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IEEE Transactions on Artificial Intelligence 2024年第1期5卷 3-22页

作者： Kabir, Shaily Wagner, Christian Ellerby, Zack Lab for Uncertainty in Data and Decision Making School of Computer Science University of Nottingham LUCID NottinghamNG7 2RD United Kingdom

Most of statistics and AI draw insights through modeling discord or variance between sources (i.e., intersource) of information. Increasingly however, research is focusing on uncertainty arising at the level of individual measurements (i.e., within- or intrasource), such as for a given sensor output or human response. Here, adopting intervals rather than numbers as the fundamental data-type provides an efficient, powerful, yet challenging way forward - offering systematic capture of uncertainty-at-source, increasing informational capacity, and ultimately potential for additional insight. Following progress in the capture of interval-valued data in particular from human participants, conducting machine learning directly upon intervals is a crucial next step. This article focuses on linear regression for interval-valued data as a recent growth area, providing an essential foundation for broader use of intervals in AI. We conduct an in-depth analysis of state-of-the-art methods, elucidating their behavior, advantages, and pitfalls when applied to synthetic and real-world datasets with different properties. Specific emphasis is given to the challenge of preserving mathematical coherence, i.e., models maintain fundamental mathematical properties of intervals. In support of real-world applicability of the regression methods, we introduce and demonstrate a novel visualization approach, the interval regression graph (IRG), which effectively communicates the impact of both position and range of variables within the regression models - offering a leap in their interpretability. Finally, this article provides practical recommendations concerning regression-method choice for interval data and highlights remaining challenges and important next steps for developing AI with the capacity to handle uncertainty-at-source. © 2020 IEEE.

关键词： data visualization

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Generating Locally Relevant Explanations Using Causal Rule Discovery

Generating Locally Relevant Explanations Using Causal Rule D...

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IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： Te Zhang Christian Wagne Lab for Uncertainty in Data and Decision Making (LUCID) School of Computer Science University of Nottingham Nottingham UK

ISBN: (数字)9798350319545

ISBN: (纸本)9798350319552

In the real-world an effect often arises via multiple causal mechanisms. Conversely, the behaviour of AI systems is commonly driven by correlations which may-or may not-be themselves linked to causal mechanisms in the associated real-world system they are modelling. From an AI and XAI point of view, it is desirable for AI systems to model and communicate primarily, if not exclusively, causal mechanisms between variables, affording strong generalisation performance and effective explanations. Indeed, as we discuss in this paper, it is critical for explanations for a given effect not only to reflect possible causal mechanisms, but to highlight the specific causal mechanisms which led to the effect in the given instance. In this light, we proceed to propose a rule generation framework which generates rules for fuzzy systems that capture possible causal mechanisms between the input variables and the target variable as discovered by data-driven causal discovery algorithms for the given data set. For a given sample, i.e., a specific set of inputs, the obtained fuzzy system provides local explanations which distinguish the locally relevant causal mechanism(s) of its effect from other possible, but not applicable causal mechanisms, and thus avoids both overly simplistic single-cause and exhaustive-potentially misleading explanations. Experiments show that the fuzzy systems obtained by the proposed framework achieve comparable performance compared to classical correlation-based approaches, and provide local explanations which indicate the specific causal mechanism for different effects.

关键词： Correlation Input variables Knowledge based systems Task analysis Fuzzy systems

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Joint Handling of data and Model uncertainty for Interpretable Interval Prediction

Joint Handling of Data and Model Uncertainty for Interpretab...

