Louis Lyons: Thanks ivana okay so Hello everybody I get to be talking about two topics in particular one is combining results from different experiments and the second is understanding how neural networks actually work.
Louis Lyons: So to start, then we combining results will start basically from the beginning and we'll talk about just combining the results.
Louis Lyons: from different experiments that emotion one quantity X each experiment has an uncertainty on information when Sigma Sigma or I is the uncertainty on the X I.
Louis Lyons: And we're going to assume, to start with their uncorrelated most of the interesting things happen when we have correlations and the answer is that the the formula and right here only one and to give you the best estimate of X from by combining these results and the uncertainty in the.
Louis Lyons: back that.
Louis Lyons: And it's given by this sort of linear combination of the exercise, now it comes actually from minimizing with respect to X bass this formula for the way to some of squares of the deviation to the side from X.
Louis Lyons: squared divided by Sigma is where and commonly This is known as Chi square I prefer to call it asked, because in some circumstances, it does behave like TAI Chi square knows it doesn't.
Louis Lyons: make you call it Chi square you end up in central saying hi square doesn't behave like how squared which sounds a little bit curious so that's why I played that Okay, so these these formulary become.
Louis Lyons: Much more.
Louis Lyons: sort of obvious looking if you define the way awaits wi as one over Sigma squared for each of the measurements and I sort of thing for this way as the inflammation.
Louis Lyons: In the data from a given experiment and a signal goes down the way those are.
Louis Lyons: it's not a formal definition, just like the way I like to think about it, and then the equations one and to become a one prime and to prime.
Louis Lyons: And you do see that X best is just the weighted average of the XI and the formula for one over Sigma squared becomes that the.
Louis Lyons: inflammation content of the combination is the sum of the inflammation contents from each of the individual experiments so.
Louis Lyons: That sounds that sounds quite nice at the bottom of the page there's this sort of overall comment about combining results, and that is that actually it's far better to combine data, but that actually is a lot more hard work than just combining results and.
Louis Lyons: graduate students or whoever did the analysis and going off into some our profession, you might not be able to combine the data you haven't taken steps to preserve it so that's why we're talking about combining those knowledge.
Louis Lyons: Just the southern side little slide on the difference between the way to the standard average and it's a story about this sort of isolated island somewhere out in the Pacific it's very conservative population, nobody.
Louis Lyons: Believes and we're interested in knowing how many married people there are island so anthropologists go out to investigate they can't the islands too big to ask everybody, so they take a sample and because it's very conservative.
Louis Lyons: island.
Louis Lyons: You have to send out two teams anthropologists a male team to interview the men and the women anthropologist to interview, the women the men go the MAC mail anthropologist find out.
Louis Lyons: Their estimates of the number of married men on the islands 100,000 plus or minus 5000 women anthropologists unfortunately because they're women they get a smaller amount of fat funding very sad.
Louis Lyons: But it means they collect a smaller sample and they have a larger uncertainty, so there aren't is 80,000 of married women plus or minus 30,000 married a plus or minus 30,000.
Louis Lyons: How many married people are there on the island, it was sort of really trivial you just add up the two, and you get 180 plus or minus 30,000.
Louis Lyons: End of story well not quite and that the only answer is that if we inject a little bit of theory into our data analysis, maybe we can come up with a better estimate.
Louis Lyons: And a little bit of theory is that maybe the people here are monogamous and so, for each married man, there is a married woman and these two are two different estimates of number of married couples.
Louis Lyons: And so, how many married couples are there on the island well if we use the phone way on the previous page we find out that there are.
Louis Lyons: The the waiting for the married man is much higher than the married women we end up with 99 plus or minus 5000 with the uncertainty being dominated by the answer.
Louis Lyons: The better measurement.
Louis Lyons: And that means the total number of married people 290 8000 plus or minus 10,000 and the contrast between these two, I want to draw your attention is not so much the difference in the.
Louis Lyons: sort of point estimate, but the fact that the uncertainty on the weighted average is much better, much smaller than the uncertainty.
Louis Lyons: is derived from just doing the addition where it's the larger uncertainty that dominates the uncertainty and Sam So what we found is that by injecting a little bit of the era with hopefully uncontroversial we get a more accurate answer.
