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Robust algorithms For Generalized Pham Systems

COMPUTATIONAL COMPLEXITY 2009年第1期18卷 105-154页

作者： Dratman, Ezequiel Matera, Guillermo Waissbein, Ariel Univ Nacl Gral Sarmiento Inst Ciencias RA-1613 Los Polvorines Argentina Consejo Nacl Invest Cient & Tecn RA-1033 Buenos Aires DF Argentina Univ Nacl Gral Sarmiento Inst Desarrollo Humano RA-1613 Los Polvorines Argentina CORE Secur Technol CoreLabs Buenos Aires DF Argentina Inst Tecnol Buenos Aires Buenos Aires DF Argentina

We discuss the complexity of robust symbolic algorithms solving a significant class of zero-dimensional square polynomial systems with rational coefficients over the complex numbers, called generalized Pham systems, which represent the class of zero-dimensional homogeneous complete-intersection systems with "no points at infinity". Our notion of robustness models the behavior of all known universal methods for solving (parametric) polynomial systems avoiding unnecessary branchings and allowing the solution of certain limit problems. We first show that any robust algorithm solving generalized Pham systems has complexity at least polynomial in the B,zout number of the system under consideration. Then we exhibit a robust probabilistic algorithm which solves generalized Pham systems with quadratic complexity in the B,zout number of the input system. The algorithm consists in a series of homotopies deforming the input system into a system which is "easy to solve", together with a "projection algorithm" which allows to move the solutions of the known instance to the solutions of an arbitrary instance along the parameter space.

关键词： Polynomial system solving robust algorithms geometric solutions Newton-Hensel lifting probabilistic algorithms complexity

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The Use of Informed Priors in Biclustering of Gene Expression with the Hierarchical Dirichlet Process

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2020年第5期17卷 1810-1821页

作者： Tercan, Bahar Acar, Aybar C. Middle East Tech Univ Canc Syst Biol Lab KanSiL TR-06800 Ankara Turkey Middle East Tech Univ Grad Sch Informat TR-06800 Ankara Turkey

We motivate and describe the application of Hierarchical Dirichlet Process (HDP) models to the "soft" biclustering of gene expression data, in which we obtain modules (biclusters) where the affiliation of genes and samples with the modules are weighted, instead of being hard memberships. As a distinct contribution, we propose a method which HDP is informed with prior beliefs, significantly increasing the quality of the biclustering in terms of both the correctness of the number of modules inferred, and the precision of these modules, especially when evidence is sparse. We outline two such informed priors;one based on co-expression relationships inherent in the data, the other based on an externally provided regulatory network. We validate these results and compare the performance of our approach to Weighted Gene Correlation Network Analysis (WGCNA), another model that features weighted modules. We have, to this end, performed experiments on semi-synthetic data. The results show that HDP, with the addition of a well-informed prior, is able to capture the correct number of modules with increased accuracy. Furthermore, the model becomes robust to changes in the strength of the prior. We conclude by discussing these results and the benefits provided by our approach for gene expression analysis and network validation.

关键词： Gene expression Analytical models Data models Cancer Biological system modeling Bioinformatics probabilistic logic Transcriptomics gene expression analysis mixed-membership models Bayesian non-parametrics hierarchical Dirichlet process (HDP) systems biology bioinformatics probabilistic algorithms

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Building Trust for Sample Voting

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INTERNATIONAL JOURNAL OF DECISION SUPPORT SYSTEM TECHNOLOGY 2018年第4期10卷 50-64页

作者： Blanchard, Nicolas K. Inst Rech Informat Fondamentale Paris France

This article explores how to build popular trust for voting systems that rely heavily on statistical tools, as they are generally counter-intuitive to the average citizen (and even to experts). By trying out the voting system in public and letting people tinker with it, a first level of familiarity can be achieved. Preliminary results from real-world experiments seem encouraging and point out the importance of psychological and sociological factors in election organization as well as the influence of user interface design. To go further, integration into a larger debating platform held by a national party could give first-hand experience to the majority of the people, and would progressively build trust as the political stakes grow higher. Finally, the authors look into how different e-democratic tools could interact in a mutually beneficial manner.

