Machine Learning

Learning is essential for unknown environments –> if designer does not have omniscience

Learning is useful as a system construction method –> expose the machine to reality, rather than trying to hardcode it

Learning modifies the machines decision mechanisms to

improve performance

learning is everything that comes trough experience and modifies the behavior

learning modifies the propability of a behavior in a certain situation

learning is a change of behavior that is not explainable with maturing, injuries, sickness or predisposition

learning makes useful changes in our mind

learning modifies representations of what is experienced

learning helps to do the same task more efficiently and effectively the next time

“A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E.“

Initial position:

• task T

• performance measurement P

• experience E with the task

Goal:

• generalize the experience in a way that allows to improve your performance on the task

learning to play games, like Backgammon

recognizing spam mail

recognizing handwritten characters

learning to classify stars

market basket analysis

supervised learning –> correct answers for each example

unsupervised learning –> correct answers are not given

reinforcement learning –> occasional rewards for good actions

inductive learning is the simplest form of learning meaning it learns a function from examples

Intitial state:

• f is the (unknown) target function

• An example is a pair (x, f(x))

Goal: find a hypothesis h

• learn from given a training set of examples

• such that h is approxamitely equal to f

Algorithm:

• construct/adjust h to agree with f on training set

• h should not be overfitting the training set

In the pigeon experiment pigeons were trained to differentiate Grandmasters of art

If their choice was correct they got a reward

They got high accuracy on the training as well as on the test set –> pigeons really recognized patterns and different styles other than just memorizing it

This sort of learning is possible trough neural networks

Use theorems of computational/statistical learning theory

try h on a new test set of examples where f is known

they model the brain and nervous system

they are based on very simple principles, but they behave in a very complex way

they can process information parallel

they have the ability to learn

applications:

• problem solving

• biological models

neurons are a tiny unit in our brain and they are connected to other neurons via synapses

if a neuron is activated, it spreads its activation to all connected neurons

a artifivial neuron can be modelled in the following way:

• it has inputs all with belonging weights

• all different inputs sum up to the input function

• the sum is then tested on the activation function

• if they pass a certain threshold the neuron is activated, if not it remains neutral

• according to that are the outputs adjusted

a perceptron is a single node in a modelled artificial neural network

it has a belonging activation function and a certain threshold which determines if it is activated or not

typical outputs are +1 and -1

a perceptron can also implement the logical functions and, or, not

but rather complex functions like xor cannot be modelled, because no linear separation is possible

f(x) is the underlying target function

h(x) is the goal function/hypothesis

a is the learning rate

Wj is the weight of the corresponding input

xj is the corresponding input

The error function for one training example may be considered as a function in a multi-dimensional space

The best weight setting for one example is where the error measure for this example is minimal

In order to find the point with the minimal error –> find the minum of the error function

We can find the minimum with gradient descent –> making small steps “downhill”

To compute this, we need a continuous and differentiable

Error Minimization activation function g

Perceptrons may have multiple output nodes

The output nodes may be combined with other perceptrons

Therefore there is one input layer, one or several hidden layers and one output layer

Information flow is unidirectional

Information is distributed

Information processing is parallel

The output nodes are trained like a normal perceptron –> minimize error function

Δi is the error term of output node i times the derivation of its inputs

the error term Δi of the output layers is propagated back to the hidden layer and so forth

Thus the information provided by the gradient flows backwards through the network –> backpropagation

Overfitting means the scenario, where :

• Training Set Error continues to decrease with increasing number of training examples / number of epochs

• Test Set Error will start to increase

In the last years, great success has been observed with training „deep“ neural networks

Successes in particular in image classification

Key ingredients:

• big data

• fast processing

• unsupervised pre-training of layers

for each pixel of an image, a new feature is computed using a weighted combination of its nxn neighborhood

these kind of neural networks allow to process sequential data by feeding back the output as the new input

Long-Short term memory allow RNN to forget

Neural networks are good for problems where the final output depends on combinations of many input features

But they don’t perform well if if explicit representations of the learned concept are needed

Neural networks are not always reliable, e.g. classifies a panda and if the image is blurred a gibbon

by the components of the performance element are to be learned

by the feedback that is available to learn these components

by the representation that is used for the components

If such a function is consistent it means that it agrees with the underlying funtion f on all examples

Ockhams’s Razor –> The best explanation is the simplest explanation that fits the data

maximize a combination of consistency and simplicity

keep a seperate validation set (different to test or training set) and stop the training if the error goes up

The error is measured by squaring the error of the perceptron learning rule

A threshold activation function is not differentiable

One can use the Sigmoid function instead

The target function may have several local minima, therefore it is often very difficult to find the global minimum

What works on the training set may destroy the performance on the test set

Machine learning is a subfield of AI and deep learning is a subfield of machine learning. Deep learning is a form of machine learning that makes use of artificial neural networks.

(Mitchell 1997): „A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E.“

Training Set Error continues to decrease with increasing number of training examples / number of epochs. An epoch is a complete pass through all training examples

Test Set Error will start to increase because of overfitting

Simple training protocol:

• keep a separate validation set to watch the performance. Validation set is different from training and test sets!

• stop training if error on validation set gets down

With the perceptron learing rule for supervised learning

The activation function has a certain threshold, if that threshold is passed the neuron is activated, if not it remains unactive

It works the same for natural and machine neural networks

A perceptron is a single linear classifier. In this case, they cannot solve tasks that are not linearly separable.

Perceptrons may have multiple output nodes

The output nodes may be combined with another perceptron

The size of this hidden layer is determined manually

Convolutional Neural Networks

• Convolution:

  for each pixel of an image, a new feature is computed using a weighted combination of its nxn neighborhood

• Convolutions can be encoded as network layers

  all possible 3x3 pixels of the input image are connected to the corresponding pixel in the next layer

• Convolutional Layers are at the heart of Image Recognition

  Several stacked on top of each other and parallel to each other

Recurrent Neural Networks (RNN)

allow to process sequential data by feeding back the output of the network into the next input

Long-Short Term Memory (LSTM)

• add „forgetting“ to RNNs

• good for mapping sequential input data into sequential output data, e.g.: text to text, or time series to time series