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
