Business Analytics at 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:

Gauss markov and unbiased, consistent and efficient estimators

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

Leave one out

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Comparing Error rates

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Bootstrap

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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:

MOdel Selection

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)

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1) linearity+ reformulations


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What is the random effects assumption?

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

Business Analytics

Gauss markov and unbiased, consistent and efficient estimators

Unbiased, if ß^=ß, 

Consist-ent, if var down, with n up

efficient, if no other linear estimates better

Gauss markov assumptions

1) linearity

2) no multicollinearity amongst predictors

3) Homoskedacity

4) No autocorrelation 

5) Expected value of residual = 0

Business Analytics

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

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

Business Analytics

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

Business Analytics

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.

Business Analytics

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

Business Analytics

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

Business Analytics

Supervised learning

y^=f(x)

�y^yy223444

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)

Business Analytics

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

Business Analytics

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.

Business Analytics

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

Business Analytics

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

Business Analytics

What is the random effects assumption?

The random effects assumption (in a random effects model) is that the
individual specific effects are uncorrelated with the independent variables
(𝑐𝑜𝑣 𝜆𝑖, 𝑥𝑗𝑖𝑡 = 0, but 𝜆𝑖 might be correlated).

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