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Noncomputable Conditional Distributions

Nathanael L. Ackerman, Cameron E. Freer, Daniel M. Roy
2011 2011 IEEE 26th Annual Symposium on Logic in Computer Science  
We prove several results giving general conditions under which conditional distributions are computable.  ...  In the discrete or dominated setting, under suitable computability hypotheses, conditional distributions are computable.  ...  We demonstrate why this is the case, by showing that there are computable joint distributions with noncomputable conditional distributions.  ... 
doi:10.1109/lics.2011.49 dblp:conf/lics/AckermanFR11 fatcat:2ak7ck55e5c2vii3oco3z7so44

The Redundancy of a Computable Code on a Noncomputable Distribution [article]

Łukasz Dębowski
2009 arXiv   pre-print
Typically for mathematical statistics, P is noncomputable (in the absolute sense).  ...  Grünwald [3, Sections 11.3 and 11.4 ] reviewed a bunch of proposed heuristic penalties, which he called the "luckiness functions" or conditional NML (normalized maximum likelihood).  ... 
arXiv:0901.2321v2 fatcat:pdela2toybhfzj5skj3n7hospa

Rate of Convergence for Consensus with Delays

Pierre-Alexander Bliman, Angelia Nedic, Asuman Ozdaglar
2008 2008 47th IEEE Conference on Decision and Control  
We study the problem of reaching a consensus in the values of a distributed system of agents with time-varying connectivity in the presence of delays.  ...  The consensus problem involves determining conditions on the agents' connectivity and interactions, including conditions on the weights a i (k), that guarantee the convergence of the estimates x i (k)  ...  Consensus algorithms also play a key role in the development of distributed optimization methods.  ... 
doi:10.1109/cdc.2008.4738941 dblp:conf/cdc/BlimanNO08 fatcat:3miwkepztvaflgll5mxqmy4lrq

Quantum Principles and Mathematical Computability

Tien D. Kieu
2005 International Journal of Theoretical Physics  
The key element of this algorithm is the computability and measurability of both the values of physical observables and of the quantum-mechanical probability distributions for these values.  ...  and the probability distributions for those values.  ...  The same conditions for tossing, i.e. the same initial conditions, will result in the same outcomes as required by the equations of classical physics.2 What is finite here is the time taken to generate  ... 
doi:10.1007/s10773-005-7070-y fatcat:e2h3tmaa7jcpjnub3wqu6ffpwe

On the Computability of Conditional Probability

Nathanael L. Ackerman, Cameron E. Freer, Daniel M. Roy
2019 Journal of the ACM  
with noncomputable conditional distributions, ruling out the prospect of general inference algorithms, even inefficient ones.  ...  Nevertheless, probabilistic inference is possible in many common modeling settings, and we prove several results giving broadly applicable conditions under which conditional distributions are computable  ...  Acknowledgments A preliminary version of this article appeared as "Noncomputable conditional distributions" in Proceedings of the 26th Annual IEEE Symposium on Logic in Computer Science, 107-116 [AFR11  ... 
doi:10.1145/3321699 fatcat:atigkacagjcbtcxy6r26repdle

Average-Case Hardness of Proving Tautologies and Theorems [article]

Hunter Monroe
2022 arXiv   pre-print
This implies the above condition.  ...  Similar conjectures that computational blind spots are manifestations of noncomputability would resolve other open problems.  ...  The set of U that are universal is noncomputable because "is universal" is a nontrivial property, so by Rice's Theorem H ′ is noncomputable.  ... 
arXiv:2205.07803v1 fatcat:bh6p2awaffgyvdq4p642zozkba

Page 479 of American Society of Civil Engineers. Collected Journals Vol. 109, Issue 4 [page]

1983 American Society of Civil Engineers. Collected Journals  
This was one of the intentions when the writer pre- sented, although in a different field, a noncomputer approach for the optimization of water distribution networks (5).  ...  In the author's graphical optimization method, one of the conditions ‘June, 1982, by Sandor Popovics (Paper 17129). *Prof., Dept. of Civ.  ... 