关键词： Citizen Trust E-Democracy End-To-End Verifiability Institution Design probabilistic algorithms Rational Ignorance Sortition

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Straight-line programs in geometric elimination theory

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JOURNAL OF PURE AND APPLIED ALGEBRA 1998年第1-3期124卷 101-146页

作者： Giusti, M Heintz, J Morais, JE Morgenstern, J Pardo, LM Ecole Polytech Ctr Math GAGE F-91228 Palaiseau France Univ Cantabria Fac Ciencias Dept Matemat Estadist & Computac E-39071 Santander Spain

We present a new method for solving symbolically zero-dimensional polynomial equation systems in the affine and toric case. The main feature of our method is the use of problem adapted data structures. arithmetic networks and straight-line programs. For sequential time complexity measured by network size we obtain the following result: it is possible to solve any affine or toric zero-dimensional equation system in nonuniform sequential time which is polynomial in the length of the input description and the "geometric degree" of the equation system. Here, the input is thought to be given by a straight-line program (or alternatively in sparse representation), and the length of the input is measured by number of variables, degree of equations and size of the program (or sparsity of the equations). The geometric degree of the input system has to be adequately defined. It is always bounded by the algebraic-combinatoric "Bezout number" of the system which is given by the Hilbert function of a suitable homogeneous ideal. However, in many important cases, the value of the geometric degree of the system is much smaller than its Bezout number since this geometric degree does not take into account multiplicities or degrees of extraneous components (which may appear at infinity in the affine case or may be contained in some coordinate hyperplane in the tonic case). Our method contains a new application of a classic tool to symbolic computation: we use Newton iteration in order to simplify straight-line programs occurring in elimination procedures. Our new technique allows for practical implementations, a meaningful characterization of the intrinsic algebraic complexity of typic elimination problems and reduces the still unanswered question of their intrinsic bit complexity to algorithmic arithmetics. However, our algorithms are not rational anymore as are the usual ones in elimination theory. They require some restricted computing with algebraic numbers. This is due to its nume

关键词： probabilistic algorithms Bounds Complexity Nullstellensatz Polynomials Time Coefficients Identities Systems Complexity input system Bound Polynomial online programming Straight line In-law personal identity

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An algorithm for the satisfiability problem of formulas in conjunctive normal form

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JOURNAL OF algorithms-COGNITION INFORMATICS AND LOGIC 2005年第1期54卷 40-44页

作者： Schuler, R Univ Ulm Abt Theoret Informat D-89069 Ulm Germany

We consider the satisfiability problem on Boolean formulas in conjunctive normal form. We show that a satisfying assignment of a formula can be found in polynomial time with a success probability of 2(-n(1 - 1/(1 + logm))), where n and m are the number of variables and the number of clauses of the formula, respectively. If the number of clauses of the formulas is bounded by V for some constant c, this gives an expected run time of O(p(n) (.) 2(n(1-1/(1+c logn)))) for a polynomial p. (C) 2004 Elsevier Inc. All rights reserved.

关键词： complexity theory NP-completeness CNF-SAT probabilistic algorithms

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SORTING NUMBERS USING LIMITED SYSTOLIC COPROCESSORS

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INFORMATION PROCESSING LETTERS 1987年第6期24卷 351-354页

作者： MULLER, H Institut für Informatik I Universität Karlsruhe P.O. Box 6380 7500 Karlsruhe Fed. Rep. Germany

A probabilistic algorithm is presented for sorting real numbers that allows a significant speed-up even under restricted parallelism. The machine model used consists of a random access machine to which 3 coprocessors are attached. The first 2 processors -- DISTRIBUTE and SORT -- are linear systolic arrays containing p processing elements. The 3rd coprocessor, RANDOM, produces a random number x between zero and one. The model is a sequential random access machine and is only augmented by some special purpose processors. The range for an improvement against sequential O(n log n) algorithms for sorting is somewhat small. The main open issue that remains is whether the time bound of Algorithm Sort can be obtained by any deterministic algorithm or can be proved impossible by giving lower bounds.

关键词： Sorting parallel computation probabilistic algorithms computational complexity

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Dynamic Propagation Modeling for Mobile Users' Position and Heading Estimation in Wireless Local Area Networks

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IEEE WIRELESS COMMUNICATIONS LETTERS 2012年第2期1卷 101-104页

作者： Atia, Mohamed Mahar Noureldin, Aboelmagd Korenberg, Michael J. Queens Univ Kingston ON K7L 3N6 Canada

A system for mobile users' position and heading estimation in IEEE 802.11 WLAN (WiFi) using received signal strength (RSS) approach is introduced. The basic contribution the system introduces is that it doesn't need offline training or extra special hardware. It makes use of the fact that only few online RSS measurements from visible access points (AP) around the user is needed to build local propagation model at run-time. Gaussian Process Regression (GPR) is used as a non-parametric modeling that handles non-equally spaced sparse data. Due to the few learning data points, Gaussian kernels calibration and prediction happen in a single step. This enables the system to autonomously adapt to environment changes. The estimated ranges from multiple access points (AP) are used to determine position using weighted least squares. Then, the rate of change of signal strength from multiple APs is used by a novel algorithm to estimate heading. Experiments show reliable meter-level positioning accuracy and heading estimation accuracy of 16.5 degrees.

