publishing on Thematic Maps

Text: Martijn ter Steege

Statistical disclose control is essential when publishing data. Public authori-ties, such as Statistics Netherlands (Dutch: CBS), do research about various topics. Some of these topics are more sensible than others: for instance publishing the average age of a group of people is not sensible, but the average income is. Therefore, the privacy of each individual within a group should be guaranteed. In short, statistical disclose control makes sure that everyone’s privacy is ensured.

The next question is, how can we make sure that each individuals privacy is ensured? In a previous paper by Douwe Hut [1], this was done by adding noise using the (p,q)-rule. This rule makes sure that it is impossible to estimate some individual data within p%, if all other contributions’ lower bound are known within q%. I won’t go into too much details, so if you want to read about this, I’d recommend you to read [1].

In my Bachelor assignment, I’ve looked into another mechanism that protects group data: the Pufferfish framework. Don’t ask me or my supervisor why this method is called Pufferfish, because we do not know. What we do know is that this method was explained in [2], but that not a lot of further research was done. Therefore, I chose to investigate into this method and t check if this method had potential to be used.

The Pufferfish framework is based on the following equations: M denotes a mechanism to protect the data, si and sj are mutually exclusive statements about the data (for instance: si: ‘individual h is not in the data set’, sj: ‘individual h is in the data set’), θ denotes all information that is known about the data. Both equations are sufficient to have Pufferfish privacy, where ε determines the strength of the privacy.

The reader can easily verify that1 these equations can be rewritten into

using some basic probability theory. Don’t look this up in my report, because I didn’t even compute this. It is good to understand the interpretation of this computation.

We can interpret

as being the initial probability that si is more likely to be true than sj. This can be seen as pre-knowledge, that is not influenced by the published data.

can be interpreted as the postknowledge, the knowledge you have after observing the data. Due to the boundaries of e±ε, and assuming that ε should be small for large privacy, we get that both boundaries are close to 1. Hence, both probability fractions should be nearly equal, so it can be assumed that no new information can be obtained by evaluating the data. That means that a mechanism M ensures privacy, when this equation holds.

1 I always wanted to use this myself! For my research, I proved that the addition of noise according to the Laplace distribution satisfies the aforementioned property. This Laplace noise is dependent on the amount of contributions in the group and the privacy parameter ε: a larger group or larger ε means less noise. I won’t go into much detail here, but if you want to see the proof, then you should read my paper.

Another mechanism I managed to create was the relative error mechanism. This mechanism does not add noise, but it has multiplicative noise. The reason why this is useful is that we can protect data relatively now: we can say that our mechanism protects the data within k%. This multiplicative noise also has Laplace distribution, but also involves a logarithm. Now we have two mechanisms that can be applied for group privacy. Looking at my research title, I haven’t talked about the publication of thematic maps. Thematic maps can be visualized in several ways, but in my research I focussed on publishing grid maps. In Figure 1 you can see such a grid map that is used by Statistics Netherlands.

Now we will focus on publishing any data on thematic maps. We can use all data of one grid cell as group, and use the mentioned privacy mechanisms to protect them. The results of the absolute error protection maps are visible in Figures 2 and 3 and the relative error protection maps are visible in Figures 4 and 5

In the Figures, we see that different cell sizes produce different scales of noise. This is an immediate consequence of the group size, and therefore logical behaviour. We see that the absolute error protection method works really well, especially with the larger cell sizes. Comparing these unprotected and protected grid maps show little differences, which is desirable for useful data publication.The relative error protection case shows less appealing grid maps. This follows since the multiplicating noise ((b) plots) of one cell is significantly larger than the others, which results in a useless protected map. This problem is only resolved when taking appropriately sized cell sizes, but that is not always possible in data publication. In all c) plots, we see the grid maps that could be published online, because this is proved to be safe. However, we notice that some cells produce negative averages, while all individual contributions of a group are non-negative. This is unrealistic behaviour and should be tackled. In my paper, I’ve also introduced a privacy mechanism with bounded output, such that negative outputs can be prevented. If you are interested in this, please check my paper via https://essay. utwente.nl/85628/. That concludes my Bachelor assignment. I have to say that my research topic was really interesting, since it was different than the typical suggested Bachelor assignments. It was really fun to do, since I had the feeling that I really contributed into new research. If you still have any questions about my Bachelor assignment, feel free to ask me, because I’m more than willing to explain everything in more detail!

References

[1] D. A. Hut. “Statistical disclosure control when publishing on thematic maps.” In: (2020). DOI: http:// dx.doi.org/10.1007/978-3-03057521-2_14.

