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bilibili_data_13232720_BV11t411A7Ym_p2_BV11t411A7Ym_p2_m4-dialogue_0616556
[S1] Now, the nice thing is, this course, not only is this course free, but these books are free as well. The elements of statistical learning has been free and, and the PDF's available on our websites. This new book is going to be free beginning of January when the course begins. And, uh, and that's a, with agreement ...
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bilibili_data_13232720_BV11t411A7Ym_p32_BV11t411A7Ym_p32_m4-dialogue_0890550
[S1] So, welcome back. Today we're going to cover model selection and regularization. But we have a special guest, my former graduate student, Daniella Witten. [S2] Hi. [S1] Welcome, Daniella. [S2] Thank you. [S1] Daniella is now at University of Washington, but maybe you want to tell students a bit about yourself and ...
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bilibili_data_13232720_BV11t411A7Ym_p32_BV11t411A7Ym_p32_m4-dialogue_0890551
[S1] Yeah, well, I, um, in college, I studied math and biology, and when I was graduating, I knew I wanted to, to go to grad school in something, but I couldn't really decide on one particular thing that I wanted to study for the rest of my life. And so I ended up doing a PhD in statistics, and I was lucky enough to do...
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bilibili_data_13232720_BV11t411A7Ym_p33_BV11t411A7Ym_p33_m4-dialogue_0302721
[S1] Um, and we, we'd want to use best subset, maybe not beyond 10 or 20, say. [S2] Yeah, I don't think I would probably even use it for 20. I mean, I think I would use best subset if I've got a handful of predictors, and if I've got 10, I wouldn't be using that anymore, most likely. [S1] Yeah, so the point is, it's no...
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bilibili_data_13232720_BV11t411A7Ym_p35_BV11t411A7Ym_p35_m4-dialogue_0407423
[S1] That's right, yeah. [S2] Unlike the RSS curve. [S1] Exactly. It's a little hard to see. [S2] Yeah. [S1] But this is slightly increasing. It's smallest- [S2] Yeah. [S1] ... with four predictors, and then it goes up a little bit. But, you know, I don't really think that there's compelling evidence here that, that fo...
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bilibili_data_13232720_BV11t411A7Ym_p35_BV11t411A7Ym_p35_m4-dialogue_0407424
[S1] So, already we see that, that CP is restricted to cases where you've got, uh, N bigger than P. [S2] That's right. [S1] And, and even if P is close to N, you're going to have a problem because you're asking if sigma squared might be, uh, far too low.
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bilibili_data_13232720_BV11t411A7Ym_p35_BV11t411A7Ym_p35_m4-dialogue_0407425
[S1] So, um, we want a large value of adjusted R squared. And, um, and so the adjusted R squared, in practice, people really like it. It tends to work really well. So some statisticians don't like it as much as, um, C-P, AIC, and BIC. [S2] [LAUGHS] [S1] And the reason is because it sort of works well empirically, but s...
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bilibili_data_13232720_BV11t411A7Ym_p35_BV11t411A7Ym_p35_m4-dialogue_0407426
[S1] But one nice thing about adjusted R-squared is like if you're working with, um, someone who's not a statistician, like scientists who aren't statisticians are really familiar with R-squared. And so from un- when to understand R-squared, adjusting R-squared is just a really small one-off and it's kind of easier to ...
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bilibili_data_13232720_BV11t411A7Ym_p37_BV11t411A7Ym_p37_m4-dialogue_0616557
[S1] And I remember when I was a student seeing this figure again and again. Actually, it was in a class that Rob was teaching and being totally confused for like three lectures. [S2] Okay. [S1] So I just want to spare everyone this confusion in case anyone shares the confusion I had. So like, if we look here, this red...
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bilibili_data_13232720_BV11t411A7Ym_p37_BV11t411A7Ym_p37_m4-dialogue_0616558
[S1] ... limit and rating take on values of around 250. And so the point is, what we're plotting here is a ton of different models for a huge grid of lambda values, and you just need to choose a value of lambda and then look at that vertical cross-section. [S2] Good. And is, so as Danielle said, if we chose the value o...
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[S1] Right, exactly. So, an equivalent picture on the right now, we've plotted the, um, the standardized coefficients as a function of the, uh, of the, the L2 norm, the sums of the squares, the square of the sum of the squares of the coefficients divided by that, the L2 norm of the fully-squared coefficients. [S2] So, ...
