scholarly journals On testing transitivity in online preference learning

2021 ◽  
Author(s):  
Björn Haddenhorst ◽  
Viktor Bengs ◽  
Eyke Hüllermeier
Keyword(s):  
State Of The Art ◽  
Hypothesis Test ◽  
Pairwise Comparisons ◽  
Sample Complexity ◽  
Logarithmic Factor ◽  
Statistical Validity ◽  
Sequential Hypothesis ◽  
Sequential Hypothesis Testing ◽  
Algorithmic Framework ◽  
Testing Algorithm

AbstractThe efficiency of state-of-the-art algorithms for the dueling bandits problem is essentially due to a clever exploitation of (stochastic) transitivity properties of pairwise comparisons: If one arm is likely to beat a second one, which in turn is likely to beat a third one, then the first is also likely to beat the third one. By now, however, there is no way to test the validity of corresponding assumptions, although this would be a key prerequisite to guarantee the meaningfulness of the results produced by an algorithm. In this paper, we investigate the problem of testing different forms of stochastic transitivity in an online manner. We derive lower bounds on the expected sample complexity of any sequential hypothesis testing algorithm for various forms of stochastic transitivity, thereby providing additional motivation to focus on weak stochastic transitivity. To this end, we introduce an algorithmic framework for the dueling bandits problem, in which the statistical validity of weak stochastic transitivity can be tested, either actively or passively, based on a multiple binomial hypothesis test. Moreover, by exploiting a connection between weak stochastic transitivity and graph theory, we suggest an enhancement to further improve the efficiency of the testing algorithm. In the active setting, both variants achieve an expected sample complexity that is optimal up to a logarithmic factor.

scholarly journals Complete Bottom-Up Predicate Invention in Meta-Interpretive Learning

2020 ◽  
Author(s):  
Céline Hocquette ◽  
Stephen H. Muggleton
Keyword(s):  
State Of The Art ◽  
Order Logic ◽  
Learning Performance ◽  
Sample Complexity ◽  
Logic Programs ◽  
Top Down ◽  
Bottom Up ◽  
Predicate Invention ◽  
Feature Discovery ◽  
Second Order Logic

Predicate Invention in Meta-Interpretive Learning (MIL) is generally based on a top-down approach, and the search for a consistent hypothesis is carried out starting from the positive examples as goals. We consider augmenting top-down MIL systems with a bottom-up step during which the background knowledge is generalised with an extension of the immediate consequence operator for second-order logic programs. This new method provides a way to perform extensive predicate invention useful for feature discovery. We demonstrate this method is complete with respect to a fragment of dyadic datalog. We theoretically prove this method reduces the number of clauses to be learned for the top-down learner, which in turn can reduce the sample complexity. We formalise an equivalence relation for predicates which is used to eliminate redundant predicates. Our experimental results suggest pairing the state-of-the-art MIL system Metagol with an initial bottom-up step can significantly improve learning performance.

Bridge Inspection Decision Making Based on Sequential Hypothesis Testing Methods

2000 ◽  
Vol 1697 (1) ◽  
pp. 14-18 ◽  
Author(s):  
Samer Madanat ◽  
Da-Jie Lin
Keyword(s):  
Decision Making ◽  
Hypothesis Testing ◽  
Mathematical Formulation ◽  
Bridge Management ◽  
Statistical Decision ◽  
Sequential Hypothesis ◽  
Bridge Structures ◽  
Technological Developments ◽  
Sequential Hypothesis Testing ◽  
The Cost

A bridge management system (BMS) is a decision support system used by a highway agency in selecting appropriate maintenance and rehabilitation (M&R) activities and in allocating available resources effectively among facilities. BMS decision making is based on the condition of bridge components, their predicted deterioration, and the cost and effectiveness of M&R activities. Traditionally, bridge condition assessments have relied mainly on human inspectors; their results have generally been qualitative and subjective. More detailed inspections requiring some degree of destruction of the bridge, like drilling the deck to inspect for chloride contamination, have also been used. With recent technological developments, methods have been developed to evaluate the condition of bridge structures in a quantitative and objective manner. Associated with the use of these technologies are questions relating to inspection frequency, sample size, and the integration of data from the various technologies and human inspections. The application of a statistical decision-making method, sequential hypothesis testing, to these questions is presented. The mathematical formulation of the sequential hypothesis testing model, the derivation of optimal inspection policies, and the implementation of these policies in the context of bridge component inspection are discussed. A parametric analysis illustrates the sensitivity of the method to the cost structure of the problem, the precision of the technologies used, and the historical information or expert judgment regarding the condition of bridge components.

A robotic Intelligent Towing Tank for learning complex fluid-structure dynamics

2019 ◽  
Vol 4 (36) ◽  
pp. eaay5063 ◽  
Author(s):  
D. Fan ◽  
G. Jodin ◽  
T. R. Consi ◽  
L. Bonfiglio ◽  
Y. Ma ◽  
...  
Keyword(s):  
Active Learning ◽  
Experimental Research ◽  
Traditional Approach ◽  
High Dimensions ◽  
Towing Tank ◽  
Sequential Hypothesis ◽  
Sequential Hypothesis Testing ◽  
Complex Fluid ◽  
Traditional Approaches ◽  
New Generation

We describe the development of the Intelligent Towing Tank, an automated experimental facility guided by active learning to conduct a sequence of vortex-induced vibration (VIV) experiments, wherein the parameters of each next experiment are selected by minimizing suitable acquisition functions of quantified uncertainties. This constitutes a potential paradigm shift in conducting experimental research, where robots, computers, and humans collaborate to accelerate discovery and to search expeditiously and effectively large parametric spaces that are impracticable with the traditional approach of sequential hypothesis testing and subsequent train-and-error execution. We describe how our research parallels efforts in other fields, providing an orders-of-magnitude reduction in the number of experiments required to explore and map the complex hydrodynamic mechanisms governing the fluid-elastic instabilities and resulting nonlinear VIV responses. We show the effectiveness of the methodology of “explore-and-exploit” in parametric spaces of high dimensions, which are intractable with traditional approaches of systematic parametric variation in experimentation. We envision that this active learning approach to experimental research can be used across disciplines and potentially lead to physical insights and a new generation of models in multi-input/multi-output nonlinear systems.

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