DEEP LEARNING FOR MEDICAL DATA

Andrew Beam, PhD

Department of Epidemiology

HSPH

twitter: @AndrewLBeam

WHAT IS DEEP LEARNING?

What is Artificial Intelligence?

What is Machine Learning?

Machine learning is a class of algorithms that learn how to do a task directly from data

Data = features (aka variables or inputs) and labels (aka the 'right' answer or outputs)

The algorithm is 'trained' to produce the correct output for a given input

What is Machine Learning?

Features

ML Algorithm

Label

Cat

Dog

What is Machine Learning?

Features

ML Algorithm

Label

“(Revenge of the Sith) marks a distinct improvement on the last two episodes, but only in the same way that dying from natural causes is preferable to crucifixion.”

Sentiment:

Negative

What is Machine Learning?

Features

ML Algorithm

Label

"I'm sorry Dave,

I can't do that"

What is Machine Learning?

Features

ML Algorithm

Label

"I'm sorry Dave,

I can't do that"

ML = box that takes input and produces output

What is Machine Learning?

Features

ML Algorithm

Label

"I'm sorry Dave,

I can't do that"

ML = box that takes input and produces output

WHAT IS DEEP LEARNING?

Deep learning is a specific kind of machine learning

- Machine learning automatically learns relationships using data

- Deep learning refers to large neural networks

- These neural networks have millions of parameters and hundreds of layers (e.g. they are structurally deep)

- Most important: Deep learning is not magic!

WHAT IS A NEURAL NET?

NEURAL NETWORK STRUCTURE

Say we want to build a model to predict the likelihood of a have a heart attack (MI) based on blood pressure (BP) and BMI

NEURAL NET STRUCTURE

A neural net is a modular way to build a classifier

BMI

Inputs

Output

Probability of MI

WHAT IS AN ARTIFICIAL NEURON?

The neuron is the basic functional unit a neural network

Inputs

Output

BMI

Probability of MI

WHAT IS AN ARTIFICIAL NEURON?

The neuron is the basic functional unit a neural network

A neuron does two things, and only two things

BMI

WHAT IS AN ARTIFICIAL NEURON?

The neuron is the basic functional unit a neural network

Weight for

A neuron does two things, and only two things

Weight for

1) Weighted sum of inputs

w_1*BP + w_2*BMI

BMI

WHAT IS AN ARTIFICIAL NEURON?

The neuron is the basic functional unit a neural network

Weight for

A neuron does two things, and only two things

Weight for

1) Weighted sum of inputs

\phi(w_1*BP + w_2*BMI)

2) Nonlinear transformation

BMI

w_1*BP + w_2*BMI

WHAT IS AN ARTIFICIAL NEURON?

\phi()

is known as the activation function

Sigmoid

Hyperbolic Tangent

WHAT IS AN ARTIFICIAL NEURON?

Summary: A neuron produces a single number that is a nonlinear transformation of its input connections

A neuron does two things, and only two things

= a number

BMI

WHAT IS AN ARTIFICIAL NEURON?

Summary: A neuron produces a single number that is a nonlinear transformation of its input connections

A neuron does two things, and only two things

= a number

BMI

This simple formula allows for an amazing amount of expressiveness

PERCEPTRON BY HAND

PERCEPTRONS

Let's say we'd like to have a single neuron learn a function

X_1

X_2

X1	X2	y
0	0	0
0	1	1
1	0	1
1	1	1

w_1

Observations

PERCEPTRONS

How do we make a prediction for each observations?

