ML

Question 1

Unsupervised Learning and how is the model trained

Answer 1

Only input data provided and models learn to extract patterns from the data

Question 2

Supervised Learning and how is the model trained

Answer 2

Each input paired with an output (target) and model trained to minimise the error

Question 3

Regression

Answer 3

Finding the relationship between two variables where the model is linear

Question 4

Classification

Answer 4

Category labels e.g. dog or bagel

Question 5

Underfitting

Answer 5

A model that is too simple which does not fit the data

Question 6

Overfitting

Answer 6

A model that fits minor variations or noise

Question 7

Model Selection and how does it work

Answer 7

Selecting correct model
Split dataset for training and validation (and testing)

Question 8

Training dataset

Answer 8

Used to train/optimise the model

Question 9

Validation dataset

Answer 9

Used for validating the model

Question 10

Test dataset

Answer 10

Used to test model for general fitting quality

Question 11

Cross-validation

Answer 11

Split data into S groups so (S-1)/S data used for training

Question 12

No free lunch theorem

Answer 12

All models are wrong, but some are useful

Question 12

Model parameters

Answer 12

Values learned from training data

Question 13

Parametric model

Answer 13

of parameters stay the same as quantity of data increases

Question 14

Non-parametric model

Answer 14

of parameters increase/decrease as quantity of data increases

Question 15

Likelihood function

Answer 15

Probability of data given model parameters

Question 16

Maximum likelihood estimation

Answer 16

Method for estimating parameters of a probabilistic model

Question 17

Linear regression model formula

Answer 17

p(y|x,w) = w^T x + e

Question 18

What is the distribution of e in the linear regression model and what is the bias parameter in the linear regression model formula and what is it for

Answer 18

Gaussian distribution with mean 0: N(0, standard deviation squared)

Within the vector w by addition of dummy variable which always has value 1 and gives extra flexibility to fit the data 1

Question 19

Linear regression to a feature vector

Answer 19

p(y|ϕ(x), w) = w^T ϕ(x) + e

Question 20

Least-squares problem for linear regression formula

Answer 20

Theta = (X^T X)^-1 X^T y

Question 21

Two key points about least-squares solutions

Answer 21

The solution has a closed-form
The solution is also the maximum likelihood solution

Question 22

What does the Linear Discriminant compute (formula) and what class is x assigned to according to y

Answer 22

y=w^T x
y>=0 means C1
Otherwise C2

Question 23

What assumptions are made for parameters to be learnt by applying MLE?

Answer 23

1. Data for each class have a Gaussian distribution
2. These two Gaussian distributions have the same covariance matrix

Question 24

Logistic sigmoid function

Answer 24

sigmoid(a) = 1/(1+e^-a)

Question 25

Logistic regression model for two classes

Answer 25

p(C1|x) = sigmoid(w^T x)
p(C2|x) = 1 - p(C1|x)

Question 26

How can the MLE parameters for logistic regression be found?

Answer 26

Using gradient descent

Question 27

Weights

Answer 27

Parameters that transform input data within each neuron

Question 28

Activation function

Answer 28

Determines whether a neuron should be activated and how to transform the input signal into an output signal

Question 29

Input layer and how many neurons

Answer 29

Consists of neurons that receive input data and pass to next layer - # of neurons = # of features in input dataset

Question 30

Hidden Layer

Answer 30

Layer of neurons between input and output which processes input data using weights and activation functions

Question 31

Output layer

Answer 31

Final layer that produces result/prediction

Question 32

Cost/Loss function

Answer 32

Measures difference between predicted and true output

Question 33

Forward pass process

Answer 33

1) Calculate activations of hidden layer, h

2) Pass result of step 1 through a nonlinear function e.g. sigmoid

3) Use step 2 to calculate activations of output layer, o

4) Compute predictions using sigmoid of step 3

Question 34

Backpropagation / backward pass and formula and what do the symbols represent

Answer 34

Algorithm used to compute gradients of loss function with respect to each weight to update weights across multiple layers based on derivative of error wrt the weight

formula is δj = h′(aj )(Sum to k of:wkj δk)

