Now let's look at the issue of distributed representation. And where we've looked and how we've looked for activation is really being guided by our prior assumptions about how brain areas represent information. And there's a long tradition from neuropsychology of thinking about a function, like face recognition as being identified with one specific area of the brain. If you knock it out, you get rid of it and so on. So it's sort of a one function, one structure kind of mapping. I'll call that a localizationist view of the world. And if that's your view of the world, and that's the truth, then all you have to do is find the area that's related to the behavior and use that for prediction. Okay. However, you might be, what I'll call a distributist. So that a function and the signals, then the neurosignals that predict it, are distributed throughout the brain or at least through some broader subsection or network of the brain. And if this is the case then the multivariate predictive effect size is relevant. And there will be no one region or no one small population of neurons that you'll be able to find that can really give you the answer. No matter how good your data actually is. And, as a principle, the more complex a function then the more likely it is to involve distributive representations across many networks. So, this is, again, ultimately an empirical question, but there have been competing views and some early proponents of distributive processing and some findings include those of Carl Ashley here who famously tried to cut out different parts of the cortex in a rat, and disrupt a memory storage, the engram, so to speak. And he really had a hard time doing it. You have to cut out a tremendous amount of the cortex to actually impair memory. So he ends up concluding that [LAUGH] that something very strange is going on, at least. And it turns out memory is probably a highly distributed process. And here's another view later from Marcel Mesalam who writes very eloquently that ensembles of neurons tune to different categories of events, form this inner digitating or partially overlapping mosaic. And then there's the prominent ensemble varies from one location to the other. So this is looking a lot like our homogenous process. And like our multi-scale organization of information that I just presented there. So there's some information at the fine grain neural level, some information at the broader spatial scales of organization and so on. So this is how I think a lot of brain process are actually organized. And if you have a weak distributed prediction where there's no one brain region but the real signals that you're interested in in predicting an outcome are distributed across regions, then you really need multivariate analysis to be able to capture those signals. So this is a simulation where I have a weak distributed signal. The true correlation between brain and outcome in each voxel is 0.18 across the brain, and I've added some noise. Now let's do our standard correlation analysis, and we'll look at the maximum correlation across the brain. And the maximum correlation turns out to be 0.57, and we actually know that the truth is it's .18, it's very weak. But we get 0.57, and that's a biased result, and the reason for that is we selected this test post hoc out of a whole family of different tests across the brain, so I get a result, but it's not a good estimate of the effect size, as we discussed earlier. Now let's look at a local search light. This is a local multivariate algorithm where I'm trying to predict from local areas. And what I get is the maximum across the brain again is .56. And because again I've selected from across the brain, then I've got a biased overoptimistic result, right, at this particular location. Again, post hoc selection. But now, when I do a multivariate prediction across the whole brain, I'm allowing all the voxels to contribute and combine to contribute to the model. Now, I can predict based on all the voxels with a very strong correlation in this simulation of .98. So by combining the signals I can really overcome the noise. And this model happens to fit the general model for that data as well, but if the real process you're modeling looks like this then this whole brain distributed multivariate prediction is going to be the way to go. And also this is unbiased because it's across the whole brain and it's cross-validated, so we're always making predictions about new observations. So here's a real data example of distributed representation. So you might not like leeches. I don't like leeches. Here's a leech. And you could ask yourself how negative do you feel when you look at this photo? I feel like a four out of five. It's bad. And that's what we're trying to predict here. So we showed participants a whole series of images that're aversive, more or less aversive. And what we're trying to develop here is a brain signature across the whole brain for how negative people find that image. How aversive on a one to five scale. So here's the signature itself, and when we apply that to both cross validated data samples and to new hold out test data sets, it really predicts very well how negative a person is feeling. So we can classify how negative they are feeling very accurately. And now the interesting final point here is what is the representational basis for this prediction? So what does this mean in terms of the neuro signs? And we can ask then, what's the minimal set of regions that's necessary to make an accurate prediction. Do I need the whole brain or just one part of the brain or what? And this is an answer where we compare regions of interest, like the amygdala, the the insula, the very emotion associated regions of interests with the whole brain. And what we see is that those regions by themselves explain very little variance. The searchlight, the maximum across the brain, which is again biased upwards, optimistically, explains only 20% of the variance. But the whole brain pattern explains 70% of the variance in a fair test in how bad people feel. So what this tells us is that in this case, the negative emotion is actually really a distributed process. We did some other analyses as well to look at networks, and there's no single network in the brain this predictive as well. So here's the distribution of the correlations from the searchlight analysis. The gray histogram shows you the distribution across the entire brain. We can even pick out the best, and the best correlation is 0.44 across the brain. Probably optimistic. And the whole brain analysis correlation with the actual ratings is 0.85. That's the end of this module. I hope you enjoyed it. And stayed tuned for more MVPA to come.