Latest / Strachey Lectures / Strachey Lecture: Probabilistic machine learning: foundations and frontiers

Transcript

Strachey Lecture: Probabilistic machine learning: foundations and frontiers · Strachey Lectures

• 0:01
  George. Okay.
• 0:18
  So I'm full blown. So I'm going to introduce our speaker for the stretch lecture this term.
• 0:22
  Firstly, I'd like to say a big thank you to Oxford Asset Management, our sponsor who makes this series of lectures possible.
• 0:28
  I've also been asked to draw your attention to our hashtag that's prominently placed in case you would like to tweet.
• 0:35
  And also anyone interested in our software engineering program can find brochures outside and people to talk to.
• 0:41
  So, okay. But onto the mean business. So it's my pleasure to introduce Stephen Carbone, who will give our Hillary term strategy lecture.
• 0:50
  Zubin is Professor of Information Engineering at Cambridge.
• 0:55
  He's a fellow of the Royal Society.
• 0:57
  I think it's fair to say that his machine learning group in Cambridge is would be one of the most influential over the last decade.
• 1:06
  It's hard to it's hard to go to any major machine learning academic group or industry lab without finding Rubin's ex-students or postdocs.
• 1:16
  So and more recently, Zubin founded Geometric Intelligence A Start-Up.
• 1:22
  And after its acquisition, he's now the co-director of Uber, Eli Labs.
• 1:27
  And maybe if you're off nicely, he might tell you a bit about that. We'll see.
• 1:32
  Okay. So you've made contributions across machine learning, particularly probabilistic inference, even deep learning.
• 1:41
  It's not surprising. He was Mike Jordan student and did his postdoctoral work with Geoff Hinton.
• 1:47
  So a pretty amazing pedigree there. So really, Zubin,
• 1:52
  seminal work is really invasion non parametric where he's really been leading this idea that
• 1:58
  it's not just enough for now machine learning research to aim for for accurate predictions.
• 2:04
  We also need to be able to quantify uncertainty. We need to be able to talk about causation.
• 2:09
  And if we really want machine learning and AI to have an impact in industry, we need to be able to tackle those things.
• 2:14
  I'm sure he will tell you all about these things. So please welcome Zubin for the talk.
• 2:27
  Thanks, Phil, for that great introduction and a great thank you to the Department of Computer Science for inviting me.
• 2:36
  Okay. Can you all hear me? Yeah. Good.
• 2:39
  So I'm going to talk about probabilistic machine learning, which is my passion, is the thing I'm really excited about.
• 2:45
  And I'll start from basics and as the talk goes on, will get into more and more current research, more of what we're actually really doing these days.
• 2:57
  So that's why the subtitle is Foundations and Frontiers. Foundations is meant to be, you know, motivation, background material.
• 3:06
  But if you're bored by that, don't worry, it'll get more technical later on.
• 3:13
  Okay, so let's start from the basics. Machine learning.
• 3:17
  Well, what is machine learning? It's just a term.
• 3:20
  There are many other related terms.
• 3:24
  You know, depending on the community that you come from, you might think about data mining or artificial intelligence or statistical modelling,
• 3:30
  neural networks, pattern recognition, sort of a bit of a more old fashioned term.
• 3:35
  All these terms are related. I'll focus on the term machine learning, but keep the context in mind in terms of academic disciplines.
• 3:46
  This is also a very interdisciplinary area in that we draw from ideas in computer science, engineering statistics,
• 3:56
  applied mathematics, and we get a lot of inspiration from cognitive science, economics, even tools from physics and neuroscience.
• 4:06
  And then why are people interested in machine learning these days?
• 4:11
  Well, it used to be kind of an interesting academic field where you sort of played around and you kind of tried to get computers to learn from data.
• 4:19
  Most people didn't care much about it, but now suddenly lots of people care.
• 4:24
  And the reason lots of people care is because there are many, many applications of machine learning.
• 4:30
  It's sort of I like to think of it as the invisible thing that's behind a lot
• 4:35
  of the more visible applications that involve computers learning from data.
• 4:43
  So let's just go through some of those applications just to motivate.
• 4:48
  Speech and language technologies is an area that has been transformed by the use of machine learning.
• 4:54
  So automatic speech recognition, machine translation, question answering dialogue systems.
• 5:01
  Then every year we seem to get more and more advances in these sorts of tools.
• 5:07
  Computer vision, again, a field that has been around for a very long time.
• 5:12
  But with the advent of large amounts of data and more powerful computational tools, we're able to now do interesting things like not just object,
• 5:25
  face and handwriting recognition, but image captioning going from an image to a bit of text that's meant to describe the image.
• 5:33
  And these are this is from a very famous paper.
• 5:39
  And, you know, you can actually pick it apart in the sense that you could say, well, these are hand chosen to make the algorithm look good.
• 5:46
  You know, man in black shirt is playing guitar.
• 5:48
  That seems pretty amazing that a computer could take an image like this and produce this description of the image.
• 5:55
  It doesn't always work that brilliantly,
• 5:59
  but I would say that most of us in the field were stunned when we saw this happen for the first time
• 6:06
  that we could actually get a system that would produce some reasonable descriptions from images.
