2017-08-24 18:58:13 +00:00
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-- #+TITLE: Deep Learning Coursera
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-- #+AUTHOR: Yann Esposito
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#+STARTUP: latexpreview
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#+TODO: TODO IN-PROGRESS WAITING | DONE CANCELED
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2017-09-02 21:54:37 +00:00
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#+COLUMNS: %TODO %3PRIORITY %40ITEM(Task) %17EFFORT(Estimated Effort){:} %CLOCKSUM %8TAGS(TAG)
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2017-08-24 18:58:13 +00:00
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* Plan
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5 courses
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** Neural Network and Deep Learning
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*** Week 1: Introduction
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*** Week 2: Basic of Neural Network programming
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*** Week 3: One hidden layer Neural Networks
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*** Week 4: Deep Neural Network
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** Improving Deep Neural Networks: Hyperparameter tuning, Regularization and Optimization
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** Structuring your Machine Learning project
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** Convolutional Neural Networks
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** Natural Language Processing: Building sequence models
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* DONE Neural Network and Deep Learning
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CLOSED: [2017-08-22 Tue 13:43]
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** Introduction
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*** What is a neural network?
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*** Supervised Learning with Neural Networks
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- Lucrative application: ads, showing the add you're most likely to click on
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- Photo tagging
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- Speech recognition
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- Machine translation
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- Autonomous driving
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***** Convolutional NN good for images
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***** Strutured data (db of data) vs Unstructured data
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- Structured data: Tables
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- Unstructured data: Audio, image, text...
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Computer are much better at interpreting unstructured data.
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*** Why is Deep Learning taking off?
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[[///Users/yaesposi/Library/Mobile%20Documents/com~apple~CloudDocs/deft/img/Scale%20drives%20deep%20learning%20progress.png]]
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- Data (lot of data)
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- Computation (faster learning loop)
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- Algorithms (ex, use ReLU instead of sigma)
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** Geoffrey Hinton interview
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** Binary Classification
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\[ (x,y) x\in \mathbb{R}^{n_x}, y \in {0,1} \]
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$m$ training examples: $$ {(x^{(1)},y^{(1)}), ... (x^{(m)},y^{(m)})} $$
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$$ m = m_{train} , m_{test} = #test examples $$
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$$ X = [ X^{(1)} ... X^{(m)} ] is an n_x x m matrix $$
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$$ X.shape (n_x,m) $$
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$$ Y = [ y^{(1)} ... y^{(m)} ] $$
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$$ Y.shape = (1,m) $$
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** Logistic Regression
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Given $X \in \mathbb{R}^{n_x}$ you want $\hat{y} = P(y=1 | X)$
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Paramters: $w \in \mathbb{R}^{n_x}, b\in \mathbb{R}$
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Output: $\hat{y} = \sigma(w^Tx + b) = \sigma(z)$
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$$\sigma(z)= \frac{1}{1 + e^{-z}}$$
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If $z \rightarrow \infty => \sigma(z) \approx 1$
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If $z \rightarrow - \infty => \sigma(z) \approx 0$
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Alternative notation not used in this course:
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$X_0=1, x\in\mathbb{R}^{n_x+1}$
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$\hat{y} = \sigma(\Theta^Tx)$
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...
