 15:44.320 --> 15:54.840 So here is a very, like, simple cover tree, and I've colored it by the total, like, the population of this node. 15:55.900 --> 15:59.800 So this color here is the relative population of this node. 15:59.860 --> 16:06.000 So about 66% of the data is underneath this node. 16:06.500 --> 16:10.220 About 33% of the data is underneath this node. 16:10.220 --> 16:12.620 And you can see that colors are kind of changing. 16:12.620 --> 16:19.820 I get a kind of a picture of how dense my data is, but that doesn't help me, because I need to make choices. 16:19.820 --> 16:22.680 It doesn't help me make the choices at all steps. 16:22.800 --> 16:26.500 So if I go here, this helps me make my choices. 16:27.040 --> 16:35.840 So here, I've got 66% of my data over here, and I've got 33% of my data over here. 16:35.840 --> 16:38.840 And then once I've taken... I have to take one of those two choices. 16:38.840 --> 16:44.380 If I take this choice, I'm now at this node, and I have two choices again. 16:44.380 --> 16:57.100 And the relative probability of taking this choice versus this one... Well, this is basically a 0.1 probability of taking this path, and this is a 0.9 probability of taking this path. 16:57.160 --> 17:03.400 And once I get to this node, I have a probability of one of going straight down, because I have no other choices. 17:03.400 --> 17:11.840 And every single point, I have a discrete distribution, like we had on page one, which tells me where I'm going. 17:11.840 --> 17:26.100 And because my tree is geometrically motivated, these choices, which were all discrete and easy to compute, and easy to count, and easy to keep track of, now I can compute the KL divergence, because it's trivial. 17:26.100 --> 17:29.880 It's all... it's just counting, taking logs, and summing things up. 17:30.960 --> 17:33.960 So this is my prior distribution. 17:33.960 --> 17:36.220 As I said, we're going to use some Bayesian statistics. 17:36.220 --> 17:37.920 And so here is my prior. 17:38.280 --> 17:40.500 How... this is built with my training set. 17:40.500 --> 17:43.080 How do I include my test set? 17:44.120 --> 17:51.980 So when I see a piece of data coming over the wire, I can make an inference of where it should belong in this tree. 17:52.020 --> 17:54.200 So if it was already... 17:54.200 --> 17:59.920 if it was in my training set and didn't get involved in building the tree, where would have it ended up? 18:00.060 --> 18:01.760 So I have a point here. 18:01.760 --> 18:04.140 So this is my new point that came over the wire. 18:04.140 --> 18:13.120 And I queried and said, oh well, this point is covered by this parent, and it's covered by that parent, and that parent, and all the way up. 18:13.180 --> 18:17.460 So the path for this point goes up this way. 18:17.460 --> 18:28.480 And now for each of those elements in those paths, I can increment my probabilistic distribution and get a posterior one that involves... that includes the new information that I got, that there's a new point over here. 18:28.840 --> 18:31.320 And now I can do that again with another point. 18:31.320 --> 18:32.420 Oh yep, cool. 18:32.420 --> 18:37.000 I have a posterior... this point's been added, and you can see that the distribution changes. 18:37.180 --> 18:40.320 And then I can add some more points, and I can add some more points. 18:40.320 --> 18:42.500 So these are all my posterior. 18:42.500 --> 18:51.120 And I can update my original thing by taking the path of each of the points and updating all the little discrete distributions that I have. 18:51.320 --> 19:02.600 So this enables me to sort of quickly make a posterior distribution out of my prior distribution, and everything is discrete. 19:02.600 --> 19:10.140 And then I can take the KL divergence between my posterior discrete distributions and my prior discrete distributions. 19:10.140 --> 19:17.800 So in this case, this one has a probability of 0.33, and here I have a probability of 0.66. 19:17.920 --> 19:24.660 And afterwards, after I've included all my training set, this is a probability of like 0.4. 19:24.660 --> 19:29.020 And this, you know, this is a probability of 0.6, and this is a probability of 0.4. 19:29.020 --> 19:30.900 And those are very different. 19:30.900 --> 19:36.280 And I can plug those into the KL divergence thing and get a positive number for the KL divergence at this node. 19:36.280 --> 19:42.220 And then I can do it for this node, and this node, and this node, and get all the KL divergences and add them up. 19:42.220 --> 19:54.680 And then I can get the total KL divergence with respect to my original tree of the posterior distribution with respect to the prior distribution, which is really useful. 