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A unified approach to evaluation algorithms for multivariate polynomials

Suresh K. Lodha, Ron Goldman
1997 Mathematics of Computation  
algorithm with computational complexities O(n s ), O(n s ) and O(n) per point respectively for the evaluation of multivariate polynomials at several points.  ...  All of the known evaluation algorithms can be generated either by considering up recursive evaluation algorithms for L-bases or by examining change of basis algorithms for L-bases.  ...  This algorithm can be used repeatedly to evaluate any bivariate L-basis on a regular rectangular lattice with an amortized cost of O(n) computations per point.  ... 
doi:10.1090/s0025-5718-97-00862-4 fatcat:37audtlqq5a4zkbodg6lmeyg64

Diversification in Firm Valuation: A Multivariate Copula Approach

Stefan Erdorf, Thomas Hartmann-Wendels, Nicolas Heinrichs
2011 Social Science Research Network  
We introduce a new discounted cash flow model which adopts the diversification effect of multi-business firms.  ...  In the bivariate case we could only focus on two business segments, but multi-business firms are often comprised of more than two segments.  ...  We assume r W ACC l to be invariant over all time points.  ... 
doi:10.2139/ssrn.1739736 fatcat:2jaswidwczd7lajmfa5e7ed3pq

Batched Point Location in SINR Diagrams via Algebraic Tools [chapter]

Boris Aronov, Matthew J. Katz
2015 Lecture Notes in Computer Science  
Moreover, the amortized query time in these results depends only on n and ε.  ...  Efficient point location in the SINR diagram, i.e., being able to build a data structure that facilitates determining, for a query point, whether any transmitter is heard there, and if so, which one, has  ...  Fact A.1 to multi-evaluate B j on all values x i ; the remaining arithmetic can be done in O(n 2 ) operations.  ... 
doi:10.1007/978-3-662-47672-7_6 fatcat:okorpezmhjabbbfdu7q7nddysq

Darlin: Recursive Proofs using Marlin [article]

Ulrich Haböck and Alberto Garoffolo and Daniele Di Benedetto
2021 arXiv   pre-print
Darlin addresses recursive proofs by integrating the amortization technique from Halo (IACR eprint 2019/099) for the non-succinct parts of the dlog verifier, and we adapt their strategy for bivariate circuit  ...  The multi-point queries to be proven by the batch evaluation argument are as follows.  ...  Here 'multi-point' refers to the different points α, α ′ , and 'multi-polynomial' to the different polynomials defined by ⃗ η, ⃗ η ′ .  ... 
arXiv:2107.04315v2 fatcat:halbog6jt5girhq7att3rxceia

The Complexity of an Adaptive Subdivision Method for Approximating Real Curves

Michael A. Burr, Shuhong Gao, Elias Tsigaridas
2017 Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17  
w 2 |α| where α = (α1, · · · , αn) ∈ N n is a multi-index.  ...  Moreover, this integral can be evaluated even when the input polynomial has complex (but not real) singularities. Examples of the evaluation of this integral appear in the remainder of this paper.  ... 
doi:10.1145/3087604.3087654 dblp:conf/issac/BurrGT17 fatcat:66yznelgcnfzvdxoahtsi57tnm

Continuous amortization and extensions: With applications to bisection-based root isolation

Michael A. Burr
2016 Journal of symbolic computation  
In this paper, the theory of continuous amortization is generalized and applied in several directions.  ...  Continuous amortization was introduced in Burr et al. (2009) as a way to bound the complexity of subdivision-based algorithms.  ...  At this point, we use an undirected multi-subgraph G of the nearest neighbor graph (Eppstein et al., 1997 ) whose edge lengths appear as the d i 's with the same multiplicities.  ... 
doi:10.1016/j.jsc.2016.01.007 fatcat:bee6vuww4zfx7bt3y2gonumqhm

Atomic Secure Multi-party Multiplication with Low Communication [chapter]

Ronald Cramer, Ivan Damgård, Robbert de Haan
2007 Lecture Notes in Computer Science  
We consider the standard secure multi-party multiplication protocol due to M. Rabin.  ...  The ideas involved can additionally be employed in the evaluation of arithmetic circuits, where under appropriate circumstances similar efficiency gains can be obtained.  ...  Atomic Secure Multi-party Multiplication with Low Communication  ... 
doi:10.1007/978-3-540-72540-4_19 fatcat:ipjkvqhxqfeezksp524f4vopm4

Bank Lending Policy, Credit Scoring, and the Survival of Loans

Kasper Roszbach
2004 Review of Economics and Statistics  
Abstract To evaluate loan applicants, banks increasingly use credit scoring models. The objective of such models typically is to minimize default rates or the number of incorrectly classified loans.  ...  In this paper a bivariate Tobit model with a variable censoring threshold and sample selection effects is estimated for (1) the decision to provide a loan or not and (2) the survival of granted loans.  ...  The starting point of every loan is the application.  ... 
doi:10.1162/0034653043125248 fatcat:uf7j3ppu5renrjm63eyo7r76xm