• 6:14
  Of course, we all have cameras in our pockets that put boxes around people's faces.
• 6:19
  If you ever ask yourself, well, how does that work? Well, that's a bit of machine learning that runs on all of your camera devices.
• 6:28
  Moving into the sciences, a lot of the sciences have become very data heavy.
• 6:34
  Fields like bioinformatics and genomics in the medical sciences,
• 6:39
  but also astronomy areas where we're now able to collect much more data than any human being could sit down and analyse manually.
• 6:49
  And so machine learning and AI tools have been very important in scientific data analysis,
• 6:57
  and that's something I'll talk about maybe a little bit later on as well.
• 7:01
  Recommender systems, we all know, but these are, you know, customers who bought this item,
• 7:06
  also bought this kind of thing that's driven by machine learning, self-driving cars, something that I'm now much more involved in.
• 7:15
  This is not a totally new thing.
• 7:18
  I mean, this self-driving car, Alvin was around about 30 years ago, and he used neural networks to drive around at 70 miles per hour on highways.
• 7:28
  That's what it says on this slide that I took from about 30 years ago.
• 7:32
  That's very scary.
• 7:33
  I would not want to be anywhere close to that truck driving at 70 miles an hour on a highway driven by a neural network that's about this big.
• 7:43
  But things have moved on and we now have pretty good self-driving systems that are just getting better every year.
• 7:54
  Robotics. I just love dogs playing football.
• 7:58
  So robotics is this this particular sort of RoboCop isn't necessarily driven by machine learning,
• 8:04
  but there are a lot of excellent uses of machine learning in robotics, automated trading, financial prediction,
• 8:12
  computer games you're all familiar with, you know, the the DeepMind landmark results first with learning Atari games,
• 8:23
  playing Atari games at a human or superhuman level, then more recently beating the world master at goal.
• 8:36
  And who knows what this is? This is Lee Brutus, a system that recently won a poker championship.
• 8:52
  And this was a very against a whole bunch of humans. This is all the numbers in parentheses are how much money the humans lost to the computer.
• 9:00
  And the very interesting thing about this is that this is quite a complicated game in that if you think about poker, what does it involve?
• 9:08
  Well, it involves things like trying to understand the state of mind of the other player and bluffing and things like that.
• 9:19
  So to be a good poker player, you have to be able to do those things. And so now we have good machine poker players as well.
• 9:25
  So what is it? Well, machine learning, if if I had to define it, I would use a sentence like this.
• 9:31
  It's an interdisciplinary field that develops both the mathematical foundations and practical applications of systems that learn from data.
• 9:39
  Here are some of the main conferences and so on associated with that field.
• 9:44
  So that's all in terms of motivation from applications.
• 9:48
  But actually when you look at machine learning systems,
• 9:51
  most of the time machine learning systems are are trying to solve one of a few canonical problems.
• 9:58
  So I'll just go through those canonical problems in my kind of introductory part of the of the lecture.
• 10:05
  So this is probably the most canonical problem, the classification problem.
• 10:08
  You have some data, you want to classify it into two or more classes.
• 10:15
  So the task is to predict some discrete class labels from input data that has lots and lots of applications.
• 10:21
  And there are a lot of buzzwords for different methods that can be used for classification.
• 10:25
  These are just different ways of trying to do classification from data.
• 10:30
  Regression, trying to predict some continuous quantity Y from some inputs X.
• 10:37
  Obviously, this has lots of applications as well.
• 10:41
  And, you know, there are lots of methods, some of which you might say, well, that's not a machine learning method, that's linear regression.
• 10:49
  It's been around for over a hundred years.
• 10:50
  But, you know, again, remember, this is all in the context of everything that's been going on in all of these neighbouring fields.
• 10:58
  And there's nothing that says, oh, this is a machine learning method and that's not a machine learning method.
• 11:03
  If it's just if it's making predictions and decisions from data, it is a machine learning method at some level clustering.
• 11:12
  The task here is the group data together so that similar points are put in the same group.
• 11:18
  Many applications, again, many different methods. Dimensionality reduction.
• 11:22
  When you have very high dimensional data, you might want to find a low dimensional representation of that data that preserves important information.
• 11:31
  Another canonical machine learning problem semi supervised learning where you might have some labelled data.
• 11:41
  Here you might have a few label points like these two label points that are minuses and these three that are pluses.
• 11:49
  And you might want to basically be able to leverage the fact that you have a lot of unlabelled data as well.
• 11:55
  And so semi supervised learning combines labelled and unlabelled data to get better predictions and reinforcement learning,
• 12:02
  which is related to sequential decision making and adaptive control.
• 12:08
  The task there is to learn to interact with an environment, making sequential decisions to maximise future rewards.
• 12:16
  So it's an interactive setting where you have an agent producing some actions or decisions in an environment.
• 12:22
  There may be some hidden state to both the agent and the environment,
• 12:26
  and then you get some observed sensory inputs and the agent has to be has to act in the environment to maximise its rewards.