19:54.680 --> 19:57.400 And so this basically, yeah, does it. 19:57.700 --> 20:10.220 And the code for doing this enables you to do it very quickly, because it's basically just counting a couple logs and some other statistical equations. 20:11.060 --> 20:15.680 And the slide just covers how you do it. 20:16.260 --> 20:21.480 So let's go back to that original test set. 20:21.480 --> 20:36.280 So I've got basically a blown up version of those slides of the Gaussian distributions where I had them, where a large number of points from my training distribution, which was a single Gaussian sampled at the center of the thing. 20:36.280 --> 20:40.440 And then I have a small number of points from a test distribution. 20:41.120 --> 20:48.300 And in this case, I have 100,000 points from my training distribution and only 500 points from my test distribution. 20:48.300 --> 20:54.340 And these both have a covariance matrix of all ones. 20:54.340 --> 20:57.860 So it's actually quite, and it's 20-dimensional. 20:57.880 --> 21:01.220 This is actually harder than most datasets. 21:01.680 --> 21:05.880 MNIST is about 10-dimensional, if you really get down to it. 21:05.880 --> 21:12.260 If you want to know what that is, you can contact me on Twitter and ask me why MNIST might be lower dimensional. 21:15.140 --> 21:23.780 And between the training distribution, I build the tree, fix it, and then I make a posterior distribution for a bunch of test distributions. 21:23.800 --> 21:26.260 And I take the KL divergence. 21:26.380 --> 21:28.300 And you can see it's a bit noisy. 21:28.480 --> 21:33.540 The reason being is I generate a lot of the exact position of your points. 21:33.540 --> 21:35.200 It's fairly sensitive to these. 21:35.340 --> 21:36.760 So this is one of the problems. 21:36.760 --> 21:45.980 And one of the things I'll talk about at the end is like, there are ways to normalize this and resolve this, because I've designed it for speed, not really for accuracy. 21:46.140 --> 21:51.460 And I'll get into why I did that afterwards, because honestly, it came to the drift stuff backwards. 21:51.620 --> 21:59.040 But you can see, the further you get, the further you separate the two distributions, the higher the number gets. 21:59.040 --> 22:03.200 So the sanity test, the unit test of does this work is correct. 22:04.860 --> 22:07.160 And I'll have to compare this to other methods. 22:07.860 --> 22:12.940 This takes big O of, sorry, Wasserstein takes big O of N to the fourth. 22:13.440 --> 22:19.960 Wasserstein is the only other drift calculator that I really know works. 22:20.740 --> 22:28.240 And is model independent and doesn't have some funny business with building an estimated distribution initially. 22:29.780 --> 22:33.500 This takes K log N. 22:33.500 --> 22:41.020 Another big difference between Wasserstein is the traditional way of doing Wasserstein requires a relatively equal size test and training set. 22:41.840 --> 22:46.160 You can't have the test set be 0.5% of the training set. 22:46.720 --> 22:51.620 That would just not work so great on the traditional method I know of. 22:51.740 --> 22:54.800 And this one, honestly, it's online. 22:54.800 --> 22:58.800 You can do, the test set can be a fraction of the size of the training set. 22:58.800 --> 23:02.240 And because it's online, it can do it in real time. 23:02.620 --> 23:05.360 And this is stupidly fast. 23:05.360 --> 23:18.100 You can track for the Ember open source, Ember malware data set, you build a reasonable couple tree, you can track 16,000 new samples per second on my laptop. 23:18.500 --> 23:24.160 So that's fast enough that inference wouldn't be, this would not be the bottleneck. 23:24.160 --> 23:32.640 Inference would be the bottleneck if you would build a cloud distribution, a cloud model, and put this as a guard in front of that cloud model. 23:33.820 --> 23:37.800 So we built it so that it can go fast enough to defend. 23:38.660 --> 23:44.420 And now here is where the thing originally came from, and then we backtracked onto Drift. 23:44.480 --> 23:46.780 So here's the test set attack. 23:47.400 --> 23:59.740 So this was originally categorized by Ian Goodfellow, and some defenses have been proposed by Nicholas Carlini and others. 24:01.540 --> 24:05.160 So, but here is the gist of the attack. 