Machine Learning

Question 1

What is supervised learning?

Answer 1

A method of training a model by observing its performance with labelled data

Question 2

What is unsupervised learning?

Answer 2

A method of identifying structures within data without the aid of response variables

Question 3

What is a regression problem?

Answer 3

A supervised learning task where the response variable is continuous

Question 4

What is a classification problem?

Answer 4

A supervised learning task where the response variable is categorical

Question 5

What is the equation we solve for when graphically fitting a logistic regression model?

Answer 5

logit(0.5) = B0 + B1x1 + B2x2 [ + … + Bpxp]

• rearranging the equation to make x2 the subject of the formula then gives us a line where the probability of “success” is equal to 0.5. Observations above and below the line will be predicted as difference classes. The feature space is partitioned

Question 6

At a high level, how to tree-based methods work?

Answer 6

The predict classes by partitioning the feature space along each of its respective dimensions. The partitioning then results in certain regions which are associated with certain responses.

Question 7

What is the R code for fitting a classification tree to a dataset and printing some information about the tree?

Answer 7

> library(tree)
treeModel = tree(Y ~ X1 + X2)
summary(treeModel)

Question 8

What is a terminal node in the context of classification trees?

Answer 8

The points at which the binary tree stops splitting. Graphically, these are the end points of the tree and represent where prediction is finalized. Also known as leaf nodes

Question 9

What process do most software packages use in rigorously determining the partition points in the feature space?

Answer 9

Recursive binary splitting

Question 10

What is the R code to fit a logistic regression model to a dataset?

Answer 10

> logisticModel = gym(Y ~ . , family = binomial(link = “logit”))
summary(logisticModel)

Question 11

What is a regression tree?

Answer 11

A classification tree where the classes are continuous numbers (eg. house valuations)

Question 12

What are the two main advantages of using tree models?

Answer 12

• tree models can handle highly non-linear data

- tree models are relatively easy to interpret despite their non-linearity

Question 13

What does RSS stand for?

Answer 13

Residual sum of squares

Question 14

What is the learning algorithm or procedure for fitting a tree?

Answer 14

Initial step: start with the entire unseparated feature space find the split positions which lead to the greatest reduction in RSS for each dimension (assuming that split point is above the RSS reduction threshold). Retain the top reduction among these.

Iterate: Split the data according to the split in the initial step. In each of the two regions, perform the same procedure as in the initial step.

Stop: If no split can be found that exceeds the minimum RSS reduction threshold then stop and return the resulting tree.

Question 15

What are impurity measures and what are 3 common impurity measures?

Answer 15

A series of methods for calculating the accuracy of classification trees. We can not use traditional RSS in the case of binary data.

3 common impurity measures:

• misclassification error
• Gini-index
• Shannon Entropy

Question 16

For a binary tree, what is the prediction of a model for region R(j)? also known as [pi hat]

Answer 16

[1/N].[sum of I(y=1)]

Question 17

What is the equation for misclassification error in the context of binary trees?

Answer 17

1 - max(pi hat, 1- pi hat)

• we want to minimize this quantity

Question 18

What is the equation for Gini-index in the context of binary trees?

Answer 18

2[pi hat].[1-(pi hat)]

Question 19

What is the equation for Shannon Entropy in the context of binary trees?

Answer 19

• refer to notes

Question 20

What is one of the downsides of using tree-based methods?

Answer 20

They are prone to overfitting

Question 21

What is overfitting?

Answer 21

Overfitting is a situation where the model replicates feature patterns seen in a particular dataset instead of “learning” the true feature patterns of the underlying data

Question 22

What is in-sample-error?

Answer 22

A measure of the performance of a model based on seen data

Question 23

What is out-of-sample-error?

Answer 23

A measure of the performance of a model based on unseen data

Question 24

What is the bias-variance tradeoff?

Answer 24

Sufficiently complex models can in theory replicate the data used to train said models almost exactly. This is not good for purposes of learning any underlying pattern. Such models exhibit high variance and will not perform well on unseen data. Though we can simplify models to remedy this, we also run the risk of simplifying the model too much

Question 25

What is a biased model?

Answer 25

A model which does not replicate salient features in the underlying pattern, also producing poor predictions

Question 26

What does parsimonious mean?

Answer 26

Unwilling to spend. In the context of machine learning, this is used to describe more conservative and simpler models

Question 27

What are the two ways of ensuring that a tree model does not overfit to the dataset?

Answer 27

• limit the number of terminal nodes by increasing the minimum RSS reduction threshold (this is not optimal because it might exclude useful partitions)
• penalize the model for producing predictions that fit the data too closely (therefore Penalized Obj = Obj + Penalty)
• we are still trying to minimize this new objective function

Question 28

Give an example of a penalized objective function that could be used for a tree-based classification model?

Answer 28

Penalized obj. = Shannon entropy + alpha|J|
* where J is the number of terminal nodes in the tree and alpha is a scaling quantity that we can choose. Alpha is therefor a hyper parameter

Question 29

What is pruning in the context of fitted tree models?