关键词： Location and heading estimation in WLAN probabilistic algorithms Gaussian process regression

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Addressing the Practical Limitations of Noisy-OR Using Conditional Inter-Causal Anti-Correlation with Ranked Nodes

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2019年第4期31卷 813-817页

作者： Noguchi, Takao Fenton, Norman Neil, Martin Queen Mary Univ London Sch Elect Engn & Comp Sci London E1 4NS England Agena Ltd Cambridge CB23 7NU England

Numerous methods have been proposed to simplify the problem of eliciting complex conditional probability tables in Bayesian networks. One of the most popular methods -"Noisy-OR"-approximates the required relationship in many real-world situations between a set of variables that are potential causes of an effect variable. However, the Noisy-OR function has the conditional inter-causal independence (CII) property which means that 'explaining away' behavior-one of the most powerful benefits of BN inference-is not present when the effect variable is observed as false. Hence, for many real-world problems where the Noisy-OR has been used or proposed, it may be deficient as an approximation of the required relationship. However, there is a very simple alternative solution, namely to define the variables as ranked nodes and to use the ranked node weighted average function. This does not have the CII property-instead, we prove it has the conditional anti-correlation property required to ensure that explaining away works in all cases. Moreover, ranked node variables are not restricted to binary states, and hence provide a more comprehensive and general solution to Noisy-OR in all cases.

关键词： Knowledge representation formalisms and methods probabilistic algorithms Bayesian networks

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An Extension to the Noisy-OR Function to Resolve the 'Explaining Away' Deficiency for Practical Bayesian Network Problems

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2019年第12期31卷 2441-2445页

作者： Fenton, Norman E. Noguchi, Takao Neil, Martin Queen Mary Univ London Sch Elect Engn & Comp Sci London E1 4NS England Agena Ltd Cambridge CB23 7NU England

The "leaky noisy-OR" function is a common and popular method used to simplify the elicitation of complex conditional probability tables in Bayesian networks involving Boolean variables. It has proven to be useful for approximating the required relationship in many real-world situations where there is a set of two or more variables that are potential causes of a single effect variable. However, one of the properties of leaky noisy-OR is Conditional Inter-causal Independence (CII). This property means that the 'explaining away' behavior-one of the most powerful benefits of BN inference-is not present when the effect variable is observed as false. Yet, for many real-world problems where the leaky noisy-OR has been considered, this behavior would be expected, meaning that leaky noisy-OR is deficient as an approximation of the required relationship in such cases. There have been previous attempts to adapt the noisy-OR to resolve this problem. However, they require too many additional parameters to be elicited. We describe a simple but powerful extension to leaky noisy-OR that requires only a single additional parameter. While it does not solve the CII problem in all cases, it does resolve most of the explaining away deficiencies that occur in practice. The problem and solution is illustrated using an example from intelligence analysis.

关键词： Noise measurement probabilistic logic Bayes methods History Tools Standards Heart Knowledge representation formalisms and methods probabilistic algorithms decision support

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Decoding interleaved Reed-Solomon codes over noisy channels

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THEORETICAL COMPUTER SCIENCE 2007年第3期379卷 348-360页

作者： Bleichenbacher, Daniel Kiayias, Aggelos Yung, Moti Univ Connecticut Dept Comp Sci & Engn Storrs CT USA Bell Labs Murray Hill NJ 07974 USA RSA Labs Bedford MA USA Columbia Univ Dept Comp Sci New York NY 10027 USA

We consider error correction over the Non-Binary Symmetric Channel (NBSC) which is a natural probabilistic extension of the Binary Symmetric Channel (BSC). We propose a new decoding algorithm for interleaved Reed-Solomon codes that attempts to correct all "interleaved" codewords simultaneously. In particular, interleaved encoding gives rise to multi-dimensional curves and more specifically to a variation of the Polynomial Reconstruction Problem, which we call Simultaneous Polynomial Reconstruction. We present and analyze a novel probabilistic algorithm that solves this problem. Our construction yields a decoding algorithm for interleaved RS codes that allows efficient transmission arbitrarily close to the channel capacity in the NBSC model. (c) 2007 Elsevier B.V. All rights reserved.

关键词： efficient decoding probabilistic algorithms Reed-Solomon codes polynomial reconstruction

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