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Artificial Intelligence (CAI), IEEE Conference on

作者： Direnc Pekaslan Christian Wagner Lab for Uncertainty in Data and Decision Making (LUCID) Computer Science University of Nottingham Nottingham UK

The presence of uncertainty, such as data uncertainty (e.g., noise) and model uncertainty (e.g., parameters), directly impacts the efficacy of prediction systems. Recent research is increasingly focusing on the explicit modelling of uncertainty within the prediction by deriving an interval-valued, rather than a point-valued prediction. The aim here is to explicitly capture uncertainty within data and model and map it systematically to the prediction outputs, in turn providing usable bounds on the expected prediction. Such bounds can convey crucial insight, such as the expected amount of renewable energy generation expected–enabling the minimal–but sufficient use of fossil fuels and other energy sources. This paper explores the viability of recent advances within non-singleton fuzzy systems to support the efficient and effective prediction of such interval-bounds, while providing an interpretable prediction model. The latter is desirable, as it affords experts not only the ability to validate the model, but allows them to interact with and change the model to adapt to unforeseen circumstances. For example, in a renewal energy context, priming a prediction system for uncommon weather patters can support its effectiveness. The proposed approach integrates both data and model uncertainty into the system recursively, generating systematic prediction intervals. To demonstrate the potential of the approach in integrating these–while supporting interpretability/interactivity, we show a series of synthetic experiments using the Mackey glass time series. The results highlight the capacity of the approach to preserve and recursively model the output uncertainty for multi-step ahead predictions. Further, the experiments demonstrate how the proposed system can provide explanations for given predictions, providing the basis for supporting expert interaction.

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Towards Causal Fuzzy System Rules Using Causal Direction

Towards Causal Fuzzy System Rules Using Causal Direction

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IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： Te Zhang Jingda Ying Christian Wagner Jonathan.M. Garibaldi Lab for Uncertainty in Data and Decision Making (LUCID) School of Computer Science University of Nottingham Nottingham UK

Generating (fuzzy) rule bases from data can provide a rapid pathway to constructing (fuzzy) systems. However, direct rule generation approaches tend to generate very large numbers of rules. One reason for this is that such techniques are not designed to differentiate between relationships of variables reflecting a causal link and those where such a link reflects a spurious correlation in the data set. In prior work, we discussed how causal discovery techniques, and specifically the subset resulting of variables within the Markov blanket can be leveraged to focus on the generation of rules for variables with a causal link. In this paper, we broaden this discussion, outlining a road-map to explain how causal discovery and its outputs-causal graphs-can be used towards refining (fuzzy) rule generation techniques. As a next step on this road-map, we present an initial approach which leverages the causal direction captured in the graph to further reduce the set of variables from those captured in the Markov blanket. Initial results show that the approach, combined with a traditional fuzzy rule generation technique such as the Wang-Mendel approach, produces competitive performance and concise rule bases-highlighting a path towards improved fuzzy system interpretability.

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JuzzyPy ― A Python Library to Create Type―1, Interval Type-2 and General Type-2 Fuzzy Logic Systems

JuzzyPy ― A Python Library to Create Type―1, Interval Type...

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IEEE Symposium Series on Computational Intelligence (SSCI)

作者： Mohammad Sameer Ahmad Christian Wagner Lab for Uncertainty in Data and Decision Making (LUCID) School of Computer Science University of Nottingham Nottingham UK

ISBN: (纸本)9781665487696

We present JuzzyPy, a Python based fuzzy logic toolkit enabling the creation of type-1, interval type-2, and general type-2 fuzzy logic systems. Fuzzy logic systems are being applied in disciplines across engineering and sectors such as cyber-security and autonomous systems, where an increasing focus on interpretability and trust is re-emphasising a focus on rule-based systems. This highlights the value of broadly accessible software resources to support both experts and non-experts in efficiently designing fuzzy systems. Python is currently the most popular programming language in the world. JuzzyPy is the first library capable of supporting the development of general type-2 systems in Python, facilitating access to these systems across engineering disciplines. In this paper we delve into the ability of the toolkit and explore its implementation. We hope that this allows for further accessibility in the use of fuzzy logic systems and provides a basis for developers, practitioners and researchers to collaborate on scientific advancement of the field and the tackling of real-world problems.

关键词： Fuzzy logic Java Autonomous systems Education data visualization Libraries Software

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A Restricted Parametrized Model for Interval-Valued Regression

A Restricted Parametrized Model for Interval-Valued Regressi...

