1. Artificial Neural Networks Artificial Neural Networks are (among other things) another technique for supervised learning k-Nearest Neighbor Decision Tree Neural Network Training Data Test DataClassification

2. Human neuron Dendrites pick up signals from other neurons When signals from dendrites reach a threshold, a signal is sent down axon to synapse

3. Connection with AI Most modern AI: “Systems that act rationally” Implementing neurons in a computer “Systems that think like humans” Why artificial neural networks then? “Universal” function fitter Potential for massive parallelism Some amount of fault-tolerance Trainable by inductive learning, like other supervised learning techniques

4. Perceptron Example 1 = malignant 0 = benign # of tumors Avg area Avg density Input Units Output Unit w1 = -0.1 w2 = 0.9 w3 = 0.1

5. The Perceptron: Input Units Input units: features in original problem If numeric, often scaled between –1 and 1 If discrete, often create one input node for each category Can also assign values for a single node (imposes ordering)

6. The Perceptron: Weights Weights: Represent importance of each input unit Combined with input units to feed output units The output unit receives as input:

7. The Perceptron: Output Unit The output unit uses an activation function to decide what the correct output is Sample activation function:

8. Simplifying the threshold Managing the threshold is cumbersome Incorporate as a “virtual” weight

9. How to learn the right weights? Need to redefine perceptron “Step function” no good – need something differentiable Replace with sigmoid approximation

10. Sigmoid function Good approximation to step function As b  infinity, sigmoid  step We’ll just take b = 1 for simplicity

11. Computing weights Think of as a gradient descent method, where weights are variables and trying to minimize error:

12. The Perceptron Learning Rule: How do we compute weights?

13. Can appropriate weights always be found? ONLY IF data is linearly separable

14. What if data is not linearly separable? Neural Network. Each hidden unit is a perceptron The output unit is another perceptron with hidden units as input VjVj O

15. Backpropagation: How do we compute weights?

16. Neural Networks and machine learning issues Neural networks can represent any training set, if enough hidden units are used How long do they take to train? How much memory? Does backprop find the best set of weights? How to deal with overfitting? How to interpret results?