# Business Analytics at TU München

## Flashcards and summaries for Business Analytics at the TU München

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## Study with flashcards and summaries for the course Business Analytics at the TU München

### Exemplary flashcards for Business Analytics at the TU München on StudySmarter:

Partial least squares

### Exemplary flashcards for Business Analytics at the TU München on StudySmarter:

5) Expected value of the residual vector, given 𝑋, is 0 (𝐸 𝜀 𝑋 = 0)

Bootstrap

Leave one out

### Exemplary flashcards for Business Analytics at the TU München on StudySmarter:

Solutions multicollinearity

MOdel Selection

### Exemplary flashcards for Business Analytics at the TU München on StudySmarter:

Model Selection and Model Assessment

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Generalization errors

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Supervised learning

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For an algorithm to be useful in a wide range of real-world
applications it must:

• Basic algorithm needs to be extended to fulfill these requirements

### Exemplary flashcards for Business Analytics at the TU München on StudySmarter:

Comparing Error rates

### Exemplary flashcards for Business Analytics at the TU München on StudySmarter:

1) linearity+ reformulations

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## Exemplary flashcards for Business Analytics at the TU München on StudySmarter:

Partial least squares

PLS uses weights to reflect covariance structure –> More difficult

5) Expected value of the residual vector, given 𝑋, is 0 (𝐸 𝜀 𝑋 = 0)

Assumption: Other factors, which are not explicitely accounted for in the
model but are contained in 𝜀, are not correlated with 𝑋 (exogeneity)

• Endogeneity is given when an independent variable is correlated with the
error term and the covariance is not null

–> Probably omitted variable bias

Bootstrap

– sampling several times (replacement from training set to bootstrap set

– some observations more than once

– bootstrap data set contains 𝑛 observations, sampled
with replacement from the original data set.
• Then the model is estimated on a bootstrap data set, and
predictions are made for original training set.
• This process is repeated many times and the resulting
statistics are averaged.

Leave one out

𝑛-Fold Cross-Validation
𝑛 instances are in the data set
Use all but one instance for training
Each iteration is evaluated by predicting the omitted instance

Maximum use of the data for training
Deterministic (no random sampling of test sets)
High computational cost
Non-stratified sample!

Solutions multicollinearity

Subset selection
best subset, backward, forward, stepwise selection of features
(already discussed in the context of the linear regression)

• Using derived input
Principal component regression
Partial least squares

• Coefficient shrinkage (regularization)
Ridge regression
Lasso (least absolute shrinkage and selection operator)

MOdel Selection

Wide-spread methods for model selection are:

• Akaike Information Criterion (AIC)
• 𝐴𝐼𝐶 = 2𝑘 − 2 ln 𝐿 , already discussed in the context of log. regression
• 𝑘 is the number of parameters, ln(𝐿) the log likelihood
• Minimum description length (Risannen, 1978)
• discussed later in this class
• Resampling methods
• Cross validation, jackknife, bootstrap, etc.

Model Selection and Model Assessment

Model selection: Estimating performances of different models to choose the
best one (produces the minimum of the test error)

Model assessment: Having chosen a model, estimating the prediction error
on new data

Generalization errors

Components of generalization error
• Bias is error from erroneous assumptions in the learning algorithm. Error might be
due to inaccurate assumptions/simplifications made by the model.
• Variance is error from sensitivity to small fluctuations in the training set. High
variance causes overfitting.
Underfitting: model is too “simple” to represent all relevant characteristics
• High bias and low variance
• High training error and high test error
Overfitting: model is too “complex” and fits irrelevant characteristics/noise
• Low bias and high variance
• Low training error and high test error

Supervised learning

y^=f(x)

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Supervised learning is inferring a function from labeled training data
Training: given a training set of labeled examples
estimate the prediction function 𝑓 by minimizing the prediction error on the
training set
Testing: apply 𝑓 to a never before seen test example 𝒙 and output the
predicted value ො𝑦 = 𝑓(𝒙)

For an algorithm to be useful in a wide range of real-world
applications it must:

• Basic algorithm needs to be extended to fulfill these requirements

– Permit numeric attributes
– Allow missing values
– Be robust in the presence of noise

• Basic algorithm needs to be extended to fulfill these requirements

Comparing Error rates

Choose lowest error rate

–

Estimated error rate is just an estimate (random)
• Student’s paired 𝑡-test tells us whether the means of two samples are
significantly different
• Construct a 𝑡-test statistic
Need variance as well as point estimates

1) linearity+ reformulations

If not applicable –> reformulate

1) polynomial regressions (if curve in data)

2) transform log if outliers

3) non linear with constant (ex Experten(..) if curve, but no negative turn

4) piecewise

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