Regression

Question 1

What is regression?

Answer 1

• Predict the value of a continuous variable based on other variables assuming a linear or nonlinear model of dependency

Predicted variable (dependent) = ^y (yhead)
Other variables (explanatory variables)

Question 2

Whats the difference between regression and classification?

Answer 2

Difference to classification is that classification predicts nominal class attributes whereas regression predicts continuous attributes

Question 3

What are regression techniques?

Answer 3

1) Linear Regression
2) Polynomial Regression
3) Local Regression
4) ANN
5) DNN
6) K-nearest-Neighbours Regression

Question 4

Explain k-nearest neighbor regression

Answer 4

• Use the numeric average of the k-nearest stations

Choose k values between 1 and 20 (Rule of thumb)

Question 5

How can you evaluate regression models?

Answer 5

Methods for Model Evaluation:

• Cross Validation: 10-fold
• Holdout Validation: 80 % random share for training, 20% for testing

Question 6

What metrics for Model Evaluation can be applied?

Answer 6

• Mean Absolute Error (MAE): computes the average deviation between predicted value and actual value
• Mean Squared Error (MSE): Places more emphasis on larger deviation
• Root Mean Squared Error (RMSE): similar scale as MAE with more emphasis on larger deviations
• Pearsons Correlation Coefficient: scores well if high (low) actual values get high (low) predictions
• R Squared: measures the part of the variation in y hat that is explainable from the explanatory variables

Question 7

How do you interpret R2

Answer 7

R2 = 1; perfect model as total variation of y can be completely explained from X

Question 8

How can you apply regression trees?

Answer 8

• In principle the same as for classification
  Differences:
  1) splits are selected by maximizing the MSE reduction (not GINI or entropy)
  2) prediction is average value of the trainings examples in a specific leaf

Question 9

What may happen if your tree has a higher depth?

Answer 9

• It may overfit

- The model learns several outliers

Question 10

What is the assumption of linear regression?

Answer 10

• The target variable y is linearly dependent on explanatory variables x

Question 11

How do you fit a regression function?

Answer 11

Least-squares approach: Find the weight vector that minimizes the sum of squared error for all training examples
Error: Difference between estimated and real value in training data

Question 12

What is ridge regularization?

Answer 12

• Variation of least squares approach (another way to fit a regression function)
• Tries to avoid overfitting by keeping weights small

alpha of 0 = normal least squares regression
alpha of 100 = strongly regularized flat curve (strong penalty)

Question 13

What problems can occur by feature selection for regression?

Answer 13

Problem 1: Highly correlated variables (height in cm and inch)
- weights are meaningless, one variable should be removed

Problem 2: Insignificant variables
- uncorrelated variables get w=0 or relatively small weights assigned

Question 14

How can you check if a variable with a small weight really is insignificant?

Answer 14

• Statistical test with H0 (w=0 as variable is insignificant)
• t-stat: number of standard deviations that w is away from 0 (center of distribution; high t-stat means that H0 is to reject)
• p-value: Probability of wrongly rejecting H0 (p-value close to 0; variable is significant

Question 15

What does Interpolation mean?

Answer 15

Interpolating regression:

• predicted values are within the range of the training data values
• is regarded as safe

Question 16

What does extrapolation mean?

Answer 16

Extrapolating regression:

• May also predict values outside of the training data interval
• Depending on the use case can also be relevant (how far will the sea level have risen by 2050) ?

An explanatory variable that is out of range could result in a predicted dependent variable out of range

Question 17

How can the results of a linear regression and a K-NN regression be described?

Answer 17

• Linear regression extrapolates
• KNN and regression trees interpolate

–> Linear regression is sensitive to outliers

Question 18

Which technique can be applied to non-linear problems?

Answer 18

• Apply transformations to the explanatory variables within the regression function (log, exp, square root; polynomial transformation)
• This allows use of linear regression techniques to fit much more complicated non-linear datasets

Question 19

Explain polynomial regression

Answer 19

• Extension of linear regression
• can be fitted using the least squares method
• Tendency to overfit training data for large degrees M (to the power of M)

Question 20

Where does a polynomial regression often overfits and which workaround can you apply to mitigate overfitting?