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** Logistic Regression Cost Function
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Search a convex loss function:
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$L(\hat{y},y) = - (y\log(\hat{y}) + (1-y)\log(1-\hat{y}))$
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If y = 1 : $L(\hat{y},y) = -\log\hat{y}$ <- want log\haty larg, want \hat{y} large
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If y = 0 : $L(\hat{y},y) = -\log\hat{y}$ <- want log (1-\hat{y}) large, want \hat{y} sall
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Cost function: $$ J(w,b) = \frac{1}{m}\sum_{i=1}^mL(\hat{y^\{(i)}},y^{(i)}) = ... $$
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** Gradient Descent
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Minize $J(w,b)$
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1. initialize w,b (generaly uses zero)
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2. Take a step in the steepest descent direction
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3. repeat 2 until reaching global optimum
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Repeat {
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$w := w - \alpha\frac{dJ(w)}{dw} = w - \alpha\mathtext{dw}$
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}
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** Derivatives
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** More Derivative Examples
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** Computaion Graph
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** Computing Derivatives
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** Computing Derivatives for multiple examples
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** Vectorization
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getting rid of explicit for loops in your code
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** Vectorizing Logistic Regression
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** Vectorizing Logistic Regression's Gradient Computation
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** Broadcasting in Python
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** Quick Tour of Jupyter / ipython notebooks
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** Neural Network Basics
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J = a*b + a*c - (b+c) = a (b + c) - (b + c) = (a - 1) (b + c)
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2017-09-02 21:54:37 +00:00
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* DONE Improving Deep Neural Networks: Hyperparameter tuning, Regularization and Optimization
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CLOSED: [2017-09-01 Fri 09:52]
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2017-08-24 18:58:13 +00:00
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** DONE Week 1: Setting up your Machine
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CLOSED: [2017-08-22 Tue 13:43]
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*** Recipe
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If *High bias*? (bad training set performance?)
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Then try:
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- Bigger network
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- Training longer
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- (NN architecture search)
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Else if *High variance*? (bad dev set performance?)
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Then try:
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- More data
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- Regularization
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- (NN architecture search)
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Deep learning, not much bias/variance tradeoff if we have a big amount of
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computer power (bigger network) and lot of data.
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*** Regularization
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**** Regularization: reduce variance
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- L2 regularization
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λ / 2m || w ||_2 ^2
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- L1 regularization: same with |w| instead of ||w||_2^2
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λ is a regularization parameter (in code named =lambd=)
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Cost = J(w^[1], b^[1], ..., w^[L], b^[L]) = 1/m \sum L(^y(i), y(i)) + λ/2m \sum_l=1^L || W^[l] ||^2
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call the "Frobenius norm"
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dW = from backprop + λ/m W^l
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update W^l = W^l - αdW^l still works
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Sometime L2 regularization called "weight decay".
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**** Dropout Regularization
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Eliminates nodes by layer randomly for each training example.
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- implementing, (inverted dropout)
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- gen random boolean vector:
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d3 = np.random.rand(a3.shape[0], a3.shape[1]) < keep_prob # (for each iteration)
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a3 = np.mulitply(a3,d3)
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a3 /= keep_prob (for normalization to be certain the a3 output still the same, reduce testing problems)
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Making prediction at test time: no drop out
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**** Over regularization methods
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- Data augmentation, (flipping images for example, random crops, random distortions, etc...)
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- Early stopping, stop earlier iteration
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*** Setting up your optimization problem
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**** Normalizing Inputs
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- μ = 1/m Sum X^(i)
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- x := x - μ (centralize)
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- σ = 1/m Sum X^(i)^2
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- x /= σ^2
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**** Gradient Checking
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***** Don't use gard check in traingin, only in debug
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***** If algorithm fail, grad check, look at component (is db? dW? dW on certain layer, etc...)
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***** Remember regularization
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***** Doesn't work with dropout, turn off drop out (put 1.0) then check
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***** Run at random initialization; perhaps again after training
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** DONE Week 2: Optimization Algorithms
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CLOSED: [2017-08-22 Tue 13:43]
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*** Mini batch
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X :: X^(1) ... X^(m)
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X,Y -> X^{i},Y^{i} where X^{i} = X^(i*batch-size ---> (i+1)*batch-size)
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*** Minibatch size
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- if mini batch size = m => Batch gradient descent (X^{1},Y^{1}) = (X,Y)
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- if mini match size = 1 => Stochastic gradient descent, every example is its own mini batch.
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- in practice in between 1 and m, m --> too long, 1 loose speedup from vectorization.
