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learn-lang-diary-part-three.lyx
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\begin_layout Title
Language Learning Diary - Part Three
\end_layout
\begin_layout Date
Sept 2021
\end_layout
\begin_layout Author
Linas Vepstas
\end_layout
\begin_layout Abstract
The language-learning effort involves research and software development
to implement the ideas concerning unsupervised learning of grammar, syntax
and semantics from corpora.
This document contains supplementary notes and a loosely-organized semi-chronol
ogical diary of results.
The notes here might not always makes sense; they are a short-hand for
my own benefit, rather than aimed at you, dear reader!
\end_layout
\begin_layout Section*
Introduction
\end_layout
\begin_layout Standard
Part Three of the diary on the language-learning effort continues work on
the English dataset.
This part is concluded, the next part is Part Four.
\end_layout
\begin_layout Section*
Summary Conclusions
\end_layout
\begin_layout Standard
A short summary of what is found here:
\end_layout
\begin_layout Itemize
Trimming the word-disjunct dataset to remove words or disjuncts or word-disjunct
pairs observed only once is a good thing, and reduces dataset size by 90%
or more.
Trimming more than this is a bad thing.
\end_layout
\begin_layout Itemize
Part of the above result may be due to a bug in the word-segmentation code:
leading/trailing double-quotes are not split from words.
The processing code then tries to escape these with backslashes, and repeated
processing creates a shower of backslashes.
This appears to pointless inflate the number of words in a dataset.
This bug needs to be fixed.
\end_layout
\begin_layout Itemize
It is not known if trimming word-pair files to remove low-count word-pairs
is a good idea or not.
This will require new (and time-consuming) experiments.
Some trimming is surely good, but how much?
\end_layout
\begin_layout Itemize
The mutual information between word-vectors is given by a Gaussian distribution.
This was seen before, but is confirmed again here.
Recall that a word-vector consists of a word, and the vector basis elements
are disjuncts.
These word-vectors are reminiscent of SkipGrams, but are constructed differentl
y.
I don't know of any theoretical work that could explain this experimental
result (or any kind of result, for that matter).
\end_layout
\begin_layout Itemize
The self-MI of a word-vector against itself appears to be given by a weak
log-normal distribution.
It is almost but not quite uniformly distributed, ranging from about 2
and gradually tapering to 30 for the dataset explored here.
An easy theoretical argument can be made that the self-MI must be positive,
but that's all.
I don't know of any theoretical work that could explain this experimental
result.
\end_layout
\begin_layout Itemize
Other ways of comparing word vectors, including basic Jaccard (vector overlap)
distance, and a conditional-Jaccard distance do correlate in general with
the MI.
An exploration of these alternate ways of exploring word similarities was
driven by work reported in the Diary part Two.
Here, nothing unusual stands out.
The distribution of these appears to be given by a log-normal curve, or
possible a log logistic curve, but the data is not refined enough to tell.
There is no theoretical basis to expect any of this.
\end_layout
\begin_layout Itemize
Examining the top-100 most similar word pairs by hand (by gut feel) suggests
that all but one or two word-pair recommendations are excellent.
This visual exam also seems to suggest that maybe MI provides better recommenda
tions than the other metrics (contradicting earlier results).
Certainly, computing MI is much faster.
\end_layout
\begin_layout Itemize
Both of the Jaccard measures have a self-distance score of exactly zero.
By contrast, the self-MI is not zero, and it suggests that there it can
be used as a natural scale to help determine when words should be classified
together.
That is, a low self-MI word is similar to everything, and maybe should
not be merged with high self-MI words.
Or perhaps it is an indicator of a word with many distinct meanings.
I don't understand this yet, and it might be a fruitful topic to examine.
\end_layout
\begin_layout Itemize
In order to make a determination to merge a pair of words, one must look
at both their similarity, and their frequency of occurrence.
One wishes to merge words that are similar and are also frequently-occurring.
To this end, the text proposes that the similarity should be combined with
the average log-frequency (log-probability) of the two words.
Combining this idea with the formula for MI gives the explicit formula
\begin_inset Formula
\[
\mbox{common}MI\left(w,u\right)=\log_{2}\frac{p\left(w,u\right)}{\sqrt{p\left(w\right)p\left(u\right)}}
\]
\end_inset
The square-root arises from the factor of 1/2 that arises from averaging
two things together.
