how to best think of the 'confidence' in simple truth value

[Apil Tamang]

Hi All,

What would be the most intuitive (and generally applicable) way of thinking about 'confidence'  in the simple-truth-value system? I know stv consists of a 'strength' and a 'confidence' part. The strength, if I remember correctly is representative of the probability of that statement being true. I'm just not sure how to think about the confidence as a guiding metric ...

Thanks...

[Nil Geisweiller]

The wiki is not very talkative about this...

Ideally you'd need to read the PLN book.

Said briefly the confidence captures the spread of the second order
distribution over the true unknown probability. If the confidence is 1
the spread is null. If the confidence is 0 the spread is uniform, that
is we know nothing about the true probability.

The spread of the second order distribution shrinks as more evidence
accumulates, so it depends on the number of observations. There is a
function to translate the count N (number of observations) into confidence

c = N / (N + K)

so as you may see as the count increases, so does the confidence. This
function is rather arbitrary, it could be something else, like say 1 -
std-dev, or anything that is monotonous and has co-domain [0, 1], but it
has the advantage of being simple.

Hope it's clearer.

Nil

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[Nil Geisweiller]

Incomplete wikified version of PLN

http://wiki.opencog.org/w/PLNBook

the whole book is available online as well somewhere (can't find it ATM).

Nil

[Ben Goertzel]

The count of a probability is the "number of observations" on which
that probability is based

The confidence of a probability is a scaling of the count into the
interval [0,1]

There are both heuristic and rigorous formulas for deriving the
confidence associated with the conclusion of a certain probabilistic
inference. Many of the PLN rules now use heuristic formulas. In the
case of inference based on natural language statements, this is
probably fine as the data is not there to feed more rigorous formulas
effectively anyway. In the case of inference based on quantitative
observations, the more rigorous formulas (based on second order
probabilities etc.) would be of value...

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Ben Goertzel, PhD
http://goertzel.org

“I tell my students, when you go to these meetings, see what direction
everyone is headed, so you can go in the opposite direction. Don’t
polish the brass on the bandwagon.” – V. S. Ramachandran

[Linas Vepstas]

On Mon, Jan 23, 2017 at 7:59 AM, 'Nil Geisweiller' via opencog
<ope...@googlegroups.com> wrote:
>
> The spread of the second order distribution shrinks as more evidence
> accumulates, so it depends on the number of observations. There is a
> function to translate the count N (number of observations) into confidence
>
> c = N / (N + K)
>
> so as you may see as the count increases, so does the confidence.

This is a rather weak sigmoid function, located at 'K'. I've often wondered
how well inference chaining would work if one used a sharper formula.
The above *eventually* approaches a confidence of 1.0, but it does
it very slowly. Pathologically slowly, even.

If I recall correctly, K is hard-coded as 800 in the code. What if, instead,
one used

c = tanh(N-K/K)

which is a much cleaner, sharper sigmoid centered at K and at least one
web page claims its very very fast, about as fast the simple formula (!!??)
https://txt.arboreus.com/2013/03/29/fast-sigmoid.html

I made a plot, see attached. The tanh formula in particular looks like it
might give much better results for TV merging in the PLN chainer.

--linas