X_1

X_2

X1	X2	y
0	0	0
0	1	1
1	0	1
1	1	1

w_1

Assume we have the following values

w1	w2	b
1	-1	-0.5

Observations

Predictions

For the first observation:

Assume we have the following values

w1	w2	b
1	-1	-0.5

X_1 = 0, X_2 = 0, y =0

Predictions

For the first observation:

Assume we have the following values

w1	w2	b
1	-1	-0.5

X_1 = 0, X_2 = 0, y =0

First compute the weighted sum:

h = w_1*X_1 + w_2*X_2 + b

h = 1*0 + -1*0 + -0.5 = -0.5

h = -0.5

Predictions

For the first observation:

Assume we have the following values

w1	w2	b
1	-1	-0.5

X_1 = 0, X_2 = 0, y =0

First compute the weighted sum:

h = w_1*X_1 + w_2*X_2 + b

h = 1*0 + -1*0 + -0.5

h = -0.5

Transform to probability:

p = \frac{1}{1+\exp(-h)}

p = \frac{1}{1+\exp(-0.5)}

p = 0.38

Predictions

For the first observation:

Assume we have the following values

w1	w2	b
1	-1	-0.5

X_1 = 0, X_2 = 0, y =0

First compute the weighted sum:

h = w_1*X_1 + w_2*X_2 + b

h = 1*0 + -1*0 + -0.5

h = -0.5

Transform to probability:

p = \frac{1}{1+\exp(-h)}

p = \frac{1}{1+\exp(-0.5)}

p = 0.38

Round to get prediction:

\hat{y} = round(p)

\hat{y} = 0

Predictions

Putting it all together:

h = w_1*X_1 + w_2*X_2 + b

p = \frac{1}{1+\exp(-h)}

\hat{y} = round(p)

Assume we have the following values

w1	w2	b
1	-1	-0.5

X1	X2	y	h	p
0	0	0	-0.5	0.38	0
0	1	1
1	0	1
1	1	1

\hat{y}

Fill out this table

Predictions

Putting it all together:

h = w_1*X_1 + w_2*X_2 + b

p = \frac{1}{1+\exp(-h)}

\hat{y} = round(p)

Assume we have the following values

w1	w2	b
1	-1	-0.5

X1	X2	y	h	p
0	0	0	-0.5	0.38	0
0	1	1	-1.5	0.18	0
1	0	1	0.5	0.62	1
1	1	1	-0.5	0.38	0

\hat{y}

Fill out this table

Room for Improvement

Our neural net isn't so great... how do we make it better?

What do I even mean by better?

Room for Improvement

Let's define how we want to measure the network's performance.

There are many ways, but let's use squared-error:

(y - p)^2

Room for Improvement

Let's define how we want to measure the network's performance.

There are many ways, but let's use squared-error:

Now we need to find values for that make this error as small as possible

(y - p)^2

w_1, w_2, b

ALL OF ML IN ONE SLIDE

Our task is learning values for such the the difference between the predicted and actual values is as small as possible.

w_1, w_2, b

Learning from Data

So, how we find the "best" values for

w_1, w_2, b

Learning from Data

So, how we find the "best" values for

hint: calculus

w_1, w_2, b

Learning from Data

Recall (without PTSD) that the derivative of a function tells you how it is changing at any given location.

If the derivative is positive, it means it's going up.

If the derivative is negative, it means it's going down.

Learning from Data

Simple strategy:

- Start with initial values for

- Take partial derivatives of loss function

with respect to

- Subtract the derivative (also called the gradient) from each

w_1, w_2, b

Learning from Data

Simple strategy:

- Start with initial values for

- Take partial derivatives of loss function

with respect to

- Subtract the derivative (also called the gradient) from each

w_1, w_2, b

To the whiteboard!

Learning Rules for each Parameter

gw_1 = (p - y)*(p*(1-p)*X_1)

gw_2 = (p - y)*(p*(1-p)*X_2)

g_b = (p - y)*(p*(1-p))

Gradient for

w^{new}_1 = w^{old}_1 - \sum gw_1

Update for

w^{new}_2 = w^{old}_2 - \sum gw_2

b^{new} = b^{old} - \sum g_b

w_1

w_2

Learning Rules for each Parameter

gw_1 = (p - y)*(p*(1-p)*X_1)

gw_2 = (p - y)*(p*(1-p)*X_2)

g_b = (p - y)*(p*(1-p))

Gradient for

w^{new}_1 = w^{old}_1 - \sum gw_1

Update for

w^{new}_2 = w^{old}_2 - \sum gw_2

b^{new} = b^{old} - \sum g_b

w_1

w_2

Fill in new table!