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+ vectorization ~1000
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1. If small training set, use batch gradient descent (m <= 2000)
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2. Typical mini-batch size: 64, 128, 256, 512, ... 2^k to fits in CPU/GPU memory
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*** Exponentially weighted average
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v_t = βv_{t-1} + (1-β)θ_t
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2017-09-02 21:54:37 +00:00
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** DONE Week 3: Hyperparameter
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CLOSED: [2017-09-01 Fri 09:52]
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*** Video 1: use random not a grid to search for hyperparameter best value
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*** Video 2: choose appropriate scale to pick hyperparameter
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- uniformly random n^[l] (number of neuron for layer l) or L (number of layers)
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- alpha: between 0.00001 to 1, then shouldn't use linear but instead use log-scale
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r = -4*np.random.rand() <- r in [-4,0]
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α = 10^r <- 10^-4 ... 10^0
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- β <- 0.9 ... 0.999 (0.9 about avg on 10 values, 0.999 avg about 1000 values)
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1-β = 0.1 .... 0.001
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r <- [-3,-1]
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1-β = 10^r
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*** Hyperparameter: Tuning in practice Panda vs caviar
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- Babysitting one model (panda) for few computer resources
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- Training many models in parallel (caviar) for lot of computer resources
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*** Batch normalization
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**** In a network
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**** Fitting Batch norm into a deep network
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**** Why Batch Normalizing?
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- don't use batch norm as a regularization even if sometime it could have this
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effect
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**** Batch Norm at test time
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μ = 1/m \sum z^(i)
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σ^2 = 1/m \sum (z^(i) - μ)^2
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z^(i)_norm = z^(i) - μ / sqrt( σ^2 + ε )
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~z^(i) = γz^(i)_norm + β
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Estimate μ and σ with exponentially weighted avg accross minibatches
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*** Multi-class classification
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**** Softmax Regression
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notation: C = #classes (0,1,2...,C-1)
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last hidden layer nb of neuron is equal to C: n^L = C
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z^[L] = w[L]a^[L-1] + b[L] (C,1)
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Activation function:
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t = e^(Z[L])
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a^[L] = e^(Z[L])/\sum_i=0^C t_i
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a^[L]_i = t_i / \sum_i=0^C t_i
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**** Training a softmax classifier
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*** Introduction to programming frameworks
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**** Deep learning frameworks
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* Structuring your Machine Learning project
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** Week 1
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*** Introduction to ML Strategy
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**** Why ML Strategy
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Try to find quick and effective way to choose a strategy
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Ways of analyzing ML problems
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**** Orthogonalization
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***** Chain of assumptions in ML
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- Fit training set well on cost function => bigger network, Adam, ...
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- Fit dev set well on cost function => Regularization, Bigger training set
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- Fit test set well on cost function => Bigger dev set
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- Perform well in real world => Change the devset or cost function
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Try not to use early stoping as it simulanously affect cost on training and dev set.
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*** Setting up your goal
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**** Single number evaluation metric
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***** First
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| Classifier | Precision | Recall |
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|------------+-----------+--------|
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| A | 95% | 90% |
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| B | 98% | 85% |
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Rather than using two number, find a new evaluation metric
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| Classifier | Precision | Recall | F1 Score |
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|------------+-----------+--------+----------|
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| A | 95% | 90% | 92.4% |
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| B | 98% | 85% | 91.0 |
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F1 score = 2 / (1/p) + (1/R) :: "Harmonic mean" of precision and recall.
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So:
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Having a good Dev set + single evaluation metric, really speed up iterating.
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***** Another example
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| Algorithm | US | China | India | Other | *Average* |
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|-----------+-----+-------+-------+-------+-----------|
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| A | 3% | 7% | 5% | 9% | |
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| ... | | | | | |
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| F | ... | ... | | | |
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Try to improve the average.
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**** Satisficing and Optimizing metric
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It's not alway easy to select on metric to optimize.