Louis Lyons: Of course, if the theory is wrong than this concept can be bias, which is sad.
Louis Lyons: it's a general point, and if you want the sort of example, corresponding to this in particle physics, it could be a kinematic fitting where we take the measured values of.
Louis Lyons: Say Jeff manages and my mentor and if we do kinematic fitting that is influencing the theoretical constraints of energy and momentum conservation among the observed quantity detector, then we can get improved values of the energy and momentum which is quite useful okay.
Louis Lyons: Fast to mainstream combining results.
Louis Lyons: And again there's this message here that is worth emphasizing combined data and combine results for various reasons, but there's a beware that applies to the formerly given back here formulating one and two or one time and to prime, and that is the fact that.
Louis Lyons: We can get into trouble when our estimated uncertainties on response to depend on the estimated value so, for instance, if we're trying to make a cross section from two different.
Louis Lyons: Data or estimating the flux of cosmic rays coming through the radio city in during the hour that i'm talking and then in the following now.
Louis Lyons: If we got in the first hour we count 100 and then the second hour we count at, then the uncertainties alliance B plus and minus can on the hundred plus and minus nine all the at, and this will give this in a larger way than for the hundred plus or minus 10.
Louis Lyons: there's a similar effect when we're determining the lifetime of particles from observing for and.
Louis Lyons: Examples of the big K of this part of measuring each of me and the K times and then do something with them define the mean life.
Louis Lyons: And if you do the very simplest method you end up with an uncertainty on tour, which is to have a square root of, and so this time.
Louis Lyons: it's the fact that the uncertainty on the lifetime tour is proportional to talk for one experiment measures, one point North north of the lifetime and the other measures, one point to note, then the one that had.
Louis Lyons: Any and both have 100 events, then the uncertainty will be plus or minus 1.9 plus minus 1.2 and the one that has fluctuated upwards of it as a larger uncertainties and one of the projects with down and have a bigger way.
Louis Lyons: That, I think, I said that at all i'm the one that fluctuated up as a larger uncertainty and hence a smaller weight is one of the larger wait again the messages likelihoods work better.
Louis Lyons: Okay, so this is just the gandy example of 100 plus or minus 10 and 18 plus or minus nine counts into identical.
Louis Lyons: Type period and the standard formula will give you 88.8 for the best value this one getting a bigger way and it's bias and and sensible and more correct approach is just to say.
Louis Lyons: In my countenance round of 100 in the first that are at in the second hour I had a total of 190 and in two hours and my basic rate is 90.
Louis Lyons: This bias actually as part of the reason that the particle beta group.
Louis Lyons: Among all the average constitutes a calculated, but in the early days of the of the discovery of the box.
Louis Lyons: Then the average being life time used to be one Peter second rather than the currently the value of around 1.5 seconds, because one experiment.
Louis Lyons: Has fluctuated down and had been given an unusually large way and that weighted average down solution well you really need to be using.
Louis Lyons: In this formula that says the weight is one over Sigma squared you really need to be using the real accuracy is not the estimated accuracies.
Louis Lyons: What are the real accuracy of these leaks round we don't know, but if they were they were using to equal time periods of equal efficiency, etc, then they're expected to have the same, you will see, whatever that is and really way.
Louis Lyons: The timings arm for how you deal with that there's a paper that.
Louis Lyons: explains how you can calculate the lifeline.
Louis Lyons: Essentially intuitively combining them were as a function of the assumed lifetime you change the uncertainties.
Louis Lyons: Because you sort of look at the way the exam was done you work out which part of the uncertainty scales, with the lifeline which is independent of lifetime read the papers, the details solution to is us likely that approach which is more like combining the data.
Louis Lyons: Right now we're going to come to some combining auditors and Essentially, these are all almost all connected with correlated.
Louis Lyons: combinations oddity number one is the fact that if you have to measurements of a quantity and they're positively correlated, then the true value can lie outside the range with people with some good reason don't tend not to lie.
Louis Lyons: And then the other oddities of the when you are combining a pair of wants is Alpha and beta from various experiments they do experiments.
Louis Lyons: Then the best values of Alpha and beta the uncertainties on them can be very much smaller than the individual answer is, and also the best values can lie outside the range of the individual maximum.
Louis Lyons: Of one variable.
