November 2018 - SIPTA News - lists.sipta.org

Re: [SIPTA] Fwd: Are there imprecise analogues of pseudo-random number generators?

by Gert De Cooman

Dear Marshall I refer to our paper about imprecise randomness (Computable randomness is inherently imprecise, De Cooman and De Bock) in the latest ISIPTA proceedings: https://biblio.ugent.be/publication/8531435/file/8531437.pdf In the paper we show that non-stationarity is indeed a source of imprecise randomness. We also prove a number of convergence results. All this for sequences of 0-1, which is the simplest case. We show, for instance, that alternating between a two un-fair coins with probabilities p and q for heads (in a deterministic fashion) will produce an imprecise random sequence of 0’s and 1’s with characterising probability interval [p,q]. The meaning of this is explained in the paper, but the underlying idea is that anyone using an interval betting model that does not include [p,q] - so for instance a precise r in this interval - can be made to lose an infinite amount of money in an infinite sequence of betting events on the digits in the sequence (using a computable strategy); and anywhere who uses a betting model that includes [p,q] is immune to such computable strategies. So this suggests an algorithm in the more general case: use an algorithm that visits the externe points of a credal set deterministically (eg, cyclically) , and for each visit to an extreme point, use the corresponding random generator to generate an outcome. Whether this also works in the case of more than two possible outcomes, still remains to be investigated, however. Best wishes, Gert > Op 13 nov. 2018, om 16:33 heeft Alessandro Antonucci <alessandro(a)idsia.ch> het volgende geschreven: > > Dear Marshall, > > For an imprecise subjectivist “the imprecision is in the eye of the > learner”. A non-stationary RNG can jump from one sampling distribution > to another but, again, this is done according to another > (second-order) distribution. The sample will be indistinguishable from > another one sampled from the marginal of that hierarchical model. The > imprecision level is basically a parameter of your learning algorithm > (e.g., s for the IDM, alpha for likelihood-based approachs), but not > something you might learn from your data. > > These are my two cents. > > Bests, > Alessandro > _________________________________ > > Alessandro Antonucci > IDSIA > Dalle Molle Institute > for Artificial Intelligence > Via Cantonale (Galleria 2) > CH-6928, Manno-Lugano, CH > > mail: alessandro(a)idsia.ch > skype: alessandro.antonucci > tel: +41 916108515 > web: www.idsia.ch/~alessandro > _________________________________ > > > ---------- Forwarded message --------- > From: Michael Smithson <Michael.Smithson(a)anu.edu.au> > Date: mar 13 nov 2018 alle ore 14:55 > Subject: Re: [SIPTA] Are there imprecise analogues of pseudo-random > number generators? > To: <alessandro.antonucci(a)gmail.com> > > > Hi Marshall, > > It isn't clear to me what you want the long-run state to be. Do you > want p(1) to settle down to having, say, a uniform distribution on > [.6,.8]? Or for the relative frequency of 1's to end up strictly > confined between .6 and .8? Or are you thinking of having p(1) fixed > at .7 and some other random variable controlling the interval width > around .7 that eventually settles on a width of .2? Or ... ? > > Kind regards, > > --Mike > > ________________________________ > From: SIPTA <sipta-bounces(a)idsia.ch> on behalf of Abrams, Marshall > <mabrams(a)uab.edu> > Sent: Tuesday, 13 November 2018 3:18:37 PM > To: sipta(a)idsia.ch > Subject: [SIPTA] Are there imprecise analogues of pseudo-random number > generators? > > I