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***** Another cat classification example
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| Classifier | Accuracy | Running Time |
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|------------+----------+--------------|
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| A | 90% | 80ms |
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| B | 92% | 95ms |
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| C | 95% | 1500ms |
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cost = accuracy - 0.5x running time
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maximize accuracy s.t. running time < 100ms
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Accuracy <- Optimizing
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Running time <- Satisficing
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If you have n metrics, pick one to optimizing, and all the other be satisficing.
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**** Train/dev/test distribution
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How you can setup these dataset to speed up your work.
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***** Cat classification dev/test sets
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Try to find a way that dev and test set come from the same distribution.
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***** True story (detail changed)
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Optimizing on dev set on load approvals for medium income zip codes.
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(repay loan?)
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Tested on low income zip codes.
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Lost 3 months
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***** Guideline
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Choose a dev set and test set to reflect data you expect to get in the future
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and consider important to do well on.
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**** Size of dev and test sets
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***** Old way of splitting
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70% train, 30% test
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60% train, 20% dev, 20% test
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For at max 10^4 examples
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But in new era, 10^6 examples:
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train: 98%, Dev 1%, Test 1%.
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***** Size of test set
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Set your test set to be big enough to give high confidence in the overall
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performance of your system. Can be far less than 30% of your data.
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For some applications, you don't need test set and only dev set.
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For example if you have a very large dev set.
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**** When to change dev/test sets and metrics?
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Metric: classification error
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Algorithm A: 3% error → letting throught a lot of porn images
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Algorithm B: 5% error → doesn't let pass porn images
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So your metric + evaluation prefer A, but you and your users prefer B.
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When this happens, mispredict your algorithm B is better.
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Error: 1/m_dev \sum_i=1^m I{y_pred^(i) /= y^(i)
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They treat pron and non pron equaly but you don't want that.
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We add a w(i) = 1 if non porn and 0 if porn in the formula
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**** Orthogonalization for cat pictures: anti-pron
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1. So far we've only discussed how to define a metric to evaluate classifier
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2. Worry separately about how to do well on this metric
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1. placing the target, and 2. is aiming the target.
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**** Another example
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Alg A: 3% err
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Alg B: 5% err
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But B does better. You see that users are using blurier images.
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You dev/test are not using the same kind of images.
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Change your metric and/or dev/test set.
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|
2017-09-13 06:55:56 +00:00
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*** Comparing to Humand-level performance
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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**** Why human-level performance
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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Human-level perf vs Bayes optimal error
|
2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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Human are generally very close to bayes perf for lot of tasks.
|
2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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- get lableld data from humans
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- gain insight from manual error analysis (why did a person get this right?)
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- better analysis of bias/variance
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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**** Avoidable bias
|
2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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***** Cat classification example
|
2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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| Humans | 1% | 7.5% |
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| Training error | 8% | 8% |
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| Dev error | 10% | 10% |
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| | focus on bias | focus on variance |
|
2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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Human level error as a proxy (estimate) for Bayes error.
|
2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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*Diff between Human err and Training err = available bias*
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*Diff between Train and Dev err = variance*
|
2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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**** Understanding Human-level performance
|
2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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***** Human-level error as proxy for Bayes error
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Medical image classification example:
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suppose
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(a) Typical human 3% err
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(b) Typical doctor 1% err
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(c) Experienced doctor 0.7% err
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(d) and team of experienced doctors 0.5% err
|
2017-09-02 21:54:37 +00:00
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|
2017-09-13 06:55:56 +00:00
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What is "human-level" error?
|
2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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Bayes error is <= to 0.5% err
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So we use that to aim as saw before.
|
2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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For a paper, (b) is good enough to talk about that.