https://bit.ly/2ux5DLJ

Learning Rules for each Parameter

gw_1 = (p - y)*(p*(1-p)*X_1)

gw_2 = (p - y)*(p*(1-p)*X_2)

g_b = (p - y)*(p*(1-p))

Gradient for

w^{new}_1 = w^{old}_1 - \sum gw_1

Update for

w^{new}_2 = w^{old}_2 - \sum gw_2

b^{new} = b^{old} - \sum g_b

w_1

w_2

Fill in new table!

https://bit.ly/2ux5DLJ

Solution:

https://bit.ly/2FHpH4z

THE BACKPROPAGATION ALGORITHM

A Simple Perceptron in R

train <- function(X,y,w,b,iter=10,lr=1) {
  w_new <- w
  b_new <- b
  for(i in 1:iter) {
    preds <- plogis(X %*% w_new + b_new)

    grad_w1 <- (preds - y)*preds*(1 - preds)*X[,1]
    grad_w2 <- (preds - y)*preds*(1 - preds)*X[,2]
    grad_b <- (preds - y)*(preds*(1 - preds))
    
    w_new[1] <- w_new[1] - lr*sum(grad_w1)
    w_new[2] <- w_new[2] - lr*sum(grad_w2)
    b_new <- b_new - lr*sum(grad_b)
    error <- (y - preds)^2
    print(paste0("Error at iteration ",i,": ",mean(error)))
  }
  return(list(w=w_new,b=b_new))
}

X <- rbind(c(0,0),c(0,1),c(1,0),c(1,1))
y <- c(0,1,1,1)
w <- as.vector(c(1,-1))
b <- -0.5

train(X,y,w,b)

https://bit.ly/2JLDJ9m

Another Example

X1	X2	y
0	0	0
0	1	0
1	0	0
1	1	1

Final Example

X1	X2	y
0	0	0
0	1	1
1	0	1
1	1	0

What Happened?

Why didn't this work?

What Happened?

Why didn't this work?

Is this relationship "harder" in some sense?

What Happened?

Why didn't this work?

Is this relationship "harder" in some sense?

NEURAL NETWORK STRUCTURE

BMI

Inputs

Output

Neural nets are organized into layers

Probability of MI

NEURAL NETWORK STRUCTURE

BMI

Inputs

Output

Neural nets are organized into layers

Probability of MI

NEURAL NETWORK STRUCTURE

Inputs

Output

Input Layer

Neural nets are organized into layers

BMI

Probability of MI

NEURAL NETWORK STRUCTURE

Inputs

Output

Neural nets are organized into layers

1st Hidden Layer

Input Layer

BMI

Probability of MI

NEURAL NETWORK STRUCTURE

Inputs

Output

Neural nets are organized into layers

A single hidden unit

1st Hidden Layer

Input Layer

BMI

Probability of MI

NEURAL NETWORK STRUCTURE

Inputs

Output

Input Layer

Neural nets are organized into layers

1st Hidden Layer

A single hidden unit

2nd Hidden Layer

BMI

Probability of MI

NEURAL NETWORK STRUCTURE

Inputs

Output

Input Layer

Neural nets are organized into layers

1st Hidden Layer

A single hidden unit

2nd Hidden Layer

Output Layer

BMI

Probability of MI

IN CLASS ASSIGNMENT

https://playground.tensorflow.org/

MODERN DEEP LEARNING

Neural networks are one of the oldest ideas in machine learning and AI

- Date back to 1940s

- Long history of "hype" cycles - boom and bust

- Were *not* state of the are machine learning technique for most of their existence

- Why are they popular now?

