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All right, so we're diving into this research paper today.

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Okay.

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It's called,

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Monte Carlo Inference for Semi-Parametric Bayesian Regression.

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Wow.

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And it's from the Journal of the American Statistical Association.

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Yeah, that sounds a little intimidating.

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Yeah, it does a little bit, but that's why we're here.

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Right.

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We're here to break it down for everyone.

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Exactly.

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See what it's all about.

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Yeah, and what's cool about this paper is it's dealing with this common problem in data analysis.

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Okay.

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Which is, how can we make our models more flexible?

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Right.

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Especially when we're dealing with real world data.

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Yeah, the messy stuff.

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Yeah, messy data, exactly.

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That doesn't always fit into those nice assumptions.

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Like not a perfect bell curve.

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Exactly, yeah, or has crazy outliers.

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Yeah.

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So one way to deal with this is through data transformations,

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which is essentially adjusting the data to better fit the model assumptions.

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Okay.

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But finding the best transformation can be really tricky.

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So what is this paper proposing?

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What's the big idea?

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So they've come up with a new method that combines data transformations with Bayesian statistics.

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Okay.

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All within this regression framework.

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So essentially they're finding a way to figure out the best transformation for your data

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at the same time as estimating the parameters of your model.

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Gotcha.

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Yeah.

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So they're doing it all at once?

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All at once.

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Okay, so how does this all work?

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How does it actually come together?

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So the key is that they've linked the transformation to the marginal distributions of the data.

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Okay.

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So think of this as looking at the overall patterns of your independent variables.

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Okay.

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The inputs and outputs to guide the choice of transformation.

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So using the data to figure out how to adjust it.

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Exactly.

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And to model these marginal distributions without making strong assumptions about their shape.

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Right.

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They use a technique called the Bayesian bootstrap.

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Okay, now hold on.

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Yeah.

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I'm not a statistician.

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What is that?

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Break that down for me.

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So the Bayesian bootstrap, it's a nonparametric method, which means we don't have to assume

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a certain distribution for the data beforehand.

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Go ahead.

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It's really flexible, adaptable.

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Right.

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And even better, it doesn't require any tuning parameters.

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So that makes it more user friendly.

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Exactly.

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Okay, so this paper, I was reading it, it highlights three main advantages to their approach.

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Yeah.

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They talk about flexibility, efficiency, and strong theoretical backing.

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Yeah.

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Let's break those down.

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Okay.

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So starting with flexibility, what makes this so flexible?

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Well, for one, it works with a wide range of data types and regression models.

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Okay.

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You can use it with linear regression, quantile regression, even more complex models like

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Gaussian processes.

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So it's not just a one-trick pony?

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Nope.

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Okay, it can be used all over the place.

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Yeah, lots of different tasks.

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All right.

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What about efficiency?

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Okay.

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Now, Bayesian methods, sometimes they have a reputation for being very computationally expensive.

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Yeah, they can be.

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Did they address that?

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They did.

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Okay.

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They use Monte Carlo sampling techniques, which are generally faster and more straightforward

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than MCMC methods.

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So they sped it up a bit.

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Yeah, made it a lot more efficient.

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Very cool.

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Okay, and then the last thing, theoretical backing.

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Right.

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So what kind of guarantees, like how do we know that this actually works?

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Well, they actually provide a mathematical proof that their method leads to what we call

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consistent posterior inference.

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Now, what is that?

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Yeah.

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For our listeners who aren't statisticians, what does that mean?

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So in Bayesian statistics, posterior inference refers to updating our beliefs about the model

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parameters based on the data.

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Right.

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So essentially, it means that our conclusions are going to be reliable and accurate, even

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if our initial model isn't perfectly specified.

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Okay.

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Yeah.

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So it's like a safety net?

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Exactly.

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Even if we're a little bit off, it's still going to get us to the right place.

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Yeah, you're still good.

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Okay.

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So they've checked off all the bosses, flexible, efficient, theoretically sound.

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Yeah.

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But how about in the real world?

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Does it actually work?

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It does.

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Okay.

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Yeah, they actually show this in the paper.

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Good.

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They have a bunch of real world examples.

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Perfect.

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Yeah, showing how the method performs with different types of regression models.

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Okay, great.

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We'll get into that after the break.

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Sounds good.

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Yeah.

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So they show how their semi-parametric Bayesian approach can be applied to things like linear

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regression,

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Okay.

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quantile regression, even Gaussian processes.

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Okay, let's break those down one by one.

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Okay.

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What did they find with linear regression?

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So they show that their method...

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Which they call, sorry to interrupt, they call it splim for short.

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Yeah, splim.

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Okay, just so we're all on the same page.

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Yes.

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Splim outperforms traditional Bayesian linear models when you've got data that needs a

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transformation that gives you more precise predictions.

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Okay, what does that mean in a practical sense?

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So think of it this way.

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Let's say we're trying to predict house prices.

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Okay.

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Based on things like size, location, number of bedrooms.

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Right.

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Their method is going to give you a more accurate prediction within a smaller range.