• 12:38
  Okay. So these are the canonical problems.
• 12:40
  It is actually quite bewildering if you start reading the machine learning literature and you're not an expert because there are many,
• 12:47
  many different methods and you know, every paper seems to present a new method.
• 12:53
  And so here is this sort of a very crude way of organising a bunch of machine learning methods.
• 12:59
  But don't give this too much input, too much weight on this.
• 13:04
  Okay. But I'm going to focus on for the first few minutes, I'm going to focus on one bubble here, which is this neural networks and deep learning one.
• 13:12
  And the reason I'm focusing on that should be for any of you who is familiar with the field,
• 13:17
  it should be pretty obvious because these methods have been really revolutionary.
• 13:22
  They've really been involved in some of the most spectacular breakthroughs in the last few years.
• 13:32
  So what are they? Well, a neural network.
• 13:39
  And I'm going to focus here on a feedforward neural network.
• 13:42
  Just for simplicity, there are other kinds, but a feedforward neural network.
• 13:45
  The most standard one is essentially just a function approximate.
• 13:50
  So it takes some inputs, called them X and it produces some outputs.
• 13:57
  Call them Y. And the way it produces them is through a sequence of transformations organised in layers.
• 14:08
  But all of that is in a sense a bit of a detail.
• 14:11
  It's just a way of representing a function that maps from X to Y via tuneable parameters called weights.
• 14:20
  Or I'm using theta t to note note the denote the parameters of the network.
• 14:27
  So neural nets are I mean, one of the important aspects of neural nets is that they're nonlinear functions
• 14:35
  and they're often both nonlinear in the input and nonlinear in the parameters.
• 14:41
  So optimising them to minimise some objective function tends to be slightly complicated.
• 14:48
  The other defining characteristic of neural networks is that they represent the function from X or Y in layers,
• 14:56
  which is essentially simply just as a composition of functions.
• 15:01
  Okay. So here is a multiplayer neural network with one hidden layer represented as a function that maps from Xs to Y through some parameters.
• 15:11
  And these super scripts here one and two you the the two layers of parameters that you have.
• 15:18
  These neural networks are usually trained to maximise some likelihood,
• 15:22
  so they fall very squarely within the world of statistical models using some variant of stochastic gradient descent optimisation.
• 15:32
  So this is where we start using tools from optimisation theory.
• 15:35
  Okay. So that's one slide on neural networks. And these things have been around for many decades.
• 15:43
  In fact,
• 15:43
  these things are what got me excited about AI back in the eighties when I was sort of an undergraduate and thinking about what to do with my life.
• 15:55
  But what's happened is that something dramatic has happened between the 1980s and now.
• 16:05
  And one of the things that's dramatic is that the terminology has changed.
• 16:09
  So people now call these deep learning systems because they have many more layers.
• 16:13
  But there are other, more interesting, dramatic things that have happened.
• 16:16
  So these deep learning systems that are involved in a lot of these very impressive
• 16:22
  benchmarks are very similar to the neural net architectures from the eighties and nineties,
• 16:30
  with some important architectural and algorithmic innovations like being able to use many layers and particular nonlinearity,
• 16:37
  such as the real you particular ways of regularising them like dropout and very useful tricks for dealing with time series like the.
• 16:49
  They are also based on vastly they're trained using vastly larger data sets, really web scale data sets.
• 16:57
  To do that, you need vastly larger compute resources, so GPUs, GPUs on clouds, etc.
• 17:04
  Importantly, there's been a major effort to democratise the software tools so that it's quite easy to actually train a neural network.
• 17:14
  So we have much better software tools, things like torch and TensorFlow.
• 17:20
  And of course, there has been vastly increased industry investment and media hype.
• 17:25
  And what that what that has meant is that there is a huge influx of people trying out different variations of neural networks on different problems.
• 17:36
  And stepping back, I kind of think of this a little bit of as the community of machine learning researchers is running a bit of a genetic algorithm,
• 17:47
  trying out lots of different ideas and variations and ideas to be able to improve on the performance of existing benchmarks.
• 17:57
  Okay. So that's that's deep learning in a in a nutshell, there's huge amounts more to say about that.
• 18:05
  And there are many better people than me to talk about that.
• 18:09
  But one thing I do want to talk about is limitations of deep learning.
• 18:13
  So let's step back from the excitement. Let's acknowledge the excitement and let's say, well, where do we go next?
• 18:20
  What do we need to focus on? And I would argue that there are a few limitations we really need to think about.
• 18:28
  So one of them is that neural nets are very data hungry.
• 18:33
  You often need millions of examples to train these large models. And that should not be surprising.
• 18:37
  If you if you know a bit of statistics,
• 18:42
  perhaps the surprising thing is that you don't need that many millions to train models with millions of parameters.
• 18:48
  People would have thought that would. That was crazy. And it is surprising that you can get away with, you know, relatively small amounts of data,
• 18:57
  even though it's large by the standards of the eighties and nineties.
• 19:01
  They're also very compute intensive to train and deploy.
• 19:07
  They're poor at representing uncertainty. And this is something that I'm particularly interested in.
