Neural Networks - Data Analysis

Neural Networks - Data Analysis

1. Tuning

   • High Bias
     • Data is too roughly modelled (underfitting)
     • Bigger Network
     • Train Longer
     • NN architecture search
   • High Variance
     • Data is too good modelled (overfitting)
     • More Data
     • Regularization
       • Weight Decay
         • L2 regularization : add (lamba/2*m)* ||W||F to cost
         • L1 regularization: add (lamba/2*m)* ||W||F to cost
         • Regularization required also to partial differential: W= W-alpha*dW
         • Intuition for param Lambda: Lambda goes High -> weights goes low -> makes NN more linear
       • Dropout
         • Randomly take out certain neurons from network
       • Data Augmentation
         • Adding more training data of distorting existing data
       • Early Stopping
         • Stop earlier, where train error and dev error are at min
   • Optimization Problem
     • Data not normalized -> slower training process
     • Normalize data to have mean=0, and std=1
     • Vanishing/ exploding gradients
       • Deep network have issue of becomming to high or two low throughout network
     • Gradient Checking
       • Compare cost function, when increased and decreased by small value epsilon
     • Optimization Algorithms
       • Mini-Batch gradient descent
         • Split the input and output (X,Y) data into small slices / batches, and calculate costs of only these batches
         • Choosing Batch Size
           • small set (m<=2000) -> batch gradient descent
           • larger set -> batch size: 64,128,256 or 512
           • Make sure batch fits CPU/GPU mem
       • Exponentially weighted averages
         • Weights are recalculated based on formula
         • Bias Correction
           • Corrects the starting values of exp. weighted averages using the formula: v(t)=v(t)/(1-beta^t)
       • Gradient Descent with Momentum
         • Aim: accelerator horizontal component of gradient descent to converge faster towards solution. Based similarly on formula for exp.weighted averages, just with gradient instead of theta
       • RMSprop
         • Aim to slower the vertical component of gradient descent and speed up the horizontal component.
       • Adam
         • Combination of RMSprop and Gradient Descent with momentum
         • Hyperparameter choice: alpha : needs to be tuned, beta1 = 0.9, beta2 = 0.999, epsilon = 1e-8
       • Learning Decay
         • A method to lowe the learning rate closer it gets to minimum.
         • Many formulas exist,the most famous is: alpha = 1/(1+decay_rate*epoch_num)
       • Tuning algorithm's hyperparameters
         • priorities: darkest - most important, lightest - least. white is fixed.
         • try random values: dont't use grid
         • Coarse to fine choice
         • randomness scale choice, e.g. for alpha - logarithmic scale
       • Batch Normalization
         • Idea of normalizing each layer input (Z, not A) of Neural Network

2. Weights/parameters initialization

   • Zeros? NO!
     • Zeros will make all neurons of neural network act the same, and behave linear, which loose the sense of having neural network.
     • Bad - Fails to break Symmetry -> gradient not decreasing
   • Random Init
     • - Initializing weights to very large random values does not work well. &nbsp;- intializing with small random values does better.&nbsp;
     • Good - Breaks Symmetry
     • Bad - large weight -> exploding gradients
   • He Init - the best!
     • sqrt(2./layers_dims[l-1])
     • Good - Ensures faster learning speed
     • works well with ReLU activations

3. Dataset Split

   • Data > 1M 98% Train, 1% Dev, 1% Test
   • Small Data, 60% Train, 20% Dev, 20% Test
   • Train set from different distribution than Dev/test sets

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