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bilibili_data_13232720_BV11t411A7Ym_p37_BV11t411A7Ym_p37_m4-dialogue_0616560
[S1] And in between we get again a shrunken coefficient. So these two pictures are really the same, but they've been flipped from left to right. [S2] And the, the x-axis are parameterized in a different way. [S1] Right. [S2] So Rob, why does, um, this x-axis on the right-hand side go from zero to one? Why does it end a...
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[S1] Right. So on the right-hand side here, on this right-hand plot, lambda is zero. [S2] Right. [S1] And so your ridge regression estimate is the same as your least squares estimate, and so that ratio is just one. [S2] Exactly. Okay. Um, I think we've actually just said all this. Thanks for the questions from Daniela....
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[S1] Um, by a certain amount. And we see the same thing on the, in this picture. [S2] And actually, this U-shaped curve that we see for the, um, the mean squared error in this figure in purple comes up again and again. [S1] Yeah. [S2] Where when we're considering, um, a bunch of different models that sort of have diffe...
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[S1] And by the way, if that looks like a total mystery, if you can like reach back to your, your distant or not so distant past, if you ever took AP calculus and you saw Lagrange multipliers in high school, this is really something that you, you might have truly seen in, in high school calculus a long time ago, but fo...
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[S1] And one thing we should mention is the, on this right-hand panel, the, the x-axis is something we haven't seen before, which is the R-squared on the training data. [S2] Right. [S1] And the reason we have that x-axis is because in this figure on the right-hand side, we're plotting both ridge regression and the lass...
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[S1] Okay, I would have noticed that detail otherwise. [S2] [LAUGHS] [S1] Okay. So now, now here's a situation where we do, we do perform better with the LASSO, and this is a case where now in the population, only two of the predictors have non-zero coefficients. So, the previous situation was, was, was dense, or non-s...
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[S1] So in a way it's sort of similar to Ridge and Lazo, right? It's still least squares, it's still a linear model in all the variables, but there's a, there's a constraint on the coefficients. [S2] That's exactly right. [S1] Right. [S2] But we're getting a constraint in a different way. We're not getting a constraint...
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[S1] Oh, yeah. And, you know, Rob, it just occurred to me that that paper we wrote 30 years ago. [S2] Still good. Still good. [S1] Still a good paper. [S2] Okay. [S1] Okay. So, here we go. Well, the first fact is the truth is never linear.
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[S1] Well, when I first saw that, I thought it was crazy, but then I realized the vertical scale is pretty stretched, right? So it's only ranging up to 0.2. [S2] Oh, good point, Rob. Good point. [S1] If you saw that from zero to one, it would look a lot more narrow.
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[S1] You can already see the advantages it has over, over polynomials, right? Th- th- this is local. Remember, with polynomials, it's a single function for the whole range of, of the, of the x variable. So, for example, if I change a, a point on the left side, it can potentially change the fit on the right side quite a...
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[S1] There's a piecewise polynomial. It's a cubic polynomial. There's the knot at 50. And it's, it's a cubic to the left and a cubic to the right. They're two different cubic polynomials. And they just fit to the data. This one's fit to the data on the left. This one's fit to the data on the right. What do you think of...
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[S1] Okay, so cubic splines, um, are used all over the place and, and you'll see we, we even got fancier versions. One fancier version is, is very handy and it's the one I tend to use all the time. It's called a natural cubic spline. If you had the choice of a cubic spline and a natural cubic spline, which one would yo...
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[S1] The standard errors you see are much wider in places for the cubic spline, especially at the boundary, which is where the act, the, the effect of the natural spline is, is taking place. And the standard errors for the natural spline are, are better there. [S2] I'm actually working on something called organic cubic...
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[S1] Okay. Fitting splines in R is easy. Um, there's a function BS, um, which takes a variable X and has some arguments. You can give it the knots, for example, and, uh, or you, uh, there's other ways of specifying the flexibility, and it'll just do the work. You, you put that in a formula and you can put one of those ...
