Developing Rules for Rental Subsidy: An Empirical Housing Study in Taiwan

Taiwan, encompassing an area of 36,197 km², is home to a population of 23 million individuals, resulting in an average population density of 669 individuals per km², placing it 16th in the global ranking. It has 6 municipalities and 13 counties, with a per capita GDP of $32,687. Fig. 1 illustrates the geographic distribution of these six municipalities as well as metropolitan areas, delineated by black lines, encompassing around 30% of Taiwan’s land area. Despite this relatively small land coverage, these municipalities host approximately 70% of the population. In recent times, metropolitan areas have witnessed a notable escalation in housing prices, attributed to the government's implementation of urban renewal initiatives and the expansion of mass rapid transit systems (Geng et al. 2015; Tsai 2018). There has been a decline in homeownership rates among all countries in the world, highlighting the formidable challenges these countries face in purchasing homes (Fung and Lee 2014; Powell et al. 2018; Fan et al. 2019). To address this issue, the government has introduced a housing rental subsidy program. However, the annual volume of applications for housing rental subsidies is substantial.

The massive volume of the data renders conventional statistical analysis inadequate for fully assessing the potential eligibility of applicants. In light of recent advancements in information technology, various fields have turned to machine learning techniques for artificial intelligence predictions (da Silva et al. 2005; Kuşan et al. 2010; Gerek 2014; Zhou et al. 2014; Zhang et al. 2017; Wang et al. 2018). Machine learning classification involves using identifiable features to classify data into separate groups and develop a predictive model for households eligible for residential subsidies. Additionally, by inputting information about a new applicant seeking residential subsidies, the model can provide a reliable prediction of the applicant's eligibility for subsidies and offer insights into their actual qualifications.

In this study, an approach, utilizing particle swarm optimization (PSO)-based fuzzy hyperrectangular composite neural networks (PFHRCNNs), is employed to categorize housing subsidy applications. The primary goal is to efficiently sort and categorize applications based on specific data attributes. This method seeks to speed up the process of identifying unqualified applications, leading to substantial savings in manpower and providing useful guidelines for reviewers, both domestically and internationally. The newly developed rapid screening tool offers applicants prompt insights into their application outcomes upon entering their information. As a result, applicants can make informed decisions about continuing their application process. Government officials in other countries facing similar circumstances can use these results as a benchmark for verification purposes.

Since its inception in 2008, the subsidy program has processed data ranging from nearly 10,000 to over 30,000 annually, accumulating to over a hundred thousand entries. Analyzing this vast database using traditional statistical methods may be somewhat inadequate, thus utilizing data mining techniques seems more appropriate. With the advancement of information technology and the maturity of data mining techniques, many scholars are using data mining techniques for research. The deeper they delve, the better they understand the limitations of statistical methods, making it a suitable tool for analyzing massive amounts of data. Performance evaluations, financial crises, medical pathology, and other fields have all demonstrated the considerable reference value of the accuracy and feasibility of results obtained through data mining analysis of massive data sets.

Building upon the aforementioned considerations, this study devised a methodology illustrated in Fig. 2.

To initiate the process, raw attributes were extracted from segments of the government database (Ministry of Interior 2023). The application procedures for rental subsidies must be completed online. All information and data entered into the system underwent error-checking procedures to ensure accurate records without any defects. The feature set covered 10 categories, including mental and physical disorders, age over 65, Taiwanese aborigine status, single-parent households, major disasters, severe injuries, family violence, prior residential subsidies, gender, and monthly rent. Following the extraction of features, the proposed model trained hyperrectangular composite neural networks (HRCNNs) for each category, resulting in a set of precise rules. However, a challenge inherent in these rules was their varying effectiveness; consequently, each definitive rule underwent transformation into a fuzzy rule, accompanied by a confidence factor to bolster their efficacy. Notably, the significance of a rule is determined by its higher confidence factor value. Subsequently, a PSO approach was employed to simultaneously streamline the rules, identify optimal confidence factors, and fine-tune the positioning of the remaining hyperrectangles to enhance their effectiveness. Ultimately, a PFHRCNN was established, comprising a compilation of fuzzy rules, facilitating the prediction of the auditing state.

The performance of PFHRCNNs in terms of recognition rates was evaluated based on the analysis of 10 key features outlined in Table 3. The initial preset tolerances include three criteria: (1) Ensuring that the sampled data achieves a minimum accuracy of 90%; (2) allowing for a 5% margin of error due to external factors, in accordance with criterion (1); and (3) requiring all data to meet a 95% confidence level.

