Saturday, 25 March 2017
A conceptual representation
we introduce here a multi-level conceptual representation, based on two morphisms : 'is linked to' and 'opposes' :
a. \( \rightarrow \) ,\( \Rightarrow \), \( \Rrightarrow \), \( \rightarrow_4 \)... : 'is linked to', level (n+)1, (n+)2, (n+)3,...
b. \( \vdash \),\( \Vdash \),\( \Vvdash \),\( \vdash_4 \)... : 'opposes', level (n+)1, (n+)2, (n+)3,...
[optional :
c. \(\circ \),\(\circ_2\),...: 'equivalence' or 'opposition', level (n+)1, (n+)2,...
d. \(. \) : under category
e. \( \leadsto\), \( \leadsto_2 \), : to, level (n+)1, (n+)2,...]
Let us give an example of implementation of this representation, in a philosophical context. (we are not trying to 'demonstrate' anything). Let Mr. X has these initial representations:
1. "Science is interested only in the reproducible : \( science \rightarrow reproductible \)
2. Moreover, science often appears as a model of truth : \(science \rightarrow truth \) (for example to people like Jacques Bouveresse)
3. The reproducible thus ends up appearing as an essential criterion of truth: \(reproducible \rightarrow truth \)
In reality the search for truth is not even a goal of science, which swears only by the reproducible. And to bring science and truth closer together is very reductive (for the concept of truth). It can be said that the metaphysical trace of science holds in the de-cision of the symmetry (i.e. its breaking):
$$ truth \rightarrow reproducible \Vdash truth \vdash reproducible "$$
Suppose now that X reads Heiddeger, in particular this passage from 'Introduction to metaphysik' [translation Fried and Polt]:
"For it cannot be decided so readily whether logic and its fundamental rules can provide any measure for the question about beings as such. It could be the other way around, that the whole logic that we know and that we treat like a gift from heaven is grounded in a very definite answer to the question about beings, and that consequently any thinking that simply follows the laws of thought of established logic is intrinsically incapable of even beginning to understand the question about beings, much less of actually unfolding it and leading it toward an answer. In truth, it is only an illusion of rigor and scientificity when one appeals to the principle of contradiction, and to logic in general, in order to prove that all thinking and talk about Nothing is contradictory and therefore senseless."
If X has the following representations on Heidegger:
\(truth \rightarrow question \, about \, beings \)
\(Logik \rightarrow science \)
\(science \vdash philosophy / poetry \)
and link his concept of reproducibility to Heidegger's Gestell (essence of technique / science)
\( Heidegger.science/Gestell \rightarrow X.reproducible \)
And if X retains his view that \(science \rightarrow reproducible \), it seems possible that he enriches his representation with:
\begin{array}{r c l}
truth \rightarrow reproducible & \Vdash & truth \vdash reproducible \\
& \Rrightarrow & \\
science & \Vdash & philosophy / poetry
\end{array}
The relative link between Heidegger concept of philosophy / poetry and X's concept of reproducibility is not necessarily a view of Heidegger, so that this link is a creative -and subjective-one (which may be ultimately true or not [or 'interesting' or not]). (We may note that if poetry is talking about Nothing (last sentence of the text above), it might appear plausible that poetry is not X.reproducible...)
Let us suppose finally that X reads Stuart Kauffman, in particular 'Investigations' and 'Humanity in a creative world'.
If X admits that his concept of \( reproducible \vdash noreproducible \) (as part of the subjective 'ecosystem' of X's thought) is close to Kauffman's \( ergodic \vdash noergodic \) $$reproducible \rightarrow ergodic$$ and if X represents core Kauffman's idea as : \( noergodic \vdash ergodic \Rightarrow physics \vdash biology / complex \)
then X can further enriched his concept of reproducibility:
\begin{array}{r c l}
noergodic \vdash ergodic & \Rightarrow & physics \vdash biology / complex \\
& \Rrightarrow & \\
noreproducible \vdash reproducible & \Rightarrow & physics \vdash biology / complex \\
\end{array}
So that X's concept of reproducibility allows X to create a link between his 'Heidegger's (thought) ecosystem' and his 'Kauffman's (thought) ecosystem' :
\begin{array}{r c l}
Heidegger & \Rrightarrow & Kauffman \\
& \rightarrow_4 & \\
norepro \vdash repro \Rightarrow philo \vdash science & \Rrightarrow & noergodic \vdash ergodic \Rightarrow bio/ complex \vdash physics
\end{array}
Obviously all X morphisms presented above are debatable. But the purpose of this example is to sketch a plausible (necessarily subjective) learning experience. The question is less to ask the objective reality of \( P = [Heidegger.science/Gestell \rightarrow X.reproducible] \) or \( P' = [reproducible \rightarrow ergodic] \) than to help X to be creative. Specifically, could it be possible to (automatically) suggest \( P \) to X ? \( P \) contribute to make X build a bridge between (his) Heidegger and (his) Kauffman through is repro concept : could this drive an Assistant algorithm to suggest \( P \) (and \( P' \) and so on) to X ?
