Key Sequence

Notation

New Concepts

• central limit theorem
• sampling statistics
  • sample mean, sample variance, standard error of the mean
• bootstrap

Important Results / Claims

• p-value from bootstrap

Questions

Interesting Factoids

Key Sequence

Notation

New Concepts

• Bernoulli distribution as an indicator
• conditional expectation
• law of total expectation

Important Results / Claims

Review: expectation. Expectation of the sums of random variables are linear regardless of whether or not the variables are IID, independent, whatever.

“expectation of the sum is the sum of the expectations”. “Can I write the expectation I want to calculate as the sum of something else?”

Questions

Interesting Factoids

\(\mathbb{E}[Y]\) =

• \(x=1\): 3
• \(x=2\): 5 + Y
• \(x=3\): 7 + Y

\begin{equation} \mathbb{E}[Y] = 3 \cdot \frac{1}{3} + (5+ \mathbb{E}[Y]) \cdot \frac{1}{3} + (7+ \mathbb{E}[Y]) \cdot \frac{1}{3} \end{equation}

Key Sequence

Notation

New Concepts

• modeling
• parameter
  • parameter learning
  • argmax

Important Results / Claims

Questions

Interesting Factoids

Key Sequence

Notation

New Concepts

• likelyhood
• Maximum Likelihood Parameter Learning
  • argmax
• maximum a posteriori estimate

Important Results / Claims

• Double Envelope Problem

Questions

Interesting Factoids

Key Sequence

Notation

For some feature input matrix, where each row is the data samples, and columns are the input features; we write

\begin{equation} x_{j}^{(i)} \end{equation}

where \(i\) are rows (datapoints), and \(j\) are columns (features)

New Concepts

• Naive Bayes

Important Results / Claims

• Naive Bayes assumption

Questions

Interesting Factoids