"We proved that for a general network stochastic process, the causal neighbors of a given node is exactly the minimal set of nodes that maximizes Causation Entropy, a key result which we refer to as the Optimal Causation Entropy Principle. Based on this principle, we introduced an algorithm for causal network inference called Optimal CSE, which utilizes two algorithms to jointly infer the set of causal neighbors of each node."
Hmm is right. Sounds all very cellular automata'ish to me. Maybe we should go NKS and run some reaction diffusion on that entropy graph. What should we reaction diffuse the entropy with? Or maybe the reaction diffusion can generate the causal nodes... or is actually the causation inference. To sum it up - using multicomponent reaction diffusion automata on sparse stochastic processes graph using Optimal CSE this can generate causation inference patterns which can then be extracted and compared with ones decompressed out of the KB for further prediction processes. Unless somehow the Hamming distance or the compression distance, the normalized compression distance NCD/NCCD from the extracted causation inference patterns to the KB patterns can be minimized so that the cross-transformation compression is reduced...like Jim Bromer was trying to so... OR you reaction diffuse the new patterns INTO the graph... to generate more causal nodes for future inference hmmm! John > -----Original Message----- > From: Ben Goertzel via AGI [mailto:[email protected]] > > Hmmm. > > This paper derives entropy-based criteria for causal inference, by tweaking > some causal Bayes net math... interesting... > > http://arxiv.org/pdf/1407.2256.pdf > > This paper defines a notion of Causation Entropy > > http://arxiv.org/pdf/1401.7574.pdf > > and derives some nice theorems about it, but their analytical methods are > only applicable when you have lots of high quality time series data > > -- ben > > > On Wed, Nov 26, 2014 at 4:31 PM, Ben Goertzel <[email protected]> wrote: > > Interesting -- these guys use some mutual information methods for > > guessing the direction of causation from the (non-temporal) expression > > data, as described in equations 3 and 4 of > > > > > http://www.clopinet.com/isabelle/Projects/NIPS2008/factsheets/LOCANET_ > > OlsenFactsheet.pdf > > > > and this poster > > > > http://www.ulb.ac.be/di/map/colsen/poster.pdf > > > > Of course, their analysis is mathematically based on assumptions that > > aren't generally true, > > > > " > > (a) causal sufficiency,(b) causal Markov and (c) faithfulness > > assumptions " > > > > (see http://mlg.eng.cam.ac.uk/zoubin/SALD/Intro-Causal.pdf for > > interpretation of these) ... > > > > but that's usually going to be true for any pragmatic computational > method... > > > > -- ben > > > > > > On Wed, Nov 26, 2014 at 12:34 PM, Ben Goertzel <[email protected]> > wrote: > >> (half-baked brainstorming below, beware.... What I'm musing about is > >> how to guess the causal direction of a correlation based on > >> non-temporal data...) > >> > >>> I've been re-reading this nice old paper on the foundations of the > Second Law.. > >>> > >>> http://necsi.edu/projects/baranger/cce.pdf > >> > >> It's a physics-y paper but I think one can apply it to AGI with some > >> appropriate set-up > >> > >> The key thing that Baranger's arguments show there is that -- Within > >> the view of a coarse-graining observer (one whose precision of > >> observation is much less than the precision of the universe he's > >> observing), it's more likely for > >> > >> -- two states that seemed the same at time T, to seem different at > >> time T+1 > >> > >> than for > >> > >> -- two states that seemed different at time T, to seem the same at > >> time T+1 > >> > >> (this is for an arbitrary trajectory in a conservative dynamical > >> system, blabla...) > >> > >> Now, suppose we apply this reasoning (hands waving kinda wildly) to a > >> space of **situations** in some universe. Each point in the state > >> space is a certain situation. A trajectory in the state space is a > >> series of situations, e.g. the series of situations encountered by > >> some agent. Suppose that the trajectories of situations encountered > >> by agents, when plotted in situation-space, are complex and > >> fractal-looking like the ones in Baranger's paper. Each agent may be > >> associated with a probability distribution over trajectories (the > >> possible histories it experiences). > >> > >> A possible commonsensical cause or effect like "rain" or "dark", in > >> this framework, corresponds to a set of situations (e.g. the > >> situations involving rain). Thus it corresponds to a certain region > >> in the situation space. Let's call these "event-sets". Each point > >> on a trajectory through situation-space is going to pass through > >> various event-sets. > >> > >> To say what it means for one event-set to cause another, relative to > >> a certain set of trajectories (or probability distribution over > >> trajectories), we can use the definitions from Luke Glynn's paper > >> http://philsci-archive.pitt.edu/9729/1/Website_Version_2.pdf > >> > >> What Baranger's line of argument (via which he derives the Second > >> Law) suggests is that overall > >> > >> -- same cause, different effects > >> > >> is more likely than > >> > >> -- different cause, same effects > >> > >> This is because "same cause, different effects" means "two different > >> situations, which are put into the same event-set by the observer, > >> lead to two different situations, which are put into different > >> event-sets by the observer", etc. > >> > >> Since event-sets are regions of situation-space, and generally > >> (because of the coarse-graining observer) an earlier time-point on a > >> trajectory is going to be less spread-out through situation-space > >> than a later time-point on the same trajectory --- therefore the > >> cause is likely to be less spread-out than the effect. > >> > >> Thus overall we might conclude: given a pair of event-sets (X,Y) > >> that are correlated (meaning e.g. that there is mutual information > >> between the distribution of particular events within category X, and > >> the distribution of particular events within category Y), > >> > >> -- the one with greater spread (i.e. the greatest differentiation, > >> i.e. the greatest entropy, among the different particular situations > >> in the event-set) is more likely to be in the future... > >> > >> The basic idea is: if event-categories X and event-categories Y are > >> sufficiently correlated that it seems likely one of > >> > >> A) The states of the universe corresponding to observation of X tend > >> to causally affect the states of the universe corresponding to > >> observation of Y [within the assumed set of trajectories along which > >> causation is being estimated] > >> > >> or > >> > >> B) The states of the universe corresponding to observation of Y tend > >> to causally affect the states of the universe corresponding to > >> observation of X [within the assumed set of trajectories along which > >> causation is being estimated] > >> > >> then, to choose between X and Y, on the average we will guess right > >> more often if we assume the lower-entropy one of X and Y is the cause > >> and the higher-entropy one is the effect ... > >> > >> So according to this way of thinking, the asymmetry required in > >> Glynn's analysis of causality could potentially be taken as entropy > >> rather than time... > >> > >> maybe ;) > >> > >> -- Ben > > > > > > > > -- > > Ben Goertzel, PhD > > http://goertzel.org > > > > "The reasonable man adapts himself to the world: the unreasonable one > > persists in trying to adapt the world to himself. Therefore all > > progress depends on the unreasonable man." -- George Bernard Shaw > > > > -- > Ben Goertzel, PhD > http://goertzel.org > > "The reasonable man adapts himself to the world: the unreasonable one > persists in trying to adapt the world to himself. Therefore all progress > depends on the unreasonable man." -- George Bernard Shaw > > ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