[2] Daniel Kifer and Ashwin Machanavajjhala. “Pufferfish: A framework for mathematical privacy definitions.” In: ACM Transactions on Database Systems 39.1 (2014), pp. 1–36. DOI: http://dx.doi. org/10.1145/2514689.

Text: Lavinia Lanting

Justus Sleurink

1. Introduce yourself. My name is Justus, I am a 5th year in the meantime. I have almost finished my bachelor and I have actually been active at Abacus all throughout my studies and I also did a board year 2 years ago. I have been a member of 10 committees in total, but that will only decrease from now on.

2. How long have you been an active member of Abacus? Way too long. No, just kidding, I can still see myself remaining active in some capacity as long as I'm still studying here.

3. Why did you decide to become an active member? Because I liked the Kick-In and liked the people and then the committee market came by and then I ended up in the Freshmen Committee. I liked it and I started doing more and more and then I did a board year. The rest will go without saying if you have nice people around you.

4. What is your favourite part about being an active member at Abacus? It's a tough question. Well…it is mainly the part of organizing nice things with nice people. The combination of organizing something together with people and working towards something, which in most cases is something nice.

5. Which committees are you currently in and in which role? Oh help. I'll just grab the list on the Abacus website. I am currently the chairman of the Advisory Council. I am still the Study Trip Committee's chairman, which is also not a committee of Abacus of course, and also of Stichting RSA. In addition, I am also still in the CoCo. I don't really have a position there at the moment and besides that I am currently still in the (H) ero committee and in the BataCo and I have no real position there either. I am an emergency response team member, so I am on the (H) ero committee and I organize the Batavieren race.

6. Which of these is your favourite and why? Of those that I'm in now? Good question. The most fun thing to do is no longer RSA at the moment, unfortunately, as we decided to cancel it last week. It takes a lot of time, but in the end there is not really a pay off at the moment, despite the fact that it was a lot of fun to work on. In the end I think I would choose the BataCo. It's fun, not too strict, not too small, not too planned.

7. Which other committees have you been in and in which role? I started with the Freshman Committee for which I was treasurer. Not much of that has remained for the rest of my career. Then I joined Ab-Actie for a year in my second year and I chaired the committee as well. I have been an Officer of Logistics for the Twick-In. I also spent a while in the Translacie: that was mainly to translate documents and then the committee was disbanded during my board year. Last year I was on the Sports Day Committee, but that was more as part of the BataCo. And I have also been on the Dies committee this year as Chairman.

8. You’ve also been a board member. Why did you choose to do a board year for Abacus? Initially because I liked it so much at Abacus and I wanted to spend more time being active. I also really learned things from it on top of the fact that it was really so much fun. My main reason was that I had had such a great time at Abacus myself by being active and I wanted to give back to the other people, I wanted to make them enthusiastic about being active and I wanted to show them how much fun it is at Abacus.

9. Are you planning on being active next year as well? If yes, which committees are you planning on being a member of next year? If it were up to me, I'd do another year in the Advisory Council. I will then see if there is something small to do next to it and if nice people want to participate, such as with the Dies this year. At the moment I am mainly thinking about another year in the Advisory Council and perhaps at Stichting RSA in the Supervisory Council after we have finished handling and found a new committee. Most of what I wanted to do I have already done.

10. Which committee that you have not joined (nor will be joining) do you think does fantastic work? In any case the Christmas dinner committee. They always give me a fantastic and pleasant evening, so they always do well as far as I am concerned, but I would never want to be in it myself, because then I have to get involved and work in-

stead of sitting and enjoying and having a good time and drinking. The (A)bac(ch)us I think does amazing work for similar reasons, but in general, all committees do just fine.

11. How would you convince non active members of Abacus to become active? There is a whole strategic approach to it. You have to get them drunk during the Kick-In, befriend them and then have them join all kinds of committees. But seriously, if you like Abacus or people from Abacus or an activity and you ever want to give something back to the association, no matter how large the committee, it is certainly worthwhile to become active. Oh yes and otherwise you have to convince people with the Active Members Weekend because that is the highlight of the year. 12. Do you have anything left to say? That is a good question. Sign up for all future activities that I organize, I would say. Just promotion for things that don't even exist yet. There you go!

Alex Schopbarteld

Study Advice first. But I really liked the activities and I really enjoy organizing things, so that's how I ended up at the Ab-Actie. As for the Christmas Dinner committee, I only helped with cooking last year and it seemed fun to organise it too. These are all things that I went to myself and that I really enjoy going to and I just really like organizing things and that's how I got active.