The square-root makes this formula look unusual, but it seems to provide
an excellent way of ranking word-pairs for merging.
The distribution again follows the normal Gaussian Bell curve.
As mentioned, the top 100 suggestions for merge candidates look very healthy.
\end_layout
\begin_layout Standard
The diary Part Four will examine a merge in gruesome detail.
\end_layout
\begin_layout Section*
September 2021
\end_layout
\begin_layout Standard
After the previous setback with grammatical clustering, it seems like more
exploratory work is in order.
Part of the exploratory effort is to discover faster ways of finding similar
words, and to find algorithms that can do incremental or continuous learning.
Some questions along this path:
\end_layout
\begin_layout Itemize
What is the distribution of disjuncts? (Yes, we've done this before, but
lets do it again for the latest
\begin_inset Quotes eld
\end_inset
clean
\begin_inset Quotes erd
\end_inset
dataset.) Create a graph showing rank vs number of times a disjunct has
been observed.
\end_layout
\begin_layout Itemize
How are disjuncts shared? Create a graph showing the rank vs.
the number of words that share this disjunct.
\end_layout
\begin_layout Itemize
Scatterplots: ...
\end_layout
\begin_layout Subsection*
Expt-4 – Trimming – Sept 2021
\end_layout
\begin_layout Standard
The above questions will be aimed at a specific dataset.
The initial choice of dataset was `
\family typewriter
run-1-en_mpg-tranche-123.rdb
\family default
`, as described earlier in the diary.
The intent is to explore two versions: the full dataset, and a lightly
trimmed dataset.
\end_layout
\begin_layout Standard
What is explored here (in expt-4) is how the size of the dataset varies
with the amount of trimming.
Trimming is desirable, since it can be used to manage dataset sizes.
Computations run faster on smaller datasets.
\end_layout
\begin_layout Standard
The outcome of trimming proves to be surprising: even
\begin_inset Quotes eld
\end_inset
mild
\begin_inset Quotes erd
\end_inset
trimming removes large parts of the word–disjunct datasets.
It removes much more than one might naively guess from a Zipfian distribution.
The underlying reason for this is confusing: it turns out that a bug in
tokenization may be ruining the distribution.
The tokenizer does not split double-quotes from the beginning/ending of
words, and later stages add backslashes to escape the quotes.
A waterfall of quotes results, polluting the dataset with oodles of backslashes.
These are observed infrequently, and how they interact with the quality
of the datasets is unclear.
\end_layout
\begin_layout Standard
Coupled with the earlier observation that even mild trimming damages the
data (as seen in expt-3, at the end of diary Part Two), this suggests that
trimming should be kept to a minimum.
By the conclusion, it emerges that perhaps the ideal trim is one that removes
all words, disjuncts and word–disjunct pairs that are observed only once.
\end_layout
\begin_layout Standard
\begin_inset Quotes eld
\end_inset
Trimming
\begin_inset Quotes erd
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means removing all words, disjuncts and word–disjunct pairs with observation
counts below some given thresholds.
The thresholds for these three counts can be set independently.
These are the three numbers below: e.g.
10-4-2 means
\begin_inset Quotes eld
\end_inset
discard all words with an observation count of 10 or less, all disjuncts
with a count of 4 or less, and all word–disjunct pairs with a count of
2 or less.
\begin_inset Quotes erd
\end_inset
\end_layout
\begin_layout Standard
The trimming process is funny: trimming (as implemented) is not idempotent
(but it should be).
Basically, the linkage filter, which guarantees that connectors have correspond
ing word entries, knocks out disjuncts and so pushes words below the cut-off.
Repeating this process then knocks out more connectors.
It needs to be run until its stable.
This is CPU consuming.
\end_layout
\begin_layout Standard
The table below shows the result of repeated trimming, interleaved with
a linkage filter to remove disjuncts with connectors in them that do not
have words any more.
Each was written to a distinct file.
\end_layout
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So that took an alarmingly large number of iterations to stabilize.
It also trimmed the dataset extremely sharply.
Alarmingly sharply.
Lets try again.
\end_layout
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Same idea, modified algo: here, instead of filtering, just delete outright.
This will shrink the AtomSpace as we go along, avoiding some of the hassle
with filtering.
Hopefully it will run faster, too.