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So less uncertainty.

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Yeah, less uncertainty.

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Okay, I like that.

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What about quantile regression?

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Okay, so quantile regression.

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That's a good one.

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Yeah, it's useful when you want to understand the full distribution of the data.

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Not just the average.

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Not just the average.

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So like if you're studying income distribution, you might be interested in not just the average

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income, but also the different percentiles.

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The spread.

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Yeah, exactly.

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Okay.

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And their method.

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Which they call?

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SBQR for semi-parametric Bayesian quantile regression.

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Okay.

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Okay.

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This significantly improved the accuracy of those quantile estimates.

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Okay.

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Especially at the tails of the distribution.

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So for those outliers.

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Yeah, exactly.

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Okay, now what about Gaussian processes?

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Right, so Gaussian processes are really flexible models.

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Okay.

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They can capture these complex nonlinear relationships.

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Yeah, very popular in machine learning.

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Yep, they're really popular.

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But one of their limitations is they assume the errors are normally distributed.

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Okay.

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Which isn't always a case.

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Right, back to that real world data problem.

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Exactly.

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So their method helps address that.

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Okay.

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By incorporating data transformations.

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Okay.

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So it makes those Gaussian processes more adaptable to different data types.

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So does it actually work?

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Did they show that it worked?

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They did, yeah.

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They tested it on a benchmark data set.

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Okay.

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Called the LIDAR data.

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Okay.

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And it significantly improved the accuracy.

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And what did they call that one?

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That one's called SBGP.

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Okay, SBGP.

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Short for Semi-terametric Bayesian Gaussian process.

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Okay.

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Quite a mouthful.

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So it can be applied to all these different types of models.

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Yeah.

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And it's still computationally efficient.

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Yeah, and they actually compared computing times.

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Okay.

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Showing that their Monte Carlo based method could be a lot faster than traditional MCMC approaches.

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So they made it faster and it works in the real world.

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Exactly.

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That's fantastic.

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They didn't stop there though.

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Oh, there's more.

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They also looked at the theoretical foundations.

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Okay.

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They actually provided mathematical proofs.

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To show that their approach leads to consistent posterior inference.

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So even if?

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Even if the model isn't perfectly specified.

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Which is usually the case.

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Yeah, usually the case in the real world.

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So this is like a really solid method that they've come up with.

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Yeah, very solid.

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Okay, very cool.

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And they also address potential issues that could come up from simplifications and approximations.

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Right.

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For example, they have this robustness adjustment.

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Okay.

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To account for potential mis-specifications.

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That's a good idea.

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Yeah, so they really thought of everything.

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They've really thought this through, haven't they?

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Yeah, they've been very thorough.

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Okay, so it's a really powerful tool for data analysis.

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It is, yeah.

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It really is.

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But are there any limitations?

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So one thing to remember is that while their method is pretty efficient.

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Okay.

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It still uses Monte Carlo sampling.

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Which can be computationally demanding.

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Okay.

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For massive data sets.

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That's all relative.

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Yeah, it's all relative.

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Right.

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So there's definitely room for further research.

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To speed it up even more.

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Yeah, optimizing it.

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Gotcha.

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Another thing is the choice of prior distributions.

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Oh, right, because it's Bayesian.

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Exactly, because it's Bayesian.

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So how do you pick those?

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Yeah, and they acknowledge this in the paper.

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Okay.

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And suggest further research into this sensitivity of their method to different prior choices.

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So more work to be done.

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Yeah, always more work to be done.

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Okay.

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But even with those limitations, it's still a really significant contribution.

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It sounds like it.

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Yeah, it addresses this common problem in data analysis.

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Right.

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Which is how can we make our models more flexible and accurate with real world data.

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Which is always messy.

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Always messy.

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Never perfect.

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Never perfect, yeah.

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And they even made it accessible.

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Oh.

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They made an R package.

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Called Sabiar.

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Sabiar.

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Yeah.

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Okay.

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And that implements their method.

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It does.

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So anyone can try it out.

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Very nice.

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I like it.

281
00:08:55,680 --> 00:08:56,080
Yeah.

282
00:08:56,080 --> 00:08:57,120
Very accessible.

283
00:08:57,120 --> 00:09:02,320
So novel approach, solid theory, good results and a package to implement it.

284
00:09:02,320 --> 00:09:02,560
Yeah.

285
00:09:02,560 --> 00:09:03,920
They really covered all the bases.

286
00:09:03,920 --> 00:09:05,120
Sounds like a great paper.

287
00:09:05,120 --> 00:09:05,520
It is.

288
00:09:05,520 --> 00:09:05,680
Yeah.

289
00:09:05,680 --> 00:09:06,800
It's a really good paper.

290
00:09:06,800 --> 00:09:06,960
Yeah.

291
00:09:06,960 --> 00:09:11,840
It's really cool how they managed to like take all this complex theory and stuff.

292
00:09:11,840 --> 00:09:14,160
And make it something that people can actually use.

293
00:09:14,160 --> 00:09:14,480
Yeah.