• 19:12
  There are some great studies that show that neural nets and deep learning systems can be easily fooled by adversarial example.
• 19:19
  So you can construct examples that will make the neural network very confidently give the wrong answer, and that should be worrying.
• 19:30
  That relates to the uncertainty thing. It's okay for a system to make mistakes,
• 19:35
  but it's not okay for it to be really confidently making mistakes because then you don't
• 19:41
  know when to trust the answers and you can't really build mission critical systems,
• 19:46
  things like in, let's say in the health care domain or in self-driving cars and so on.
• 19:51
  If you really can't trust the confidences of your model, they're finicky to optimise.
• 19:59
  You know, optimisation is non convex and there are many different parametric architectural choices that need to be made.
• 20:06
  And they're generally on interpretable black boxes, lacking in transparency and difficult to trust.
• 20:13
  Okay, of course people are working on all of these things,
• 20:16
  but I wanted to put them on a slide to sort of motivate us to move towards the interesting challenges that we have.
• 20:24
  A particular area that that I'm really interested in, which Phil mentioned in the introduction,
• 20:33
  is thinking about machine learning as probabilistic modelling.
• 20:37
  So let's go beyond deep learning. I'll come back to neural nets and deep learning in a minute in the context of probabilistic modelling.
• 20:44
  Let's go beyond deep learning and let's talk about a particular view of machine learning
• 20:50
  that's grounded in the idea that we want systems that will build models from data,
• 20:57
  probabilistic models from data. So what do I mean by a model?
• 21:00
  The term model gets used by many people in different contexts. What I mean is a model describes data that one could observe from a system.
• 21:13
  Okay. So it should models should be able to make predictions.
• 21:19
  It should it should say make statements about observable data.
• 21:22
  If it doesn't do that, then it's very difficult to know if you have a good model or not, whether you have a falsifiable model, for example, or not.
• 21:31
  Now, if a model is making statements about possible data that could be observed,
• 21:38
  then what we're going to do is we're going to use the mathematics of probability
• 21:43
  theory to express all forms of uncertainty and noise associated with our model.
• 21:48
  So think about a simple model. Let's take a let's say a model that does forecasting of the weather tomorrow.
• 21:58
  Okay. That's not a necessarily simple model. One could certainly build a simple version of that.
• 22:02
  Okay. Now, you don't want models that make forecasts that don't tell you how uncertain they are.
• 22:10
  And now you have to consider where are all the different sources of uncertainty that you could have in predicting the weather tomorrow?
• 22:18
  You might have uncertainty that's coming from the noise in the sensor data that you collected.
• 22:26
  You might have uncertainty that's coming from the fact that there are unpredictable effects that your model did not consider.
• 22:33
  Your model might have parameters and you might be uncertain about what the right parameters are.
• 22:38
  All of those sources of uncertainty we need to deal with somehow.
• 22:42
  And what we're going to do is we're going to use the language of probability theory to express uncertainty.
• 22:47
  And to me, that is as fundamental as saying that we use calculus as the language to express rates of change.
• 22:55
  Probability theory is the language of uncertainty. Then the good news is that we don't have to invoke anything else.
• 23:03
  We can just stay within the framework of probability theory to infer aspects of the model from data,
• 23:11
  to adapt our model to data, to make predictions, etc. So it all ends up being very, very simple.
• 23:21
  And here is what it looks like. Here is Bayes rule, which is the sort of engine that drives learning from data.
• 23:32
  And I'm colour coding things into two classes data and hypotheses.
• 23:40
  And what I mean by data is anything that's actually measured a measured quantity.
• 23:47
  And what I mean by hypotheses is everything else okay?
• 23:51
  The world, from a basic point of view, is divided into two kinds of things.
• 23:55
  Stuff you're measuring and stuff you're not measuring.
• 23:59
  Okay? And the stuff you're measuring, you've measured.
• 24:02
  So you kind of know what it is. It could be noisy, but you've measured it.
• 24:06
  And the stuff you're not measuring, you better represent the fact that you're uncertain about it because you didn't measure it.
• 24:13
  Okay, so all of those things we call hypotheses.
• 24:19
  Okay. So that's not the only thing there. I said that these hypotheses, if we think about these, is as if we're trying to express models of data.
• 24:31
  We're going to use probability theory to express our models. So basically for every potential configuration of our hypotheses,
• 24:41
  we should be able to describe what is the probability of the observed data under that hypothesis.
• 24:49
  That's the term that's called the likelihood,
• 24:51
  and that's actually what drives most neural network learning is maximising likelihood or penalised likelihood of some kind.
• 25:00
  But forget about neural nets. Now we're talking much more generally.
• 25:03
  We have this term, which is the likelihood, which gives you the probability of the data given the hypothesis.
• 25:09
  And then we have this term, which is called the prior. And the prior is our representation of our uncertainty about everything we haven't observed.
• 25:20
  Before we get our data. So the game goes like this.
• 25:25
  Before we have our data, we have to place our bets on all the unobserved things we use the language of probability theory to do that.
• 25:34
  So we put a probability distribution over our space of hypotheses.