Its not too much difficult to trace the path
\( Bergson \leadsto Whitehead \leadsto Wittgenstein \leadsto Kauffman \)
as Kauffman give (verly light) mention of Whitehead, and then if you google \( Whitehead \circ Kauffman \) you get
\( Whitehead \circ Kauffman \leadsto Shaviro \)
and Prof. Shaviro site give typically more plausible '\( \leadsto \)' genealogy as above (Bergson...)
But maybe X would have more interest in a (hidden) \( Heidegger \leadsto Kauffman \) story ?
Wednesday, 22 March 2017
Learning Fallacy II
In 'Learning Fallacy' LF we began the reflexion on the model / data duality :
a. what kind of data are relevant for my problem - i.e. am I not typically biased towards over-reducing/localising the problem ?
b. how much specific is my model - that is am I not typically biased towards overfiting, i.e. under-symmetrising my model ?
We call the corresponding heuristic :
a. Data Expansion
b. Large Symmetry
The data expansion heuristic is not a more-data-is-better tale. Here we are talking of perspective on 'reality' [recall that your reality is a work-in-progress...] : what kind of implicit (over-simplifying) hypothesis am I doing by leaving seemingly not relevant data ?
Ex a : We already mentioned the RFIM hypothesis on Finance, which precisely is considered to be relevant more broadly for social domain.
The transdisciplinary (or not) paradigm is one manifestation of the Data Expansion problem : a typical example is given in 'Natural language / neuro economics II'.
Ex b : recall the paradoxical behavior of Markowitz in FL : the Portfolio theoretician adopts a fully symmetrised approach for his skin-in-the-game private financial strategy...
'Learning as categorification IV' propose simple examples where symmetries are explicitly declared the essential part of the problem.
a. what kind of data are relevant for my problem - i.e. am I not typically biased towards over-reducing/localising the problem ?
b. how much specific is my model - that is am I not typically biased towards overfiting, i.e. under-symmetrising my model ?
We call the corresponding heuristic :
a. Data Expansion
b. Large Symmetry
The data expansion heuristic is not a more-data-is-better tale. Here we are talking of perspective on 'reality' [recall that your reality is a work-in-progress...] : what kind of implicit (over-simplifying) hypothesis am I doing by leaving seemingly not relevant data ?
Ex a : We already mentioned the RFIM hypothesis on Finance, which precisely is considered to be relevant more broadly for social domain.
The transdisciplinary (or not) paradigm is one manifestation of the Data Expansion problem : a typical example is given in 'Natural language / neuro economics II'.
Ex b : recall the paradoxical behavior of Markowitz in FL : the Portfolio theoretician adopts a fully symmetrised approach for his skin-in-the-game private financial strategy...
'Learning as categorification IV' propose simple examples where symmetries are explicitly declared the essential part of the problem.
Saturday, 11 March 2017
Natural language / neuro economics II
we had a first round over NL in the post NL / neuro economics [NLNE]. Curiously, at that time our (rapid) web foraging missed the important "faculty of language" Hauser et al. 2002 paper [FL]. We will go further in the subject with the 2016 Hauser Watumull 'UGF' and 2014 'On recusion' papers.
FL is interesting for us for two reasons :
a. it links to Learning Fallacy II [LF]
b. it links with NLNE and A Conceptual Representation CR
FL has a clear comparative approach, and its semantics fields builds on the Data Expandion DE Large Symmetry LS tradeoff of LF : 'compar' : 39, 'analog' : 10, 'homolog' 12, specif : 18, uniq : 30.
$$FL \rightarrow Data \,Expansion / Large \, Symmetry$$
In detail :
a. "We hypothesize that FLN only includes recursion and is the only uniquely human component of the faculty of language".
$$FL.animals \rightarrow DE $$"Although scholars interested in language evolution have often ignored comparative data altogether or focused narrowly on data from nonhuman primates, current thinking in neuroscience, molecular biology, and developmental biology indicates that many aspects of neural and developmental function are highly conserved, encouraging the extension of the comparative method to all vertebrates (and perhaps beyond) ."
"Although this line of reasoning may appear obvious, it is surprisingly common for a trait to be held up as uniquely human before any appropriate comparative data are available."
b. "We further argue that FLN may have evolved for reasons other than language, hence comparative studies might look for evidence of such computations outside of the domain of communication (for example, number, navigation, and social relations)."