would like to ask a theoretical and practical question. (No > conference announcement here!) > > tl;dr: Are there imprecise analogues of pseudo-random number generators? > > If that question doesn't make sense, please feel free to read on, with > my thanks for doing so. (Sorry the following is so long; I was worried > that what I was asking would be unclear otherwise.) > > I am interested in imprecise chance, that is, objective imprecise > probability; this idea has been discussed in different ways by > Terrence Fine and his colleagues, Marco Cattaneo, Luke Glynn, Alan > Hajek, Suppes and Zanotti, Stephan Hartmann, Igor Gorban, and probably > others. > > In an agent-based model, (precise) chance can be modeled using a PRNG. > Can this be generalized to base an ABM on a model of imprecise chance? > I had thought this would be impossible, but now I am not so sure. A > good PRNG such as a Mersenne Twister is of course not truly chancy, > and its output even has low Kolmogorov complexity, but it's still a > good way to model chance in many contexts. Why couldn't imprecise > chance be modeled in an ABM using a deterministic algorithm as well? > > What would the output of a pseudo imprecise random number generator > (PIRNG) look like? > > Well, suppose one wrote a function that used a normal PRNG to generate > 0's and 1's with probability 0.7 for 1. Then over most large sets of > outputs, we would find the frequency of 1 to be close to 0.7, and as > we increased the size of such a set, the frequency would usually get > closer to 0.7 > > Similarly, using a PIRNG, one ought to be able to write a function > that generates 0's and 1's with (for example) an interval probability > of [0.6, 0.8] for 1. Then over most large lets of outputs, the > frequency of 1 should lie in or near [0.6, 0.8], and as we increased > the size of such a set, the frequency would remain near [0.6, 0.8] but > would usually wander without settling down to any precise value within > that interval. > > Are there known algorithms that might have this kind of behavior? Or > could this kind of behavior be simulated using PRNGs for sequences > that are not extremely long? i.e. maybe one can write a function > using a PRNG such that over the not-too-long-run, sequences would > appear to be imprecisely chancy, but they would eventually settle down > to precise values in the very very long run. That might be good > enough for some ABMs. > > Or am I just confused? (I think this is not unlikely.) > > Any suggestions about what sort of literature I should look at or what > kinds of keywords to search on would be welcome. > > [In some parts of Fierens, Rego, and Fine's "A frequentist > understanding of sets of measures" (2009), it sounds as if such a > class of algorithms might be described, at least in a loose, general > way, but if that is so, I have not understood the article well enough > to see how what's given there does so. Their model uses sequence > specified to be of intermediate Kolmogorov complexity, which itself > seems like a difficult thing to generate.] > > > Thank you! > > Marshall > > > Marshall Abrams, Associate Professor > Department of Philosophy, University of Alabama at Birmingham > Email: mabrams(a)uab.edu; Phone: (205) 996-7483; Fax: (205) 975-6610 > Mail: HB 414A, 900 13th Street South, Birmingham, AL 35294-1260; Office: HB 418 > Website: http://members.logical.net/~marshall > > _______________________________________________ > SIPTA mailing list > SIPTA(a)idsia.ch > http://mailman2.ti-edu.ch/mailman/listinfo/sipta > _______________________________________________ > SIPTA mailing list > SIPTA(a)idsia.ch > http://mailman2.ti-edu.ch/mailman/listinfo/sipta

