Bayesian Deep Probabilistic Differentiable Programming

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# Bayesian Deep Probabilistic Differentiable Programming

## A Journey Towards Scientific AI

Michael Green

MCnet Machine Learning training, Lund University 2020

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# What are we doing today?

- The current state of AI
- Probabilistic programming
- Differentiable programming
- The scientific principle
  ]
.right-column[
## Part 2

- A paradigm shift
- Foundations of uncertainty
- Decision making

]

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## Education · Timeline

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                I'm not putting that on paper.
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          <q-timeline-entry
            title="MSc Computer Science and Mathematics"
            subtitle="2000-2003"
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                Thesis on machine learning in Robots for soccer playing purposes
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            title="PhD Theoretical Physics"
            subtitle="2004-2008"
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                Machine Learning Research directed at Neural network ensembles
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            title="SimCorp A/S"
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            subtitle="2008-2009"
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                MCMC methods for market price movements
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            title="GroupM A/S"
            subtitle="2009-2013"
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                Development of statistical methods for the predicton of sales
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            subtitle="2013-Present"
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                Founded the worlds first automated AI driven media agency
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            title="AI α Lab ApS"
            subtitle="2018-Present"
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                Founded an AI driven and risk management investment company
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            title="Desupervised ApS"
            subtitle="2018-Present"
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                Founded an AGI company building software for solving
                intelligence
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## My personal goal with AI research

> Build software that allows machines to see, learn and think like people do

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![](static/ai-types.png.webp)

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# What is intelligence?

![](static/datatowizdom.svg)

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## Breakdown

Basically data is compressed into information.
Information is in turn assimilated into knowledge
Knowledge eventually can transcend into wizdom

Wizdom allows an agent to search for knowledge
This also makes it realize that this requires information
Which can come from data or prior information

]

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## The AGI process

### What do we have?

Imagine any task to pose to an AGI in the real world. What do we have to do?

- Perception is hard
- Localization is solved
- Planning is extra hard
- Control is easy
]

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## Intelligence

AI is the behaviour shown by an agent in an environment that seems to optimize the concept of future freedom
<br />
<br />

]

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## The Bayesian brain

### What do we have?

Imagine any task to pose to an AGI in the real world. What do we have to do?

- Perception is hard
- Localization is solved
- Planning is extra hard
- Control is easy
]

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# The probabilistic modeling pipeline

![](static/probabilisticmodelingpipeline.svg)

]
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## Breakdown

Our AI engine works with two major ingredients: A questions and a dataset. It
uses all knowledge it can receive about the question as well as the dataset to
form hypotheses. These hypotheses are then continuously tested through models
which is also criticized and revised

]

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## What is deep probabilistic programming?

### Learning

$$\hat{\theta}=\underset{\theta}{\mathrm{argmax}}~p(y | \theta, x, m)$$

### Predicting

$$p(\hat{y}|\hat{\theta}, x, y, m)$$

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### Learning

$$p\left(\theta|y, x, m\right)=\frac{p\left(y|\theta,x,m\right)p\left(\theta|x,m\right)}{\int p\left(y,\theta|x,m\right)d\theta}$$

### Predicting

$$p\left(\hat{y}|y,x,m\right)=\int p(\hat{y}|\theta, y, x, m)p(\theta|y, x, m)d\theta$$

### Comparing

$$p(m|y,x)=\frac{p(y|x,m)p(m|x)}{p(y|x)}$$

]

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## An important reminder

<small>Not evaluating uncertainty for every prediction is a fundamental mistake.</small>

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## Uncertainty is absolutely crucial

<small>Not evaluating uncertainty for every prediction is a fundamental mistake.</small>

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## The scientific principle

You cannot do science without assumptions and the best way to specify those
assumptions are through probabilistic modeling.
<br />
<br />

]

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## What do we get from this?

Probabilistic programming creates systems that help make decisions in the face of uncertainty. Probabilistic reasoning combines knowledge of a situation with the laws of probability. Until recently, probabilistic reasoning systems have been limited in scope, and have not successfully addressed real world situations.

- It allows us to specify the models as we see fit
- Curse of dimensionality is gone
- We get uncertainty measures for all parameters
- We can stay true to the scientific principle
- We do not need to be experts in MCMC to use it!

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## About autodifferentiation

- Two major approaches
  - Forward mode
  - Reverse mode
- Three major implementation directions
  - Static compiled graph (Tensorflow et. al.)
  - Operator overloading dynamic graph (Pytorch)
  - Source to source (Zygote)

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![](static/differentiateallthethingsmeme2.png)

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# Part two

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## Borrowing from Mr. Twain

The problem with our models is not that they know too little; It's that they
know so many things that just ain't so.
]

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## What about some real life examples?

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## What my model doesn't know....

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## A "new" language to the rescue

- Julia is an excellent platform for doing Deep probabilistic differentiable
programming
- Liberates you from "frameworks", as we can differentiate all things
- Your code can differentiate functions from packages whose authors never
thought about it
- Solves the two language problem

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# How do we get started?

f(x) = 5x + 3

f(10), f'(10)
# (53, 5)

@code_llvm f'(10)
# define i64 @"julia_#625_38792"(i64) {
# top:
#   ret i64 5
# }
```
]

This is a nice example of source-to-source autodiff in actiona. The compiler
generates the backwards pass for you!

]

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# Direct support of all language features

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```julia
import Base: +, -

struct Point
  x::Float64
  y::Float64
end

a::Point + b::Point = Point(a.x + b.x, a.y + b.y)
a::Point - b::Point = Point(a.x - b.x, a.y - b.y)
dist(p::Point) = sqrt(p.x^2 + p.y^2)
```
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```julia
a = Point(1, 2)
# Point(1.0, 2.0)

b = Point(3, 4)
# Point(3.0, 4.0)

dist(a + b)
# 7.211102550927978

gradient(a -> dist(a + b), a)[1]
# (x = 0.5547001962252291, y = 0.8320502943378437)
```
]

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# Simple machine learning model

```julia
struct Linear
  W
  b
end

(l::Linear)(x) = l.W * x .+ l.b

model = Linear(rand(2, 5), rand(2))
# Linear([0.267663 … 0.334385], [0.0386873, 0.0203294])

dmodel = gradient(model -> sum(model(x)), model)[1]
# (W = [0.652543 … 0.683588], b = [1.0, 1.0])
```

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# Neural ODEs is a cinch!

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## Going vanilla?

```julia
using Flux
using DifferentialEquations

m = Chain(
  Dense(28^2, 32, relu),
  # this would require an ODE of 32 parameters
  p -> solve(prob,Tsit5(),p=p,saveat=0.1)[1,:],
  Dense(32, 10),
  softmax)
```
]

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## Wanna do it with convolutions?

```julia
m = Chain(
  Conv((2,2), 1=>16, relu),
  x -> maxpool(x, (2,2)),
  Conv((2,2), 16=>8, relu),
  x -> maxpool(x, (2,2)),
  x -> reshape(x, :, size(x, 4)),
  x -> solve(prob,Tsit5(),x=x,saveat=0.1)[1,:],
  Dense(288, 10), softmax) |> gpu
```
]

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# How about graph neural networks?

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# Summary

- Inductive bias is key
- View models as programs which can be differentiated
- Free yourself from the bonds of Deep Learning
- Always Quantify uncertainty

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# Thanks for listening!

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