24:05.160 --> 24:06.720 Normal users just query. 24:06.720 --> 24:10.840 They don't care about whether they got a false positive or a false negative, they just keep querying. 24:11.820 --> 24:36.160 And for us, we think of a normal user as being like an enterprise user, trying to figure out whether all the reports coming over the wire of new binaries are malicious or benign, or they'd be submitting every single binary that they see on their network to a service that will tell them whether it was malicious or benign for an ADV product. 24:37.600 --> 24:43.640 But a malicious user would be submitting things with a specific goal in mind. 24:43.640 --> 24:51.620 They don't care about what they care deeply what the label is, and they care deeply about defining a false negative. 24:51.620 --> 24:54.780 They want to find a malicious sample we classify as benign. 24:54.780 --> 25:09.340 So what they'll do is they'll try a bunch of stuff until they find something that is misclassified as benign and is actually malicious and bypasses our model, and then they deploy it as far as much as possible. 25:09.700 --> 25:20.420 So if you do, if you apply this to, you know, the fast drift calculators to that, you can attach a little drift calculator to each user. 25:20.560 --> 25:25.720 And as samples come over the wire, you track it for that user. 25:26.440 --> 25:35.020 And if the user starts exploiting something, they're going to get a very boring distribution where it's just one point repeated over and over again. 25:37.420 --> 25:47.620 And you spike your distribution, your KL divergence spikes up and then becomes very normal because it's essentially you're tracing the same path over and over and over again. 25:49.160 --> 25:59.040 And you can see that there's an exploration phase where the malicious users try to look for a benign misclassified sample, and when they find one, there's an exploitation phase. 25:59.040 --> 26:01.480 And the KL divergence rises rapidly. 26:01.480 --> 26:06.280 You can see that that this is in log of scale. 26:06.280 --> 26:11.220 So this is literally hundreds of times more KL divergence than the benign samples. 26:11.220 --> 26:13.380 And here, it's the same thing. 26:13.380 --> 26:19.640 Hundreds of times more KL divergence than the benign and the attackers were unsuccessful. 26:20.780 --> 26:30.460 Because of this, you can build, you can probably build a very good online defense of your system against a set attack. 26:32.900 --> 26:46.560 And here's where basically the system was originally built sort of with this mind and other attacks in mind, because I'm more interested in defending my models than calculating drift. 26:47.340 --> 26:50.420 But because it's so bloody fast, it does this really well. 26:50.420 --> 26:53.220 And because it's so bloody fast, you can retrofit it. 26:53.220 --> 26:59.160 So here's where I'll talk about some next steps. 26:59.180 --> 27:02.740 So as I mentioned previously, this thing is a bit noisy. 27:02.740 --> 27:04.500 There are ways to fix it. 27:04.500 --> 27:14.940 In this case, window sizes and some tuning things that I didn't go into in these slides because I've already got 20 minutes. 27:15.060 --> 27:20.940 There are some tuning systems you can use to really clean up and de-noise. 27:20.940 --> 27:39.880 There's also some interesting waking functions you can do inside the tree because there's some noise from an overactive leaf node might end up just building a very high KL divergence for just that one node and it throws everything off. 27:40.300 --> 27:44.980 And there's a couple other little things like that that still need to be cleaned up before this goes into production. 27:45.000 --> 27:54.440 But the system itself is looking very promising and is honestly the fastest of its kind that I can see in the world. 27:55.900 --> 28:09.180 And that's basically it for Gokul's ability to detect benign test set and other drift things. 28:09.180 --> 28:15.540 The library is at elastic.com, oh sorry, github slash elastic slash Gokul. 28:15.880 --> 28:22.180 It's named after my grandmother because the base algorithm for this thing is called GRMA. 28:22.180 --> 28:24.820 And if you say that while drunk, you can kind of get grandma. 28:25.160 --> 28:30.940 And grandma's a bit too on the nose, so I named it Gokul. 28:32.680 --> 28:38.640 Anyway, well, looking forward to hearing you guys on Twitter and Twitch and Slack or whatever. 28:38.980 --> 28:40.980 So thank you very much and good night.