"We consider the possibility that certain specific aspects of the faculty of language are “spandrels”—by-products of preexisting constraints rather than end products of a history of natural selection (39). This possibility, which opens the door to other empirical lines of inquiry, is perfectly compatible with our firm support of the adaptationist program. Indeed, it follows directly from the foundational notion that adaptation is an “onerous concept” to be invoked only when alternative explanations fail."$$FL.(bio)functions \rightarrow LS$$ in more detail:
$$communication, number, navigation, social \, relations \rightarrow FLN \\ \Rightarrow universal \, constraint \,(computational \, and \, biological) \\ \Rrightarrow LS $$ (it should be read recursively : \( [[x \rightarrow y] \Rightarrow z] \Rrightarrow u \)
This reasoning line dwells on the computational perspective of our NLNE: the problem of NL is a computational one, then a simplicity / creativity one, so essentially - as much as we learnt from Nature eons trial and error 'foraging', recursion is 'nearly optimal'. FL makes clear reference to the Minimalist program : "Recent work on FLN (4, 41–43) suggests the possibility that at least the narrow-syntactic component satisfies conditions of highly efficient computation to an extent previously unsuspected."
$$FL \rightarrow recursion$$
As already mentioned in NLNE, First Order Logic expressiveness is not enough, your need more 'deepness'. The 2-Cat concept in category theory is not proper neither for a conceptual representation, and CR is a tentative trial to a general Creative Assistant.
Friday, 17 February 2017
learning as categorification V
1. Much of what we have in mind – inside I mean, mind as a [private] room… - is what could be called unstructured data. Some people say: ‘mind is full of scorpions’… but more generally, memory is a fantastic recipient, a grimoire full of … mysteries. Γνῶθι σεαυτόν might be read : clean your mansionry. And getting older, it can only go from bad to worse: mind is a great hoarder. How tidying it up ?
2. we should be here bold and resolute, as any (young) theorician : build our own theory, that is classification
$$ (natsci / philo ... )theorician\quad \rightarrow \quad (private \quad real \quad life) \quad learner $$
classify means : you have an \( x \), an \( y \), and (boldly) draw
$$ x \rightarrow y $$
3. Easy ? This is a negative, most of the time…
\( y \) is not of the same nature as \( x \): \( y \) is a ‘symmetry’, \( x \) is some real life ‘object’ : anything from minimal experience to macro ontos.
\( x \) is well-known-from-me, something-I-m-not-indifferent-to : a personal experience, something-I-often-play-with. Even conceptual, \( x \) is concrete-to-me.
\( y \) is eventually some abstract concept, more symmetrical… somehow more simple – balancing this with abstraction - than any \( x \), so that the compression \( x \rightarrow y \) could be significant : our purpose is to make…room.
4. As pointed out by Brown and Porter, the all point is to move from a ‘concrete’ (to the learner at least) collection of \( x_{\omega} \) to some more abstract \( y \)
One path to do that is to find some explicit relations between these \( x_{\omega} \)
The classic example of ‘cardinality’, our \( y \), as in https://golem.ph.utexas.edu/category/2008/10/what_is_categorification.html, make explicit the isomorphism between any finite set. Somehow, any child did that at some point…
Abstracting the detailed structure of these \( x_{\omega} \) unveils the symmetry \( y \).
5. Paradoxically, (student) learning is a long trip to forget (art of explicit building of) isomorphisms and keeping only \( y \) in mind. But real (life) learning tends to be rather a never ending explicit building of morphisms as new \( x_{\omega} \) flow in your mind…
That is : you should enforce your learning to learn ability, that is the art to design new \( y \) and new → between (old and new) \( x_{\omega} \) and (old and new) \( y \)
Hopefully, the more you do it, the more you are good at it… Note that be good at doing something, having learned it, is not as be good at learning anything !...
2. we should be here bold and resolute, as any (young) theorician : build our own theory, that is classification
$$ (natsci / philo ... )theorician\quad \rightarrow \quad (private \quad real \quad life) \quad learner $$
classify means : you have an \( x \), an \( y \), and (boldly) draw
$$ x \rightarrow y $$
3. Easy ? This is a negative, most of the time…
\( y \) is not of the same nature as \( x \): \( y \) is a ‘symmetry’, \( x \) is some real life ‘object’ : anything from minimal experience to macro ontos.
\( x \) is well-known-from-me, something-I-m-not-indifferent-to : a personal experience, something-I-often-play-with. Even conceptual, \( x \) is concrete-to-me.
\( y \) is eventually some abstract concept, more symmetrical… somehow more simple – balancing this with abstraction - than any \( x \), so that the compression \( x \rightarrow y \) could be significant : our purpose is to make…room.
4. As pointed out by Brown and Porter, the all point is to move from a ‘concrete’ (to the learner at least) collection of \( x_{\omega} \) to some more abstract \( y \)
One path to do that is to find some explicit relations between these \( x_{\omega} \)
The classic example of ‘cardinality’, our \( y \), as in https://golem.ph.utexas.edu/category/2008/10/what_is_categorification.html, make explicit the isomorphism between any finite set. Somehow, any child did that at some point…
Abstracting the detailed structure of these \( x_{\omega} \) unveils the symmetry \( y \).