Answer 29

The process of rolling the tree back to smaller sub-trees to avoid overfitting

Question 30

What is cost-complexity pruning the context of fitted tree models?

Answer 30

The process of reducing the complexity of a tree by using an adjusted cost function which penalizes overfitting

Question 31

What is a balanced tree in the context of fitted tree models?

Answer 31

An optimal sub-tree which is sufficiently generalizable for the prediction problem at hand

Question 32

How do we select optimal tree size when looking at a graph of cost-complexity parameter (cp) and error?

Answer 32

We select the simplest model which overlaps (in terms of standard deviations) with the best performing tree on the training data

Question 33

What is the validation set approach to splitting our data when modeling?

Answer 33

We divide the data into:

• training set which will be used to train the model
• validation set which will be used to tweak the model and validate its performance
• test set which we only use once when reporting the true performance of the model

Question 34

What is the K-fold cross-validation approach to splitting our data when modeling?

Answer 34

• We split the data into K partitions
• K-1 folds/partitions are used to train the data and remaining fold is used for validation
• the folds are then cycled until all folds have been used for training and validation
• test set is left untouched until reporting time
• we utilize more of our data for training
• we have a small sample size of K for our validation errors which we can then calculate mean and variance from

Question 35

What is a neural network?

Answer 35

A type of non-linear model which uses interconnected nodes and mathematical functions to produce responses. They are primarily used for supervised learning but can be easily adapted to unsupervised learning tasks

Question 36

In a graphical presentation of a neural network, what does a node represent?

Answer 36

An activation (or activation function)

Question 37

In a graphical presentation of a neural network, what does an edge represent?

Answer 37

A weight (or parameter)

Question 38

Why do we refer to the a hidden layer as “hidden”?

Answer 38

Since the nodes in this layer do not contain any direct observations, their state cannot be known

Question 39

How do we calculate the depth of a neural network?

Answer 39

The number of hidden layers + 1

Question 40

What does a(j)^l denote?

Answer 40

The jth node in the lth layer of the network

Question 41

What does d(l) denote?

Answer 41

The number of nodes in the lth layer of the network

Question 42

What does w(kj)^l denote?

Answer 42

The weight parameter linking the kth node in layer l-1 and the jth node in layer l

Question 43

What does b(j)^l denote?

Answer 43

The jth bias in layer l

Question 44

What is the R code for creating a random sample of size n from a uniform distribution over bounds a and b?

Answer 44

> runif(n , a , b)

Question 45

What is the R code for creating a data object using matrices?

Answer 45

> data.frame(Y=someVector, X=someMatrix/Vector)

Question 46

What is the R code for fitting a neural net with two hidden layers of size n and n-1? (and also printing the fitted network)

Answer 46

> library(neuralnet)
neuralNetModel = neuralnet(Y~X, hidden = c(n, n-1), data = yourData)
plot(neuralNetModel)

Question 47

What does DGP stand for?

Answer 47

Data generating process (i.e. the true underlying function which is producing the data)

Question 48

What is the name of the optimization technique used to fit neural networks and how does it work?

Answer 48

The gradient descent algorithm. It assesses the plane defined by the cost function and updates the parameters based on the partial derivatives (slope of the plane) leading to a local minimum

x(i+1) = xi + lambda.g(xi)

• where g() represents the partial derivative of the plane
• where lambda represents the learning rate

Question 49

When will the gradient decent algorithm stop updating parameters?

Answer 49

Either
- after some predefined number of steps
or
- when some predefined step size is achieved (i.e. gradient levels out to some tolerance level)

Question 50

What does MSE stand for?

Answer 50

Mean Square Error

Question 51

How do you calculate MSE for a neural network?

Answer 51

[1/N].sum of [prediction - actual]²

Question 52

What are the 4 main activation functions used in neural networks?

Answer 52

• the logistic function [output between 0 and 1]
• the rectified linear units functions (ReLU) [output between 0 and inf]
• the hyperbolic tangent function (tan-h) [output between -1 and 1]
• the identity function [output is -inf to inf] *typically for regression problems

*refer to notes for their equations

Question 53

What is an objective function?

Answer 53

A function which we are trying to maximize or minimize

Question 54

What kind of objective functions do we use for neural networks?

Answer 54

• MSE for regression problems
• Cross-Entropy Error for classification problems
• refer to notes for cross entropy equation

Question 55

What is regularization in the context of neural networks?

Answer 55

A method of penalizing overfitting

Question 56

What is L2 regularization in the context of neural networks?

Answer 56

The adding of a penalty term to the objective function which penalizes the model for overfitting

Question 57

What is the procedure for fitting an optimal neural network for a given architecture?

Answer 57

1) Start with an over specified unconstrained model

2) Find a value for the L2 regularization parameter which optimizes validation performance

Question 58

What does the term “epochs” refer to in the context of machine learning?

Answer 58

The number of passes of the entire training set the machine learning algorithm has completed. If the batch size is the entire training set, then the number of epochs will be the number of iterations.