|
2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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***** Error analysis example
|
2017-09-02 21:54:37 +00:00
|
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|
2017-09-13 06:55:56 +00:00
|
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| Human (proxy for bayes err) | 1, 0.7, 0.5% | 1, 0.7, 0.5 | 1, 0.7, 0.5 |
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| Train err | 5% | 1% | 0.7% |
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| Dev err | 6% | 5% | 0.8% |
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| | | | |
|
2017-09-02 21:54:37 +00:00
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|
2017-09-13 06:55:56 +00:00
|
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|
Case 1:
|
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|
|
For this example it doesn't matter because avoidable bias (5 - 1%), is bigger
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|
than variance (6-5)
|
2017-09-02 21:54:37 +00:00
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|
2017-09-13 06:55:56 +00:00
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Case 2: focus on variance
|
2017-09-02 21:54:37 +00:00
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|
2017-09-13 06:55:56 +00:00
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Case 3, very important you use 0.5 as your "human-level" error. Because it show
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|
that you should focus on bias and not on variance.
|
2017-09-02 21:54:37 +00:00
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|
2017-09-13 06:55:56 +00:00
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|
This problem arose only when you're doing very good.
|
2017-09-02 21:54:37 +00:00
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|
2017-09-13 06:55:56 +00:00
|
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***** Summary of bias/variance with human-level perf
|
2017-09-02 21:54:37 +00:00
|
|
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|
2017-09-13 06:55:56 +00:00
|
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|
Human-level error (proxy for Bayes err)
|
2017-09-02 21:54:37 +00:00
|
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|
2017-09-13 06:55:56 +00:00
|
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|
^
|
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|
|
| "Avoidable bias"
|
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|
|
v
|
2017-09-02 21:54:37 +00:00
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|
2017-09-13 06:55:56 +00:00
|
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Training error
|
2017-09-02 21:54:37 +00:00
|
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|
2017-09-13 06:55:56 +00:00
|
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|
^
|
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|
|
| "Variance"
|
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|
v
|
2017-09-02 21:54:37 +00:00
|
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|
2017-09-13 06:55:56 +00:00
|
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|
Dev error
|
2017-09-02 21:54:37 +00:00
|
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|
**** Surpassing human-level performance
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|
2017-09-13 06:55:56 +00:00
|
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|
|
***** Surpassing human-level performance
|
|
|
|
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|
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|
|
| Team | 0.5% | 0.5% |
|
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|
| One human | 1% | 1% |
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|
|
| Training error | 0.6% | 0.3% |
|
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|
|
| Dev error | 0.8% | 0.4% |
|
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|
|
|-----------------+-------+------------|
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|
|
| Avoidable bias? | ~0.5% | can't know |
|
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|
|
***** Problems where ML significantly surpasses human-level performance
|
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|
|
- Online advertising
|
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|
|
- Product recommendations
|
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|
|
- Logistics (predicting transit time)
|
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|
|
- Loan approvals
|
|
|
|
|
|
|
|
|
|
all thoses examples:
|
|
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|
|
+ come from structured data
|
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|
|
+ not natural perception problems
|
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|
|
+ Lots of data
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|
Also, Speech recognition, Some image recognition, Medical, ECG, skin cancer,
|
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|
|
etc...
|
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|
|
**** Improving your model performance
|
|
|
|
|
|
|
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|
|
Set of guidelines
|
|
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|
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|
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|
|
***** The two fundamental assumptions of supervised learning
|
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|
|
1. You can fit the training set pretty well (~ avoidable bias)
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|
|
2. The training set performance generalizes pretty well to the dev/test set
|
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|
***** Reducing (avoidable) bias and variance
|
|
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|
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|
|
Human-level error (proxy for Bayes err)
|
|
|
|
|
|
|
|
|
|
^
|
|
|
|
|
| train bigger model
|
|
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|
|
| "Avoidable bias" => train longer/better optimization algorithms (momentum, RMSprop, Adam)
|
|
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|
|
| NN architecture/hyperparameters search (RSS, CNN...)
|
|
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|
|
v
|
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|
Training error
|
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|
^
|
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|
|
| More data
|
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|
|
| "variance" => Regulraization (L2, dropout, data augmentation)
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|
| NN architecture/hyperparameters search
|
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|
v
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|
Dev error
|
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|
|
These concepts are easy to learn, hard to master.
|
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|
|
You'll be more systematics than most ML teams.
|
|
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|
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|
|
** Week 2
|
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|
|
*** Error Analysis
|
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|
**** Error Analysis
|
|
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|
|
***** Carrying out error analysis
|
|
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|
|
- Imagine your cat algo doesn't work as good as expected.
|
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|
|
- One of your colaborator think you should focus on working on dogs.