Following the three specified tolerances mentioned previously, 500 samples were randomly chosen from a data set containing 36,086 entries, which accounts for roughly 1.4% of the entire data set. These samples were utilized for training purposes using SSDL until achieving 100% accuracy. The remaining data were kept aside for accuracy assessment. Nine sets of training data and one set of testing data were established (10-fold cross validation), each defining distinct rule sets. This methodology aimed to identify which rule configurations provided the most accurate application predictions. The results obtained from the testing samples revealed the highest accuracy rate of 98.6%, which corresponds to the highest accuracy rate observed among all trials presented in Table 3. Notably, the average accuracy percentage ranged from approximately 94.25%–99.3%, highlighting the robust performance of this identifier. In particular, the highest test accuracy rate of 98.6% was linked with 66 rules, suggesting a positive correlation between the number of rules and the accuracy of test samples.

The PFHRCNN model identification aptly captures the authentic attributes of applicants. Furthermore, it effectively discerns the pivotal rules that determine the qualification status of a rental subsidy application, thereby furnishing valuable guidance for individuals. The salient findings are encapsulated within the rules elucidated in Table 4, which encompass four crucial rules spanning an extensive spectrum of household classifications. For instance, the numerical range of [0, 20] encompasses 21 distinct counties in Taiwan, with the exception of Lianjiang County (an offshore island depicted in Fig. 1), which was not included in this research. Likewise, the value range [0, 353] corresponds to 354 diverse regional townships. Demographic attributes, such as mental and physical disorders, age exceeding 65, Taiwanese aborigine status, single-parent families, major disasters, major injuries, family violence, previous receipt of residential subsidies, and gender-related criteria, are represented with [1, 1] to denote significant factors influencing subsidy eligibility. Conversely, [0, 1] signifies minimal impact on the subsidy outcome. The range [0, 195,000] for monthly rent indicates that rent amounts span from 0 to 195,000 NTD (0–6,500 USD). Interpreting the extracted prediction rules yields several noteworthy insights: Rule 1 underscores that applicants from single-parent families who have previously received residential subsidies are more likely to be approved. Rule 2 states that individuals residing outside Chiayi, Pingtung, Hualien, Penghu, and Kinmen Counties qualify for the subsidy if their monthly rent ranges from 8,000 to 13,000 NTD (266–433 USD). These counties, as illustrated in Fig. 1, are primarily located in the southern region or offshore islands. Consequently, residents in the northern areas have a greater likelihood of securing the subsidy within this range. Rule 3 suggests that residents in the southern region of Hsinchu, as well as the islands of Kinmen and Penghu Counties, could pass the audit if they have successfully applied for subsidies before. Rule 4 highlights that individuals aged over 65 paying less than 11,999 NTD (400 USD) in monthly rent are deemed to pass the audit.

The objective of this study is to create a proficient and accurate tool for promptly assessing and filtering out ineligible applications, alongside establishing uniform review standards for cities and townships throughout Taiwan. Among the 36,086 data sets, the PFHRCNN model yielded its highest classification accuracy at approximately 98.6% with 66 rules. The four major and crucial rules span an extensive spectrum of household classifications. The evaluation of the model commenced by randomly selecting 500 samples from a data set comprising 36,086 entries, representing roughly 1.4% of the complete data set. Through a 10-fold cross-validation process, the average accuracy percentage ranged from about 94.25% to 99.3%, demonstrating the robust performance of this identifier.

This work makes significant contributions in two key areas: (1) the suitability of PFHRCNNS as a predictive tool for residential rental subsidies, not only domestically but also internationally, and (2) the establishment of 66 rules, with particular emphasis on the four major rules. By scrutinizing detailed data features and rules, these contributions can be implemented in other countries with social and economic development similar to Taiwan. These rules outline specific criteria for passing the audit, including single-parent families, monthly rent range, specific regions, and individuals aged 65 years and older. The rapid auditing tool benefits both government agencies and applicants. By inputting basic information, applicants can assess the likelihood of successful auditing outcomes, enabling them to decide on pursuing further document preparation. Concurrently, government bodies can employ the tool for initial screening, suggesting direct rejection for applications with persistently low success rates, thus enhancing efficiency and impartiality. Subsequent studies will focus on refining the algorithm and developing a user-friendly interface. It is also recommended to incorporate different features as inputs in various countries or regions to tailor the findings to address more specific issues.

All data, models, and codes generated or used during the study appear in the published article.

The authors extend their gratitude for the partial support provided for this research by the Taiwan Ministry of Science and Technology (MOST)/National Science and Technology Council (NSTC) under grant numbers MOST-108-2221-E-008-002-MY3, MOST-109-2622-E-008-018-CC2, MOST-110-2622-E-008-018-CC2, MOST-110-2221-E-008-052-MY3, NSTC-111-2622-E-008-017, and NSTC-111-2221-E-008-027-MY3. It is important to note that any opinions, findings, conclusions, and recommendations presented in this paper solely belong to the authors and do not necessarily reflect the perspectives of the MOST/NSTC.