5. Paradoxically, (student) learning is a long trip to forget (art of explicit building of) isomorphisms and keeping only \( y \) in mind. But real (life) learning tends to be rather a never ending explicit building of morphisms as new \( x_{\omega} \) flow in your mind…
That is : you should enforce your learning to learn ability, that is the art to design new \( y \) and new → between (old and new) \( x_{\omega} \) and (old and new) \( y \)
Hopefully, the more you do it, the more you are good at it… Note that be good at doing something, having learned it, is not as be good at learning anything !...
Wednesday, 25 January 2017
Lean management categorification
A. \( LM \rightarrow \quad learning \)
It is surprising and very comforting to note that the very popular 'lean startup' by Eric Ries or the 'getting to plan B' by Mullins & Komisar (KM) demonstrates an obvious relationship between learning to learn (L2L) and lean management (LM)
$$ LM \rightarrow \quad learning $$
Maybe because entrepreneurs have essentially skin in the game , as should have all learner / modeler.
At the heart of lean management, there is the idea that the company is essentially a place of learning; let's count words:
Learn: 292
Know: 123
Problem: 177
Solv: 38
And precisely, a scientific process:
Hypotheses: 67
Assumption: 73
Theor: 31
Test: 206
Feedback: 86
Valid: 74
Experiment: 171
System: 139
Scien: 47
Fail: 132 (yes, failure is included in the scientific learning package!)
LM is the place of a surprising symmetry:
\begin{array}{r c l}
\ product & \quad & startup \\
\uparrow \quad \downarrow \quad & \rightarrow & \uparrow \quad \downarrow \quad \\
learning & \quad & customer \\
\end{array}
The traditional causality is: I learn to produce; LM puts forward : I produce to learn!
Fordism approach is in (product) push mode: Ford produces, the customer buys
LM is in (informational) pull mode: the startup learns from its customer
"The learning about how to build a sustainable business is the outcome of those experiments. For startups, that information is much more important than dollars, awards, or mentions in the press, because it can influence and reshape the next set of ideas. "
"For startups, the role of strategy is to help figure out the right questions to ask"
In detail, the functor LM → Learning is:
\begin{array}{r c l}
\ product & \quad & model \\
\uparrow \quad \downarrow \quad & \rightarrow & \uparrow \quad \downarrow \quad \\
customer & \quad & data \\
\end{array}
More precisely, everything is dynamic: at all times \( t \) LM seeks a minimum viable product, hence the correspondence
\begin{array}{r c l}
\ MVP_t & \rightarrow & model_t \\
\ customer_t & \rightarrow & data_t \\
\end{array}
In fact a set \( data_t \) of data is attached to \( MVP_t \) ( \( model_t \) ): this is the information available at \(t \)
B. Overfit, Regularization
The key to the endless process LM is what corresponds in ML to Active Learning: sequential acquisition of new data:
$$ Model_t → data_t → model_{t + 1} \rightarrow data_{t + 1} ...$$
or in the form of a cycle :
\begin{array}{r c l}
\ model & & \\
\ \downarrow \quad \uparrow & & \\
\ data & & \\
\end{array}
So what we have here is really a learning path
The model is at once:
a. A representation of the domain and,
b. A decision function that allows the exploration of the domain in order to acquire new data.
This learning diagram is similar to the Multi-Armed Bandit (MAB): at each \( t \), one decides which arm to operate, and one observes the reward.
a. Ex1: A / B testing protocol
b. Ex2: H&M in KM, different styles are tested almost simultaneously, and one favors the most successful.
Obviously exploration is expensive, and the whole question is to stay alive until the (relative) completion of the learning process ... this is where the concept of lean / waste (82 occurrences in the text) is looming.
Ries is particularly good at telling his own experience at IMVU. The whole pararagraph 'Talking to customers' is a piece of anthology, absolutely hilarious: the confrontation between the engineer and the 'seventeen-year-old girl' announces a tragi-comedy, and was for Ries the revelation that he has basically lost his time for 6 months! 'There's obviously something wrong', 'deal breaker', 'utterly / fundamentally flawed'...
Ries : 'Here's the question that bothered me most of all: if the goal of these months was to learn these important insights about customers, why did it take so long? How much of our effort contributed to the essential lessons we needed to learn? Could we have learned those lessons earlier if I had not been focused on making the product "better" by adding features and fixing bugs?
Here Ries has a seemingly surprising paragraph if one reads it from the coign of vantage of Statistical Learning: 'optimization versus learning'. In the context of statiscal learning, optimization is almost synonymous with learning.
In line with 'learning fallacy', I would say we have here a case of 'tree hiding the forest': the 6 months lost developing unnecessary features to IMVU, this is an example of over-optimization : This 'model' is demolished when confronting new data.
Carrying the metaphor / functor \( Lean \rightarrow Learn \) further, we get
$$ waste \rightarrow overfit$$
We can be tempted to talk about dynamic regularization: we are looking for the simplest and least expensive model (product) that 'fit' the data.