294
00:09:14,480 --> 00:09:18,640
It shows you how much they care about making sure that people can actually use this.

295
00:09:18,640 --> 00:09:19,520
It's not just theory.

296
00:09:19,520 --> 00:09:20,480
They made a tool.

297
00:09:20,480 --> 00:09:21,280
That's really cool.

298
00:09:21,280 --> 00:09:21,520
Yeah.

299
00:09:21,520 --> 00:09:26,720
It's like they gave us this really well put together toolbox.

300
00:09:26,720 --> 00:09:27,200
Yeah.

301
00:09:27,200 --> 00:09:28,240
With instructions.

302
00:09:28,240 --> 00:09:28,480
Yeah.

303
00:09:28,480 --> 00:09:30,720
And all the tools are right there ready to go.

304
00:09:30,720 --> 00:09:31,440
That's awesome.

305
00:09:31,440 --> 00:09:33,840
And they even talked about like what we can do next.

306
00:09:33,840 --> 00:09:34,080
Right.

307
00:09:34,080 --> 00:09:36,000
Like where this research can go.

308
00:09:36,000 --> 00:09:36,080
Yeah.

309
00:09:36,080 --> 00:09:36,800
Yeah.

310
00:09:36,800 --> 00:09:37,840
I brought up all these questions.

311
00:09:37,840 --> 00:09:40,400
Like they said we could use this with even bigger data sets.

312
00:09:40,400 --> 00:09:40,640
Right.

313
00:09:40,640 --> 00:09:42,160
Like high dimensional data.

314
00:09:42,160 --> 00:09:42,480
Yeah.

315
00:09:42,480 --> 00:09:45,040
And even like really complex models.

316
00:09:45,040 --> 00:09:46,160
They're really complex stuff.

317
00:09:46,160 --> 00:09:46,320
Yeah.

318
00:09:46,320 --> 00:09:47,760
Like deep learning models.

319
00:09:47,760 --> 00:09:48,000
Yeah.

320
00:09:48,000 --> 00:09:49,760
Imagine if we could do all this with those.

321
00:09:49,760 --> 00:09:51,280
Oh, that'd be incredible.

322
00:09:51,280 --> 00:09:51,600
Yeah.

323
00:09:51,600 --> 00:09:52,640
That'd be a game changer.

324
00:09:52,640 --> 00:09:53,440
It really would.

325
00:09:53,440 --> 00:09:53,600
Yeah.

326
00:09:53,600 --> 00:09:57,200
It's like they planted a seed and a whole bunch of new ideas can come from this.

327
00:09:57,200 --> 00:09:57,520
Yeah.

328
00:09:57,520 --> 00:09:59,360
And they're inviting everyone to join them.

329
00:09:59,360 --> 00:09:59,840
Yeah.

330
00:09:59,840 --> 00:10:00,960
Come explore with us.

331
00:10:00,960 --> 00:10:03,760
It's a really cool time to be working in this area.

332
00:10:03,760 --> 00:10:04,160
It is.

333
00:10:04,160 --> 00:10:05,120
Well, this has been awesome.

334
00:10:05,120 --> 00:10:07,040
I'm really glad we got to dive into this paper.

335
00:10:07,040 --> 00:10:07,680
Me too.

336
00:10:07,680 --> 00:10:07,840
Yeah.

337
00:10:07,840 --> 00:10:09,040
It's really interesting stuff.

338
00:10:09,040 --> 00:10:11,440
And it just shows like what's possible.

339
00:10:11,440 --> 00:10:11,840
Definitely.

340
00:10:11,840 --> 00:10:14,800
When you combine smart ideas, good methods,

341
00:10:14,800 --> 00:10:16,080
and you want to make a difference.

342
00:10:16,080 --> 00:10:16,320
Yeah.

343
00:10:16,320 --> 00:10:17,600
It's not just about the theory.

344
00:10:17,600 --> 00:10:19,600
It's about making an impact.

345
00:10:19,600 --> 00:10:20,000
Totally.

346
00:10:20,000 --> 00:10:21,600
Well, thanks for breaking this down for us.

347
00:10:21,600 --> 00:10:22,080
Of course.

348
00:10:22,080 --> 00:10:23,360
Happy to be here.

349
00:10:23,360 --> 00:10:26,880
And to all our listeners out there, thanks for tuning in.

350
00:10:26,880 --> 00:10:28,800
Keep on learning.

351
00:10:28,800 --> 00:10:29,040
Yeah.

352
00:10:29,040 --> 00:10:29,760
Check out the paper.

353
00:10:29,760 --> 00:10:30,800
Check out the package.

354
00:10:30,800 --> 00:10:32,400
And see what you can discover.

355
00:10:32,400 --> 00:10:32,720
Yeah.

356
00:10:32,720 --> 00:10:33,600
Have fun with it.

357
00:10:33,600 --> 00:10:35,360
Happy analyzing.

358
00:10:35,360 --> 00:10:35,680
All right.

359
00:10:35,680 --> 00:10:36,480
That's it for us.

360
00:10:36,480 --> 00:10:54,240
See you next time.