4.What is your favourite part about being an active member at Abacus? I just really like the people. You are in a meeting and you are working on something, but I really enjoy being together with the group and I enjoy devising and organizing activities and that it is appreciated.

1. Introduce yourself. My name is Alex, I am a 2nd year student in Applied Mathematics and Applied Physics. In my spare time I try to play the guitar. I always play D&D with my friends on weekends. I really enjoy cooking, that's a really big hobby of mine, and I'm also an active member. I don't have a lot of time left next to all of this. 5. Which committees are you currently in and in which role? I am the secretary of the Christmas Dinner committee, I am the treasurer of the Twick-In and I am the poster boy of the Ab-Actie. I also like it so much that I am listed on the website as poster boy. I think that's an honor actually.

2. How long have you been an active member of Abacus? From the beginning of this year, so that's approximately ¾ of a year

3. Why did you decide to become an active member? I already wanted to in my first year, but I wanted to get my Binding 6. Which of these is your favourite and why? I think I like making the poster is the most when I have the time. When I have little time for it, I don't like it very much because I feel like I have to rush it. I can just spend too much time on it because I like it so much. 7. Are you planning on being active next year as well? If yes, which committees are you planning on being a member of next year? I do want to stay in the Ab-Actie. I think they also will be very happy with that. I really enjoyed the Christmas Dinner Committee this year, but it is a pity that it is not allowed to take place physically, so maybe I will stay in it for another year so that I can also organize it physically, but maybe there is something else I could do.

8. Which committee that you have not joined (nor will be joining) do you think does fantastic work? I like the PixCie and the Ideaal! very nice. I don't see myself walking around with a camera though. I also haven't been on a trip yet, so I don't know for certain if they do a good job, but I'm sure they do.

9. How would you convince non active members of Abacus to become active? I just really like it myself and I think everyone who likes the activities will also enjoy organizing them. I think you should just try it out and if it is something for you, you will notice right away.

10. Do you have anything left to say? No not really. When will this come out? Do I still have to promote the Christmas Dinner?

Wessel Heerink

1. Introduce yourself. My name is Wessel and I am 20 years old. I am a 2nd year Applied Mathematics student and I live in Nijverdaal.

2. How long have you been an active member of Abacus? Ever since my first year as member of the Freshmen Committee and of the www.com.

3. Why did you decide to become an active member? At first I joined the www.com because I love programming myself. Then only one person had registered with the Freshmen Committee and then I thought: sure, I can do that too.

4. What is your favourite part about being an active member at Abacus? It's just fun. You have, especially in this time, people to speak to every week instead of just sitting alone in your room. I also like organizing things, so that's why I'm also part of the Twick-In and Christmas Dinner Committee this year.

5. Which committees are you currently in and in which role? I am in the www.com, but we have no real roles there. Everyone just works on the website. I have no real role within the Christmas Dinner Committee and I am secretary of the Twick-In.

6. Which of these is your favourite and why? I think that would be the Twick-In. Surely it is special that I can organize something so big. A lot has to be done, but with our efforts it still all works out fine.

7. Which other committees have you been in and in which role? I was chairman of the Freshmen Committee. 8. Are you planning on being active next year as well? If yes, which committees are you planning on being a member of next year? I think I will only be member of the www.com next year. The Christmas Dinner committee is a bit less fun than I expected, but maybe that's also because of Covid.

9. Which committee that you have not joined (nor will be joining) do you think does fantastic work? I always like the activities of the AbActie. It doesn't really matter what it is, but I really enjoy being with others.

10. How would you convince non active members of Abacus to become active? You get to know other people from other years. You build up contacts with people who also study mathematics and it is simply recommended.

11. Do you have anything left to say? Not really. The Ideaal! comes out too late to promote the Christmas Dinner.

Hugo Hof

1. Introduce yourself. My name is Hugo, I am 6th year and I am now in the first year of my master. I am doing the master DMMP and I live in the center of Enschede. I am vegan and I really love to make music.

2. How long have you been an active member of Abacus? From my second year, I think.

3. Why did you decide to become an active member? At first for the fun and I thought the Twick-In would be great because I was allowed to participate in the Kick-In one more time. It felt worth it, also because it was so wonderful for everyone at Abacus. I also joined the (A)bac(ch)us for the same reason: because I liked the drinks so much and I wanted to offer the same experience to others.

4. What is your favourite part about being an active member at Abacus? I like committees in which you have to communicate a lot with people. I