This course, Advanced Machine Learning, and Signal Processing is part of the IBM Advanced Data Science Specialization which IBM is currently creating, and gives you easy access to the invaluable insights into Supervised and Unsupervised Machine Learning Models used by experts in many fields relevant disciplines.

We’ll learn about the fundamentals of Linear Algebra to understand how machine learning modes work. Then we introduce the most popular Machine Learning Frameworks for python Scikit-Learn and SparkML.

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#### Quiz : Machine Learning

Q1. Please order the following terms on their dimensionality

• scalar, vector, matrix, tensor
• scalar, matrix, vector, tensor
• vector, scalar, matrix, tensor

Q2. A line can seperate two point clouds in 2D space. How would you call a line of separation in 3D space?

Q3. A line can seperate two point clouds in 2D space. How would you call a line of separation in 4D space?

Q4. How do you call the process of predicting a continuous value?

• Classification
• Regression
• Clustering

Q5. How do you call the process of predicting a discrete (categorical) value?

• Classification
• Clustering
• Regression

Q6. How do you call the process of finding data points which belong together?

• Clustering
• Classification
• Regression

#### Quiz : ML Pipelines

Q1. What are Machine Learning Pipelines?

• A way to do feature engineering within the pipeline framework
• A way of expressing your complete end-2-end machine learning flow within a single framework with a homogeneous API
• A way of making ML algorithms run faster
• A way of speeding up ML development

Q2. How is the class called which transforms a string class label to a class index in SparkML?

• Bucketizer
• OneHotEncoder
• StringIndexer
• VectorAssembler

Q3. What is the class called which transforms a set of columns in a data frame to a single DenseVector representation in SparkML?1 point

• VectorAssembler
• OneHotEncoder
• Bucketizer
• StringIndexer

#### Quiz : Linear Regression

Q1. Consider the following linear regression model.

y = b + w1x1 + w2x2 + w3x3 + w4x4

• x1 – x4 are used to predict y
• y is used to predict w1 – w4
• y is used to predict x1 – x4
• w1 – w4 are used to predict y

Q2. Consider the following linear regression model.

y = b + w1x1 + w2x2 + w3x3 + w4x4

What is the dimensionality of the training data set?

Q3. Consider the following linear regression model.

y = b + w1x1 + w2x2 + w3x3 + w4x4

Now consider that the influence of x3 to predict y is very low. On other words, independently of the value of x3, y doesn’t change a lot, therefore x3 and y are weakly correlated.

Please choose a value for w3 to reflect this behaviour

#### Quiz : Splitting and Overfitting

Q1. When do we have an over-fitting problem?

• If we perform well on the validation set and poorly on the training set
• If we perform well on the validation set and well on the training set
• If we perform poorly on the validation set and poorly on the training set
• If we perform well on the training set and poorly on the validation set

#### Quiz : Evaluation Measures

Q1. What’s the accuracy given the true labels t and the predicted labels p

Note: This is a classification problem, so the value needs to be between 0 and 1

t = (1,3,2,4,3,2,1,4,3,2,3,4)

p = (1,2,2,4,4,2,1,4,1,2,3,4)

Format: 0.XX

#### Quiz : Logistic Regression

Q1. Which statement is correct?

• Logistic Regression is a supervised machine learning model to predict a discrete (categorical) value
• Logistic Regression is a supervised machine learning model to predict a continuous value
• Logistic Regression is a unsupervised machine learning model to predict a continuous value
• Logistic Regression is a unsupervised machine learning model to predict a discrete (categorical) value

#### Quiz : Naive Bayes

Q1. Bayes’ theorem is used for reversing the order of joint probabilities.

• True
• False

Q2. A box contains 3 lemons and 6 apples. We draw two fruits at random. What’s the probability of getting 2 lemons? Please round your answer to 3 decimal places.

Q3. You roll a six sided die. What’s the probability of rolling a 3 or a 6? Please round your answer to 3 decimal places.

Q4. Bayesian inference is a method of inference where the probability of a _________________ is updated as new evidence becomes available.

• prior
• hypothesis
• posterior
• distribution

Q5. Why is the Gaussian distribution often used in machine learning?

• The process of sampling any random distribution with finite variance and adding the numbers together produces a Gaussian distribution (Central Limit Theorem)
• Occurs naturally in many situations (age, height of people, blood pressure readings etc.)
• It is easily described (you only need a mean and a variance)
• All of the above

Q6. The process of Bayesian inference involves the following steps:

1. Collect data
2. Calculate the likelihood
3. Obtain a posterior
4. Obtain a prior

What is the correct order of executing the above steps?

• 4, 1, 2, 3
• 1, 4, 2, 3
• 3, 1, 2, 4
• 4, 2, 1, 3

Q7. In Bayesian statistics, MAP stands for

• Mean accuracy projection
• Maximum a posteriori probability
• Manifold associated probability

Q8. Naive Bayes is considered “naive” because

• it is an outdated technique and better methods exist nowadays.
• the input features are considered to be independent.
• it can be used only with a Gaussian distribution.
• it can’t handle multiple input features.

#### Quiz : Support Vector Machines

Q1. Why are Support Vector Machines also called “maximum margin classifier”?

• Because margins from the distances are maximized when computing the boundaries of separation
• Because distances from the margin are maximized when computing the boundaries of separation
• Because distances from the decision boundaries are maximized when computing the hyper-plane of separation

#### Quiz : Testing, X-Validation, GridSearch

Q1. What is the purpose of a test set in contrast of a train and validation set?