• 25:38
  Then we observe the data. Aha! That's the beautiful moment where we can now compute the likelihood,
• 25:44
  the probability of the data, given the hypotheses and the simple rules of probability,
• 25:47
  tell you you multiply these two, you re normalise over all the hypotheses that you've been considering.
• 25:55
  And then what you get is your new state of knowledge, the posterior distribution of your hypotheses,
• 26:00
  given the data, and that is the prior that you would use if you got any more data.
• 26:05
  So there's nothing really fundamentally different between the prior and the posterior.
• 26:09
  It's just the representation of your state of knowledge at any point in the process with the data you've observed so far.
• 26:17
  Okay, so learning and prediction can be seen as forms of inference using this this rule.
• 26:27
  And here is the slide that I it's a one slide description of Bayesian machine learning that I always use apologies for people who've seen it.
• 26:37
  But the point is that even Bayes rule that I had on the previous slide is not a fundamental rule.
• 26:44
  The fundamental rules of probability theory are these two simple rules the thumb rule and the product rule.
• 26:50
  And the sum rule tells you that the probability of some unknown quantity X is the sum over some other unknown quantity Y of the joint probability.
• 27:00
  So the this is called also sometimes called the marginalisation rule.
• 27:07
  And the product rule says that the joint probability of X and Y can be factored into
• 27:12
  the probability of X times the probability of Y given X or the other way around.
• 27:18
  So from these two simple rules, if we substitute X and Y with data and hypotheses, we can get Bayes rule, which we got in the previous slide.
• 27:29
  If we use the following symbols theta to represent the parameters of our Model D,
• 27:35
  to represent the observed data, and M to represent the model class that we've assumed.
• 27:42
  Then we get this expression here, which is just Bayes rule apply to parameters of our model.
• 27:50
  What would the parameters be? For example, in a neural net they would be the weights in the neural net and linear regression,
• 27:55
  they would be the linear regression coefficients, etc. Every model has parameters in this world.
• 28:02
  Okay. And this is the prior that's the likelihood.
• 28:06
  And this term here is the normalising constant, which is itself quite interesting.
• 28:11
  It's called the marginal likelihood. Now this follows from the salmon product rule.
• 28:17
  If you want to make predictions about any unknown quantity X given the data, then the salmon product will tell you that the way you make predictions,
• 28:26
  there's only one valid way under this framework, and that one valid way is you consider the predictions made by every possible parameter value.
• 28:38
  So those are these terms, and then you weight them by this term in green,
• 28:43
  which is the posterior probability of the parameters given the data and the model class.
• 28:48
  So the act of forecasting or predicting any unknown quantity X given the observed data is by the salmon
• 28:56
  product rule an averaging process you have to average over all the hypotheses that you've considered.
• 29:02
  You don't pick the best one or your favourite one, or you don't flip a coin or anything like that.
• 29:07
  You're supposed to average over the space of hypotheses in this particular way.
• 29:12
  And if you now want to compare different model classes, then you might apply Bayes rule at the level of model classes.
• 29:23
  And that looks like this where this term in red, the marginal likelihood now appears in the numerator and denominator.
• 29:29
  None of this is actually mysterious. They all follow from from these two rules.
• 29:34
  What do I mean by model? Comparison. Model comparison might the story might go like this.
• 29:40
  Okay, let's say I'm a biologist. I do an experiment and I have a colleague and my colleague says, I believe that,
• 29:49
  you know, this transposition transcription factor regulates these genes.
• 29:54
  And I say, no, I have a different model. I believe that it doesn't and that this one does or something like that.
• 29:59
  So my colleague and I have two different models now.
• 30:03
  We could argue about it in words, but if we follow this probabilistic framework,
• 30:07
  what we should do is both of us should write down the model to the specification level that it could make predictions about observable data.
• 30:15
  We could assign a probability to the observable data, and then we observe the data.
• 30:22
  D And now we can settle the argument.
• 30:25
  We basically say, All right, what is the marginal likelihood that that your model gave to my data?
• 30:32
  What is the marginal likelihood my model gives to the data? Well, both of our models had some free parameters.
• 30:38
  Maybe your model had 17 free parameters, and my model had three free parameters.
• 30:43
  So my model is simpler somehow. And I want I don't know, I get nervous, I say, that seems unfair.
• 30:51
  Okay, so your model had more parameters if if my colleague goes and optimises those 17 parameters,
• 30:57
  then sure enough she can fit the data much better than I can.
• 31:02
  Right. But that's not the game optimisation doesn't follow from the some rule in a product rule.
• 31:07
  It doesn't matter that my colleague has 17 parameters and I have three.
• 31:11
  If we can both compute the marginal likelihood, then we can settle this argument.
• 31:16
  Okay, so I actually really strongly believe that in an ideal world, science would be done like this.
• 31:22
  People wouldn't just publish their papers in open journals and share their data in an open manner.
• 31:29
  I think actually people should write down their models in a way that one could evaluate with future data,
• 31:38
  maybe write them as probabilistic programs, which I'll talk about later. And then we could really do objective.