Nov. 13, 2018

[SIPTA] Fwd: Are there imprecise analogues of pseudo-random number generators?

by Alessandro Antonucci

Dear Marshall, For an imprecise subjectivist “the imprecision is in the eye of the learner”. A non-stationary RNG can jump from one sampling distribution to another but, again, this is done according to another (second-order) distribution. The sample will be indistinguishable from another one sampled from the marginal of that hierarchical model. The imprecision level is basically a parameter of your learning algorithm (e.g., s for the IDM, alpha for likelihood-based approachs), but not something you might learn from your data. These are my two cents. Bests, Alessandro _________________________________ Alessandro Antonucci IDSIA Dalle Molle Institute for Artificial Intelligence Via Cantonale (Galleria 2) CH-6928, Manno-Lugano, CH mail: alessandro(a)idsia.ch skype: alessandro.antonucci tel: +41 916108515 web: www.idsia.ch/~alessandro _________________________________ ---------- Forwarded message --------- From: Michael Smithson <Michael.Smithson(a)anu.edu.au> Date: mar 13 nov 2018 alle ore 14:55 Subject: Re: [SIPTA] Are there imprecise analogues of pseudo-random number generators? To: <alessandro.antonucci(a)gmail.com> Hi Marshall, It isn't clear to me what you want the long-run state to be. Do you want p(1) to settle down to having, say, a uniform distribution on [.6,.8]? Or for the relative frequency of 1's to end up strictly confined between .6 and .8? Or are you thinking of having p(1) fixed at .7 and some other random variable controlling the interval width around .7 that eventually settles on a width of .2? Or ... ? Kind regards, --Mike ________________________________ From: SIPTA <sipta-bounces(a)idsia.ch> on behalf of Abrams, Marshall <mabrams(a)uab.edu> Sent: Tuesday, 13 November 2018 3:18:37 PM To: sipta(a)idsia.ch Subject: [SIPTA] Are there imprecise analogues of pseudo-random number generators? I would like to ask a theoretical and practical question. (No conference announcement here!) tl;dr: Are there imprecise analogues of pseudo-random number generators? If that question doesn't make sense, please feel free to read on, with my thanks for doing so. (Sorry the following is so long; I was worried that what I was asking would be unclear otherwise.) I am interested in imprecise chance, that is, objective imprecise probability; this idea has been discussed in different ways by Terrence Fine and his colleagues, Marco Cattaneo, Luke Glynn, Alan Hajek, Suppes and Zanotti, Stephan Hartmann, Igor Gorban, and probably others. In an agent-based model, (precise) chance can be modeled using a PRNG. Can this be generalized to base an ABM on a model of imprecise chance? I had thought this would be impossible, but now I am not so sure. A good PRNG such as a Mersenne Twister is of course not truly chancy, and its output even has low Kolmogorov complexity, but it's still a good way to model chance in many contexts. Why couldn't imprecise chance be modeled in an ABM using a deterministic algorithm as well? What would the output of a pseudo imprecise random number generator (PIRNG) look like? Well, suppose one wrote a function that used a normal PRNG to generate 0's and 1's with probability 0.7 for 1. Then over most large sets of outputs, we would find the frequency of 1 to be close to 0.7, and as we increased the size of such a set, the frequency would usually get closer to 0.7 Similarly, using a PIRNG, one ought to be able to write a function that generates 0's and 1's with (for example) an interval probability of [0.6, 0.8] for 1. Then over most large lets of outputs, the frequency of 1 should lie in or near [0.6, 0.8], and as we increased the size of such a set, the frequency would remain near [0.6, 0.8] but would usually wander without settling down to any precise value within that interval. Are there known algorithms that might have this kind of behavior? Or could this kind of behavior be simulated using PRNGs for sequences that are not extremely long? i.e. maybe one can write a function using a PRNG such that over the not-too-long-run, sequences would appear to be imprecisely chancy, but they would eventually settle down to precise values in the very very long run. That might be good enough for some ABMs. Or am I just confused? (I think this is not unlikely.) Any suggestions about what sort of literature I should look at or what kinds of keywords to search on would be welcome. [In some parts of Fierens, Rego, and Fine's "A frequentist understanding of sets of measures" (2009), it sounds as if such a class of algorithms might be described, at least in a loose, general way, but if that is so, I have not understood the article well enough to see how what's given there does so. Their model uses sequence specified to be of intermediate Kolmogorov complexity, which itself seems like a difficult thing to generate.] Thank you! Marshall Marshall Abrams, Associate Professor Department of Philosophy, University of Alabama at Birmingham Email: mabrams(a)uab.edu; Phone: (205) 996-7483; Fax: (205) 975-6610 Mail: HB 414A, 900 13th Street South, Birmingham, AL 35294-1260; Office: HB 418 Website: http://members.logical.net/~marshall _______________________________________________ SIPTA mailing list SIPTA(a)idsia.ch http://mailman2.ti-edu.ch/mailman/listinfo/sipta

Nov. 13, 2018

Re: [SIPTA] Are there imprecise analogues of pseudo-random number generators?

