we need to keep two sequences aligned; so in addition to minimum edit distance we need to know how to transform one sequence into another.

To do this, we keep a pointer of what cell we came from.

This is similar to edit distance with DP, but we keep a pointer of each cell of the action: point DOWN (less j) if inserting, point LEFT (less i) if deleting, and point diagonally if substituting.

Bag of Words is an order-free representation of a corpus. Specifically, each word has a count which we assign to each word without any other information about ordering, etc.

With the Bayes Theorem, we have:

\begin{equation} C_{MAP} = \arg\max_{c \in C} P(d|c)P( c) \end{equation}

where \(d\) is the document, and \(c\) is the class.

So, given a document is a set of a bunch of words:

\begin{equation} C_{MAP} = \arg\max_{c\in C} P(x_1, \dots, x_{n}|c)P( c) \end{equation}

DOI: 10.3389/fnagi.2021.635945

One-Liner

extracted lexicographic and syntactical features from ADReSS Challenge data and trained it on various models, with BERT performing the best.

Novelty

???????

Seems like results here are a strict subset of Zhu 2021. Same sets of dataprep of Antonsson 2021 but trained on a BERT now. Seem to do worse than Antonsson 2021 too.

Notable Methods

Essentially Antonsson 2021

• Also performed MMSE score regression.

Key Figs

Table 7 training result

This figure shows us that the results attained by training on extracted feature is past the state-of-the-art at the time.

A basis is a list of vectors in \(V\) that spans \(V\) and is linearly independent

constituents

• a LIST! of vectors in vector space \(V\)

requirements

• the list is…
  • linear independent
  • spans \(V\)

additional information

criteria for basis

A list \(v_1, \dots v_{n}\) of vectors in \(V\) is a basis of \(V\) IFF every \(v \in V\) can be written uniquely as:

\begin{equation} v = a_1v_1+ \dots + a_{n}v_{n} \end{equation}

where \(a_1, \dots, a_{n} \in \mathbb{F}\).

forward direction

Suppose we have \(v_1, \dots, v_{n}\) as the basis in \(V\). We desire that \(v_1, \dots v_{n}\) uniquely constructs each \(v \in V\).

Suppose \(v_1, \dots v_{n} \in V\) is a basis of some vector space \(V\); \(w_1, \dots w_{n} \in W\) is just a good’ol list of length \(n= \dim V\) in \(W\).

There exists a unique linear map \(T \in \mathcal{L}(V,W)\) such that…

\begin{equation} Tv_{j} = w_{j} \end{equation}

for each \(j = 1, \dots n\)

Intuition

The layperson’s explanation of this result: 1) that, for everywhere you want to take the basis of one space, there’s always a unique linear map to take you there. 2) that, a linear map is determined uniquely by what it does to the basis of its domain.