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|
|
- Anaylize manually 100 mislabeled dev set examples
|
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|
|
- Count up how many are dogs
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|
|
- Supose 5% are dogs. So at most you could go from 10% err to 9.5% so not much useful.
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- Supose taht 50% of them are dogs error, so you could go down from 10% to 5%,
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so you could be more confident.
|
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|
|
***** Evaluate multiple idea in parallel
|
|
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|
|
- fix pictures of dogs
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|
- fix great cats (lion, panthers, ...)
|
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|
|
- improve performance of blurry images
|
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|
Create spreadsheet:
|
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| Image | Dog | Great cats | Bluring |
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| 1 | ok | | |
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| 2 | | | ok |
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| 3 | | ok | ok |
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| ... | | | |
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|
| % of total | 8% | 43% | 61% |
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|
You sometime notice other dimensions like instagram filters...
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|
Could easily know where you should improve.
|
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|
|
**** Cleaning up incorrectly labeled dataset
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|
|
***** Incorrectly labeled examples
|
|
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|
|
If you have incorrectly labeled data.
|
|
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|
|
First lets consider the training set.
|
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|
So long as you don't have too much errors, DL is quite robust to random errors.
|
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|
But this is a problem for systematic errors.
|
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|
***** Error analysis
|
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|
|
| Image | Dog | Great cats | Bluring | Comments |
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| ... | | | | |
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|
| 98 | ok | | | labeler missed cat in background |
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| 99 | | | ok | |
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|
| 100 | | ok | ok | drawing of a cat not a real cat |
|
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|
| % of total | 8% | 43% | 61% | |
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|
|
1st case:
|
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|
|
Overall dev set error: 10%
|
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|
|
Error due incorrect labels: 0.6%
|
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|
|
Errors due to other causes: 9.4%
|
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|
2nd case:
|
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|
|
|
|
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|
|
Overall dev set error: 2%
|
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|
|
Error due incorrect labels: 0.6%
|
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|
|
Errors due to other causes: 1.4%
|
|
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|
|
|
|
|
|
|
In 2nd case, take the time to fix mislabeled examples.
|
|
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|
|
***** Correctin incorrect dev/test set examples
|
|
|
|
|
|
|
|
|
|
- Apply same process to your dev and test sets to make sure they continue to
|
|
|
|
|
come from the same distribution.
|
|
|
|
|
- Consider examining examples your algorithm gor right as well as ones it got
|
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|
|
wrong.
|
|
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|
|
- Train and dev/test data may now crom from slightly different distributions
|
|
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|
|
**** Buid your first system quickly then iterate
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|
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|
|
***** Speech recognition example
|
|
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|
|
- noisy background
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|
- café noise
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|
- car noise
|
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|
- Accented speech
|
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|
- Far from microphone
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|
|
- young children's speech
|
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|
|
- stuttering, uh, ah, um...
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|
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|
|
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|
|
50 directions you could go, on which should you focus on?
|
|
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|
|
|
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|
|
1. Set up dev/test set and metric
|
|
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|
|
2. Build initial system quickly
|
|
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|
|
3. Use Bias/Variance analysis & Error Analysis to prioritize next steps
|
|
|
|
|
|
|
|
|
|
Guideline: *Build your first system quickly then iterate*
|
|
|
|
|
|
|
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|
|
Do not otherthink, build something quick and dirty first.
|
|
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|
|
*** Mismatched training and dev/test set
|
|
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|
|
**** Training and testing on different distributions
|
|
|
|
|
***** Cat app example
|
|
|
|
|
Two sources of data:
|
|
|
|
|
- data from webpages
|
|
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|
|
- data from mobile app
|
|
|
|
|
|
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|
|
Let's say you don't have lot of users (~10k from mobile, 200k from web)
|
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You care about doing well on mobile images. You don't want to use only the 10k,
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but the dilema is the 200k aren't from the same distribution.
