MINI: Bayesian Belief Networks

Key Takeaways

[Music] data skeptic is the official podcast of datas skeptic.com bringing you stories interviews and mini episodes on topics in data science machine learning statistics and artificial intelligence all right Linda So today we're going to talk about basian networks so a basian network is a probabilistic as cyclic directed graph I don't know what that means all right so let's get into it start with graph graph it's a chart A visual representation of data that's normally a good answer a lot of people think that way I'm using it in like the data structure way so graph like a graph of the internet all of the nodes are websites and the edges are links between them like a social network that's a graph yeah we call that a graph listen so what is your definition of a graph a graph is a collection of nodes and edges and an edge is visual it can be I mean you definitely visualize them but you can just do it on paper too if you want to so you can just have coordinates there is no position you just talk relatively speaking there's something called an adjacency Matrix that just indicates if two edges have a link between them or not so it could be a chart that says link yes or no yeah yeah and that's a graph yeah so like somewhere at Facebook there's probably a database table that says like friend one friend two and those are just the links you know like Kyle Linda friend okay so that's a graph now a directed a cyclic graph means that the edges between it don't form a cycle so they always go in one Direction kind of like a tree you know a tree branches out the tree's limbs never connect back to its roots we don't know how peanuts grow so why what's wrong with peanuts peanut you know I learned this in elementary school they taught me about this peanut plant so it grows upward but then it puts the pods under the ground so it goes up and then goes that sounds like an urban legend no I'm pretty sure it's a diagram if my third grade memory serves me right well all right we'll have to look that one of lastly it's probabilistic in that in a basian network is a special kind of use case of a graph so keeping in mind that a graph is kind of like a social network but in our case a basian network the nodes are not people they're ideas they're random variables a random variable if it was a problem about a car could be like how long ago you got an oil changed whether or not it has a flat tire just any sort of detail you would have another node could be like is the check engine light on now there's many things that can turn the check engine light on right oh yeah at least with the Toyotas yeah especially our car I don't think we've ever had it off really for a very extended period of time y I'm just used to that false alarm right there that's what we call a type two error just because it's on doesn't tell us necessarily what the problem is yep and just says check engine although it's probably independent of whether or not we have a flat tire right they have another light for a flat tire if we were drawing a basian network of the car there'd be a node for you know is the tire flat or not and there'd be a node for the check engine light and they wouldn't directly link because the flat tire would not cause the check engine light to go on but the random variable of how much oil you have in the car that would be linked to the check engine light because if it gets low there's some probability it'll turn the light on a node like uh whether or not the check engine light goes on it has a bunch of incoming links from other nodes and then there's something inside of it called a conditional probability table and it describes the likelihood of the state of that node based on all of the inputs so in the case of let's say this check engine light if the input is the level of oil if the reading is full then there's a very there should be a low likelihood the light is on if the level of oil is very low there should be a high probability that the light is on right um yeah assuming the light works yeah the accuracy of the system how well tuned of a Metrology device it is that's going to be captured in this conditional probability table so we say what are the probabilities that this variable will be in these different states or have these different values given the input it has which you may or may not know right MH but you can describe what you know about those other nodes probabilistically so you can say like well I think these things might be true and then the whole basian network the reason it's basian is because it updates all of the beliefs you have over those different random values like can you give an example let's put a basan network in the context of like a a medical application like in a doctor's office or something like that hypothetically you go in complaining of fever the doctor in their mind or maybe they have a piece of software that actually does this has all of these things they can measure about you your blood pressure your temperature any complaints you have the amount of pain you report to be and these sorts of things and then they have some nodes some random variables that represent that like what it could be caused by so for example if you're report like feeling dizzy well that could be related to blood pressure or it could be related to I don't know probably two or three other things and all those things could be related to you having a certain syndrome or disease or virus or something like that okay there's things that cause other things and you can narrow them down based on symptoms yep and you know the relationship between them so for example if I go in complaining that I have a headache the doctor's probably not going to x-ray my my bones to see if I have a broken bone right well you're saying they would rule something out yes so the doctor has a belief over your medical State and it and you can express that belief in the basian network as a belief over the value of every node how about the belief you have malaria do you think if you