More precisely: if we calculate the difference between:
a. the ex-post reward \( r_t \): not only measurement of the product's suitability to customer, but more generally learning rate
b. and the ex-ante cost of R&D \(c_t \),
The regularization at \( t + 1 \) is done according to \( r_t - c_t \).
It is obviously advantageous for this measurement to be as continuous as possible: this is the key message of the LM: the increment of time, or cycle duration, must be as low as possible. 'The biggest advantage of working in small batches is that quality problems can be identified much sooner'.
The evaluation of \( r_t \) is anything but obvious. As Ries explains at length, growth or other 'vanity metrics' do not prove that \( r_t-c_t > 0 \). The 'actionable metrics' must make it possible to correctly evaluate \( r_t \), according to Ries.
Of course the LM approach gives no guaranty to converge before running out of cash!
C. symmetries?
But most notably, Ries gives no explicit method to guess the symmetries of the domain.
This part is entirely human black box, discretionary. Assumptions come from art, not science. 'As far as exploration is costless and continuous, you can explore randomly' seems to be the cartoon message of Ries. For example, in the case of Caroline at HP, nothing is said except 'testing'.
When Ries insists on metrics (or post analysis), in fact it is indeed representation, therefore symmetries fundamentally. For example, in the case of Grockit, the initial assumption itself is revised: 'In fact, over time, through dozens of tests, it became clear that the key to student engagement was to offer them a combination of social and solo features. Students preferred having a choice of how to study.'
But a fully symmetrized $$ Social \leftrightarrow solo $$
would have warned against a pure social approach.
Actually, we can argue that Ries gives tree heuristics to guess the symmetries:
a. The five whys has a strong flavor of hierarchical discovery, and in fact target (ground) symmetries.
b. Transfer learning: notably from manufacturing, and Toyota.
c. Catalog of Pivots:
Zoom-in / out
Customer segment (or need)
Value capture
Engine of growth
..
In all cases, Category Theory is closer : isn't "Pivot" a wonderful intuition of ... symmetry ?
Of course, MK's 'analogs and antilogs' is quite in line with Cat.
Incidentally, Ries gives examples of \( Learn * customer \), \( Learn *student \) actions without ever giving a model other than 'testing'. To give a single example, the \( social \leftrightarrow solo \) symmetry seems linked to concepts like mimicry (CF for example the recent theory of mirror neurons) on the one hand and to something as a need of intellectual order / Compression (CF the magical theory of creativity of Schmidhuber)
The statistical learning is: \( Learn * data \), and many methods exist.
But it is especially in the case of Sciences (Mathematics, Physics, Biology, ...) that the action
$$ S = Learn * phenomena $$
manifests oneself through a gigantic theoretical and empirical production.
If the action is \( Learn * Object \), then it seems interesting to learn the functor
$$ Learn * X \rightarrow S $$
whatever X is
In finance (and beyond in social science), the functor was formalized through the econophysics. To give an example: RFIM = Random Field Ising model is according to Bouchaud et al. a paradigm - i.e. a symmetry - plausible, CF eg "Crises and collective socio-economic phenomena: simple models and challenges"
Incidentally, the recent interest of physics for statistical learning (CF Mezard 'physics-statistics-and-information-the-defi-of-mass-data' in La Jaune et la Rouge, the Mallat site at ENS, "Learning as categorification III ", etc.) marks a re-symmetrization:
$$ S \leftrightarrow Learn * X $$
But as Mezard says: "Contrary to what is sometimes said, the irruption of massive data into the study of complex systems is not going to take the place of theory. It is always necessary and even more difficult to understand, analyze, and build a model, but the theorist can rely on new and powerful statistical tools. "
Conclusion: The Lean Management approach is motivated mainly by the constraint of profitability. This constraint, if it has the merit of bringing reflection (from the entrepreneur) back to (the objective observation of) reality, is essentially a transfer from the (~millenary) experimental method in sciences.
Why not to push this transfer / Categorification further ?
It is surprising and very comforting to note that the very popular 'lean startup' by Eric Ries or the 'getting to plan B' by Mullins & Komisar (KM) demonstrates an obvious relationship between learning to learn (L2L) and lean management (LM)
$$ LM \rightarrow \quad learning $$
Maybe because entrepreneurs have essentially skin in the game , as should have all learner / modeler.
At the heart of lean management, there is the idea that the company is essentially a place of learning; let's count words:
Learn: 292
Know: 123
Problem: 177
Solv: 38
And precisely, a scientific process:
Hypotheses: 67
Assumption: 73
Theor: 31
Test: 206
Feedback: 86
Valid: 74
Experiment: 171
System: 139
Scien: 47
Fail: 132 (yes, failure is included in the scientific learning package!)
LM is the place of a surprising symmetry:
\begin{array}{r c l}
\ product & \quad & startup \\
\uparrow \quad \downarrow \quad & \rightarrow & \uparrow \quad \downarrow \quad \\
learning & \quad & customer \\
\end{array}
The traditional causality is: I learn to produce; LM puts forward : I produce to learn!