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[S1] I can see you don't like the name. [S2] No. [S1] No, don't get rude, Rob. Um, and that's for cubic splines and for natural splines, NS. And here we see a function of age. Here's a natural cubic spline. You can see it's got three knots, interior knots, um, and is a function of age and gives you a very nice fit, sta...
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[S1] It's not as, as crazy a function as you like because the roughness penalty controls how wiggly the function can be. [S2] It's pretty amazing that this has a solution at all, right? It has a nice simple solution. [S1] Exactly. [S2] And I guess the, a clue as to why it's a cubic spline is that the second derivative ...
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[S1] So if you like these kind of mathematical things, it's a, it's a fun proof to go through. [S2] Yeah. And it might show up in one of the quizzes. [S1] [LAUGHS] [S2] No. Okay. A few details. As I said, they, smoothine splines avoid the knot selection issues and, and we have a single lambda that needs to be chosen. T...
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[S1] Okay. Well, so we already got a, a long list of, of, of ways of, of fitting nonlinear functions. There's another whole family of, of methods called local regression. In fact, Rob, wasn't there a PhD thesis from Stanford on, on local regression? [S2] I don't remember. [S1] Rob's PhD thesis was called Local Likeliho...
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[S1] I wouldn't say wildly. [S2] You're too modest, Rob. [S1] Yes, yes.
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[S1] ... probably fair to say that, uh, Lowe's and cubic splines are, cubic smoothing splines are probably the two best ways of doing smoothing. And if you set the degrees of freedom of both to, to be equal, roughly, they look pretty similar too, in general. Would you agree? [S2] That's right. [S1] So, either one of th...
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[S1] One, uh, node per observation. [S2] So a very bushy tree has got high variance in. [S1] Right, it's got high variance, uh, low- [S2] It's overfitting the data. [S1] Low bias, but is overfitting and probably not gonna predict well.
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[S1] We, we set aside one part, we fit trees of various sizes on the K-1 parts, and then evaluate the, the, the prediction error on the part we've left out. [S2] Oh, so that's clever. The whole thing's controlled by alpha, then. Alpha decides how big the tree is, and you use cross-validation just to pick alpha. [S1] Ex...
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[S1] Right. And so we, we choose the alpha and we'll see cross validation curves in a few slides, but it's going to tell us the, a good idea of the, the best value of alpha to trade off the fit with the size of the tree. Um, having chosen alpha, we then go back to the, the, the, the full tree and find the sub-tree that...
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[S1] ... the size of the, the, the term- we, we don't split a terminal node that has fewer than, say, five observations. And that gave us this tree with how many nodes? One, two, three, four, five, six, seven, eight, nine, 10, 11, 12. Right? But probably not all of these are, are, are, are predictive. [S2] Why, why are...
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[S1] Not me. It's a good idea though. [S2] So it's the, whoever the author of the tree growing program in R is. [S1] Yeah. [S2] Okay. So here's the result of cross validation, which is going to give us the pruned tree. So what do we see here? Well, we see along the horizontal axis, tree size, which is the alpha paramet...
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[S1] So cross validation, on the other hand, you fit for a while, it's, it's, it's, it's, it's happy with the splits, and then it looks like it's overfitting, just increasing variance and, and not helping prediction error. Uh, the test error, which we're, we can evaluate here because we have, we've set aside a separate...
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[S1] And so we gr- we ran the tree growing process with cross-validation, and we see what we get in the next figure. At the top, you see the full tree grown to- to all the data, and you can see it's quite a bushy tree, um, with an early split- uh, split on thal. [S2] It's actually, it's a- it's a thalium stress test. [...
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[S1] And, and then the two, the left and right nodes were split on, on CA. [S2] Uh, calcium, I think. [S1] Which is calcium. And, and then the subsequent splits, it's hard to see here, but you get, um, this, these pictures are in the book. So quite a bushy tree.
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[S1] If we go over the left here, we'll see actually results of a single tree. So in this case, bagging proved a single tree maybe just by 1% error. [S2] Actually, the dotted line is a single tree, right? [S1] Okay.
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[S1] ... training sample, if you run this, if you grow two tre- two trees, you'll get two different trees, 'cause- [S2] Exactly. [S1] ... by chance, it'll pick different variables each time. [S2] Okay, so let's see how Random Forest does in the-
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[S1] That's a good question. Is it, is it cheating? Is it biasing things? Well, it's not because when, when, the, the outcome, the class is not being used to, to choose the genes. It would have been a problem if we chose the genes that, that, that, that vary the most from one class to another. In other words, if we, if...