went in if you went to the doctor complaining of a fever would the doctor assume that you have malaria well assuming you live in the US and that's where you hang out with most of your time then they'd probably not look towards malaria but they would ask some questions so they would ask do you travel malaria is present in tropical countries and climates where mosquitoes breed a lot more so the doctor begins with this maybe low probability that you have malaria and then you report hey I've been having fevers now what changes in their beliefs a lot of things change their belief that you have just a standard fever grows up their belief that you probably have a wide array of other possible diseases including but not limited to malaria goes up a little bit because something is causing the fever and it could be one of a lot of things right that's just a common immune response so then the doctor is like well I want to learn you know can I figure out the causal aspects of why this person has a fever so they'll start asking other questions where essentially they get new information that they can't observe so the doctor can't directly observe if you have malaria well I mean I guess they could take a blood test that's pretty much a direct observation but before they do that they'll ask you questions good one was have you traveled recently now what do you think think if you you don't tell the doctor where you went you just say yes how does that affect the doctor's belief that you have malaria well I think the odds of getting malaria are probably greater if you've traveled recently maybe not massively greater cuz maybe you travel to the Arctic or you traveled to France where there's not that much malaria but yeah maybe you travel to somewhere tropical and you were exposed so that as soon as they know you've traveled their belief goes up a little bit that it might be a malaria probably not like doubling or anything it's still un likely I would imagine but up a little bit but also other conditions go up right any other you know travel related illnesses you're likely to catch certain things when you travel more so than when you're at home let's take a break from our show today to talk about our sponsor Periscope data instead of telling you about some of the features of their product like I usually do today I wanted to give you a little bit of a personal testimonial about the way I use Periscope data so there's a company I did some machine learning work for so as every data scientist will tell you garbage in garbage out if the data is no good the models aren't going to work at all so as is typical I spent a lot of time building up the right filters how to exclude things that for whatever reason didn't count and you know test accounts and all this kind of stuff and I built up a view that really worked for me that I could power my model with but of course I was left with the nagging uncertainty that what if the underlying data shifts and that somehow screws up my model or causes drift in an unpredictable way well I solved that with Periscope data I built myself a nice dashboard that tracks of the key metrics and inputs that were going into my model I set that to email myself every day so I could just keep an eye on the stats I wanted to make sure that the summary statistic to describe the data set I cared about didn't shift if you'd like to get your own custombuilt dashboards in your email box at Whatever frequency you want and also have the luxury of getting alerts that you design you've got to check out Periscope data to get started head over to Periscope data.com [Music] Skeptics so what do you think the doctor's next question would be after learning that you've been traveling where have you traveled and where was the riskiest place you and I have ever traveled I don't know the riskiest but one place we traveled a few years ago was Vietnam uhh and they have higher cases incidences of malaria than the US in fact we had to look at a map to see if we were in danger zones right yeah there's certain areas in Vietnam that are at higher risk for getting malaria um so if then you report oh I just got back from Vietnam and I have a fever well then I think the doctor's belief of the possibility of malaria obviously they're not certain this could be a fever for any number of other reasons but now it's a little bit suspicious right suspicious that you might have malaria yeah because you traveled if you had to throw out a random number I know you're not a doctor or or you don't work for the CDC or anything like that but if you came back from Vietnam with a fever what do you think are the odds it's malaria I don't know you could have had food just gotten sick from the food so I mean I feel like there's at least that's a greater chance that you're just sick from food let's say malarious 10% chance you know that's exactly what I was going to guess because as much as that's maybe alarmingly high that one out of 10 people are expected to have it and you know you definitely want to do whatever the follow-ups are it's still not like a guarantee it's still not the sky is falling we can't Panic we have to think statistically and the doctor actually has to make a judgment call right they have to decide what to do next I don't know how you treat malaria yeah I don't either I guess the point I'm making here is that there's something about it that's external to the basian network at this point the doctor has to make a judgment call but they make it informed by this basian network which represents the most up-to-date version of all the beliefs the you know the culmination of knowledge they've acquired about you and it does this in an efficient way so what do you mean by efficient the main thing I mean is that you can add new information and that new information can propagate throughout the whole network in a really really quick way so you don't have to wait a long time given that and also some algorithmic details that I'm kind of skipping over here because we don't represent the full probability like