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Option 1: take the 210k images and split between train/dev/test (train 205k, 2.5k, 2.5k)
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- avantage, same distribution
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- disavantage, perform on web instead of web.
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- only 119 other the 2.5k will be from mobile.
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Option 1 not recommended
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Option 2:
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- train set have 200k images from the web and 5k from the mobile.
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- dev and test all mobile app images.
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- avantage you know aiming your target where you want it to be.
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- disavantage, your training distribution is different
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But other the long term it will get you better performance
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***** Speech recognition example
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- Speech artificial rearview mirror. (real product in China)
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1. Training: take all the speech data you have; purshased data, smart speaker control, voice keyboard... (500k)
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2. Dev/test: speech activated, rearview mirror (20k)
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Set your training set to be 500k from 1. and Dev/Test from 2.
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The training set could be 510k (500k from 1 and 10k from 2.) and Dev/Test set (5k+5k from the rest of 2.)
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Much bigger training set.
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**** Bias and Variance with mismatched data distribution
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***** Cat classifier example
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Assume humans get ~0% error.
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| Training error | 1% |
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| Dev error | 10% |
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Maybe there isn't a variance pb as the distribution is different.
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Training-dev set: Same distrib as training set but not used for training.
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Train / dev / test ==> Train split in train-2 and train-dev
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So now you learn only on train-2 and check on train-dev and dev and test.
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| Train err% | 1% | 1% |
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| Train-dev err% | 9% | 1.5% |
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| dev err% | 10% | 10% |
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| | Var pb | data mismatch pb |
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Other examples:
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| Human err% | 0% | 0% |
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| Train err% | 10% | 10% |
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| Train-dev err% | 11% | 11% |
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| dev err% | 12% | 20% |
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| | Bias pb | Bias + data mismatch pb |
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***** Bias/variance on mismatched trainig and dev/test sets
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| Human level | 4% |
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avoidable bias
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| Training set error | 7% |
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variance
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| Training-dev set error | 10% |
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data mismatch
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| Dev error | 12% |
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degree of overfitting to dev set
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| Test error | 12% |
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Example, training is much harder than dev/test set distribution:
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| Human level | 4% |
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| Training set error | 7% |
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| Training-dev set error | 10% |
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| Dev error | 6% |
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| Test error | 6% |
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***** More general formulation
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The numbers can be place onto a table:
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| | General Speech rec tasks | Rearview mirror speech data |
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|--------------------+--------------------------+-----------------------------|
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| Human lvl | "Human level err" (4%) | 6% |
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| err on trained on | "Training err" (7%) | 6% |
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| err not trained on | "Training-dev err" (10%) | "Dev/Test err" (6%) |
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**** Addressing data mismatch
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There are not any systematic way to address that.
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But there are things you can try.
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***** Addressing data mismatch
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- Carry out manual error analysis to try to understand difference between
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training and dev/test sets.
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ex: you might find that a lot of dev set is noisy (car noise)
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- Make training data more similar, or collect more data similar to dev/test sets.
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ex: simulate noisy in-car data.
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***** Artificial data synthesis
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- Clean + car noise = synthetized in-car audio
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Create more data, and can be a reasonable process.
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Let's say you have 10k hrs of sound and only 1hr of car noise.
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There is a risk your algorithm will overfit your 1hr car noise.
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***** Artificial data synthesis (2)
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Car recognition
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Using car generated by computer vs just photos. You might overfit generated
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cars. A video game might have only 20 cars, so overfit these 20 cars.