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[S1] Its error is, um, upwards of 50 or 60%. Now remember, there's 15 classes, so an error of 60 or 70% isn't crazy, right? Um, because there's so many classes, but it's still, it's still not very good. [S2] It's interesting, Rob, how quickly the error comes down with random forests. [S1] Right. [S2] And then sort of l...
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[S1] So there's these two components, growing a tree to the residuals and then adding in some shrunken version of it into your current model. [S2] And that lambda's pretty small, right? It's like, we're going to see about 0.01, for example, as a value of lambda. [S1] So really shrinking-
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[S1] four and eight. That might be a typical example, depending on, on the size of your data set and the number of predictors. [S2] Oh, so if, if D is one, each little tree can only involve a single variable. [S1] Right. So it's, it's actually an, an additive function of, of single variables, so there's no interactions...
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[S1] Unlike in random forest where the number of trees, you just went far enough so that you, uh, till you stopped, uh, getting the benefit of averaging. [S2] Right. I think it's still the case that, that the number of trees is not a hugely important parameter. It's possible to overfit, but it takes, I think, a very la...
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[S1] Um, x2 squared, x1 cubed, x1, x2, and so on, right? Polynomial expansions. So you can go from a p dimensional space, in this case, two, to a higher dimensional space. And the more transform variables you add, um, the more likely you are to be, to be able to get separation in this higher dimensional space. [S2] I j...
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[S1] Okay. Thank you. That was a bad choice of, uh, of letter. [S2] That's usually the kind of mistake I make. [S1] [LAUGHS] [S2] I'm glad, I'm glad I caught you on one, finally. [S1] It's the kind of mistake I hate making.
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[S1] That's a good point, Robin. You know, and when you think of it like that, you say, suppose you had a thousand points, and it ends up that there's 10 support points. You think, "Oh, great, you could have thrown away the other 990 points." Well, not really, because you had to have them all there to decide which ones...
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[S1] You'll notice when you, if you, if you went through this little example over here, you'll notice that it was a, it did give you the inner product between a degree two polynomial, but there were coefficients in front of these, and those are, are what give you the squashing factors. [S2] So Trevor, in that example, ...
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[S1] You'd run into trouble raising power of... [S2] Right. [S1] ... to a million. [S2] Yeah, with a polynomial kernel, I can get away with that. [S1] You can get away with it, yeah. [S2] And that's because of the squishing. [S1] Because of all the squishing down, yeah.
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[S1] So if gamma's really large, it's like having a small standard deviation, and, and you get much more wiggly decision boundaries. Whereas if gamma's small, the, the decision boundaries gets smoother. [S2] That's a good point. [S1] So we're gonna take this machinery in, in the next segment and, and look at a, a, an e...
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[S1] In the left panel. [S2] In the right panel. [S1] In the right panel, we compare the linear support vector classifier, which is the red curve, to the SVM using a radial kernel, um, with different values of gamma, right? And you'll notice that it's not monotone. So when gamma is 10 to the minus 1, we seem to do real...
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[S1] Which means gamma is another tuning parameter for the support vector, uh, classifier. [S2] And just keep in mind, what they're telling us, it's not really a fair comparison on the right panel, right? 'Cause the, the, uh, gamma smaller has more complexity, so it's gonna fit more. So, and this is a bigger? [S1] Yeah...
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[S1] ... or group them into, into, uh, uh, customers that are similar with regard to these features. And why do we want to do that? Because m- maybe if they're similar with regard to these features, then the, the, the, the kind of advertising we use for that subgroup will be, uh, important. So we use a certain kind of ...
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[S1] It's, what's also interesting, Rob, is that variables that are somewhat responsible for clusters, like for example, this, this second variable- [S2] Mm-hmm. [S1] ... that we have over here, um, also tend to have high variance because, you know, if, if they separate the data in, in, in, in clusters, they, there ten...
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[S1] So, that's just the detail of the previous figure, which we talked about. Now, oh, sorry, I missed a point here, which is that it's not, this algorithm, although it gives you a, a local minimum, it's not guaranteed to give a global minimum. Why not? Well- [S2] What does that mean, Rob? A local minimum? [S1] Oh.