by Professor Bickis

Hello Marshall: I think I understand what you are looking for. The law of large numbers says that with probability one, a sequence of i.i.d. random bits will settle down to a relative frequency corresponding to the probability of a 1. i.e., the lim sup and the lim inf of the relative frequency would both converge to the same number. What you are looking for is a generator of a sequence in which the lim sup is (e.g.) 0.8 and the lim inf is 0.6. Certainly such sequences exist, and with some ingenuity one could construct a way of generating such sequences. However, I am skeptical about what kind of probabilistic interpretation could be given to them, considering what the law of large numbers says. I imagine you would have to build in some kind of memory to the process, violating the independence of the trials. The obvious trick would be to vary the underlying probability that generates the sequence, but I don’t that would work. The relative frequency would just settle down to the average of the probabilities. My understanding of imprecise probability is that it is purely epistemic, but I note that you reference a (relatively) recent paper by Fine et al. about objective imprecise probability. I’ll have to look that up. These are just my immediate thoughts. It is an interesting theoretical question. I am not quite clear about what the application might be. Just an afterthought. There is a concept in analysis called “almost periodic sequences”, which are related to the phenomenon of quasi-crystals, and things like Penrose tilings. I don’t know much about these, but there may be a connection. Mik Bickis Professor Emeritus Department of Mathematics and Statistics University of Saskatchewan > On Nov 13, 2018, at 06:34 AM, Michael Smithson <Michael.Smithson(a)anu.edu.au> wrote: > > Hi Marshall, > It isn't clear to me what you want the long-run state to be. Do you want p(1) to settle down to having, say, a uniform distribution on [.6,.8]? Or for the relative frequency of 1's to end up strictly confined between .6 and .8? Or are you thinking of having p(1) fixed at .7 and some other random variable controlling the interval width around .7 that eventually settles on a width of .2? Or ... ? > Kind regards, > --Mike > From: SIPTA <sipta-bounces(a)idsia.ch> on behalf of Abrams, Marshall <mabrams(a)uab.edu> > Sent: Tuesday, 13 November 2018 3:18:37 PM > To: sipta(a)idsia.ch > Subject: [SIPTA] Are there imprecise analogues of pseudo-random number generators? > > I would like to ask a theoretical and practical question. (No conference announcement here!) > > tl;dr: Are there imprecise analogues of pseudo-random number generators? > > If that question doesn't make sense, please feel free to read on, with my thanks for doing so. (Sorry the following is so long; I was worried that what I was asking would be unclear otherwise.) > > I am interested in imprecise chance, that is, objective imprecise probability; this idea has been discussed in different ways by Terrence Fine and his colleagues, Marco Cattaneo, Luke Glynn, Alan Hajek, Suppes and Zanotti, Stephan Hartmann, Igor Gorban, and probably others. > > In an agent-based model, (precise) chance can be modeled using a PRNG. Can this be generalized to base an ABM on a model of imprecise chance? I had thought this would be impossible, but now I am not so sure. A good PRNG such as a Mersenne Twister is of course not truly chancy, and its output even has low Kolmogorov complexity, but it's still a good way to model chance in many contexts. Why couldn't imprecise chance be modeled in an ABM using a deterministic algorithm as well? > > What would the output of a pseudo imprecise random number generator (PIRNG) look like? > > Well, suppose one wrote a function that used a normal PRNG to generate 0's and 1's with probability 0.7 for 1. Then over most large sets of outputs, we would find the frequency of 1 to be close to 0.7, and as we increased the size of such a set, the frequency would usually get closer to 0.7 > > Similarly, using a PIRNG, one ought to be able to write a function that generates 0's and 1's with (for example) an interval probability of [0.6, 0.8] for 1. Then over most large lets of outputs, the frequency of 1 should lie in or near [0.6, 0.8], and as we increased the size of such a set, the frequency would remain near [0.6, 0.8] but would usually wander without settling down to any precise value within that interval. > > Are there known algorithms that might have this kind of behavior? Or could this kind of behavior be simulated using PRNGs for sequences that are not extremely long? i.e. maybe one can write a function using a PRNG such that over the not-too-long-run, sequences would appear to be imprecisely chancy, but they would eventually settle down to precise values in the very very long run. That might be good enough for some ABMs. > > Or am I just confused? (I think this is not unlikely.) > > Any suggestions about what sort of literature I should look at or what kinds of keywords to search on would be welcome. > > [In some parts of Fierens, Rego, and Fine's "A frequentist understanding of sets of measures" (2009), it sounds as if such a class of algorithms might be described, at least in a loose, general way, but if that is so, I have not understood the article well enough to see how what's given there does so. Their model uses sequence specified to be of intermediate Kolmogorov complexity, which itself seems like a difficult thing to generate.] > > > Thank you! > > Marshall > > > Marshall Abrams, Associate Professor > Department of Philosophy, University of Alabama at Birmingham > Email: mabrams(a)uab.edu; Phone: (205) 996-7483; Fax: (205) 975-6610 > Mail: HB 414A, 900 13th Street South, Birmingham, AL 35294-1260; Office: HB 418 > Website: http://members.logical.net/~marshall > > _______________________________________________ > SIPTA mailing list > SIPTA(a)idsia.ch > http://mailman2.ti-edu.ch/mailman/listinfo/sipta