• 31:43
  Well, actually, it's subjective, but, you know,
• 31:46
  we could do a sort of principled comparison of models giving different subjective opinions about what the hypotheses are.
• 31:56
  Okay, so one side on basic machine learning.
• 32:00
  So why should we care about all this?
• 32:02
  We've had a revolution in machine learning with wonderful, fantastic, deep learning methods that never talk about base anywhere in them.
• 32:12
  So why should we care about all this Bayesian stuff? Well, the reason I care is that I'd really like models with calibrated senses of uncertainty.
• 32:23
  So I want to be able to trust my system. If it says the probability of there being a pedestrian in front of my car is 0.1,
• 32:35
  I want that to mean 10% and I can take actions that correspond to that calibrated probability.
• 32:44
  Getting systems that know when they don't know, I feel, is very important.
• 32:48
  Also, there's a very beautiful thing about all of this, which is that unease about like 17 parameters,
• 32:54
  which the three parameters or different structures of models.
• 32:57
  Well, this framework actually gives you automatic tools to compare models of different complexity and to automate the learning of models from data.
• 33:07
  And this is called Bayesian Occam's Razor. And it's something I will use in the latter part of my talk.
• 33:14
  Okay. So let's go back to our neural networks and just to ground the discussion a little bit.
• 33:23
  Here's a neural network and maps from X to why there are different sources of uncertainty here.
• 33:29
  One of them is parameter uncertainty. We have weights in the neural network.
• 33:34
  And, you know, given any finite amount of data, we're not sure what those weights should be.
• 33:39
  So we need to represent our uncertainty. But we also have structural uncertainty.
• 33:43
  We've made some structural choices like the architecture, a number of hidden units, our choice of activation functions.
• 33:50
  And that's also a source of uncertainty. So it would be great if we could represent all of that.
• 33:56
  And that's not a new idea.
• 34:00
  None of this is really new ideas.
• 34:03
  In fact, the idea of doing Bayesian analysis of neural networks has been around since the early nineties, at least to actually late eighties years.
• 34:16
  A bit of a history of a few different methods. Here is a depiction of what we'd really like.
• 34:23
  So here's a system that was trained to do some regression on some data.
• 34:26
  And what we'd really like is this sort of behaviour that outside of the range of its training data,
• 34:32
  it should say, I don't really know and there are many ways of doing that.
• 34:37
  These are all different ways of doing that. And we had a nice workshop at NIPS on Bayesian Deep Learning,
• 34:44
  where we kind of brought that history together and looked at some of the current state of the art.
• 34:51
  So this world machine learning often has camps and people think that you have to be in one or another camp,
• 34:58
  but you don't actually you have to understand what all the tools are in the different camps,
• 35:02
  and there's a lot of fertile ground at the intersection of these camps.
• 35:06
  And that's this is one example of those things. So when do we need probabilities?
• 35:12
  Well, we need them when we, our system are, you know, learning an intelligence problem depends crucially on representing uncertainty.
• 35:24
  I've sort of said that. But let me describe some examples of that.
• 35:28
  So any time we're doing forecasting and, you know, that could be financial forecasting,
• 35:35
  weather forecasting, forecasting demand at Uber or for Amazon products or whatever.
• 35:42
  We need to represent our uncertainty decision making.
• 35:46
  Generally, when you make decisions, you're thinking about the consequences of your actions into the future.
• 35:53
  And it's really useful to represent uncertainty there.
• 35:56
  It's hard to imagine not doing that at some level when you're learning from limited, noisy and missing data.
• 36:03
  So if you imagine dealing with, say, medical records, if you're trying to do machine learning and medical records,
• 36:10
  you have patients, your patients and each of them has lots of things that are unobserved.
• 36:16
  They maybe there are few medical tests that have been done on each patient.
• 36:20
  Most of the data is actually missing. If you look at that, look at it that way if you want to learn complex personalised models.
• 36:27
  So it might be, again, whether it's in a medical domain or in a retail domain or something like that,
• 36:34
  you might have you might think you have a huge data set, but actually for every patient or every customer, you only have a little bit of data, right?
• 36:44
  So it's not really a big data problem. You need to represent uncertainty about that individual.
• 36:50
  The whole field of data compression is based on probabilistic modelling and a lot of
• 36:54
  my interest in automatic model discovery and experiment design is really based on.
• 37:02
  Uncertainty. Now, over the last three months, I've been involved in setting up Uber's AA labs.
• 37:08
  I'll just mention that in one slide. Why would Uber care about any of this?
• 37:14
  Well, if you look at many of the problems that a large technology company has to solve.
• 37:24
  There are problems that deal with uncertainty, decision making, personalisation and so on.
• 37:31
  There are huge number of problems.
• 37:33
  There are huge number of opportunities around any of the major technology companies for learning from data and for using uncertainty in there.
• 37:42
  And, you know, fairly obviously, if you're trying to build a very complicated system that makes decisions in the real world like a self-driving car,
• 37:53
  you'd really like to have calibrated uncertainties in that system. Okay.
• 37:58
  So here is the one slide picture of my current passions, my current research interests,
• 38:09
  and then the next few minutes and I leave a few minutes for questions at the end.