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[S1] Remember, starting the algorithm was this random assignment of points to, to the number of clusters you're using. [S2] Right. So when we start the algorithm from different places, we get actually quite different solutions. Don't worry about the fact that the colors are chosen differently. Like this, these are gold...
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[S1] ... three or four different, three different, yeah, three different solutions, right, I guess. [S2] The one, the ones you colored in red at the top all have exactly the same distance. [S1] Yeah. [S2] So they're actually all the same. The colorings are different, but as Rob said, the colorings are arbitrary. [S1] Y...
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[S1] Well, we have a guest here today, Dr. John Chambers. Um, John was the inventor of the S-language, which is the language that we use in, in R. John was also my department head at AT&T Bell Labs when I worked there in the, in the 80s and 90s. So, John, welcome. [S2] Okay. [S1] And- [S2] Great to be here. [S1] Thank ...
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[S1] Uh, and meanwhile, the next event, uh, on the floor above us at Murray Hill, there were some guys in computer science research who were busy creating a new kind of operating system, which eventually was called UNIX. [S2] Oh. [S1] And in particular, in around 1978 or so, a new version of UNIX was developed that was...
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[S1] Not, not so similar. There, there were, uh, two books that Rick and I wrote that described that. If you looked at it and just looked at what somebody written down, say, to do a linear regression, it would look similar. [S2] Yeah. [S1] But as soon as you started to do anything non-trivial, it was very different. [S...
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[S1] Uh, and on that date, version 1.0 of R was, was produced. I wasn't part of R-Core at that time, but I was very friendly with them, and one of my most treasured souvenirs is serial number one of the CD-ROMs, uh, that were produced at that time for R, autographed by all the members of- [S2] Oh, fantastic. [S1] ... t...
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[S1] for many things now, not all, but many things now, people produce the code, they produce an R package, and instantly, everyone else can use what they've got freely and contribute their ideas to let things evolve. And that, I think, is, to my mind, the most beneficial result that's happened. [S2] Well, thank you ve...
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[S1] No, I don't think that's the case. Um, the thing is for us, you know, a lot of what we do is actually sometimes a lot of it is traveling. So you would be very bored sometimes, I think, on your own. [S2] Yeah. [S1] And, um, it's really good to have each other around and, and kind of buzz off each other. And even wi...
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[S1] I've already been to Eiffel Tower twice. [S2] Yeah. [S1] So, and I do love it, but I would, I think I'd just go to a really nice French restaurant. [S2] Yeah. [S1] I'd actually, I've never tried, like, snails or what else is the French signature? [S2] Frog's legs? [S1] Frog's legs, yeah. Never tried either, and I ...
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[S1] Elon Musk, great to see you. How are you? [S2] Good, how are you? [S1] I mean, we're here at the Texas Giga Factory the day before this thing opens. It's been pretty crazy out there. Thank you so much for making time. [S2] Very welcome. [S1] I would love you to help us kind of cast our minds, I don't know, 10, 20,...
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[S1] And help us try to picture what it would take to build a future that's worth getting excited about. You've often said it. [S2] Sure. [S1] The last time you spoke at ten, you said that, that was really just a big driver. It's, you know, you can talk about lots of other reasons to do the work you're doing, but funda...
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[S1] And then, uh, ultimately, uh, you, you, it's not really possible to make electric rockets, but you can make the propellant used in, in, in rockets, uh, using sustainable energy. [S2] Right. [S1] So, uh, ultimately we can have a fully sustainable energy economy, uh, and, um, and it's, it's those three things, solar...
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[S1] If, if, if that's the, the, the- [S2] That's the angle. [S1] ... rough, very rough numbers. And I certainly would invite others to check our calculations, 'cause they may arrive at a different, a different conclusions. But, um, in order to, uh, transition, uh, not just, um, current electricity production, but also...
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[S1] We'll probably do more than that, but yes, that's, hopefully we get there within a couple of years. [S2] Right. But I mean, that, so that is one- [S1] Point, point, point one terawatt hours. [S2] But that's still one, one hundredth of what's needed. How much of the rest of that 100 is, is Tesla planning to take on...