MODERN DEEP LEARNING

Several key advancements have enabled the modern deep learning revolution

GPU enable training of huge neural nets on extremely large datasets

Several key advancements have enabled the modern deep learning revolution

MODERN DEEP LEARNING

Transfer Learning

Train big model

on large dataset

Refine model

on smaller dataset

Several key advancements have enabled the modern deep learning revolution

Methodological advancements have made deeper networks easier to train

Architecture

Optimizers

Activation Functions

MODERN DEEP LEARNING

Several key advancements have enabled the modern deep learning revolution

Easy to use frameworks dramatically lower the barrier to entry

Automatic differentiation allows easy prototyping

MODERN DEEP LEARNING

Deep Learning Comes of Age

CONVOLUTIONAL NEURAL NETWORKS

CONVOLUTIONAL NEURAL NETS (CNNs)

Dates back to the late 1980s

Responsible for Deep Learning revival
Invented by in 1989 Yann Lecun at Bell Labs - "Lenet"
Integrated into handwriting recognition systems
in the 90s
Huge flurry of activity after the Alexnet paper

THE BREAKTHROUGH (2012)

Imagenet Database

Millions of labeled images
Objects in images fall into 1 of a possible 1,000 categories
Relatively high-resolution
Bounding boxes giving exact location of object - useful for both classification and localization

Large Scale Visual

Recognition Challenge (ILSVRC)

Annual Imagenet Challenge starting in 2010
Successor to smaller PASCAL VOC challenge
Many tracks including classification and localization
Standardized training and test set. Competitors upload predictions for test set and are automatically scored

THE BREAKTHROUGH (2012)

Pivotal event occurred in 2012 which laid the blueprint for successful deep learning model

Massive amounts of labeled images
Training with GPUs
Methodological innovations that enabled training deeper networks while minimizing overfitting

THE BREAKTHROUGH (2012)

In 2011, a misclassification rate of 25% was near state of the art on ILSVRC

In 2012, Geoff Hinton and two graduate students, Alex Krizhevsky and Ilya Sutskever, entered ILSVRC with one of the first deep neural networks trained on GPUs, now known as "Alexnet"

Result: An error rate of 16%, nearly half what the second place entry was able to achieve.

The computer vision world immediately took notice

THE ILSVRC AFTERMATH (2012-2014)

Alexnet paper has ~ 37,000 citations since being published in 2012!

Most algorithms expect "tabular" data

WHY CNNS WORK

y	X1	X2	X3	X4
0	7	52	17	654
0	23	2752	4	1
1	786	27	0	5
0	354	7527	89	68

The problem with tabular data

What is this a picture of?

WHY CNNS WORK

What is this a picture of?

The problem with tabular data

WHY CNNS WORK

What is this a picture of?

Tabular data throws away too much information!

The problem with tabular data

WHY CNNS WORK

CONVOLUTIONAL NEURAL NETS

Images are just 2D arrays of numbers

Goal is to build f(image) = 1

CONVOLUTIONAL NEURAL NETS

CNNs look at small connected groups of pixels using "filters"

Image credit: http://deeplearning.stanford.edu/wiki/index.php/Feature_extraction_using_convolution

Images have a local correlation structure

Near by pixels are likely to be more similar than pixels that are far away

CNNs exploit this through convolutions of small image patches

WHY DO CNNs WORK SO WELL?

Based on solid image priors
Exploit properties of images, e.g. local correlations and invariances
Mimic generative distribution with augmentation to reduce over fitting
Results in end-to-end visual recognition system trained with SGD on GPUs: pixels in -> classifications out

CNNs exploit strong prior information about images

ALPHAGO DISCUSSION

DEEP LEARNING HAS MASTERED GO

Source: https://deepmind.com/blog/alphago-zero-learning-scratch/

Human data no longer needed

DEEP LEARNING HAS MASTERED GO

SUMMARY & CONCLUSIONS

CONCLUSIONS

Deep learning models are like legos, but you need to know what blocks you have and how they fit together
Could potentially impact many fields -> understand concepts so you have deep learning "insurance"
Impact of medical imaging seems inevitable
Prereqs: Data (lots) + GPUs (more = better)

Review Articles

Additional Resources

http://beamandrew.github.io

Copy of HMS Computational Medicine Lecture (March 2022)

By beamandrew

Copy of HMS Computational Medicine Lecture (March 2022)