• 38:12
  In the next few minutes, I'm going to touch on a few of these topics.
• 38:19
  And it's fairly modular, so I can stop to give us time for questions.
• 38:23
  But I want to put this slide up here because.
• 38:28
  Well, actually, because I had this slide.
• 38:31
  So that's one reason because and the reason I had this slide is that I was asked to give a talk about a year ago and they told me,
• 38:42
  summarise your work in one slide. So that forced me to produce this slide.
• 38:46
  And then when I produced it, I thought it was actually kind of a useful exercise.
• 38:50
  So so the, the useful exercise is that it crystallised in my mind the thing that really drives me.
• 38:58
  And, you know, it's not that I'm a Bayesian and I just love probabilities or anything like that.
• 39:04
  It turns out the thing that really drives me is that.
• 39:11
  I like stuff that's automated. I don't I want things to be systematic and automated.
• 39:18
  And computer scientists are very good at that. Like computer science, if you put your computer science hat on,
• 39:23
  you do something three times and you think, Oh, I need to write a computer program to do that for me.
• 39:29
  Three times was two times too many. Right. And.
• 39:33
  And the sorry state of machine learning is that stuff is not really automated.
• 39:41
  There still is tremendous amounts of human labour, arbitrary decision making and tweaking involved in deploying machine learning systems.
• 39:53
  Which is ironic. The whole field is about getting systems to learn from data.
• 39:58
  But then there's there there are a lot of well-paid researchers and engineers tweaking those systems that learn from data.
• 40:05
  So let's think about automating these things.
• 40:09
  And this is what drives me. So if you look at some of these topics, which I'm going to talk about.
• 40:14
  So automatic statistician, what is that about? And I'll I'll talk about that in a couple of minutes.
• 40:18
  That's about automating the process of model discovery from data.
• 40:23
  So searching for a good model from data. Probabilistic programming.
• 40:29
  Something that Frank Wood, who is at Oxford, is a world expert in policy programming,
• 40:36
  is automating the process of doing inference from a very general probabilistic model.
• 40:45
  We also want to automate. Optimisation.
• 40:49
  So optimisation is actually a sequential decision problem.
• 40:52
  If you have an OPTIMISER that's trying to optimise a function, it's making decisions about where to evaluate the function next.
• 40:59
  Collecting some data and then moving on to another point and so on.
• 41:03
  People don't think about optimisation that way. They just think about, here's an algorithm and here's something I can prove about the algorithm.
• 41:08
  But actually optimisation is very much like, you know.
• 41:14
  Bend it problems, reinforcement learning problems,
• 41:17
  sequential decision making under uncertainty is something that drives this because we want to optimise sorry,
• 41:23
  we want to automate the allocation of computational resources.
• 41:27
  So especially now that machine learning systems are very complex.
• 41:32
  Right. These these systems use a lot of memory, a lot of CPU.
• 41:37
  The datasets are very big. So we can't afford to just tinker about and run a few experiments on a single computer.
• 41:47
  And when we run major experiments, we actually have to worry about the fact that this is running on a big, you know, cloud of computers.
• 41:56
  And, you know, that's using energy and energy costs money and it's not good for the world, right, using energy like that.
• 42:05
  So optimising resource allocation. So these are the things that drive me these days.
• 42:10
  I'm going to talk about a couple of them very quickly.
• 42:13
  Probabilistic programming is one of them.
• 42:17
  The problem here is that developing probabilistic models and deriving inference algorithms is generally a very time consuming and error prone process.
• 42:30
  And the solution is to develop probabilistic programming languages.
• 42:34
  So what are these things? This is a very beautiful marriage between probabilistic modelling and programming languages, worlds.
• 42:42
  And the idea is that you have a probabilistic programming language, which is a way of expressing probabilistic models.
• 42:49
  And the modern ones, the ones that people are very interested in, like Frank Wood and myself these days, are completely general programming languages,
• 42:58
  sort of Turing complete programming languages that can express any computable probability distribution.
• 43:05
  That's the expression part. But what do you do with that?
• 43:08
  Well, well, first of all, how do you do that? You express your model as a simulator, a simulator that would generate data.
• 43:17
  That's one canonical way of doing that. And that's a very natural concept.
• 43:22
  You could say, okay, I have a model for the weather.
• 43:26
  Well, that's actually kind of a simulator. Okay. And I write it as a computer program.
• 43:31
  I have a model for my gene expression network, and that's going to be a simulator that, you know, simulates gene expression data.
• 43:40
  Okay. That's the modelling part.
• 43:44
  But then you have some data, you have a simulator and you have some data,
• 43:48
  and what you're really interested in is inferring or learning parameters of your simulator, of your model, given the data.
• 43:58
  And the very incredible thing is that we can actually come up with universal inference engines.
• 44:04
  We can come up with inference engines that in principle could compute the probability
• 44:11
  distribution over the hidden variables in our computer program given the data.
• 44:17
  So it's basically running Bayes rule on computer programs.
• 44:20
  We're all used to running computer programs in the forward direction. You take some inputs and you produce some outputs.
