Vulturemox commented on a change in pull request #1119:
URL: https://github.com/apache/systemds/pull/1119#discussion_r533320677
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File path: scripts/staging/datawig/DesignDocument.md
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+# DataWig Design Document
+Julian Rakuschek, Noah Ruhmer
+### Basic Idea
+Let us assume the following table as presented in the corresponding Paper by
Prof. Biessmann [1]:
+
+| Type | Description | Size | Color |
+| :-----------: | :------------------- | :------------: | :-----------: |
+| Shoes | ideal for running | 12UK | Black |
+| SD Card | for saving files | 8GB | Blue |
+| Dress | This yellow dress ...| M | ??? |
+
+The goal is obviously to impute the Color `Yellow` for the Dress, but how do
we get there?
+
+First we select the feature columns which are `Type`, `Description` and
`Size`, the label column alias to-be-imputed shall be `Color`
+
+#### Numerical Encoding x<sup>c</sup>
+The first stage is the transformation from strings and categorical data into
their numerical representation:
+
+| Type | Description | Size | Color |
+| :-----------: | :------------------- | :------------: | :-----------: |
+| OHE | Sequential Encoding | OHE | OHE |
+
+Here we can use a One-Hot Encoder (OHE) for categorical data and a sequential
encoding for strings. As SystemDS already has the bultin function `toOneHot` we
plan on using that and for the sequential data we would implement a new builtin
function `sequentialEncode` which would look like this:
+* Let's say Row 1 contains "Shoes" and Row2 "SD Card"
+* First we assign each unique character a unique index, e.g.
+ * `{S: 1, h: 2, o: 3, e: 4, s: 5, D: 6, " ": 7, C: 8, a: 9, r: 10, d: 11}`
+* Then we replace each character in the string with the corresponding
token-index, which would yield two arrays:
+ * `[1, 2, 3, 4, 5]`
+ * `[1, 6, 7, 8, 9, 10, 11]`
+* This is also the way how the SequentialEncoder in the Python-Implementation
of DataWig works
+
+#### Feature Extraction
+This is the part where we yet don't fully understand on how this should work.
In the paper [1], Prof. Biessmann uses one Featurizer for each column, namely
for One-hot encoded data he uses an embedding and for sequential data they
either use: "an n-gram representation or a character-based embedding using a
long short-term memory (LSTM) recurrent neural network" [1, chapter 3]
+
+However, we think that it could also be possible to use the PCA algorithm
which is already implemented in SystemDS as a Feature Extraction Layer. What we
yet don't know is whether we should apply PCA to all columns at once and reduce
them to a dimension of one, or use PCA on each column like Prof. Biessmann.
+
+| Type | Description | Size |
+| :-----------: | :------------------- | :------------: |
+| PCA | PCA | PCA |
+
+The resulting columns would then all be concatenated to a single vector X, but
in case we use PCA on all columns at once, this step can be omitted.
+
+Also a side note: In the table above you can see that we only apply the
Feature Extraction to the feature columns, the label-column will then be used
in the Imputation Equation.
+
+#### Imputation
+For the imputation we have to calculate the probability of each possible
missing value replacement and choose the likeliest value: `P(y | X, Θ)`
+Thereby we want the probability of y fitting in the column given the Feature
Extraction *and* the trained parameter Θ
+
+Θ is then calculated with the equation presentation in Prof. Biessmanns paper
[1], if we understand that right, we calculate this equation once every epoch.
The remaining question is what the parameters in Θ stand for, namely they are:
`Θ = (W, z, b)`
Review comment:
Thanks for the additional material, I'll have a look at it!
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