Learning from Data.

• Deals with obtaining the features (inputs) from data

• Deals with predictive tasks such as:

• Forecasting

• Anomaly Detection

• Missing Data Imputation

• Classifying

• Ranking

• Recommendation/Decision

Learning From Data (When)

• Data Rich Environment

• Lack of Human Expertise

• Difficult to explain Human Expertise

• Dynamic Systems, Changing with time

• Needs for adaptation

Departments of Business Where Analytics are valuable:

- Finance

• Marketing and Sales

• Supply Chaing and Logistics

• …

Statistical Learning: Lots of Keywords

Learning:

• Supervised Learning

• Unsupervised Learning

• Semi-Supervised Learning

• Reinforcement Learning

• Deep Learning (Part of both Supervised and Unsupervised Learning)

• etc.

Task and Data:

• Regression

• Classification

• Clustering

• Forecasting

• etc.

Why Statistical Learning in Business

• Huge Amount of data

• 100s of covariates

• It becomes more fashionable

• It’s algorithms become more available

• Computers are more powerful

• Need to use different data types in modelling

• Data to Pattern to [hopefully] theory is promising

• …

Learning

Supervised Learning	Unsupervised Learning	Reinforcement Learning
{Y;X} available	{X} available	Ex: Game
\(E[Y \: given \: X]\)	Pattern inside data
\(P(Y=y \: given \:X=x)\)	Homogeneous Groups
Ex: Regression	Ex: Clustering

Data Rich Environment: [Very] High Dimensionality

• The main Goal is:

\(Data=Pattern(s)+Error(s)\)

Example: Standard Regression

\(y=\beta_0+\beta_1 x_1+\beta_2 x_2+ \cdots + \beta_k x_k + \varepsilon\)
for some \(k>>2\)

This is equivalent to

\(Pattern=\beta_0+\beta_1 x_1+\beta_2 x_2+ \cdots + \beta_k x_k \; and \; \; error=\varepsilon\)
(Assumptions are skipped)

Or put in another form:

\(\mu(X)=E[Y|X=x]=\hat \beta_0+\hat \beta_1 x_1+\hat \beta_2 x_2+ \cdots +\hat \beta_k x_k\)

given \(E[\varepsilon]=0\) and \(\hat \beta_i\) are the estimated coefficients.

How to find the parameters, \(\hat \beta_i\):

• An example: minimize Mean Squared Errors (MSE) (or Ordinary Least Squared Estimation)

\(MSE=\frac{1}{N+1} \sum_{i=0}^{N} (y_i-\mu(x_i))^2=\frac{1}{N+1} \sum_{i=0}^{N} \varepsilon_i^2\)

In Econometrics

• In most of the cases, number of observations, \(N\) is grater than number of covariates (parameters), \(P\), \(N>>P\)

• If \(N \sim P\) then one might talk about some failure due to degrees of freedom (and overfitting)

• if \(N < P\) OLS fails.

\(\implies\) high dimensionality comes with difficulties.

In Economics

• Causal Relationships are very important

Means:

Correlation vs Causation must be discussed (this one is the main critique)

Error structure is important

Behavioral assessments to model is crucial

Goodness of fit is not the main focus (though it is important)

In Econometrics

• Theories (Thought Exercise: Idea)

• Lots of assumptions without a plausible way to test them (many of them are unrealistic)

• Theories \(\implies\) Models

• Estimate Models (OLS, IV Regression, Max Likelihood GMM etc.)

• Conclude with estimated parameters and standard errors

Fundamental Table

Data	Causal	Predictive
Observational	Good/Bad	Good/Bad
Experimental	Good/Bad	Good/Bad

Lets think two variables, \(y\) and \(x\), and the causality structure such that \(X\) causes \(Y\). All of the alternatives are:

• \(X\) causes \(Y\), (or shown as \(X \implies Y\))

• \(Y\) causes \(X\), \(Y \implies X\)

• \(Z\) causes both \(X\) and \(Y\), \(Z \implies {Y, X}\) (but \(z\) may or may not be available)

• By Chance, [remember p-value ]

• By Selection

Causality (Will be back to this topic later)

• Experiment to remove the effects of potential confounding factors? (may solve some of the cases)

• Sample split randomly

It is possible then,

\(X \implies Y\)

\(Y\) do not causes \(X\) since the sample is splitt by chance then chance causes \(X\)

\(Z\) may cause both possible but by chance

It could still be by chance

It could be by selection, but it should be excluded by the experimenter

Why Data Analytics in Business

OPEN DISCUSSION (ONCE MORE)

An R Example

https://www.youtube.com/watch?v=GTgZfCltMm8