• 44:26
  But this is kind of doing it backwards.
• 44:29
  You have a computer program that takes some inputs and some calls the random number generators and produces some outputs.
• 44:35
  These are random outputs. That's the data.
• 44:37
  And now we say, well, what should the inputs and the cost of the random number generators have been to observe this output for the computer program?
• 44:48
  That's Bayes rule on the program. And there are many languages.
• 44:55
  Now, Anglican is the one that Frank Wood's team has been developing one of the state of the art languages.
• 45:02
  Our group in Cambridge has a language called Turing, which is much less developed but also exciting.
• 45:08
  It's based on Julia. There are many different languages developed by different groups and there are many
• 45:14
  different inference algorithms that can generally run on models in those languages.
• 45:23
  Here is, for example, a hidden Markov model written in in Turing.
• 45:30
  It's fairly easy to read if you uncomment one line of this model.
• 45:35
  You go from a regular hidden Markov model to a Bayesian hidden Markov model.
• 45:38
  So changing models around is as easy as sort of adding and removing a few lines of your probabilistic program.
• 45:47
  And I really think that, you know, if our vision actually plays out, this could really revolutionise scientific modelling.
• 45:53
  If people were actually willing to write probabilistic programs for all of their models and they shared them,
• 45:59
  then people could take somebody else's model, run it on their data, improve it, etc.
• 46:05
  A few resources here. I'll just give you a few examples. These are now slides from my postdoc, Hong.
• 46:11
  Okay. It's a little bit about Turing.
• 46:15
  I'll skip through that. That's our H&M example, but much bigger. This is a Bayesian neural network.
• 46:20
  Most of this is specifying the prior on the on the weights.
• 46:26
  And then this is the actual, you know, Bayesian neural network that's just sort of the neural network function and so on.
• 46:32
  And then you could just run inference using, you know, Hamiltonian Monte Carlo or something.
• 46:38
  You don't have to even know what that is. It abstracts away the model specification from the inference and ah language.
• 46:47
  Turing is pretty competitive. It's,
• 46:50
  it's sort of in the same ballpark is Anglican occasionally a bit faster but I know that the Anglican team keeps improving their language as well.
• 47:00
  Another topic I want to talk about is Bayesian optimisation.
• 47:04
  I have basically a couple of slides on that.
• 47:07
  So the problem here is you want to find ideally a global optimum, maybe that's too much ask of some black box function that is expensive to evaluate.
• 47:18
  So you can't just evaluate in lots and lots of places. You need to think about where you're going to evaluate your function next.
• 47:25
  And we don't want to do that manually. We want to automate the algorithm that thinks about that.
• 47:30
  So the solution is to treat the problem as sequential decision making under uncertainty.
• 47:36
  And what we're uncertain about is what the actual function is. And this has huge number of applications.
• 47:41
  And I'm actually you know, I'll say a couple words about the automatic statistician, but I do want to leave some time for questions.
• 47:46
  So the automatic statistician is automating is trying to automate model discovery.
• 47:54
  And the idea here is what we'd like is the system where we can just give it data.
• 48:00
  It searches over a large space of models,
• 48:04
  evaluating models according to some principled metric that trades off model complexity with the amount of data that you have.
• 48:12
  And actually the marginal likelihood, which I described, is one such metric, it produces a model and then interestingly,
• 48:19
  it translates that into a report that is then interpretable by a human being.
• 48:23
  So this is the opposite of a black box. We really want a transparent box, something that the human will be able to understand.
• 48:33
  Okay. And again, you know, I'll actually skip over most of this because I do want to leave time for questions.
• 48:40
  So we do a search over models. This is the automatic statistician applied to some time series.
• 48:45
  It finds a good model. Then it comes up with a description of that model.
• 48:49
  It produces the text itself. So this is the executive summary of the text.
• 48:54
  Actually, the text is in the form of these documents, which are, you know, 5 to 10 pages long.
• 49:01
  And, you know, we can have here is the report writing demo.
• 49:06
  You know, we could run this and this is a slightly different version of this, which actually does clustering.
• 49:15
  It tries to visualise things, it tells you what it's found, etc.
• 49:20
  Okay. And it tends to perform well at prediction because actually being systematic pays off.
• 49:31
  Okay. And we've applied this to classification as well, to regression, to clustering and so on.
• 49:36
  And we're going to have a release of it, I keep saying very soon, but this time I really mean it very soon means in a couple of months, I think.
• 49:45
  Okay. So I'm going to wrap up there.
• 49:50
  This probabilistic modelling framework isn't the only way to do machine learning, but it's a really useful organising principle.
• 49:58
  There is there are many layers and it's completely compatible with the choice of models that
• 50:03
  you have and whether you like deep learning or even logic and other frameworks and so on.
• 50:09
  We we really can hybridise a lot of these methods to produce interesting systems that reason about uncertainty and learn from data.
• 50:19
  I've briefly reviewed three topics is the review paper I wrote a couple of years ago that summarised
• 50:24
  this line of work and I wanted to end by thanking a whole bunch of collaborators I've had.