If we know that \(a,b\) are both Gaussian distributions, then we have that:

\begin{equation} \mqty[a \\ b] \sim \mathcal{N} \qty(\mqty[\mu_{a} \\mu_{b}], \mqty[A & C \\ C^{T} & B]) \end{equation}

whereby:

• \(A\) is the covariance of each element of \(A\)
• \(B\) is the covariance of each element of \(B\)
• \(C\) is the covariance of \(A\) against \(B\)

To perform inference:

\begin{equation} p(a|b) = \mathcal{N}(a | \mu_{a|B}, \Sigma_{a|b}) \end{equation}

wherby:

\begin{equation} \mu_{a|b} = \mu_{a} + CB^{-1}(b-\mu_{b}) \end{equation}

Information Retrival is trying to find material within large collections which is unstructured which satisfies an information need (of structured info).

Unstructured information has had a massive outburst after the millennium.

IMPORTANTLY: evaluating Information Retrival is based on Precision/Recall/F on information need and not the query.

For ranked system, we can come up with a curve of precision-recall curve by selecting increasing \(k\), or mean average precision.

Basic Terminology

collection

a set of documents—could by static, or dynamically added

Information Units are unique entities mentioned during an utterance; for a sentence like “There is a boy. The boy is a brother. He is stealing a cookie. The sister is watching.”, “boy, cookie, sister” are possible IUs.