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IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： Jingda Ying Shaily Kabir Christian Wagner Lab for Uncertainty in Data and Decision Making (LUCID) School of Computer Science University of Nottingham Nottingham UK Department of Computer Science and Engineering University of Dhaka Bangladesh

This paper explores the parameter generation of the existing ‘Parametrized Model’ (PM) as the state-of-the-art linear interval-valued regression model, highlighting that its strong performance may arise from unexpected behavior. Focusing on the approach's core idea of using dynamic reference points from the regressor variables to describe and regress interval-valued data, this paper shows that key parameters in the PM method are not actually restricted, and explores the impact this has on model generation. As part of this analysis, we propose a Restricted Parametrized Model (RPM) which ensures parameter bounds are maintained. We evaluate the approach by conducting linear regression for a series of synthetic interval-valued data sets with different features, discussing its performance against the original PM and other linear interval regression models. The experiments confirm empirically that the PM model violates restrictions on parameter bounds, resulting in the selection of reference points—outside—the regressor intervals–nevertheless producing strongly performing regression models which outperform other models, including RPM, when parameter bounds are violated. We conclude by discussing that the mechanism underpinning the PM regression is different to what is expected, i.e. it commonly selects reference points which are not from the regressor variables, warranting further research to explore whether the PM's parameter bounds can be relaxed, or whether this exposes potential problems, for example for edge cases.

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The Joint Weighted Average (JWA) Operator

arXiv

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arXiv 2023年

作者： Broomell, Stephen B. Wagner, Christian GRID – Global Risk and Individual Decisions Laboratory Purdue University West LafayetteIN47907 United States LUCID – Lab for Uncertainty in Data and Decision Making University of Nottingham Nottingham United Kingdom

Information aggregation is a vital tool for human and machine decision making in the presence of uncertainty. Traditionally, approaches to aggregation broadly diverge into two categories, those which attribute a worth or weight to information sources and those which attribute said worth to the evidence arising from said sources. The latter is pervasive in the physical sciences, underpinning linear order statistics and enabling non-linear aggregation. The former is popular in the social sciences, providing interpretable insight on the sources. While prior work has identified the need to apply both approaches simultaneously, it has yet to conceptually integrate both approaches and provide a semantic interpretation of the arising aggregation approach. Here, we conceptually integrate both approaches in a novel joint weighted averaging operator. We leverage compositional geometry to underpin this integration, showing how it provides a systematic basis for the combination of weighted aggregation operators–which has thus far not been considered in the literature. We proceed to show how the resulting operator systematically integrates a priori beliefs about the worth of both sources and evidence, reflecting the semantic integration of both weighting strategies. We conclude and highlight the potential of the operator across disciplines, from machine learning to psychology. © 2023, CC BY.

关键词： decision making

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Learning Causal Fuzzy Logic Rules by Leveraging Markov Blankets

Learning Causal Fuzzy Logic Rules by Leveraging Markov Blank...

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IEEE International Conference on Systems, Man and Cybernetics

作者： Te Zhang Christian Wagner Lab for Uncertainty in Data and Decision Making School of Computer Science University of Nottingham Nottingham UK

ISBN: (纸本)9781665442084

An important property of fuzzy systems is the interpretability provided by their rules. However, if a fuzzy system is derived through machine learning algorithms, its interpretability is often greatly diminished as membership functions and rules are adjusted to minimize error in respect to a data set. To address part of this challenge, we propose a novel two-step fuzzy rule generation framework leveraging the concept of the Markov blanket, i.e., the set of variables which are causally related to a target variable – such as a system’s output. By estimating the Markov blanket for a given application, we restrict rule learning to (only) the variables which are causally linked to the system output, thus minimising the generation of spurious rules (based on spurious correlations of variables). This decreases the complexity of fuzzy systems and maintains a causal link between rules’ antecedents and consequent(s) – as expected by humans when viewing rules. The proposed framework can improve the interpretability of fuzzy rule based systems which are tuned using machine learning techniques, while also providing performance advantages as are commonly associated with feature selection techniques. Experiment results show that even the initial implementation of the framework proposed here can generate more concise and interpretable rule bases without compromising performance.