everything related to everything we only represent the probabilistic relationships between the things that matter you know like fever and travel matters but fever and uh your X-ray reading shouldn't relate to one another because those independences are captured in the network by the absence of an edge we can better propagate the beliefs through the network in an efficient way you can compute your updated beliefs given the new information in a short period of time well the computer is doing the Computing right yeah okay so you're saying for some various reasons it's light and easy to update and doesn't take that long to compute that's right the handwave answer to why is because we're taking advantage of the statistical structure of the system if people want more details let me know in the comments maybe I'll do like a detailed blog post cuz I actually think it's an important result but a little bit too deep maybe for the mini episode basically we should walk away knowing that a basian network is this it's some kind of graph with nodes that's right yeah so each node is one random variable one property you know about a system and all the edges just describe the conditional dependencies and as you recall when we talked about last time conditional Independence that property shows up in kind of a cool way here if there's a conditional Independence between two nodes usually because know something that you know is in between that relates them to one another if you know the middle information then receiving new information about either variable doesn't cause a a belief update to happen across the rest of the network because you know if your smoke detector is going off that's a good signal that your house is on fire but if the fire department is actively there already then the smoke detector doesn't tell you any new information MH Bas and networks I like them because you can do statistical queries against the network you can keep adding adding new information and then look and say okay well given this new piece of information how does that affect what I believe about some other related piece of information so as a a data structure that has an efficient way you can compute those things you can have a really good probabilistic representation of whatever sort of system or project you're working on okay well then just to round it up I just wanted to clarify to our audience that we did not contract malaria that's right just that was an open question and then secondly our Prius does not have the check engine light on so we are all good and safe yeah how did you turn that off I didn't I thought you did no I didn't now I'm a little worried a long time ago I thought you took it in to get an oil change and that was it all right well Lindy what do you think is the most interesting part of this basian network's topic there's a network it makes decisions it seems very binary oh no it's not binary at all it's probabilistic well I'm not really sure we discussed why it's probabilistic oh let's get into that then so every node has I keep saying a belief over it that belief is a probability so the pro the likelihood that the check engine light is on that's between zero and 100% And I can go check it and if I see it on or off then I'll immediately like set the value right I'll say like it's definitely off right now I know that to be true because I trust my eyes but if maybe I heard from you as I did a moment ago that it's off and I'm not sure if I believe you well I just update my beliefs that I'm now like maybe 90% sure it's off cuz I think you might be right but you're not a totally reliable source of information no offense so the question is not is the light on the question is what's the probability that the light is on yeah okay so just for our audience then some of our questions should be rephrased yeah I sometimes speak maybe a little bit too binary maybe that's what you mean the variable itself the node in the network might be light on or off that's binary but your Bel well actually we should say it's light on is the name of the node and then your belief that that is true is the probabilistic part okay so it's about your what's the probability of X being whatever likely or on or what exactly okay so my summary is now it's a probabilistic network you got it you nailed it on this one basian networks are really cool and very useful maybe not as widely known or widely used as you know other things like just good old machine learning classification and deep learning and stuff like that but I love bayy networks I find them very useful I've had the a pleasant opportunity to have deployed them on two occasions in my career so that's pretty cool two occasions yep is that right or is that often uh well it seems a little rare I've done other tasks more frequently you know like just I've done I don't even know how many other machine learning models tons dozens at least I've only deployed bayy and networks twice is there an industry that it applies more to not necessarily an industry I would say a class of problems if I at least that's the way I look at it it's when knowledge representation is important when you know you have a lot of different observable and unobservable variables like maybe an industrial setting and some Factory would be a good use case where you have measurements from the Telemetry of all the different gauges and then certain things you can't measure and you want to be able to ask questions about the state of the factory not just like is the factory going to experience a problem which could be a fun prediction or classification problem but you want to say okay if this gauge gets to this temperature what do I think the pressure in this area will be and you can run you know sort of statistical queries like that anyway thank you as always for joining me Lindy thank you and until next time I just want to remind everyone to keep thinking skeptically of and with data data skeptic is a listener supported program to support the show visit datas skeptic.com and click on the membership tab