Nov. 13, 2018

Re: [SIPTA] Are there imprecise analogues of pseudo-random number generators?

by Michael Smithson

Nov. 13, 2018

[SIPTA] AlCoB 2019: 1st call for papers

by IRDTA

Nov. 13, 2018

[SIPTA] Are there imprecise analogues of pseudo-random number generators?

by Abrams

Nov. 13, 2018

[SIPTA] FW: EUSFLAT 2019 - Call for papers

by Kreinovich

Nov. 10, 2018

[SIPTA] FW: open position in computational science

by Kreinovich

Nov. 8, 2018

[SIPTA] 2018 Lotfi A. Zadeh Pioneer Award

by Kreinovich

Dear Friends, I have just learned that Ronald R. Yager was aearded the 2018 Lotfi A. Zadeh Pioneer Award from the IEEE Systems, Man, and Cybernetics Society. The award is given to honor a person with outstanding and pioneering contributions to academic and/or industrial research in systems science and engineering, human-machine systems, and/or cybernetics. Dr. Yager is a pioneer in many areas of fuzzy research. He also had published several pioneering seminal papers on interval-valued probabilities and other imprecise probability topics. Congratulations to Dr. Yager!

Nov. 7, 2018

[SIPTA] [UR @ FLAIRS 32] CALL FOR PAPERS

by Alessandro Antonucci

*** Apologies for multiple postings *** Special Track on Uncertain Reasoning at Flairs 32 - Call for Papers Special Track on Uncertain Reasoning at the 32nd Florida Artificial Intelligence Research Society Conference (FLAIRS-32) May 19-22, 2019 - Sarasota, Florida (US) Paper submission deadline: November 19, 2018 Conference website: http://www.flairs-32.info Special track website: http://w3.uqo.ca/allimo01/UR_2019/ur19.html ::: Call for Papers ::: Many problems in AI (in reasoning, planning, learning, perception and robotics) require the agent to operate with incomplete or uncertain information. The objective of this track is to present and discuss a broad and diverse range of current work on uncertain reasoning, including theoretical and applied research based on different paradigms. We hope that the variety and richness of this track will help to promote cross fertilization among the different approaches for uncertain reasoning, and in this way foster the development of new ideas and paradigms. The Special Track on Uncertain Reasoning (UR) is the oldest track in FLAIRS conferences, running annually since 1996. The UR '19 Special Track at the 32nd International Florida Artificial Intelligence Research Society Conference (FLAIRS-32) is the 24th in the series. Like the past tracks, UR'19 seeks to bring together researchers working on broad issues related to reasoning under uncertainty. Papers on all aspects of uncertain reasoning are invited. Papers of particular interest include, but are not limited to: - Uncertain reasoning formalisms, calculi and methodologies - Reasoning with probability, possibility, fuzzy logic, belief function, vagueness, granularity, rough sets, and probability logics - Modeling and reasoning using imprecise and indeterminate information, such as: Choquet capacities, comparative orderings, convex sets of measures, and interval-valued probabilities - Exact, approximate and qualitative uncertain reasoning - Inference and learning with graphical models of uncertainty (e.g., Bayesian networks) - Multi-agent uncertain reasoning and decision making - Decision-theoretic planning and Markov decision process - Temporal reasoning and uncertainty; nonmonotonic reasoning; similarity-based reasoning - Conditional logics, description logic, logic programming - Argumentation - Belief change and merging - Construction of models from elicitation, data mining and knowledge discovery - Uncertain reasoning in information retrieval, filtering, fusion, diagnosis, prediction, situation assessment - Uncertain reasoning in data management - Practical applications of uncertain reasoning (e.g., machine learning, computer vision and animation) All accepted papers will be published as FLAIRS proceedings by AAAI Press. A special issue of an international journal will be devoted to extended versions of the top papers at the track. ::: Program Committee ::: : Track Chairs : - Mohand Said Allili (University of Quebec in Outaouais, Canada) - Alessandro Antonucci (IDSIA, Switzerland) - Salem Benferhat (University of Artois, France) : PC Members : - Ofer Arieli (The Academic College of Tel-Aviv, Israel) - Nizar Bouguila (Concordia University, Canada) - Cory Butz (University of Regina, Canada) - Ameur Bensefia (Higher Colleges of Technology, UAE) - Martine Ceberio (University of Texas at El Paso, US) - Sebastien Destercke (University of Technology of Compiègne, France) - Love Ekenberg (Stockholm University, Sweden) - Lluis Godo (Spanish National Research Council, Spain) - Christophe Gonzales (LIP6, France) - Ilyes Jenhani (Prince Mohammad Bin Fahd University, Saudi Arabia) - Amanda Hicks (University of Florida, US) - Sedki Karima (University of Paris 13, France) - Gabriele Kern-Isberner (Technical University of Dortmund, Germany) - Vladik Kreinovich (University of Texas at El Paso, US) - Rafael Peñaloza (Free University of Bozen-Bolzano, Italy) - Philippe Leray (University of Nantes, France) - Lalintha G. Polpitiya (University of Miami, US) - Choh Man Teng (Institute for Human and Machine Cognition, US) - Steven Schockaert (Cardiff University, UK) - Karim Tabia (Artois University, France) - Barbara Vantaggi (Sapienza University of Rome, Italy) - Ronald Yager (Iona College, USA) ::: Other Information ::: FLAIRS 32 will be held in Sarasota, Florida. Additional information on the conference location and travel planning can be found here. Feel free to write the organizers (alessandro(a)idsia.ch or MohandSaid.allili(a)uqo.ca) for any further information about the special track. ::: Submission ::: Interested authors should format their papers according to AAAI formatting guidelines. The papers should be original work (i.e., not submitted, in submission, or submitted to another conference while in review). Papers should not exceed 6 pages (4 pages for a poster) and are due by November 19, 2018. For FLAIRS-32, the 2019 conference, the reviewing is a double blind process. Author names and affiliations must be omitted on submitted papers to provide double-blind reviewing. The papers will be reviewed by at least three reviewers. Papers must be submitted as PDF through the EasyChair conference system, which can also be accessed through the main conference web site. Authors should indicate the special track "Uncertain Reasoning" for submissions. The proceedings of FLAIRS-32 will be published by the AAAI. Authors of accepted papers will be required to sign a form transferring copyright of their contribution to AAAI. At least one author of each accepted paper is required to register, attend, and present the paper at FLAIRS-32. _________________________________ Alessandro Antonucci IDSIA Dalle Molle Institute for Artificial Intelligence Via Cantonale (Galleria 2) CH-6928, Manno-Lugano, CH mail: alessandro(a)idsia.ch web: www.idsia.ch/~alessandro _________________________________

Nov. 5, 2018