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Machine-Learning

Various machine learning algorithms broken down in basic and readable python code. Useful for studying and learning how the algorithms function.

• MultiLayerPerceptron.py - Basic multilayer perceptron neural network written with numpy. With weight decay regularization, learning rate decay, softmax or logistic sigmoid output layer, and tanh hidden layer.

• LinearRegression.py - Gradient descent linear regression with l2 regularization.

• LogisticRegression.py - Gradient descent logistic regression with l2 regularization.

Usage

MultiLayerPerceptron

Parameters

-input (int): Size of input layer, must match the number of features in the input dataset.

-hidden (int): Size of hidden layer, more hidden neurons can model more complex data at the cost of potentially overfitting.

-output (int): Size of output layers, must match the number of possible classes. Can use 1 for binary classification.

-iterations (int): controls the number of passes over the traning data (aka epochs). Defaults to 50

-learning_rate (float): The learning rate constant controls how much weights are updated on each iteration. Defaults to 0.01.

-l2_in (float): Weight decay regularization term for the input layer weights, keeps weights low to avoid overfitting. Useful when hidden layer is large. Defaults to 0 (off).

-l2_out (float): Weight decay regularization term for the hidden layer weights, keeps weights low to avoid overfitting. Useful when hidden layer is large. Defaults to 0 (off).

-momentum (float): Adds a fraction of the previous weight update to the current weight update. Is used to help system from converging at a local minimum. A high value can increase the learning speed but risks overshooting the minimum. A low momentum can get stuck in a local minimum and decreases the speed of learning. Defaults to 0 (off).

-rate_decay (float): How much to decrease learning rate on each iteration. The idea is to start with a high learning rate to avoid local minima and then slow down as the global minimum is approached. Defaults to 0 (off).

-output_layer (string): Which activation function to use for the output layer. Currently accepts 'logistic' for logistic sigmoid or 'softmax' for softmax. Use softmax when the outputs are mutually exclusive. Defaults to 'logistic'.

-verbose (bool): Whether to print current error rate while training. Defaults to True.

Fitting and predicting

1. Initialize the network and setting up the size of each layer.

NN = MLP_Classifier(64, 100, 10)

2. Train the network with the training dataset. The training dataset must be in the following format with y values one hot encoded. There is an example in the demo function of the MLP on how to import data with numpy and get it into the appropriate format.

	[[[x1, x2, x3, ..., xn], [y1, y2, ..., yn]],
    [[[x1, x2, x3, ..., xn], [y1, y2, ..., yn]],
    ...
    [[[x1, x2, x3, ..., xn], [y1, y2, ..., yn]]]

NN.fit(train)

3. Make predictions on testing dataset. Same format as training dataset without the list of y values. Will return a list of predictions.

NN.predict(X_test)

Linear and Logistic Regression

Parameters

-learning_rate (float): The learning rate constant controls how much weights are updated on each iteration. Defaults to 0.01.

-iterations (int): controls the number of passes over the traning data (aka epochs). Defaults to 50.

-intercept (bool): Whether or not to fit an intercept. Defaults to True.

-L2 (float): Weight decay regularization term for the weights, keeps weights low to avoid overfitting. Defaults to 0 (off).

-tolerance (float): The error value in which to stop training. Defaults to 0 (off).

-verbose (bool): Whether to print current error rate while training. Defaults to True.

Fitting and predicting

1. Initialize the linear model.

linearReg = LinReg(learning_rate = 0.1, iterations = 500, verbose = True, l2 = 0.001)

2. Train the model with the training dataset. The training dataset has to be a numpy array, the X and y values must be seperated into two different arrays.

linearReg.fit(X = X_train, y = y_train)

3. Make predictions on testing dataset. Same format as training dataset without the array of y values. Will return a list of predictions.

linearReg.predict(X_test)

Logistic regression has one extra parameter for .predict. If labels is set to 'True' the predicted class is returned, otherwise the probability of the class being label 1 is returned.

logit.predict(X_test, labels = True)