Louis Lyons: So what do we do and we combining.
Louis Lyons: Combining more than one nation.
Louis Lyons: With.
Louis Lyons: correlated uncertainties and so the first five lines, or so it just repeating the procedure for the uncorrelated variables when this is my expression SPF.
Louis Lyons: Whereas if we have correlated variables, we have to expand the definition to ask prime involving the matrix in between these two.
Louis Lyons: The backbone and transpose the vector of the different axes compared with the best value and the matrix and is the inverse of the covariance matrix so here it's written down the.
Louis Lyons: Center to measurement Sigma this would be Sigma squared plus B squared and we have the covariance expressing the correlation between the management and the end is the inverse of the covariance matrix and what happens is that when we.
Louis Lyons: Do the same procedures we did with the uncorrelated face when we maximize s prime with respect to X best we find the value of X best.
Louis Lyons: And what what happens is that it lies outside the range of X one X two when the covariance is larger than the smaller of the two uncertainties here or, if you prefer, reading it in terms of the correlation coefficient bro.
Louis Lyons: row is larger than the smaller the ratio of the small to the large.
Louis Lyons: uncertainties.
Louis Lyons: So if you want to avoid this extrapolation effect for X bears then.
Louis Lyons: One situation where you get large row, is it too similar allows these are gone within the same.
Louis Lyons: thing collaboration on the same data provide two different groups using somewhat different methods.
Louis Lyons: So that because it's the same data, the results are going to be very correlated with each other, the answer that really is that if you want to avoid extrapolating find the best value then don't combine the two values try and get.
Louis Lyons: A little bit more inflammation out of the combination them from either one but it's better instead to use the better results and use the other as hopefully confirm the truth.
Louis Lyons: Where battery is defined as the smaller expected uncertainty.
Louis Lyons: And the reason for not extrapolate wanting to extrapolate is the amount of extrapolating you have to do depends on the exact values of the Sigma the uncertainties and the population.
Louis Lyons: This this extrapolation of that actually is known as people's person and parcel and P, or has sort of practice in.
Louis Lyons: an outbreak memorandum that actually i've been unable to find and the dates back from 1987 and it was about combining cross sections for neutrons plus the nuclei.
Louis Lyons: which the neutron Community was very interested in doing now, what do you do about this, and the answer is that the extrapolation sometimes it's very reasonable and you want to do it, and sometimes it's it's unreasonable for instance aluminum if you tried to combine the.
Louis Lyons: The data from one of the legs experiments from one year, not the air, then you probably have a luminosity uncertainty.
Louis Lyons: Which is correlated between the two years and then, if you're not careful, on luminosity uncertainties large compared with on certain days uncertainties, then it can result in this extrapolation from.
Louis Lyons: To get the best combined yourself as compared to the individual results, and there are numerous solutions as possible, and the answer, of course, is that it depends on the circumstances, whether you do, or you don't want to extrapolate i'll give you an example where you do in a second.
Louis Lyons: And one of the problems of course and the reasons you bet you would get involved in extrapolation when you don't want to is again that we.
Louis Lyons: can use estimated uncertainty is an equal level luminosity uncertainty is proportional is a sort of scale factor, which means that if things like actually a.
Louis Lyons: They get different.
Louis Lyons: Uncertain absolute closer.
Louis Lyons: Look, you don't really want.
Louis Lyons: Okay, you also can go get when you do this combination, you can get.
Louis Lyons: Small.
Louis Lyons: very small uncertainties on the combination and again that can be reasonable will see very soon.
Louis Lyons: And sort of combined with this is the statement that.
Louis Lyons: That it can be very reasonable about get these very small uncertainties and if you just end up by combining profile like birds, you can lose this.
Louis Lyons: advantage that you're supposed to get so the very simple example we're going to have is sort of tracking example with no magnetic field and it's just the TV set to a straight line to some things that some of the factors, so if it in y equals a plus cx to some tracks in.
Louis Lyons: detect too expensive to sub detectors each have three flames, so, if you like, here's, why is that this is one sub detector with the point shown in red.
Louis Lyons: And this is the other sub detector with the point showing in blue and then we're going to fit the track to some detectors individually and then overall.
Louis Lyons: The whole of the detector and you can see straight away without doing anything complicated that we're going to have a very large uncertainty in the gradient from these individual sub detectors because this offline to close together.