δj = error signal for jth hidden unit
wkj = weight connecting hidden unit j to output unit k
h’(aj) = derivative of activation function
δ k = error signal at kth output unit

Question 35

Vanishing gradient problem

Answer 35

When gradients used to update the weights during backpropagation become too small which slows down/stops learning process

Question 36

Exploding gradient problem

Answer 36

When gradients grow too large during backpropagation, causing weights to become large and degrading model performance

Question 37

Gradient clipping and formula and what do the variables mean

Answer 37

Used to cap magnitude of gradient :
g’ = min(1, c/||g|| ) g
c = constant value to limit size of gradient

Question 38

Residual network and formula

Answer 38

Each layer has the form of a residual layer which is like a shortcut for gradients to flow directly from output to previous layer defined to be:
F1’ = F1(x)+x where F1(x) is the standard mapping (linear transformation and then actication)

Question 38

Non-saturating activation function

Answer 38

Activation functions that don’t compress inputs into a limited range, avoiding vanishing gradients

Question 39

Parameter initialisation significance

Answer 39

Necessary to choose good initial parameters to avoid issues with gradient descent

Question 40

Early stopping

Answer 40

Process of creating a validation set and stopping training once the error on the validation step starts to increase

Question 41

Weight decay formula

Answer 41

Adds a term: (lambda)w^T w to the loss function where user chooses value of lambda>0 to penalise large weights

Question 42

Dropout and pro

Answer 42

When all outgoing connections from a unit with some given probability are turned off during training to ensure that each unit can perform well without depending on other units

This can drastically reduce overfitting

Question 43

Classification tree

Answer 43

Decision tree where each internal node represents decision based on a feature and each leaf represents a class label

Question 44

Regression tree

Answer 44

Decision tree where each internal node represents a decision based on a feature and each leaf node represents a predicted value

Question 45

Are trees parametric or non-parametric?

Answer 45

Non-parametric

Question 46

CART (Classification And Regression Trees) algorithm

Answer 46

Learning the tree structure greedy algorithm:
1) Start from root node
2) Run exhaustive search over each possible variable and threshold for a new node:
For each variable and threshold:
a. Compute average of target variable for each leaf of the proposed node
b. Compute error if we stop adding nodes here
3) Choose variable and threshold that minimise the error
4) Add a new node for the chosen variable and threshold
5) Repeat step 2 until there are only n data points associated with each leaf node
6) Prune back the tree to remove branches that do not reduce error by more than a small tolerance value, e

Pruning:
1) Start with a tree T0
2) Consider pruning each node in T0 by combining branches to obtain tree T
3) Compute C(T) = (Sum from T=1 to |T|) et(T) + lambda |T| where
- |T| is # of leaves
- et(T) is error associated with t’th leaf of tree
- lambda is a penalty added for the # of leaves in the tree
4) If C(T) <= C(T0) keep the pruned tree, otherwise reinstate the pruned node

Question 47

Kernel function and example

Answer 47

Used to compute dot product between two data points e.g.
For two vectors, x and x’, possible kernel function K(x,x’) = ϕ(x).ϕ(x’) where ϕ is mapping to a higher-dimensional space

Question 48

Kernel trick

Answer 48

We just need the kernel function to make a prediction so evaluate the kernel function values e.g. k(x1, x) without first computing ϕ(x1) and ϕ(x) and then compute their scalar product

Question 49

Dual parameter

Answer 49

Indicate how much each training sample contributes to the decision boundary

Question 50

Gram matrix

Answer 50

Defined to be K = ϕϕ^T so Knm = ϕ(xn)^T ϕ(xm) which is the similarity between the nth and mth datapoint

Question 51

Margin

Answer 51

Distance from decision boundary (hyperplane) to closest training datapoint

Question 52

Support vectors

Answer 52

Data points that lie closest to decision boundary (margin)

Question 53

Soft margin

Answer 53

Allows points to lie on wrong side of hyperplane in exchange for a penalty which is controlled by a regularisation parameter

Question 54

Slack variables

Answer 54

Measures distance of misclassified points from decision boundary

Question 55

How can SVMs be extended to more than two classes? (for k classes)

Answer 55

One-versus-one = train k(k-1)/2 SVM classifiers to distinguish between each pair of classes and take a vote for the predicted class

One-versus-the-rest = train k SVM classifiers to distinguish between each class and all other classes

Question 56

Bayesian network

Answer 56

Graphical model that represents a set of random variables and their conditional dependencies via a DAG

Question 57

What is needed to construct a Bayesian network to represent a given joint distribution?