The wave equation with computable initial data such that its unique solution is not computable

Marian Boykan Pour-El, Ian Richards
1981 Advances in Mathematics  
(Just as the initial conditions are computable, the energy integral in our examples is also a computable real.)  ...  It is well known that the solution U(X, y, z, t) is uniquely determined by two initial conditions: the values of u and au/at at time t = 0.  ...  Regarding the initial conditions, we must now verify property (c). In general, distributions on IR4 do not admit restriction to hyperplanes {t = t,) within lR4. However, in this case they do.  ... 
doi:10.1016/0001-8708(81)90001-3 fatcat:62mf62dzo5dehh7jqrjpfmgu6y

Schnorr randomness for noncomputable measures [article]

Jason Rute
2017 arXiv   pre-print
This paper explores a novel definition of Schnorr randomness for noncomputable measures.  ...  We prove a number of theorems demonstrating that this is the correct definition which enjoys many of the same properties as Martin-Löf randomness for noncomputable measures.  ...  The conditional probability P(· | T = a) is the probability distribution associated with being a Brownian motion path ω which satisfies ω(1) = a.  ... 
arXiv:1607.04679v3 fatcat:hwbohm6xo5hmjhnngl35yugbgu

The impact of computers on cognitive psychology

Doris Aaronson, Edward Grupsmith, May Aaronson
1976 Behavior Research Methods & Instrumentation  
A tabulation of journal articles relevant to computer-based cognitive research shows the distribution of articles over various categories of hardware and software development.  ...  A quantitative analysis of federal funding for computer-based and noncomputer research compares costs over the past 9 years for the areas of perception, memory, learning, and thinking.  ...  Figure 7 shows how grant funds are distributed among expense categories. We have graphed the percentage of the average grantee's budget spent for personnel. equipment. supplies, and other expenses.  ... 
doi:10.3758/bf03201760 fatcat:lr3eschcmfgwdnlp3wfnwhpoty

Page 5225 of Mathematical Reviews Vol. , Issue 93i [page]

1993 Mathematical Reviews  
is independent of the initial conditions of the model. (2) Averages over “independent villages” give average behaviors close to the average of the limit distribution. (3) Mistakes generate global convergence  ...  In particular, he presents general conditions under which a general class of learning models will give convergence.  ... 

Page 203 of American Society of Civil Engineers. Collected Journals Vol. 109, Issue 1 [page]

1983 American Society of Civil Engineers. Collected Journals  
The network cost minimization model using LP tech- niques is then formulated and its solution is briefly outlined for the D- and Q-specified conditions.  ...  ., “Noncomputer Optimization of Single-Source Networks,” Jour- nal of the Environmental Engineering Division, ASCE, Vol. 104, No. EE4, Proc. Paper 13956, Aug., 1978, pp. 799-814. . Bhave, P.  ... 

On the computability of conditional probability [article]

Nathanael L. Ackerman, Cameron E. Freer, Daniel M. Roy
2019 arXiv   pre-print
We show that there are computable joint distributions with noncomputable conditional distributions, ruling out the prospect of general inference algorithms, even inefficient ones.  ...  Nevertheless, probabilistic inference is possible in many common modeling settings, and we prove several results giving broadly applicable conditions under which conditional distributions are computable  ...  Despite the noncomputability of conditioning in general, conditional distribution maps are often computable in practice.  ... 
arXiv:1005.3014v3 fatcat:52slkre5h5delbclkpizcutzkm

Achieving Linear Convergence in Distributed Asynchronous Multi-agent Optimization [article]

Ye Tian, Ying Sun, Gesualdo Scutari
2019 arXiv   pre-print
To the best of our knowledge, this is the first distributed algorithm with provable geometric convergence rate in such a general asynchronous setting.  ...  We propose a general distributed asynchronous algorithmic framework whereby i) agents can update their local variables as well as communicate with their neighbors at any time, without any form of coordination  ...  See Appendix C. (43) Then following results are instrumental to find a sufficient condition for ρ(T) < 1. Proof. See Appendix F.  ... 
arXiv:1803.10359v4 fatcat:qdeplzkdxfbddgzkuwlkhky7l4

Computing the non-computable

Tien D. Kieu
2003 Contemporary physics (Print)  
Generalised quantum algorithms are also considered for some other mathematical noncomputables in the same and of different noncomputability classes.  ...  The key element of all these algorithms is the measurability of both the values of physical observables and of the quantum-mechanical probability distributions for these values.  ...  outcomes because of illposed initial conditions.  ... 
doi:10.1080/00107510302712 fatcat:r66suu6zlnfovc637qzrbe7jnq
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