Louis Lyons: Do the combination we've got quite a nice lever arms, so the uncertainty is very much reduced with.
Louis Lyons: Your answer is not just a factor of squares into because we've got to estimate, it can be very much more, better than that if he's widely separated from each other.
Louis Lyons: So here actually looking at covariance matrix we're looking at the covariance.
Louis Lyons: matrix but the the red lips, is the sort of.
Louis Lyons: preferred values of A and B from the Red points and there's a negative correlation between gradient in the intercept because, if I fit some line through here.
Louis Lyons: If I have a line with a bigger gradient because smaller intercept so the uncertainty lips like that the Blue ones it's the other way around it, a straight line.
Louis Lyons: and get some intercepted by us a bigger Brady and i'll get a bigger set the covariance is proportional to minus the next.
Louis Lyons: And so you can see that these are the preferred values.
Louis Lyons: And so the overall preferred is not the overlap region but it's sort of related to that, but we're going to get a region sort of around here.
Louis Lyons: For the best value, so it is reasonable, but you do get a much smaller uncertainty on the combination when you think the new venture values there and it's all due to the correlations is actually a specific example of that rather than just tracking.
Louis Lyons: From cosmology So what is shown here is the fraction of the matter in the universe, and the fraction of dark energy in the universe as estimated from different cosmological backgrounds.
Louis Lyons: Different cosmological phenomena, this is the cosmic microwave background, this is the no thing, and this is clusters of galaxies and what you see is that the era estimates from each of them are sort of these ellipses the one supernovae different levels of confidence.
Louis Lyons: And the important thing is that they have different correlations, this is a very high negative correlation between the uncertainties on the practice of dark matter and dark energy.
Louis Lyons: Whereas.
Louis Lyons: This one is sort of almost uncorrelated misses the mild positive correlation.
Louis Lyons: And if you look at any of these individual measurements, you see, that means blue or.
Louis Lyons: Green or the brown their lives they all have big uncertainties in the fraction of dark energy and yet when you combine them because they had different correlations you end up with them.
Louis Lyons: Quite a tightly defined by you know Point seven something with a small uncertainty, so you certainly want to make use of the fact that they have different populations.
Louis Lyons: Also, you can get in this situation again like in a somewhat like the situation with just a single variable you can get a set of data, like like this one to two sub detectors That means that when you fit straight lines to.
Louis Lyons: The nba individual detectors you get.
Louis Lyons: lines like this.
Louis Lyons: that's the red line goes just with the red points the blue line goes through the blue points and the black line is the Professor combined line and so here the.
Louis Lyons: intercept of the best line is above, I both the individual intercepts and the gradient has actually the opposite sign to the individual gradient so entirely possible not not amazing.
Louis Lyons: Nothing magic about it, and you can have a hypothesis, and this really I was expressing this in terms of the parameters about us and being, but you can also actually have this for you can turn it into a hypothesis testing example I mean the hypothesis might be that the gradient.
Louis Lyons: Of the line here being the gradient of the line is is positive or negative and the lead to very interesting different cases and you.
Louis Lyons: Both the individual sets of data same gradient as positive the combined line says the dragon is negative, you favor the other hypothesis, I mean this might be relevant to.
Louis Lyons: The fact that when Nova and cheap to pay experiments measuring trying to determine which of the two you know mass hierarchies is.
Louis Lyons: The correct one the combined results from the two experiments seems to be different from the results from either the individual experiments.
Louis Lyons: So that might be this might be part of the story, why.
Louis Lyons: Okay, in the interest of time Let it come on to the visit the final example where.
Louis Lyons: correlations grossing well this actually is again a case where the combined result differs from the individual results.
Louis Lyons: With your combine combining but there aren't even any correlations of all here, so this is known as the your Simpson paradox and you've been against this in very many forms, you can imagine, this one being a.
Louis Lyons: topical issue.
Louis Lyons: Then it's giving patients abroad.
Louis Lyons: and
Louis Lyons: how effective it is and we're dividing patients to categories not young and old, but depending on their medical history, whether they were they had asthma, or they didn't have asthma.
Louis Lyons: And this is received, yet the drug day or vaccination a, and this is vaccination Bead and we're giving people are sort of ascribed a ma.