Answer 20

• Overfitting often happens in sparse regions

Workarounds:

• decrease M
• increase amount of training data
• Local Regression

Question 21

What is the idea behind local regression?

Answer 21

Assumption: non-linear problems are approximately linear in local areas
Idea: use linear regression locally for the data point at hand (lazy learning)
- Combination of k-NN and linear regression

Question 22

How does local regression work?

Answer 22

Given a datapoint:

1) retrieve the k nearest neighbors
2) learn a regression model for those neighbors
3) use the learned model to predict the y value

Question 23

What are the advantages of local regression?

Answer 23

Advantage: fits non-linear models well

• good local approximation
• often better than pure k-NN (local regression does not compute the average of the neighbors but a regression function that is often more accurate)

Question 24

What are the disadvantages of local regression?

Answer 24

Disadvantage:

• slow at runtime
• for each test example:
  
  • find k nearest neighbors
  • compute local model

Question 25

How do ANNs for regression differ from ANNs for classification?

Answer 25

- ANN for classification uses a threshold to determine if the class is true or false - ANN for regression does not use a cutoff for true or false predictions; it leaves the numbers as they are (between 0 and 1)

Question 26

Can you learn non-linear models with ANNs?

Answer 26

- No, its a linear model where the target variable is a linear combination of the input variables - non-linear regressions can be approximated by using multiple hidden layers (Deep ANNs allow arbitrary functions) But: the flexibility of Deep ANNs can result in overfitting -> lot of training data necessary

Question 27

What is a time series?

Answer 27

- Data points are indexed in time order | - e.g. Stock market prices, Temperature

Question 28

What is the difference in predicting Time series?

Answer 28

- Predict data points that continue the series into the future - There is a order in the data - other regression techniques do not use time explicitly - aims to predict future values of the same variable

Question 29

What are the different approaches for time series forecasting?

Answer 29

1) Data-driven: Smoothing 2) Model-driven: 1) component models of time series 2) other regression techniques

Question 30

How does smoothing work?

Answer 30

Principle: Use more recent values, as they might matter more Simple Moving Average (SMA) - average of last n values Exponential Moving Average (EMA) - exponentially decrease weight of older values

Question 31

Explain component models of time series

Answer 31

Assume time series to consist of four components: 1) Long-term trend 2) Cyclical effect 3) Seasonal effect 4) Random variation

Question 32

Explain Windowing as time series method

Answer 32

Idea: Transform forecasting problem int classical learning problem (classification or regression) - Only use the last k time periods E.g. Weather forecasting: Assumption: - use the weather from the k previous days - the older past is irrelevant

Question 33

What are the components of the generalization error?

Answer 33

- Bias: Error due to wrong model complexity (model underfits the training and test data) - Variance: Models excessive sensitivity to small variations in the training data (flexible models are likely to overfit) - Irreducible error: Due to noisiness of the data itself (need to clean the training data)

Question 34

Explain the Bias / Variance-Tradeoff

Answer 34

- The more flexible a model is the higher is the degree of overfitting - the less flexible a model is the higher is the degree of underfitting ``` Both cases (too flexible and too static) result in higher errors -> find the ideal flexibility that results in the lowest error! ```

Question 35

How can you find the ideal flexibility (bias/variance-tradeoff)

Answer 35

1) Test different learning methods (models that are more biased (Linear Regression) and more flexible (polynomial regression) 2) Test different hyperparameters - Degree of polynomial, ridge - max depth of tree, min examples branch - number of hidden layers of ANN 3a: increase amount of training data 3b: include data with corner cases (make data more interesting) 3c: cleanse the training data

Question 36

How does the learning curve for a low flexibility model look like in dependence of training set size?

Answer 36

- Underfitting: High training and test errors due to bias | - Error remains even if more data is added

Question 37

How does the learning curve for a high flexibility model look like in dependence of training set size?

Answer 37

- Overfitting: Generalization error decreases for increasing training set size - using more training data you can also use more flexible models (like Deep Learning)