A parametrized approach for linear regression of interval data

Souza, Leandro Carlos de; Souza, Renata M. C. R. de; Amaral, Getúlio José Amorim do; Filho, Telmo M. Silva

doi:10.1016/j.knosys.2017.06.012

Cited by 42 publications

(51 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For this problem, Guo et al [22] proposed a constraint center-and-range method in which two constraints were added into equation ( 8): (1) e right end value of the predicted interval is greater than or equal to the left end value of the corresponding observed interval, as shown in the first set of constraints ( 9); (2) e left end value of the predicted interval is less than or equal to the right end value of the corresponding observed interval, as shown in the second set of constraints (9). is improved CCRM model (called CCRM + for simplicity) can be expressed as (8), (9).…”

Section: Ccrm + Methodmentioning

confidence: 99%

“…e min-max method is one of the classic EP methods in which the left and right endpoint data series of interval data are considered as two independent series, respectively [7]. A typical min-max method uses a convex combination of the left and right endpoints of interval independent variables to express the interval data, and finally to utilize Ordinary Least Squares (called as OLS for simplicity) method to obtain the regression coefficients [8]. Compared to the EP method, the MR method uses the midpoint series to represent the changing trend of interval data and utilizes the radius series to represent the uncertainty of interval data.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Robust Approach to CCRM Interval Regression considering Interval Coincidence Degree

Wang

Shilin

2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Traditional CCRMs (Constrained Center-and-Range Methods) in solving the problem of interval regression could hardly make tradeoffs between the overall fitting accuracy and the coincidence degree between the observed and predicted intervals and could also hardly reduce the number of disjoint elements between the observed and predicted intervals, as well as raise the average ratio of all predicted intervals contained within their observed intervals. This paper constructed a nonlinear regression model based on center-and-range method, in which the maximization of coincidence degree for the sample with the worst coincidence degree between the observed and predicted interval was incorporated into the traditional CCRM model’s objective. This novel nonlinear programming model was proven to be a convex one that satisfied K-T condition. Monte Carlo simulation shows that the model is degenerated to the compared CCRM+ model as the objective only contains the minimization of the overall fitting accuracy for both center and range sample series. In this situation, it could obtain a better solution than the use of the compared CCRM model. In addition, when the proposed model only takes into account the maximization of coincidence degree for the sample with the worst coincidence degree between the observed and predicted interval, the model shows a better performance than the CCRM+ model in terms of the average ratio of all predicted intervals contained within their observed intervals, as well as the average number of forecasts with 0% accuracy.

show abstract

Section: Ccrm + Methodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Robust Approach to CCRM Interval Regression considering Interval Coincidence Degree

Wang

Shilin

2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…Current linear regression models for intervals use different reference points, such as the regressors' center values, their lower and upper bounds, or both their center and range (width), to estimate the interval-valued regressand [21]. All earlier interval regression approaches [15]- [17] risk 'flipping' the interval bounds or generating a negative interval range, and thus breaking mathematical coherence (i.e., the value of the left endpoint is greater than the value of the right endpoint, violating the definition of the interval).…”

Section: Introductionmentioning

confidence: 99%

“…All earlier interval regression approaches [15]- [17] risk 'flipping' the interval bounds or generating a negative interval range, and thus breaking mathematical coherence (i.e., the value of the left endpoint is greater than the value of the right endpoint, violating the definition of the interval). The more recent approaches [18]- [21] impose either positivity restrictions on parameters or design the regression model so as to ensure that the lower bound does not exceed the upper bound. For instance, Neto and Carvalho [18] apply the Lawson and Hanson's algorithm (LHA) [23], Wang et al [19] use Moore's linear combination [24], and Souza et al [21] the Box-Cox transformation [25] to guarantee mathematical coherence.…”

Section: Introductionmentioning

confidence: 99%

“…The more recent approaches [18]- [21] impose either positivity restrictions on parameters or design the regression model so as to ensure that the lower bound does not exceed the upper bound. For instance, Neto and Carvalho [18] apply the Lawson and Hanson's algorithm (LHA) [23], Wang et al [19] use Moore's linear combination [24], and Souza et al [21] the Box-Cox transformation [25] to guarantee mathematical coherence.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Towards Handling Uncertainty-at-Source in AI -- A Review and Next Steps for Interval Regression