关键词： Fuzzy logic Machine learning algorithms Knowledge based systems Machine learning Markov processes Feature extraction Inference algorithms

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Compositional Linear Regression on Interval-valued data

Compositional Linear Regression on Interval-valued Data

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IEEE Symposium Series on Computational Intelligence (SSCI)

作者： Direnc Pekaslan Christian Wagner Lab for Uncertainty in Data and Decision Making (LUCID) School of Computer Science University of Nottingham UK

ISBN: (纸本)9781728190495

uncertainty is pervasive in data and decision making, manifesting in various forms, from lack-of-information to vagueness. Interval-valued data provide an efficient and effective way to capture this uncertainty not afforded by using point-values such as numbers. Once interval-valued data have been captured, insights pertaining to their inherent range can be explored and communicated. Approaches to analysis span from exploring summary statistics, such as the average range/uncertainty, to inferential statistics such as regression and more complex machine learning techniques. In recent years, approaches in particular to regression for interval-valued data have attracted increasing interest, with advances affording improved regression model accuracy and increased resilience to parameter flipping, i.e. ‘loss of mathematical coherence’. This paper explores the application of a branch of statistics-compositional data analysis, for the computation of inferential statistics and specifically regression for interval-valued data. We articulate how, why and when a compositional representation of interval-valued data may be appropriate, and how intervals on a fixed domain can be easily converted to a compositional representation. Finally, we show how regression for compositional (interval) data can be conducted, and how this can provide an elegant means to mitigating some of the challenges faced by traditional approaches, including preserving mathematical coherence by virtue of the compositional representation.

关键词： uncertainty Linear regression decision making Focusing Estimation Coherence Machine learning

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Interval Agreement Weighted Average - Sensitivity to data Set Features

Interval Agreement Weighted Average - Sensitivity to Data Se...

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IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： Yu Zhao Christian Wagner Brendan Ryan Direnc Pekaslan Javier Navarro Lab for Uncertainty in Data and Decision Making (LUCID) School of Computer Science University of Nottingham United Kingdom Human Factors Research Group Faculty of Engineering University of Nottingham School of Engineering and Sciences United Kingdom School of Engineering and Sciences Technological Institute of Higher Studies of Monterrey Mexico

ISBN: (数字)9798350319545

ISBN: (纸本)9798350319552

The growing use of intervals in fields like survey analysis necessitates effective aggregation methods that can summarize and represent such uncertain data representations. The Interval Agreement Approach (IAA) addresses this by aggregating interval responses into Fuzzy Sets (FSs), capturing both intra- and inter-participant agreement, while minimizing information loss. While offering a powerful modeling tool, the IAA does not natively offer a measure of central tendency, which is itself an interval of particular utility in real-world applications. In contrast, the Interval Weighted Average (IWA) has been used for directly measuring the central tendency of intervals. While straightforward and effective, it is not designed, nor able to, summarize interval data in terms of their agreement, as the IAA does. To bridge this gap, this paper introduces Interval Agreement Weighted Average (IAWA), which is specifically designed to reflect both the central tendency and agreement. This is achieved by first modeling interval agreement as FSs using the IAA, and then transforming these FSs into intervals using the IWA. We demonstrate the approach by conducting sensitivity analyses to explore the behavior of the proposed approach in detail. Our findings suggest that the IAWA is a highly effective measure of central tendency. Additionally, it also partially inherits IAA's ability to reflect the agreement of sets of intervals. We conclude by highlighting the potential and growth of the use of intervals in information elicitation, within, and beyond survey research, underpinning a new degree of understanding of both intra- and inter-source uncertainty.

关键词： Surveys Weight measurement Bridges Fuzzy sets uncertainty Sensitivity analysis Fuzzy systems

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