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[S1] I mean, these are just guesses. I mean, um, so please, you know, people just shouldn't hold me to these things. It's not like this is like, uh, some, what, what does happen is I'll, I'll, I'll, I'll make some, like, you know, best guess and then people will, in five years, there'll be some jerk that writes an arti...
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[S1] that same grid probably is offering the world really low cost energy, isn't it? Compared, compared with now. [S2] Yeah. [S1] And I'm, I'm curious about, like, do, should people, are people entitled to get a little bit excited about the possibilities of that, that world?
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[S1] ... use a lot of energy. But if you've got, um, a lot of s- uh, sustainable energy from wind and solar, uh, you can actually sequester carbon, so you can re- reverse the CO2- [S2] Right. [S1] ... uh, p- parts per million of the atmosphere and- and- and oceans. Um, and- and also, uh, uh, you can really have as much...
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[S1] Yes, exactly. [S2] Yeah, yeah. [S1] 'Cause like, like when you, when you burn fossil fuels, there's all, there's all these like, uh, side reactions and, and, and, and toxic gases of various kinds. Um, and like, like, like, sort of, uh, little particulates that, that are bad for your lungs. Like, there's, there's a...
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[S1] I want us to switch now t- to think a bit about artificial intelligence. And, but the segue there, let, you, you mentioned how, how annoying it is when people call you up for bad predictions in the past. So, I'm, I'm possibly gonna be, um, uh, annoying now. But, um, I, I, I'm curious about- [S2] Yeah. [S1] ... you...
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[S1] You did almost exactly half of it. You were scoffed in 2014 because no one- [S2] Yeah. [S1] ... since Henry Ford with the Model T had, had come close to that kind of growth rate- [S2] Yes. [S1] ... for, for cars. You were scoffed and you actually hit 500,000 cars and- [S2] Yeah. [S1] ... and 510,000 or whatever pr...
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[S1] Last time you came to TED, we, um, I asked you about full self-driving and, um, you said, "Yep, this very year, where I am confident that we will have a car going from LA to New York, uh, without any intervention." [S2] Yeah, I, I don't want to blow your mind, but I'm not always right. [S1] [LAUGHS] [S2] Um... [S1...
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[S1] Uh, you, you just hit a ceiling. Um, and, and, uh, uh, if you, because what happened, if you, if you were to plot the progress, the, the progress looks like a log curve. So it's like, yeah, a series of log curves. So, uh, most people don't know what a log curve is, I suppose, but it, it, it- [S2] Sure, sure, the s...
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[S1] It goes, it goes up sort of a, you know, sort of a fairly straight way and then it starts tailing off and, and, and, and you start- [S2] And there's a kind of ocean. [S1] ... getting diminishing returns. Uh, yeah, and, and you're like, uh-oh, this, it was trending up and now it's sort of curving over and not, and,...
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[S1] Well, I mean, admittedly, these, these, uh, may be an infamous, uh, last words, but I, I actually am confident that we will solve it this year. Uh, that we will exceed, uh, you're, you're saying, like, what, the, the probability of an accident, uh, at what point do you exceed that of the average person? [S2] Right...
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[S1] ... ambiguity. But if you look at a, at a video segment of a few seconds of video, that ambiguity resolves. [S2] Mm-hmm. [S1] Um, so the, so the first thing we have to do is sort of tie all eight cameras together so they're syn- they're synchronized, so the, all, all the frames are looked at simultaneously and lab...
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[S1] create, uh, an order labeling, uh, create order labeling software to amplify the efficiency of human labelers because it's quite hard to label video. It takes, in the beginning it was taking several hours to label a 10 second video clip. [S2] Mm-hmm. [S1] This is not scalable. [S2] Right.
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[S1] What you're saying is that, uh, that you, you think that, I mean, the, the result of this is that you're effectively giving the car a 3D model of the actual objects that are all around it. It knows what they are, and it knows how fast they are moving. And th- the remaining task is to- [S2] Yes. [S1] ... is to pred...
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[S1] What the quirky behaviors are, that, that, you know, that when a pedestrian is walking down the road with a smaller pedestrian, that maybe that smaller pedestrian might do something unpredictable or, like things like that. [S2] Yeah. [S1] You have to build into it before you can really call it safe.
