scholarly journals Provable Guarantees on the Robustness of Decision Rules to Causal Interventions

2021 ◽  
Author(s):  
Benjie Wang ◽  
Clare Lyle ◽  
Marta Kwiatkowska
Keyword(s):  
Decision Making ◽  
Bayesian Networks ◽  
Lower Bounds ◽  
Decision Rules ◽  
Experimental Results ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Data Generating Process ◽  
Causal Bayesian Networks ◽  
Novel Model

Robustness of decision rules to shifts in the data-generating process is crucial to the successful deployment of decision-making systems. Such shifts can be viewed as interventions on a causal graph, which capture (possibly hypothetical) changes in the data-generating process, whether due to natural reasons or by the action of an adversary. We consider causal Bayesian networks and formally define the interventional robustness problem, a novel model-based notion of robustness for decision functions that measures worst-case performance with respect to a set of interventions that denote changes to parameters and/or causal influences. By relying on a tractable representation of Bayesian networks as arithmetic circuits, we provide efficient algorithms for computing guaranteed upper and lower bounds on the interventional robustness probabilities. Experimental results demonstrate that the methods yield useful and interpretable bounds for a range of practical networks, paving the way towards provably causally robust decision-making systems.

Rough Set Application in Customer Classification

2011 ◽  
Vol 267 ◽  
pp. 46-49 ◽  
Author(s):  
Ju Li ◽  
Wen Bin Xu ◽  
Wei Yuan Tu ◽  
Xing Wang ◽  
Wei Zhang ◽  
...  
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Customer Relationship Management ◽  
Decision Rules ◽  
Relationship Management ◽  
Experimental Results ◽  
Customer Relationship ◽  
Decision Table ◽  
Final Decision ◽  
Customer Classification

Based on the study of customer relationship management. First, we got the data from the database, transformed the corresponding decision table, then got the data in decision-making table for further simplification, generated the final decision rules. and got good results, experimental results showed that the method provided some practical value.

scholarly journals The stretch-length tradeoff in geometric networks: average case and worst case study

2015 ◽  
Vol 159 (1) ◽  
pp. 125-151
Author(s):  
DAVID ALDOUS ◽  
TAMAR LANDO
Keyword(s):  
Lower Bounds ◽  
Poisson Point Process ◽  
Euclidean Distance ◽  
Unit Area ◽  
Average Density ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Average Case ◽  
Route Length

AbstractConsider a network linking the points of a rate-1 Poisson point process on the plane. Write Ψave(s) for the minimum possible mean length per unit area of such a network, subject to the constraint that the route-length between every pair of points is at moststimes the Euclidean distance. We give upper and lower bounds on the function Ψave(s), and on the analogous “worst-case” function Ψworst(s) where the point configuration is arbitrary subject to average density one per unit area. Our bounds are numerically crude, but raise the question of whether there is an exponent α such that each function has Ψ(s) ≍ (s− 1)−αass↓ 1.

scholarly journals Refined Expected Value Decision Rules under Orthopair Fuzzy Environment

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 442 ◽  
Author(s):  
Yige Xue ◽  
Yong Deng
Keyword(s):  
Decision Making ◽  
Choquet Integral ◽  
Decision Rules ◽  
Expected Value ◽  
Experimental Results ◽  
Numerical Examples ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Expected Values ◽  
Function Measure

Refined expected value decision rules can refine the calculation of the expected value and make decisions by estimating the expected values of different alternatives, which use many theories, such as Choquet integral, PM function, measure and so on. However, the refined expected value decision rules have not been applied to the orthopair fuzzy environment yet. To address this issue, in this paper we propose the refined expected value decision rules under the orthopair fuzzy environment, which can apply the refined expected value decision rules on the issues of decision making that is described in the orthopair fuzzy environment. Numerical examples were applied to verify the availability and flexibility of the new refined expected value decision rules model. The experimental results demonstrate that the proposed model can apply refined expected value decision rules in the orthopair fuzzy environment and solve the decision making issues with the orthopair fuzzy environment successfully.

scholarly journals Fully-Dynamic and Kinetic Conflict-Free Coloring of Intervals with Respect to Points

2019 ◽  
Vol 29 (01) ◽  
pp. 49-72
Author(s):  
Mark de Berg ◽  
Tim Leijsen ◽  
Aleksandar Markovic ◽  
André van Renssen ◽  
Marcel Roeloffzen ◽  
...  
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Insertions And Deletions ◽  
Coloring Problem ◽  
Trade Offs ◽  
Special Cases ◽  
The Cost ◽  
Case Number

We introduce the fully-dynamic conflict-free coloring problem for a set [Formula: see text] of intervals in [Formula: see text] with respect to points, where the goal is to maintain a conflict-free coloring for [Formula: see text] under insertions and deletions. A coloring is conflict-free if for each point [Formula: see text] contained in some interval, [Formula: see text] is contained in an interval whose color is not shared with any other interval containing [Formula: see text]. We investigate trade-offs between the number of colors used and the number of intervals that are recolored upon insertion or deletion of an interval. Our results include: a lower bound on the number of recolorings as a function of the number of colors, which implies that with [Formula: see text] recolorings per update the worst-case number of colors is [Formula: see text], and that any strategy using [Formula: see text] colors needs [Formula: see text] recolorings; a coloring strategy that uses [Formula: see text] colors at the cost of [Formula: see text] recolorings, and another strategy that uses [Formula: see text] colors at the cost of [Formula: see text] recolorings; stronger upper and lower bounds for special cases. We also consider the kinetic setting where the intervals move continuously (but there are no insertions or deletions); here we show how to maintain a coloring with only four colors at the cost of three recolorings per event and show this is tight.