Fordism approach is in (product) push mode: Ford produces, the customer buys
LM is in (informational) pull mode: the startup learns from its customer
"The learning about how to build a sustainable business is the outcome of those experiments. For startups, that information is much more important than dollars, awards, or mentions in the press, because it can influence and reshape the next set of ideas. "
"For startups, the role of strategy is to help figure out the right questions to ask"
In detail, the functor LM → Learning is:
\begin{array}{r c l}
\ product & \quad & model \\
\uparrow \quad \downarrow \quad & \rightarrow & \uparrow \quad \downarrow \quad \\
customer & \quad & data \\
\end{array}
More precisely, everything is dynamic: at all times \( t \) LM seeks a minimum viable product, hence the correspondence
\begin{array}{r c l}
\ MVP_t & \rightarrow & model_t \\
\ customer_t & \rightarrow & data_t \\
\end{array}
In fact a set \( data_t \) of data is attached to \( MVP_t \) ( \( model_t \) ): this is the information available at \(t \)
B. Overfit, Regularization
The key to the endless process LM is what corresponds in ML to Active Learning: sequential acquisition of new data:
$$ Model_t → data_t → model_{t + 1} \rightarrow data_{t + 1} ...$$
or in the form of a cycle :
\begin{array}{r c l}
\ model & & \\
\ \downarrow \quad \uparrow & & \\
\ data & & \\
\end{array}
So what we have here is really a learning path
The model is at once:
a. A representation of the domain and,
b. A decision function that allows the exploration of the domain in order to acquire new data.
This learning diagram is similar to the Multi-Armed Bandit (MAB): at each \( t \), one decides which arm to operate, and one observes the reward.
a. Ex1: A / B testing protocol
b. Ex2: H&M in KM, different styles are tested almost simultaneously, and one favors the most successful.
Obviously exploration is expensive, and the whole question is to stay alive until the (relative) completion of the learning process ... this is where the concept of lean / waste (82 occurrences in the text) is looming.
Ries is particularly good at telling his own experience at IMVU. The whole pararagraph 'Talking to customers' is a piece of anthology, absolutely hilarious: the confrontation between the engineer and the 'seventeen-year-old girl' announces a tragi-comedy, and was for Ries the revelation that he has basically lost his time for 6 months! 'There's obviously something wrong', 'deal breaker', 'utterly / fundamentally flawed'...
Ries : 'Here's the question that bothered me most of all: if the goal of these months was to learn these important insights about customers, why did it take so long? How much of our effort contributed to the essential lessons we needed to learn? Could we have learned those lessons earlier if I had not been focused on making the product "better" by adding features and fixing bugs?
Here Ries has a seemingly surprising paragraph if one reads it from the coign of vantage of Statistical Learning: 'optimization versus learning'. In the context of statiscal learning, optimization is almost synonymous with learning.
In line with 'learning fallacy', I would say we have here a case of 'tree hiding the forest': the 6 months lost developing unnecessary features to IMVU, this is an example of over-optimization : This 'model' is demolished when confronting new data.
Carrying the metaphor / functor \( Lean \rightarrow Learn \) further, we get
$$ waste \rightarrow overfit$$
We can be tempted to talk about dynamic regularization: we are looking for the simplest and least expensive model (product) that 'fit' the data.
More precisely: if we calculate the difference between:
a. the ex-post reward \( r_t \): not only measurement of the product's suitability to customer, but more generally learning rate
b. and the ex-ante cost of R&D \(c_t \),
The regularization at \( t + 1 \) is done according to \( r_t - c_t \).
It is obviously advantageous for this measurement to be as continuous as possible: this is the key message of the LM: the increment of time, or cycle duration, must be as low as possible. 'The biggest advantage of working in small batches is that quality problems can be identified much sooner'.
The evaluation of \( r_t \) is anything but obvious. As Ries explains at length, growth or other 'vanity metrics' do not prove that \( r_t-c_t > 0 \). The 'actionable metrics' must make it possible to correctly evaluate \( r_t \), according to Ries.
Of course the LM approach gives no guaranty to converge before running out of cash!
C. symmetries?
But most notably, Ries gives no explicit method to guess the symmetries of the domain.
This part is entirely human black box, discretionary. Assumptions come from art, not science. 'As far as exploration is costless and continuous, you can explore randomly' seems to be the cartoon message of Ries. For example, in the case of Caroline at HP, nothing is said except 'testing'.
When Ries insists on metrics (or post analysis), in fact it is indeed representation, therefore symmetries fundamentally. For example, in the case of Grockit, the initial assumption itself is revised: 'In fact, over time, through dozens of tests, it became clear that the key to student engagement was to offer them a combination of social and solo features. Students preferred having a choice of how to study.'
But a fully symmetrized $$ Social \leftrightarrow solo $$
would have warned against a pure social approach.