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[S1] So you have to say, how much are you going to try to remember? Um, and, but like if, it's very common for things to be occluded. So like if you talk about, say, a, a pedestrian walking past a, a truck where you saw the p- pedestrian, um, st- start on one side of the truck, then they, then they're occluded by the t...
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[S1] ... computer doesn't know until it's full. [S2] So you need to slow down. [S1] I mean, a skeptic is going to say that every year for the last five years, you've kind of said, "Well, no, this is the year." We're confident that it, we're, we're there in a year or two or, you know, like it's, it's always been about t...
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[S1] Um, yes. I mean, the, the car currently drives me around Austin most of the time with no interventions. So it's not like, um, and, and, and, and we, we have, uh, over 100,000 people in our, uh, uh, full-stop driving beard program. Uh, so you can look at the videos that they post online. Um- [S2] I do. [S1] Okay, g...
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[S1] Okay, great. Um, and, uh- [S2] Some of them are great and some of them are a little terrifying. I mean, occasionally- [S1] Yeah. [S2] ... the car seems to sort of like veer off and scare the hell out of people. Um, but, um- [S1] It's still better. [S2] [LAUGHS] It's still better. But, but you, but the, the, but yo...
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[S1] drive people to be ambitious. Without that, nothing gets done. [S2] Well, I generally believe, um, in terms of internal, uh, timelines that we want to set, set the most aggressive timeline that we can, um, uh, because there's sort of like a law of gases expansion where, for schedules where whatever time you set, i...
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[S1] ... percent. [S2] Yes. [S1] So, uh, but they don't mention that one. Uh, so it, it, I mean, I'm not sure what my exact track record is on predictions. They're more optimistic than pessimistic, but they're not all optimistic. Um, some of them, uh, are exceeded, uh, probably more are later, um, but they, uh,
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[S1] they, they do come true. It's very rare that they do not come true. It's sort of like, uh, you know, uh, you know, if, if, if there's some radical technology prediction, uh, the, the point is not that it was a few years late, but that it happened at all. [S2] Right. [S1] Yeah, that's the, that's the more important...
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[S1] ... generalize that to a robot on legs as well. The, the two hard parts, I think, like it's not, obviously companies like Boston Dynamics have shown that it's possible to make, uh, uh, quite compelling, sometimes alarming robots. [S2] Right. [S1] Um, you know, so, so this is, from a sensors and actuator standpoint...
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[S1] So let's dig into exactly that. I mean, in one way, it's actually an easier problem than full self-driving because you, instead of an object going along at 60 miles an hour, which if it gets it wrong, someone will die, this is an object that's engineered to only go at, what, 3 or 4 or 5 miles an hour. [S2] Yeah, c...
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[S1] Right. [S2] [LAUGHS] [S1] But, um, but so, so talk about, I mean, I, I think the first applications you, you've mentioned are probably going to be manufacturing, but eventually the vision is to, to have these available for people at home. [S2] Right. [S1] If you had a robot that really understood the 3D architectu...
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[S1] When it could recognize, obviously recognize everyone in the home. [S2] Yeah. [S1] Could play catch with your kids.
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[S1] That, that sounds wise. [S2] And I do think there should be a regulatory agency for AI. I've said this for many years. I don't, I don't love being regulated, but I, you know, I think this is an important thing for public safety. [S1] Let, let, let's come back to that. But I'm, I'm just, I, I don't think many peopl...
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[S1] Do you think there will be basically like in say, say 2050 or whatever, that like a, a, a robot in most homes is, is what there will be and people will, will- [S2] Yeah, I think there probably will. [S1] ... will love them and count on them. You'll have your own butler basically. [S2] Yeah, you'll have your sort o...
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[S1] I mean, it's probably inevitable. I mean, I did promise the internet that I would make cat girls. We, we could make a robot cat girl. [S2] [LAUGHS] [S1] I mean, I mean, I mean, I mean, it's- [S2] Be careful what you promise the internet, you know? [LAUGHS] [S1] Yeah. Um, so, yeah, I, I guess, uh, it'll be what, wh...
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[S1] Initially just selling to businesses, or when do you picture you'll sell, you'll start selling them where you can buy your parents one for Christmas or something? [S2] I'd say less than 10 years. [S1] How, how, how, how, help me on the economics of this. So, what, what do you picture the cost of one of these being...
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