DEEP LEARNING FOR MEDICAL DATA
Andrew Beam, PhD
Department of Biomedical Informatics
February 23rd, 2018
twitter: @AndrewLBeam
WHAT IS DEEP LEARNING?
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
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
BP
BMI
Inputs
Output
Probability of MI
WHAT IS AN ARTIFICIAL NEURON?
The neuron is the basic functional unit a neural network
Inputs
Output
BP
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
BP
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
BP
BMI
BP
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
BP
BMI
BP
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
BP
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
BP
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 neural learn a simple function
y
X_1
X_2
| X1 | X2 | y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
w_1
w_1
b
Observations
PERCEPTRONS
How do we make a prediction for each observations?
y
X_1
X_2
| X1 | X2 | y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
w_1
w_1
b
Assume we have the following values
| w1 | w2 | b |
|---|---|---|
| 1 | -1 | 0 |
Observations
Predictions
For the first observation:
Assume we have the following values
| w1 | w2 | b |
|---|---|---|
| 1 | -1 | 0 |
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 |
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 = 0
h = 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
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
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
w_1, w_2, b
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
Gradient for
Gradient for
w^{new}_1 = w^{old}_1 - \sum gw_1
Update for
Update for
Update for
w^{new}_2 = w^{old}_2 - \sum gw_2
b^{new} = b^{old} - \sum g_b
w_1
w_1
w_2
w_2
b
b
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
Gradient for
Gradient for
w^{new}_1 = w^{old}_1 - \sum gw_1
Update for
Update for
Update for
w^{new}_2 = w^{old}_2 - \sum gw_2
b^{new} = b^{old} - \sum g_b
w_1
w_1
w_2
w_2
b
b
Fill in new table!
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)
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?
Let's plot it and see.
NEURAL NETWORK STRUCTURE
BP
BMI
Inputs
Output
Neural nets are organized into layers
Probability of MI
NEURAL NETWORK STRUCTURE
BP
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
BP
BMI
Probability of MI
NEURAL NETWORK STRUCTURE
Inputs
Output
Neural nets are organized into layers
1st Hidden Layer
Input Layer
BP
BMI
Probability of MI
NEURAL NETWORK STRUCTURE
Inputs
Output
Neural nets are organized into layers
A single hidden unit
1st Hidden Layer
Input Layer
BP
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
BP
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
BP
BMI
Probability of MI
IN CLASS ASSIGNMENT
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
+
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 ~ 16,000 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
CASE STUDY
DIABETIC RETINOPATHY
In 2016 Google built a deep learning model to automatically diagnose patients with diabetic retinopathy
- Input data: Labeled fundus photographs of the eye
- Large database of 128,000 images they created for this project
- Hired ophthalmologists to annotate the images ($$$)
DIABETIC RETINOPATHY
DIABETIC RETINOPATHY
Why did this work so well?
- Huge dataset of over 100,000 images
- High quality annotations - each image was rated by 3-7 opthamologists
- Transfer learning - neural network was originally trained on Imagenet!
- For the cost of a GPU (~$1,000) it's possible to read 240 million images/day at accuracy on par with best ophthalmologists!
DIABETIC RETINOPATHY
Implications
- Many subsequent studies have followed this formula
- Ingredients: Deep learning + high quality database of ~100,000 medical images + transfer learning
- Many medical imaging tasks in radiology, pathology, dermatology, and opthamology can be fully automated in a similar manner
- Similar results emerging from non-image data
How will this technology change medical practice, reimbursement, and other policies?
AUTOMATIC X-RAY READING
https://arxiv.org/pdf/1711.05225.pdf
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)
Additional Resources
http://beamandrew.github.io
ASIC Lecture
By beamandrew