• A test set is used to assess over-fitting hyper-parameters
• A test set is used to improve model performance
• A test set is used to prevent over-fitting hyper-parameters

Q2. When adding pipeline or model hyper-parameters to the search grid – what is the relation between number of tune-able hyper-parameters and the growth in computational complexity?

• linear
• exponential
• logarithmic
• cubic

#### Quiz : Enselble Learning

Q1. How are Random Forest different in re-sampling from Gradient Boosted Trees?

• Re-sampling doesn’t differ in those models
• Sampling is done using Bootstrapping in RandomForests wheres Gradient Boosted Trees use Boosting
• Sampling is done using Boosting in RandomForests wheres Gradient Boosted Trees use Bootstrapping

Q2. Which model is mostly prune to overfitting?

• Random Forest
• Decision Trees

#### Quiz : Regularization

Q1. Which regularization technique is penalizing large model parameters most?

• L1 Regularization
• L2 Regularization

Q2. When is it appropriate to use Regularization

• To prevent underfitting
• To prevent overfitting

#### Quiz : Clustering

Q1. Which of the following algorithms needs you to pre-specify the expexted number of clusters?

• kmeans
• Distribution-based clustering
• Density-based clustering
• Hierarchical clustering

Q2. Which algorithm let’s you visually determine a good number of clusters based on it’s output?

• kmeans
• Density-based clustering
• Distribution-based clustering
• Hierarchical clustering

#### Quiz : PCA

Q1. What are the implications of using highly dimensional data?

• Data becomes sparse as we add dimensions
• Adding more dimensions reduces the size of the data set
• Distances loose meaning in high dimensions
• Adding more dimensions reduces the collinearity in the data

Q2. The process of reducing the number of random variables by obtaining a smaller set of artificial features is known as

• feature reduction
• feature selection

Q3. What are some linear methods for dimensionality reduction?

• Principal Component Analysis (PCA)
• Linear Discriminant Analysis (LDA)
• Self-organising Maps (SOM)
• Autoencoders

Q4. Which line gives the direction of greatest variance in the data set plotted above?

• orange
• green
• red
• blue

Q5. We use _______________ to measure how a group of random variables vary together.

• correlation
• direction of variance
• covariance
• Kullback–Leibler divergence

Q6. Using PCA to reduce the dimensionality of a data set involves the following steps:

1. Centre the data

2. Find the eigenvalues and eigenvectors of Sigma

3. Compute the covariance matrix

4. Select new dimensions and project the data

Put the steps in the correct order.

• 1, 4, 3, 2
• 1, 2, 4, 3
• 1, 3, 2, 4
• 4, 1, 3, 2

Q7. In PCA, the second principal component is ______________ to the first principal component.

• perpendicular
• parallel
• opposite
• identical

Q8. SystemML provides an out-of-the-box implementation of PCA.

• True
• False

#### Quiz : Fourier Transform

Q1. The Fourier transform is an invertible transformation between the time and frequency domain representations of a signal.

• True
• False

Q2. The figure above shows two signals A and B, that have the same frequency and phase shift, but different amplitudes. What would the sum (A+B) of these two signals look like?

• The sum of A and B would be • The sum of A and B would be • The sum of A and B would be • The sum of A and B would be Q3. The plot above shows a signal in the

• time domain
• frequency domain

Q4. The reduction of a continuous time signal to a discrete time signal is known as

• anti-aliasing
• sampling
• Z-transforming
• low-pass filtering

Q5. You have the following continuous signal but when sampled its plot looks like this: What is the most likely explanation for this effect?

• The ADC is not functioning correctly
• The sampling rate is too high
• The sampling rate is too low
• The ADC resolution is too low to handle this frequency

Q6. You have the following frequency domain plot of a signal that’s been generated by adding two separate signals (A and B) together. What can the plot tell you about the components of the original signal? Assume that the axes follow the same convention that’s been used so far in this module.

• The frequencies of A and B are 3.0 and 5.0 Hz.
• The frequencies of A and B are 2.0 and 3.0 Hz.
• The amplitudes of A and B are 2.0 and 3.0
• The amplitudes of A and B are 3.0 and 5.0

Q7. A known limitation of FT/DFT is that it requires an infinite series of sinusoids to represent a signal, so it cannot be used efficiently in a discrete setting.

• True
• False

Q8. Discrete Fourier Transform is slower compared to Fast Fourier Transform.

• Correct. The computational complexity of DFT is O(n^2) in contrast to O(nlog(n)) for FFT.
• This is incorrect. Please, review the lecture on FFT.

#### Quiz : Wavelet Transform

Q1. A signal that does not change in time is said to be generated by

• a stationary process
• a non-stationary process

Q2. Which of the following signals are generated by a stationary process

• white noise (a signal containing many frequencies with equal intensities)
• electrocardiogram (ECG)
• a sum of multiple sine waves, each having a fixed frequency and amplitude
• the sound of a fireworks display

Q3. A key limitation of Fourier transform is that it cannot provide information on when specific frequencies occur in the signal.

• True
• False

Q4. The visual representation of a wavelet transform is called

• a histogram
• a spectrogram
• a scaleogram
• a sonograph

Q5. The wavelet defined by the function ψ(t) and used in the scaling and translation process is called

• base wavelet
• initial wavelet
• mother wavelet
• pseudo-wavelet

Q6. The x and y axes of a 2D scaleogram represent=

• time
• amplitude
• scale
• frequency

Q7. Passing the signal through a series of low pass and high pass filters is a step in the calculation of=

• Discrete Wavelet Transform (DWT)
• Continuous Wavelet Transform (CWT)
• Fast Fourier Transform (FFT)
• Fourier Transform (FT)

Q8. The signal shown on the plot above has been generated by

• a stationary process
• a non-stationary process
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