speaker-0: Yeah, so a lot of kernels that we use a lot have a parameter in it called the length scale. there's all kinds of kernels that don't have length scale parameters, they have other parameters. There's useful kernels that don't have any parameters, you just say they're similar and you go from there. there's kernels over graphs, there's kernels over trees, there's kernels over all kinds of weird data things, but working in just sort of regular data where if x is five and another x is ten, the length scale parameter says, okay, is five and ten, they're five apart. Is are we going to think of that as similar or not? You know? And the length scale what it basically does is scale the inputs. That's the simplest way to think about it. And you can do a little do a little algebra on a kernel function like the exponential quadratic, and you can see that the length scale just defines just divides each x by a scale. And you know you can divide x equals five and x equals ten, you know, by divide them both by five and now they're one and two. So now they're only one unit apart. And then you go, okay, well that's pretty similar if the length scale is five. But if your length scale is like a hundred, then five and ten are hardly different, right? That's basically the same number. and if your length scale is like point zero zero one, then five and ten are really, really far apart. And those are Hardly the same thing at all. And so your y if you have x is five and another x is ten, then your y values there shouldn't be related to each other at all. They have no really nothing to do with each other. And so that's that's what a length scale is doing in in a lot of the common kernels like the ones from the Matern family and the exponentiated quadratic that you'll that you'll see if you look at the prime C examples or or most examples with GPs. Yeah.
speaker-2: Mm-hmm.
speaker-1: Yeah and actually so you'll tell me. Students understand about length scale and amplitude.
speaker-2: I used the first, I think the most probably the most useful function of the whole PyMC package is the GP Author during your with the envelopes and first the colors are amazing with GPs because they are so, you know, like uniform and continuous. It's just always extremely beautiful and pleasing.
speaker-0: Pretty plots. That's that's honestly another.
speaker-2: They make amazing pots. Yeah, yeah. And you can use and you know you can use the best
speaker-1: Color palettes, from Matlotlibla.
speaker-2: Like you the VRDs and CVDs and Magman they work. Whereas usually if it's like if you've got categorical data it's such boring palettes, you know, it's just like, you know, it's just one discrete color after the other. It's like, my god. Yeah. GPs are great because continuous.
speaker-1: So car piges that for
speaker-2: The function is amazing because you can see really the GP if it's to D of course.
speaker-1: And then so thanks to that, once you have that plot, basically the x-axis is the length scale. And it's gonna like the length scale is basically gonna tell you how far do the relation go on the x-axis. Yes. and it's like kind of a memory process. the memory of the process, because like if it's a long memory, then the length scale is gonna be long. If it's a short memory, short length scale. And also sometimes the length scale can be the memory can be spiky. It can be like if it's periodic, or actually every
speaker-2: Corner.
speaker-1: you remember about something, you know, it's like or like every my taxes, you know, so it's like that's like the the annual parody taxes, parody kernel, you know. so yeah, that's the length scale. And then y axis gives you the amplitude.
speaker-2: Mm-hmm.
speaker-1: Yeah and actually so you'll tell me. Students understand about length scale and amplitude.
speaker-2: I used the first, I think the most probably the most useful function of the whole PyMC package is the GP Author during your with the envelopes and first the colors are amazing with GPs because they are so, you know, like uniform and continuous. It's just always extremely beautiful and pleasing.
speaker-0: Pretty plots. That's that's honestly another.
speaker-2: They make amazing pots. Yeah, yeah. And you can use and you know you can use the best
speaker-1: Color palettes, from Matlotlibla.
speaker-2: Like you the VRDs and CVDs and Magman they work. Whereas usually if it's like if you've got categorical data it's such boring palettes, you know, it's just like, you know, it's just one discrete color after the other. It's like, my god. Yeah. GPs are great because continuous.
speaker-1: So car piges that for
speaker-2: The function is amazing because you can see really the GP if it's to D of course.
speaker-1: And then so thanks to that, once you have that plot, basically the x-axis is the length scale. And it's gonna like the length scale is basically gonna tell you how far do the relation go on the x-axis. Yes. and it's like kind of a memory process. the memory of the process, because like if it's a long memory, then the length scale is gonna be long. If it's a short memory, short length scale. And also sometimes the length scale can be the memory can be spiky. It can be like if it's periodic, or actually every
speaker-2: Corner.
speaker-1: you remember about something, you know, it's like or like every my taxes, you know, so it's like that's like the the annual parody taxes, parody kernel, you know. so yeah, that's the length scale. And then y axis gives you the amplitude.