Louis Lyons: For how well they're doing the upgrade have this strong and so here the dragon a the the average month is 14 and here without with patients who didn't have asked her patients with as mothers was actually 18.
Louis Lyons: And the drug be the scores will be a mighty for these places and.
Louis Lyons: When you combine the results by adding up the number of patients, the sum total marks here the combined score is 70 to define it between 40 and 70 no problem.
Louis Lyons: Here the combined score CPA no problem is between 50 and 19 but what you notice is that we know asthma drug be was better with asthma drug.
Louis Lyons: Being is better again but combined drug a is better, and so you get like what's called the doctors dilemma.
Louis Lyons: In the patient comes along and if they've had asthma, then the doctor says okay will people with asthma drug is better than the next patient has no asthma.
Louis Lyons: And again, the doctor will say drug be is better, and the third patient comes along and says, I don't know whether I have asthma or not.
Louis Lyons: And so, Dr uses the combined score and said oh drug a is better, despite the fact that this patient either had asked why they use or didn't have asthma.
Louis Lyons: And in either case, they would have been giving the other drug so a real dilemma for the doctor, so I mean this you can be expressed in that, in terms of different schools and whether boys and girls and that sort of results that you might find sort of politically incorrect so.
Louis Lyons: i'll just leave you to think about that one and let's get on to the.
Louis Lyons: sort of Okay, the summary of the combination oddities, then, is that theory can help.
Louis Lyons: With.
Louis Lyons: If you introduce theory into your analysis, you can get more precise answer you have to be careful with estimated uncertainties which depend on the numerical value your estimate of.
Louis Lyons: Whatever physical quantity, it is you're trying to measure.
Louis Lyons: there's the heels pertinent paradox, where a combination, the outside the range of individual values and the fact that extrapolation can indeed be the correct procedure insensible quickly yeah.
Louis Lyons: being combined on certainly can be very much more women into uncertainties, a point that I didn't mention it in the stress, as I went through is that if you use profile likelihoods combining the day to lose this.
Louis Lyons: correlation information between the among the nuisance brand profile over, and so you can fail to get this.
Louis Lyons: back the combined Sigma can reasonably be very much mobile individual Sigma and that extrapolation as in the doctors dilemma.
Louis Lyons: Essentially, can.
Louis Lyons: extrapolate that's not the right word it is sort of flipping between.
Louis Lyons: 1% a year or another, or who did well at school, this can occur without any actual correlations.
Louis Lyons: And I think I gotta leave out this a couple of slides on not combining resolved combining P values, and I will just say that it's again much better to combine the data and combine P values.
Louis Lyons: And the other thing that I will say, without going into details, is there are various methods for combining P values it's not a unique proceed gay Defense the best method depends on information beyond just the information contained in the p values, and if you want to read the.
Louis Lyons: paper that gives you a comparison between, on the performance of the different methods they're due to the Boston.
Louis Lyons: So let's spend the last 10 minutes or so.
Louis Lyons: So again, spend the last 10 minutes or so just talking about your networks and how they were so.
Louis Lyons: Okay.
Louis Lyons: Right so neural networks, what we are trying to do in this specific application of your networks is to separate signal from background so i'm imagining the say the blue points or signal points and the red points background.
Louis Lyons: In terms of to kinematic variables V1 and V2 and we're going to try and use neural network to separate them so we've got these from Monte Carlo or from some samples of real data in regions where miraculously we've got your signal and.
Louis Lyons: We will also combined regions where background only that's easier and we're going to try and use a neural network in order to.
Louis Lyons: select these events for the banks, the purity and again any given efficiency, Nice and there are many ways of doing dealing with this, and I mean to start with, you can guess use your human generated selection.
Louis Lyons: Low dimensional parameters space that might be the best we, the one we're going to concentrate neural network simple neural networks, mainly with one hidden layer and nowadays we could use the networks with with many different levels so.
Louis Lyons: Looking at it very much from the outside and we're going to do better than this for us.
Louis Lyons: here's my little black new box, which contains the neural network we're going to feed in various features from the event.
Louis Lyons: That we have a game and we're going to tell the network which of these events signal on with your background and we're going to.