scholarly journals EXACT MINIMIZATION OF AND–EXOR EXPRESSIONS OF PRACTICAL BENCHMARK FUNCTIONS

2009 ◽  
Vol 18 (03) ◽  
pp. 465-486 ◽  
Author(s):  
TAKASHI HIRAYAMA ◽  
YASUAKI NISHITANI
Keyword(s):  
Lower Bounds ◽  
Search Space ◽  
Computing Methods ◽  
Experimental Results ◽  
Upper And Lower Bounds ◽  
Search Procedure ◽  
Minimization Algorithm ◽  
Original Algorithm ◽  
Sum Of Products ◽  
Exclusive Or

We propose faster-computing methods for the minimization algorithm of AND–EXOR expressions, or exclusive-or sum-of-products expressions (ESOPs), and obtain the exact minimum ESOPs of benchmark functions. These methods improve the search procedure for ESOPs, which is the most time-consuming part of the original algorithm. For faster computation, the search space for ESOPs is reduced by checking the upper and lower bounds on the size of ESOPs. Experimental results to demonstrate the effectiveness of these methods are presented. The exact minimum ESOPs of many practical benchmark functions have been revealed by this improved algorithm.

scholarly journals Cuckoo Hashing

2001 ◽  
Vol 8 (32) ◽  
Author(s):  
Rasmus Pagh ◽  
Flemming Friche Rodler
Keyword(s):  
Lower Bounds ◽  
Binary Search ◽  
Upper And Lower Bounds ◽  
Binary Search Trees ◽  
Search Trees ◽  
Worst Case ◽  
Average Case ◽  
Cuckoo Hashing ◽  
Perfect Hashing ◽  
Theoretical Performance

We present a simple and efficient dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. (<em>Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738-761, 1994</em>). The space usage is similar to that of binary search trees, i.e., three words per key on average. The practicality of the scheme is backed by extensive experiments and comparisons with known methods, showing it to be quite competitive also in the average case.

scholarly journals Quantum SDP-Solvers: Better upper and lower bounds

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 230 ◽  
Author(s):  
Joran van Apeldoorn ◽  
András Gilyén ◽  
Sander Gribling ◽  
Ronald de Wolf
Keyword(s):  
Combinatorial Optimization ◽  
Lower Bounds ◽  
Optimization Problems ◽  
Quantum Algorithms ◽  
Upper And Lower Bounds ◽  
Smooth Functions ◽  
Worst Case ◽  
Semidefinite Programs ◽  
New Techniques ◽  
Combinatorial Optimization Problems

Brandão and Svore \cite{brandao2016QSDPSpeedup} recently gave quantum algorithms for approximately solving semidefinite programs, which in some regimes are faster than the best-possible classical algorithms in terms of the dimension n of the problem and the number m of constraints, but worse in terms of various other parameters. In this paper we improve their algorithms in several ways, getting better dependence on those other parameters. To this end we develop new techniques for quantum algorithms, for instance a general way to efficiently implement smooth functions of sparse Hamiltonians, and a generalized minimum-finding procedure.We also show limits on this approach to quantum SDP-solvers, for instance for combinatorial optimization problems that have a lot of symmetry. Finally, we prove some general lower bounds showing that in the worst case, the complexity of every quantum LP-solver (and hence also SDP-solver) has to scale linearly with mn when m≈n, which is the same as classical.

MINIMIZING CONGESTION OF LAYOUTS FOR ATM NETWORKS WITH FAULTY LINKS

1999 ◽  
Vol 10 (04) ◽  
pp. 503-512 ◽  
Author(s):  
LESZEK GASIENIEC ◽  
EVANGELOS KRANAKIS ◽  
DANNY KRIZANC ◽  
ANDREZEJ PELC
Keyword(s):  
Lower Bounds ◽  
High Probability ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Atm Networks ◽  
Worst Case ◽  
Precise Analysis ◽  
Order Of Magnitude ◽  
Bounded Size ◽  
Fault Distribution

We consider the problem of constructing virtual path layouts for an ATM network consisting of a complete network Kn of n processors in which a certain number of links may fail. Our main goal is to construct layouts which tolerate any configuration of up to f faults and have the least possible congestion. First, we study the minimal congestion of 1-hop f-tolerant layouts in Kn. For any positive integer f we give upper and lower bounds on this minimal congestion and construct f-tolerant layouts with congestion corresponding to the upper bounds. Our results are based on a precise analysis of the diameter of the network Kn[ℱ] which results from Kn by deleting links from a set ℱ of bounded size. Next we study the minimal congestion of h-hop f-tolerant layouts in Kn, for larger values of the number h of hops. We give upper and lower bounds on the order of magnitude of this congestion, based on results for 1-hop layouts. Finally, we consider a random, rather than worst case, fault distribution where links fail independently with constant probability p<1. Our goal now is to construct layouts with low congestion that tolerate the existing faults with high probability. For any p<1, we show the existence of 1-hop layouts in Kn, with congestion O( log n).

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