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*** Learning from multiple tasks
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**** Transfer learning
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Learning recognize cats to help to read x-ray scans.
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***** Transfer learning
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Create new NN by changing just the last layer (the output).
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(X,Y) now become (radiology images, diagnosis)
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retrain the W^[Z], b^[Z].
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You might want to train just the last layer, you all the layers.
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The rule of thumb, just the last layer on few data.
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The rule of thumb, all the layer on lot of datas.
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pre-training, and fine-tuning.
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A lot of low-level features learning from a very large data set might help.
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- Another example. Speech recognition system:
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X (audio) y (speech recognintion) (wakeword, trigger word (ok google, hey siri, etc...))
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You could add several new layers, and retrain the new layers or even more layers.
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It make sense to transfer make sense when you have a very different number of examples.
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- 10^6 image recognintion, but only 100 radiology data.
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- 10k hrs sounds, but only 1h data for wake words...
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Transfering from lot of data to small number of data.
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It doesn't make sense to transfer the other way.
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***** When transfer learning makes sense
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Task from A to B
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- Task A and B have the same input X
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- You have a lot more data for Task A than Task B
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- Low level features from A could be helpful for learning B
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**** Multi-task learning
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Simultaneously learn multiple tasks.
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***** Simplified autonomous driving example
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| | y^(i) | (4,1)
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|----------------+-------|
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| pedestrians | 0 |
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| cars | 1 |
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| stop signs | 1 |
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| traffic lights | 0 |
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Y = [ y^(1) y^(2) .... y^(m) ]
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***** Neural network architecture
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x -> [] -> [] .... -> ^y in R^4
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Loss: y(i) -> 1/m \sum_i=1^m \sum_j=1^4 (L(y^(i)_j , y^(i)_j))
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L is the usual loss function.
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Unlike softmax regression, one image can have multiple labels.
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- One NN doing 4 things is better than learning 4 different NN for each task.
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Some examples might not be fully labelled.
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And you can train by summing only other 0/1 label and not on ? mark (un labeled values).
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So you can use more informations.
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***** When multi-task learning makes sens.
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- Training on set of tasks taht could benefit from having shared lower-level features
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- Usually: amount of data you have for each task is quite similar
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- Can train a big enough neural network to do well on all the tasks
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Multi-task learning used a lot more than transfer learning.
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*** End-to-end deep learning
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**** What is end-to-end deep learning?
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***** What is end-to-end deep learning?
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Speech recognition example
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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audio - MFCC -> features -- ML --> phonemes -> words -> transcript
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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audio ------------------------------------------------> transcript
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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You might need a lot of data.
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3k hrs of data, classical approach better.
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10k to 100k hurs then end-to-end approach generally shines.
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***** Face recognition
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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Multi state approach works better:
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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1. detect face, zoom-in and crop to center the face
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2. then feed this croped image to find identity. Generally comparing to all
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employes.
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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Why?
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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- Have a lot of data for task 1
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- Have a lot of data for task 2
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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If you were to try to learn everything at the same time you wouldn't have enough
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data.
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***** More examples
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Machine translation:
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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English -> text analysis -> ... -> French
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English -------------------------> French
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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Because we have lot of (x,y) examples.
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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Estimating child's age from scan of the hand:
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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Image -> bones -> age
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Image ----------> age (there is not enough data)
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**** Whether to use end-to-end deep learning
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***** Pros and cons of end-to-end learning
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Pros:
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- let the data speak (no human preconception)
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- Less hand-designing of components needed
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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Cons:
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- May need a large amount of data: input end ----> output end (x,y)
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- Excludes potentially useful hand-designed components. Data, Hand-design
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***** Applying end-to-end deep learning
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Key question: do you have sufficient data to learn a function of the complexity
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needed to map x to y?
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2017-09-02 21:54:37 +00:00
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2017-09-13 06:55:56 +00:00
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- choose X->Y mapping
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- pure deep learning approch not appropriate if hard to find end-to-end exmaples.
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