Louis Lyons: we've got to adjust more parameters in here basically weights and thresholds, but there's some parameters that we've been the network or fiddle around with.
Louis Lyons: To try and optimize the output, so the output is is near as one, as we can get for the signal and as needed to zero for the background so here's your network out output and here we've done some sort of reasonably good job of getting the signal me at one in the background.
Louis Lyons: or zero so.
Louis Lyons: it's going to be a learning process from the events.
Louis Lyons: So, how does it work.
Louis Lyons: So what we've got inside our little black box we simplified it down to just two inputs one output and there are three nodes in here in the hidden layer and.
Louis Lyons: Basically, everything all the input nodes or two of them are connected to each of the hidden layer three hidden layer nodes and then these are connected to the output and each of these nodes here.
Louis Lyons: And the output node again to take a linear combination of the import to to that So here we take an in the linear combination of.
Louis Lyons: These two inputs, the JAR from the the input variables of the event and it's going to sort of from them it's going to calculate and output.
Louis Lyons: And that is done buyers sigmoid function, so it is this linear combination is the input and the some output there, and here, this is a part of the output.
Louis Lyons: As a function unlabeled, this is the output on the y axis, and here the input on the X axis and it's the sort of sigmoid function like this one, over one plus two is correct and fellow beater it.
Louis Lyons: All of these sigmoid function so from zero negative values to want a positive values.
Louis Lyons: And that low be drink does it slowly a high beta it does it more sharply and a very high beta it just becomes essential step function between being off the negative invoice and on the positive and book Okay, so I think we're ready to.
Louis Lyons: Go.
Louis Lyons: So what we're going to do here is slightly different combination of.
Louis Lyons: blue background event in purple and what we're going to do is we're going to use the first note here, the first in the top in that mode in order to.
Louis Lyons: divide the.
Louis Lyons: By the region in multi dimensional dimensional space by this division line where the input is going to be the low.
Louis Lyons: Car or the input above zero so that we produce either.
Louis Lyons: The output is going to be either a one or a zero depending on this linear combination here is the big one, is the be too nice little way.
Louis Lyons: associated with these two purple ones in the diagram here's the threshold, which is another of the parameters of the network and what we again to do is we're going to ensure that.
Louis Lyons: What if this is greater than zero The network will be a link, there will be on with the.
Louis Lyons: One here, and if it's The other side is here zero, it will be off and what happened, so the dividing line between.
Louis Lyons: zero, and this is the equation of a higher plane, which in two dimensions for the straight line.
Louis Lyons: And so, this is the dividing line between where the network is going to be off for these and on all the events are delaying the diagonal here so.
Louis Lyons: we've got two more nodes and similar thing happens for the these nodes here with the Green lines and again with suitably chosen weights and threshold we can arrange the network will arrange for us that line to be here.
Louis Lyons: So, again on the road here and have below the green line and, finally, the third line is there, so we put them all together.
Louis Lyons: And these are the three lines that we have corresponding to these green.
Louis Lyons: The outputs from these three hidden layers and now what we want to do is, we want to insist that all three of them, give us an on.
Louis Lyons: Because, then that will select inside is trained or there was a pretty good job of collecting the blue points and not have been to many of the red triangles there, and so that will give us quite a nice optimization of our engine and so all we have to do is use weights like or.
Louis Lyons: Not like board, but each of these notes here the output from these nodes wait for them and the threshold of minus one, and so in order and remember H1 and H2 and a brain the.
Louis Lyons: outfits here are going to be all more to one, so the only way, you can get this positive is to have all of them on, and then we get positive about it, so this way, we got one out what.
Louis Lyons: All these events and zero out for all the others, and where we are happy so.
Louis Lyons: A couple of things to know the complexity of the final region in slack obviously it depends on the number of nodes and if I want to use the hex hexagons sagamore region, I will have six in here, and the second thing is that.
Louis Lyons: have been very large so that the transition from on to our occurs in a very your region across here, we can have a.
Louis Lyons: finite value.
Louis Lyons: That will have the effects of rounding the corner is.
Louis Lyons: desirable to be able to have so we've almost understood how networks work in in producing very flexible regions but.
Louis Lyons: The only source of regions can produce with a single hidden layer these solar comebacks regions so come back to the region is one where.