Actually, we can argue that Ries gives tree heuristics to guess the symmetries:
a. The five whys has a strong flavor of hierarchical discovery, and in fact target (ground) symmetries.
b. Transfer learning: notably from manufacturing, and Toyota.
c. Catalog of Pivots:
Zoom-in / out
Customer segment (or need)
Value capture
Engine of growth
..
In all cases, Category Theory is closer : isn't "Pivot" a wonderful intuition of ... symmetry ?
Of course, MK's 'analogs and antilogs' is quite in line with Cat.
Incidentally, Ries gives examples of \( Learn * customer \), \( Learn *student \) actions without ever giving a model other than 'testing'. To give a single example, the \( social \leftrightarrow solo \) symmetry seems linked to concepts like mimicry (CF for example the recent theory of mirror neurons) on the one hand and to something as a need of intellectual order / Compression (CF the magical theory of creativity of Schmidhuber)
The statistical learning is: \( Learn * data \), and many methods exist.
But it is especially in the case of Sciences (Mathematics, Physics, Biology, ...) that the action
$$ S = Learn * phenomena $$
manifests oneself through a gigantic theoretical and empirical production.
If the action is \( Learn * Object \), then it seems interesting to learn the functor
$$ Learn * X \rightarrow S $$
whatever X is
In finance (and beyond in social science), the functor was formalized through the econophysics. To give an example: RFIM = Random Field Ising model is according to Bouchaud et al. a paradigm - i.e. a symmetry - plausible, CF eg "Crises and collective socio-economic phenomena: simple models and challenges"
Incidentally, the recent interest of physics for statistical learning (CF Mezard 'physics-statistics-and-information-the-defi-of-mass-data' in La Jaune et la Rouge, the Mallat site at ENS, "Learning as categorification III ", etc.) marks a re-symmetrization:
$$ S \leftrightarrow Learn * X $$
But as Mezard says: "Contrary to what is sometimes said, the irruption of massive data into the study of complex systems is not going to take the place of theory. It is always necessary and even more difficult to understand, analyze, and build a model, but the theorist can rely on new and powerful statistical tools. "
Conclusion: The Lean Management approach is motivated mainly by the constraint of profitability. This constraint, if it has the merit of bringing reflection (from the entrepreneur) back to (the objective observation of) reality, is essentially a transfer from the (~millenary) experimental method in sciences.
Why not to push this transfer / Categorification further ?
Tuesday, 17 January 2017
No equilibrium theorem
1. in the classic "How markets slowly digest", Bouchaud et. al (B): "Then begins a kind of hide and seek game, where each side attempts to guess the available liquidity on the other side. A 'tit-for-tat' process then starts, whereby market orders trigger limit orders and limit orders attracts market orders ", 6.5.4
2. Incidentally, tit-for-tat (TT) refers to a strategy of the iterated PD (prisoner dilemma)
3. what can be the meaning of the looming of game theory GT within a paper at distance of Rational Equilibrium approach and critic of K85?
4. We can argue a methodological isomorphism between theoretical physics TP (Physics and learning) and GT
\begin{array}{r c l}
\ TP & \leftrightarrow & GT \\
(SO (3) / local / etc) \quad symmetries & \rightarrow & (infinite) \quad strategic \quad regress \\
\end{array}
5. See, for example, 'Rational interaction', 'game theory, symmetry, and scientific discovery', HW Brock
6. We would be tempted to conclude that B "fail to learn": he does not recognize the natural (theoretical) space of the domain he is studying, i.e. the symmetries of the domain
But GT suggests that "physical" dynamics have a good chance of lapsing in finance
7. In physics the causality \( F ^ i = m * a ^ i \) (or even the equations of the field in RG) establishes the causal link between force and acceleration
8. K is still in this paradigm: \( imb = 1 / λ * δp \) CF 'mm second law'
9. As is often the case with this type of article, equilibrium is obtained conditionally only by assumptions of implicit coordination that are not realistic (K explicitly excludes any form of manipulation, insider and mm assume the optimal strategy of other agents)
10. A natural framework is rather the PD: in a game of sharing P&L (= long term equilibrium), the two agents can play cooperation, ie a kind of à la Kyle equilibrium corresponding to a kind of average historical behavior of these Agents), or deviate significantly from them, fooling other expectations
11. More precisely, in K, the fundamental symmetry is written simply
\begin{array}{r c l}
\ & K & \\
mm & \rightarrow & insider \\
\end{array}
Mm and insider know all about one another, the reasoning rules are CK (common knowledge). They could reverse their respective roles, but they do not, symmetry is only valid in K(nowledge) and not in A(ct)
12. The literature on PD is considerable (and for good reason), but in iterated strategies such as TT or win-stay lose-switch appear not only theoretically (including in an evolutionary framework) but empirically observed (CF Axelrod 84, 'Evolutionary dynamics', Nowak)
13. Note that this takes place in a framework of payoff without any uncertainty: the matrix of the payoffs is perfectly known.