Bank Lending Policy, Credit Scoring and the Survival of Loans

Kasper F. Roszbach
2004 Social Science Research Network  
Abstract To evaluate loan applicants, banks increasingly use credit scoring models. The objective of such models typically is to minimize default rates or the number of incorrectly classified loans.  ...  In this paper a bivariate Tobit model with a variable censoring threshold and sample selection effects is estimated for (1) the decision to provide a loan or not and (2) the survival of granted loans.  ...  The starting point of every loan is the application.  ... 
doi:10.2139/ssrn.488522 fatcat:qi6ckefspvgevgvxp7vuhmijau

Amortized Inference for Causal Structure Learning [article]

Lars Lorch, Scott Sussex, Jonas Rothfuss, Andreas Krause, Bernhard Schölkopf
2022 arXiv   pre-print
In this work, we propose to amortize the process of causal structure learning.  ...  Learning causal structure poses a combinatorial search problem that typically involves evaluating structures using a score or independence test.  ...  While amortized inference has gained increasing popularity in recent years (Amos, 2022) , prior work applying it to causal discovery only studied narrowly defined subproblems like the bivariate case or  ... 
arXiv:2205.12934v1 fatcat:o7jwjhf4vrhehkchihc4yclala

Batched Point Location in SINR Diagrams via Algebraic Tools [article]

Boris Aronov, Matthew J. Katz
2017 arXiv   pre-print
Moreover, the amortized query time in these results depends only on n and ε.  ...  Efficient point location in the SINR diagram, i.e., building a data structure to determine, for a query point, whether any transmitter is heard there, and if so, which one, has been recently investigated  ...  Fact A.7 (Bivariate Evaluation and Interpolation over a Grid [11, 29] ).  ... 
arXiv:1412.0962v3 fatcat:4vaosbvud5gz5c2jlth4crqbim

Lattices and Algorithms for Bivariate Bernstein, Lagrange, Newton, and Other Related Polynomial Bases Based on Duality betweenL-Bases andB-Bases

Suresh Kumar Lodha, Ron Goldman
1998 Journal of Approximation Theory  
A new geometric point-line duality between L-bases and B-bases is described: lines in L-bases correspond to points or vectors in B-bases and concurrent lines map to collinear points and vice versa.  ...  We describe, in particular, a new change of basis algorithm from a bivariate Lagrange L-basis to a bivariate Bernstein basis with computational complexity O(n 3 ). Academic Press  ...  Again when the L-basis is a Lagrange basis, this change of basis algorithm evaluates the B-patch at O(n 2 ) points with an amortized cost of O(n) computations per point.  ... 
doi:10.1006/jath.1997.3162 fatcat:bo4prnb6hjbq3nk3l4mjielfgq

Batch codes and their applications

Yuval Ishai, Eyal Kushilevitz, Rafail Ostrovsky, Amit Sahai
2004 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04  
We also demonstrate the usefulness of batch codes by presenting two types of applications: trading maximal load for storage in certain load-balancing scenarios, and amortizing the computational cost of  ...  Recall that the Reed-Muller (RM) code is defined as the evaluation of all degree d polynomials on all |F | evaluation points.  ...  Let S 1 , S 2 , S 3 denote the disjoint subsets of evaluation points used for decoding the multiset {i, i, i}.  ... 
doi:10.1145/1007352.1007396 dblp:conf/stoc/IshaiKOS04 fatcat:nxtwnfqxnjh2bnnjwtvpy4g3ky

Solving bivariate systems using Rational Univariate Representations

Yacine Bouzidi, Sylvain Lazard, Guillaume Moroz, Marc Pouget, Fabrice Rouillier, Michael Sagraloff
2016 Journal of Complexity  
A key ingredient of our proofs of complexity is an amortized analysis of the triangular decomposition algorithm via subresultants, which is of independent interest.  ...  Such representations require the computation of a separating form for the system, that is a linear combination of the variables that takes different values when evaluated at the distinct solutions of the  ...  We present in Section 4 our amortized analysis of the triangular decomposition and a related luckiness certificate which is a key feature of the following multi-modular algorithms.  ... 
doi:10.1016/j.jco.2016.07.002 fatcat:3eg6wmdymzfunpc4bwww6ddyvm

BayesFlow: Learning complex stochastic models with invertible neural networks [article]

Stefan T. Radev, Ulf K. Mertens, Andreass Voss, Lynton Ardizzone, Ullrich Köthe
2020 arXiv   pre-print
With this work, we propose a novel method for globally amortized Bayesian inference based on invertible neural networks which we call BayesFlow.  ...  We argue that BayesFlow provides a general framework for building amortized Bayesian parameter estimation machines for any forward model from which data can be simulated.  ...  Evaluating this model for specific observations x o 1:N is then very fast, so that the training effort amortizes over repeated evaluations (see Figure 1 for a graphical illustration).  ... 
arXiv:2003.06281v4 fatcat:fsoeg74glrdkxkn63d6fdjbtzm
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