Louis Lyons: It can connect any coupons in the range and it lives within the region, whereas here's a non combat we can where you can connect this point with that one goes across.
Louis Lyons: outside the region so if I want to produce a region.
Louis Lyons: select my signature events like this, or like this, then I need a little bit more complex, I need an extra hidden layer so these little bets.
Louis Lyons: For imagine this picture here on the left these hidden bits this bit of the network here is very much like in the previous slide so we can arrange the this bit to be on for that region.
Louis Lyons: And this bed, giving us this ha here giving us on to this rage and and what we want is, we want the out what the on the Bible uses on so this time instead of requiring all of them to be on we want either of these to be alarming, so our.
Louis Lyons: Our output node can be doing it sigmoid on, for instance, the output from.
Louis Lyons: Age seven output from the top there and ha.
Louis Lyons: ha to the below a bit and these in my simple example I have an older one, and so, if I subtract a half of this if either of these is on, then the output will be on until we select this region or well or this region.
Louis Lyons: And Similarly, I can now sort of get used to.
Louis Lyons: The same example of emerged as one region, not the same region, which again has gone from backstage which requires an extra layer so.
Louis Lyons: We can get more complex layers and if I want to have a whole series of and adores I would have to.
Louis Lyons: sort of have extra layers in my in my overall network connection So these are not actually completely connected networks in that, for instance, the the be one input goes just to.
Louis Lyons: My upper box here and not to the lower box, so I can even if I did connect this fully I couldn't really be more exotic things that I don't quite understand, but this is the level of understanding.
Louis Lyons: of how simple ish neural networks with one or perhaps do a few more hidden layers where.
Louis Lyons: We were was just general statements about using neural networks and.
Louis Lyons: I think we've come to the summary of being you're being your network, and that is that the advantages of course they're very flexible calculations Okay, and you can have a tune the top.
Louis Lyons: desire for selecting thing the disadvantages that takes time or long time, very long time there's a tendency to include too many variables.
Louis Lyons: and
Louis Lyons: That the neural network in the world and finding out what's useful and what isn't and also that it can be treated still can be treating someone as a black box, especially when you come to.
Louis Lyons: The multi layer network and the attitudes neural networks, certainly has changed considerably over the years.
Louis Lyons: At the beginning of the last year.
Louis Lyons: A few we're going to use your network, you have Convention columns, but it was not completely ridiculous thing to do, whereas towards the end of roadmap era.
Louis Lyons: It was getting to the case that if you didn't use your own networks, then you are asked why you weren't using them, and I suppose now in the future is why aren't you using a deep network to do all the work for you.
Louis Lyons: So overall conclusions, which are not specific actually the topics that i've been talking about is that there's a lot of software that exists.
Louis Lyons: Doing many statistical procedures for you.
Louis Lyons: So there's a slight complaint is a little bit too easy to use, without understanding what it's doing, and it really is important to try and understand what it's doing because.
Louis Lyons: You sort of get one of your pieces of information that we're getting instructing the program what to do if you get it wrong, you want to be big enough aware of what is your network is supposed to be doing in order.
Louis Lyons: Software others doing in order to protect.
Louis Lyons: Those simple arrows.
Louis Lyons: For all these topics books exist for now much more information on the web, these are some books, written by particle physicists about.
Louis Lyons: Statistics so much easier for particle physics, in general, to understand them, and then to understand books, written by.
Louis Lyons: Genuine statisticians populate groups got seconds on probability statistics and Monte Carlo and the big experiments down has statistics committees that you go to their website to be involved for advice and another source of information, the five step series of workshops.
Louis Lyons: which the last few years have been devoted rather than to specific areas of physics physics in general and there's also now there's the fights that series of lectures.
Louis Lyons: happen about once a month with lecture given by real statisticians and also by particle physicists special interest in.
Louis Lyons: physics and the final comment is that if you think you've got some use of this.
Louis Lyons: problem that you have to resolve before you reinvent the wheel transit statisticians or even particle physics, have already found a solution.
Louis Lyons: For your statistical analysis problem and then particular don't use your own square wheel circular with all That being said, so good luck to your analysis and thanks.
Ivana Hristova: Thank you very much, Louis for the very nice overview and the comprehensive explanations of these interesting topics, so let me stop the recording.