Answer 57

1) The DAG (structure of the BN)
2) Conditional probability distributions p(xk|pak) (parameters of the BN)

Question 58

Collider

Answer 58

A node is a collider on a path if both arrows point to it on the path

Question 59

Blocked path

Answer 59

A path is blocked by S if at least one of the following:

1) There is a collider that is not in S and none of its desendants are in S

2) There is a non-collider on the path that is in S

Question 60

How can you represent the joint probability distribution for a Bayesian network?

Answer 60

If the network has nodes X1,X2,…,Xn the joint probability distribution is: P(X1,X2,..,Xn)=∏ i=1to n (P(Xi)|Parents(Xi))

Question 61

What is plate notation

Answer 61

A plate is drawn around a subset of variables, and the number of repetitions is indicated on the plate.

Question 62

How would you translate a ML model to a BN?

Answer 62

To translate a machine learning model into a Bayesian network, you identify the random variables in the model and their dependencies.

Question 63

What does d-separated mean? What is its significance?

Answer 63

If all paths from node x to node y are blocked given nodes S then x and y are d-separated by S. This means x and y are conditionally independent given S in the DAG.

Question 64

Prior distribution

Answer 64

Represents our beliefs about the parameters of a model before observing any data.

Question 65

Posterior distribution

Answer 65

Combines the prior distribution and the likelihood to provide an updated belief about the parameters after observing the data.

Question 66

What do we know about parameters and data in the Bayesian approach?

Answer 66

Parameters (unknown quantities we try to estimate) and latent variables (unobserved variables that influence the model) are treated as random variables

Data (observed variables) are also considered random but are known quantities

Question 67

Ancestral sampling and example for: P(A,B,C,D,E) = p(A)p(B)p(C|A,B)p(D|C)p(E|B,C)

Answer 67

Generates samples from a joint probability distribution from parents to children
e.g. We first sample values for A and B, suppose we get A=0, B=1. Then we sample from C from the conditional distribution P(C|A=0, B=1) and so on

Question 68

Rejection sampling example for P(A,B,C,D,E) = p(A)p(B)p(C|A,B)p(D|C)p(E|B,C)

Answer 68

If we wanted to sample from P(B,D|E=1) we would sample from the marginal distribution P(B,D,E) and throw away those samples where E!=1

Question 69

Markov chain

Answer 69

Series of random variables z1,…,zm such that the following holds for mE{1,…,M-1}:
p(zm+1|z1,…,zm) = p(zm+1|zm)

Question 70

Homogeneous Markov chain

Answer 70

If p(zm+1|zm) is the same for all m

Question 71

Initial distribution in Markov chain

Answer 71

p(z1)

Question 72

Transition distribution in Markov chain

Answer 72

It captures how likely it is to transition from the current state to any possible next state.

Question 73

Markov chain Monte Carlo and significance of samples

Answer 73

Sample a sequence of distributions which eventually get close to desired distribution:
1) Draw sample from each distribution in the sequence
2) Only keep samples when we get close enough to desired distribution

*These samples are not independent

Question 74

Target probability distribution

Answer 74

Used to construct a Markov chain
For Bayesian ML this will be P(theta|D=d), the posterior distribution of the model parameters given the observed data

Question 75

Metropolis-Hastings Algorithm

Answer 75

Define single transition probability distribution for a homogeneous Markov chain.
Let current state be z^(T).
Generate a value z* by sampling from a proposal distribution q(z|z^(T))
Accept z* as the new state with certain acceptance probability in which case z^(T+1)=z. If we don’t accept z then stay where you are so z^(T+1)=z^(T)

Question 75

Metropolis algorithm

Answer 75

Special case of the Metropolis-Hastings algorithm where the proposal distribution is symmetric (i.e., the probability of proposing a move to a state is the same as proposing a move back)