Kabir¹,

Wagner²,

Ellerby³

2021

Preprint

View full text Add to dashboard Cite

Most of statistics and AI draw insights through modelling discord or variance between sources of information (i.e., inter-source uncertainty). Increasingly, however, research is focusing upon uncertainty arising at the level of individual measurements (i.e., within-or intra-source), 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 insight. Following recent progress in the capture of interval-valued data, including from human participants, conducting machine learning directly upon intervals is a crucial next step. This paper 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-ofthe-art methods, elucidating their behaviour, advantages, and pitfalls when applied to datasets with different properties. Specific emphasis is given to the challenge of preserving mathematical coherence -i.e., ensuring that models maintain fundamental mathematical properties of intervals throughout -and the paper puts forward extensions to an existing approach to guarantee this. Carefully designed experiments, using both synthetic and real-world data, are conducted -with findings presented alongside novel visualizations for interval-valued regression outputs, designed to maximise model interpretability. Finally, the paper makes recommendations concerning method suitability for data sets with specific properties and highlights remaining challenges and important next steps for developing AI with the capacity to handle uncertainty-at-source. 1 Impact Statement-Capturing information as intervals, rather than numbers, provides a powerful means for handling uncertainty and inherent range in data. This paper focuses on a basic building block of statistics and AI: linear regression. In recent years, regression for intervals has become a topic of interest in AI, and has been applied to domains ranging from marketing to cyber-security. It allows direct modelling of relationships not only between variables per-se, but also concerning their associated uncertainty. For example, we can infer not only how a snack's nutritional benefits impact consumer purchase intention, but also how uncertainty about these benefits impacts purchase intention and its own associated uncertainty. Nonetheless, while there are considerable upsides to interval-valued regression and AI, substantial challenges remain. This paper reviews, analyses and extends state-of-the-art interval regression methods, presenting in-depth experimental results and introducing novel visualisations, to enhance model interpretability and provide context and data-specific recommendations for algorithm selection.

show abstract

Interval time series forecasting: A systematic literature review

Wang,

Gurmani,

Tao

et al. 2023

Journal of Forecasting

View full text Add to dashboard Cite

Interval time series forecasting can be used for forecasting special symbolic data comprising lower and upper bounds and plays an important role in handling the complexity, instability, and uncertainty of observed objects. The purpose of this research is to identify the most widely used definition of interval time series; classify existing research into mature research, current research focus, and research gaps within the defined framework; and recommend future directions for interval forecasting research. To achieve this goal, we have conducted a systematic literature review, comprising search strategy planning, screening mechanism determination, document analysis, and report generation. During the search strategy planning stage, eight literature search libraries are selected to obtain the most extensive studies (total of 525 targets). In the screening‐mechanism determination stage, through the inclusion and exclusion mechanism, the literature that is repetitive, of low‐relevance, and from other fields are discarded, and 125 studies are finally selected. In the document analysis stage, tag‐based methods and classification grids are selected to analyze the shortlisted studies. The results show that there are still numerous research gaps in interval time series forecasting, such as the establishment of hybrid models, application of multisource information, development and application of evaluation techniques, and expansion of application scenarios. In the report‐generation stage, the problems that have been solved and encountered in interval forecasting are summarized, and future research directions are proposed. Finally, the most significant contribution of this research is to provide an overview of interval time series forecasting for easy reference by researchers and to facilitate further research.

show abstract

A parametrized approach for linear regression of interval data

Cited by 42 publications

References 13 publications

A Robust Approach to CCRM Interval Regression considering Interval Coincidence Degree

A Robust Approach to CCRM Interval Regression considering Interval Coincidence Degree

Towards Handling Uncertainty-at-Source in AI -- A Review and Next Steps for Interval Regression

Interval time series forecasting: A systematic literature review

Contact Info

Product

Resources

About