There is therefore no stake in learning a representation of the world
14. Projected in the framework of K, this amounts to saying that the representation (imb) is not an issue
On the other hand, \( \lambda \) can not be stable
And this non-stationarity is fundamental, in the sense that it results from the space symmetry of space (GT) space (finance)
In a GT frame, we now have a substitution in Act between mm and insider:
\begin{array}{r c l}
\ & K, A & \\
mm & \rightarrow & insider \\
\end{array}
The mm can mimic the insider, and reciprocally
2. Incidentally, tit-for-tat (TT) refers to a strategy of the iterated PD (prisoner dilemma)
3. what can be the meaning of the looming of game theory GT within a paper at distance of Rational Equilibrium approach and critic of K85?
4. We can argue a methodological isomorphism between theoretical physics TP (Physics and learning) and GT
\begin{array}{r c l}
\ TP & \leftrightarrow & GT \\
(SO (3) / local / etc) \quad symmetries & \rightarrow & (infinite) \quad strategic \quad regress \\
\end{array}
5. See, for example, 'Rational interaction', 'game theory, symmetry, and scientific discovery', HW Brock
6. We would be tempted to conclude that B "fail to learn": he does not recognize the natural (theoretical) space of the domain he is studying, i.e. the symmetries of the domain
But GT suggests that "physical" dynamics have a good chance of lapsing in finance
7. In physics the causality \( F ^ i = m * a ^ i \) (or even the equations of the field in RG) establishes the causal link between force and acceleration
8. K is still in this paradigm: \( imb = 1 / λ * δp \) CF 'mm second law'
9. As is often the case with this type of article, equilibrium is obtained conditionally only by assumptions of implicit coordination that are not realistic (K explicitly excludes any form of manipulation, insider and mm assume the optimal strategy of other agents)
10. A natural framework is rather the PD: in a game of sharing P&L (= long term equilibrium), the two agents can play cooperation, ie a kind of à la Kyle equilibrium corresponding to a kind of average historical behavior of these Agents), or deviate significantly from them, fooling other expectations
11. More precisely, in K, the fundamental symmetry is written simply
\begin{array}{r c l}
\ & K & \\
mm & \rightarrow & insider \\
\end{array}
Mm and insider know all about one another, the reasoning rules are CK (common knowledge). They could reverse their respective roles, but they do not, symmetry is only valid in K(nowledge) and not in A(ct)
12. The literature on PD is considerable (and for good reason), but in iterated strategies such as TT or win-stay lose-switch appear not only theoretically (including in an evolutionary framework) but empirically observed (CF Axelrod 84, 'Evolutionary dynamics', Nowak)
13. Note that this takes place in a framework of payoff without any uncertainty: the matrix of the payoffs is perfectly known.
There is therefore no stake in learning a representation of the world
14. Projected in the framework of K, this amounts to saying that the representation (imb) is not an issue
On the other hand, \( \lambda \) can not be stable
And this non-stationarity is fundamental, in the sense that it results from the space symmetry of space (GT) space (finance)
In a GT frame, we now have a substitution in Act between mm and insider:
\begin{array}{r c l}
\ & K, A & \\
mm & \rightarrow & insider \\
\end{array}
The mm can mimic the insider, and reciprocally
On agent-based models' symmetries
1. I see 4 questions on the methodology of agents-based models, emphasizing the MG: CF 'Minority Games', Challet, Marsili, Zhang
2. pb1: minority (for MG): why not a majority game?
CF 'the $ -game', Andersen, Sornette
3. pb2: rationality of agents? For example for MGs:
a. Basic MG: always active
b. Grand canonical MG: active or not, one single strategy, does not take into account its market impact
c. 'Nash' MG: takes into account his market impact, but does not reason on the presence of others
4. pb3: microstructure? For example for MGs:
a. basic MG: no producers, no market maker
b. evolved MG: producers, no market maker (but see 'the $ -game')
Econophysics have only been recently focused on microstructure (CF eg Farmer)
5. pb4: what is the right symmetry: unconscious (/ emergence / animal / ecology) or conscious (/ convention / human / economy) cooperation?
6. pb4 is perhaps the bottom line: if the market logic is the division between producer and speculator (in MG, or market maker in the $ -game), is it rational from these (types of ' ) Agents not to re-examine (periodically) the terms of partition?
If so, then the framework of analysis is - a conceptual notch above the ABM - that of the iterated PD: CF 'no equilibrium theorem'
7. the ecological approach, CF Farmer 'market force, ecology, and evolution' adopts a symmetry of physicist / biologist: no cross-speculation.
In the mainstream economic literature, a fortiori in the Game Theory, the symmetry 'infinite regress' is a basic axiom.
But even without assuming this 'difficult' faculty, the iterated prisoner dilemma approach, which falls well within the bounded rationality category (H Simon), goes in the direction of a consciousness of the agents of the strategic essence of the game.
8. In the 'insider / market impact' dialogue, the non-cooperative behaviors are
a. Insider: market impact ++
b. Market maker: front-running
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