Question 76

Proposal distribution

Answer 76

Distribution from which samples are drawn to general potential states in Markov chain

Question 77

Acceptance probability for MH and M algorithm

Answer 77

MH: α(x,y) = min(1, π(y)q(y|x)/π(x)q(x|y) )
where π is target distribution and q is proposal distribution

M: α(x,y) = min(1, π(y)/π(x))

Question 78

Burn-in and what for

Answer 78

Initial period of MCMC simulation during which samples are discarded because early samples might not represent the target distribution well due to influence of initial state

Question 79

Convergence in MCMC

Answer 79

Process by which distribution of samples generated by Markov chain approaches the target distribution

Question 80

Why do we run several chains during MCMC?

Answer 80

Helps to diagnose convergence and explore parameter space

Question 81

What can a sample from a distribution be used for

Answer 81

Can be used to approximate an expected value defined by that distribution

Question 82

What is R hat used for?

Answer 82

Value computed from an MCMC run used to check for convergence.
If the run is successful ie. there’s been a convergence, it will be close to 1

Question 83

Clustering

Answer 83

Unsupervised learning technique to group similar data points into groups

Question 84

Soft clustering

Answer 84

Assigns data points to clusters probabilistically by applying MLE to a Gaussian mixture model, rather than strictly assigning each point to single cluster

Question 85

Gaussian mixture model

Answer 85

Probabilistic model that assumes data is generated from a mixture of several Gaussian distributions (type of soft clustering model)

Question 86

Mixing coefficient

Answer 86

Represents the proportion of the kth component in the overall distribution as a probability between 0 and 1

Question 87

Responsibility in mixture model

Answer 87

The probability that a specific data point was generated by a particular cluster in the model

Question 88

K-means algorithm

Answer 88

• Randomly initialise K cluster centroids
• Assign each data point to the closest cluster centroid based on Euclidean distance
• Recompute the centroids by calculating the mean of all data points assigned to each cluster
• Repeat the assignment and update steps until convergence ie. when the cluster assignments no longer change significantly

Question 89

EM algorithm purpose and steps

Answer 89

MLE for Gaussian mixtures:
Intialise by choosing starting variables for u (mean), covariance, pi

Then compute iterations of:
E step: Compute values for the responsibilities given the current parameter values

M step: Re-estimate the parameters using the current responsibilities

Question 90

Hinderance of EM algorithm

Answer 90

There is no guarantee that it will succeed in maximising the log-likelihood. It may converge to a local maximum which is not a global maximum of the log-likelihood function.

Question 91

3 EM equations

Answer 91

(log likelihood of observed data X given parameters theta) ln p(X∣θ)=L(q,θ)+KL(q∣∣p)

(Lower bound on log-likelihood) L(q,θ)= (sum to Z) q(Z) ln(p(X,Z∣θ)/q(Z))
q(Z) = distribution over latent variables Z
P(X, Z|θ) = joint probability of observed data X and latent variables Z given parameters

(Kullback-Leibler divergence between probability distributions p1 and p2) KL(q||p)= -(sum to Z) q(Z) ln(p(Z∣X,θ)/q(Z))

Question 92

Key fact about Kullback-Leibler

Answer 92

KL(q||p) ≥ 0 for any choice of q, so L(q, θ) ≤ ln p(X|θ).

Question 93

What is increased in E-step?

Answer 93

We increase L(q, θ) by updating q (and leaving θ fixed)

Question 94

What is increased in M step?

Answer 94

We increase L(q, θ) by updating θ (and leaving q fixed)

Question 95

Why does the EM algorithm work?

Answer 95

After the E-step we have L(q, θ) = ln p(X|θ) (and so KL(q||p) = 0), so that in the following M-step increasing L(q, θ) will also increase ln p(X|θ).

Question 96

What is the ReLU function and where is it not differentiable (what do we do here instead)?

Answer 96

Straight line with slope 1 for positive values of 𝑥 and a horizontal line at 0 for negative values of 𝑥.
It is not differentiable at 0 but we just impose a gradient of 0.