Fairness-Aware Loan Recommendation for Microfinance Services

Eric L. Lee, Jing-Kai Lou, Wei-Ming Chen,
Yen-Chi Chen, Shou-De Lin, Yen-Sheng Chiang, and Kuan-Ta Chen

PDF Version | Contact Us

Abstract

Up to date, more than 15 billion US dollars have been invested in microfinance that benefited more than 160 million people in developing countries. The Kiva organization is one of the successful examples that use a decentralized matching process to match lenders and borrowers. Interested lenders from around the world can look for cases among thousands of applicants they found promising to lend the money to. But how can loan borrowers and lenders be successfully matched up in a microfinance platform like Kiva? We argue that a sophisticate recommender not only pairs up loan lenders and borrowers in accordance to their preferences, but should also help to diversify the distribution of donations to reduce the inequality of loans is highly demanded, as altruism, like any resource, can be congestible.
In this paper, we propose a fairness-aware recommendation system based on one-class collaborative-filtering techniques for charity and micro-loan platform such as Kiva.org. Our experiments on real dataset indicates that the proposed method can largely improve the loan distribution fairness while retaining the accuracy of recommendations.

1  Introduction

Since the pioneering endeavor by Yunus and Yusus [14], microfinance has received intense attention and been widely adopted around the world. Up to date, more than 15 billion US dollars have been invested in microfinance that benefited more than 160 million people in developing countries. As a successful financial and philanthropic model, microfinance has attracted researchers from different disciplines to investigate what mechanisms underlie its success. Microfinance successfully overcomes two hurdles that prevent poor people from getting loans from the traditional financial institutions. First and foremost, the risk problem-how can we decrease delinquency rates of loans provided to the economically disadvantaged? Second, how can we find willing loan providers? Practitioners of microfinance solve the first problem in reference to social theories, using the mechanism of collective monitoring and punishment to minimize incidents of delinquency [8,7,9,4]. Advocates of microfinance solve the second problem by linking microfinance to philanthropy [13], motivating loan providers to treat lending money to the poor as an act of kindness. With the two major problems being solved, it remains a question how to screen out potential loan borrowers and lenders.
Proposal. In this paper, we propose a matching algorithm for microfinance whose goal is to not only maximizing the opportunity of successful matching but also diversifying the resources of loan providers. The concepts of fairness and recommendation are, to some extent, contradict to each other. If one only cares about fairness, then there is no need to perform recommendation as we can simply equally divide the resources to every person in need. On the contrary, the goal of performing recommendation is indeed to break the fair situation so that some specific loan is recommended to certain lenders. Thus, a successful fairness-aware matching system needs to take such trade-off into consideration.
Since only partial binary decision labels (whether a contribution was made) of each lender to each loan is available, we formulate the problem as an one-class collaborative filtering (OCCF) problem [11], where negative (i.e. not interested) and unlabeled (i.e. not seen) examples are mixed together. To solve the one-class collaborative filtering problem, we adopt the Bayesian Personalized Ranking idea to a Matrix Factorization engine. We propose two methods take fairness into consideration: 1) Item-Based regularization method and 2) the fairness-aware BPRMF method. The first model exploits a regularization term to build the distribution of ratings to avoid skewed recommendation, but suffer the drawback of high computational cost. The second approach dynamically adjusts the learning step in the stochastic gradient descent process to achieve the goal of balancing recommendation, that is relatively efficient and yields good results.
Contribution. We propose a fairness-aware recommendation system for charity and micro-loan platform such as Kiva.org, and conduct experiments to verify the effectiveness of the system. To our knowledge, this is the first-ever loan recommendation algorithm that takes fairness into consideration.
The remainder of this paper is organized as follows. Section 2 describes related works on recommendation systems. We present an overview of the Kiva ecosystem in Section 3. In Section 4, we propose a fairness-aware loan recommender system for microloaning services and then evaluate its performance in Section 4.2. Finally, Section 6 draws our conclusion and future work.

2  Related Work

From the viewpoint of fairness-aware recommendation systems, the closest works we have seen are the ones that emphasize on the diversification of recommendation [1,15,16]. The core concept of diversification is to recommend different kinds of items to improve users' satisfaction. However, it is very different from the concept of fairness where we want to diversify the matching between lenders and loan applicants.
Choo et al.[5] have focused on building personalized loan recommendation system which is based on content-based filtering techniques using specialized feature integration techniques and gradient boosting tree (GBtree). The goal is similar to ours except that fairness has not yet been taken into consideration in their design. In the authors' follow-up work [6], they continued to analyze the lending terms' behavior: How they choose which borrowers to lend money and when they would perform the next loaning? The results show that their Maxent-based model can be used to discover diverse team characteristics and predict team affiliation.

3  The Kiva ecosystem

In this section, we describe the Kiva dataset, post-processing steps, and the user behavior of loan applicants and providers.
glob_gender_ranking.png (a) Borrower gender glob_sector_ranking.png (b) Loan sector glob_country_ranking.png (c) Borrower country
Figure 1: Distributions of major loan attributes

3.1  Data Description

On their own website, the Kiva organization provides three public datasets which contain the information about the loan applicants (i.e., borrowers), the lenders, and the connections between them. Since Kiva's launch in April 2005, till December 2013, there have been 643,495 loans coming from 80 countries, and 1,196,283 lenders registered on the website. Since each loan can be contributed by a number of lenders (each loan contribution can be ranged from $25 up to $500 USD), the lenders have in the lump made 15,355,805 contributions to the loans worldwide through the Kiva platform.
The loans on Kiva contains descriptive information such as the personal biography of the borrowers (normally their gender and marital status are included), the purpose of the needs, and the amount of money needed. The timestamps of when a loan is posted and funded, as well as its repayment schedule, are also provided. The repayment schedule can be any of three types: monthly (66.5%), irregularly (25.4%), and at end of term (7.9%). A loan can be classified into one of six statuses based on their posted and funded timestamps.
Table 1: Loan summary in the full and reduced datasets
Status Full dataset Reduced dataset
Fundraising 5,672 (0.91%) 0 (0%)
Fully funded 280 (0.04%) 57 (0.02%)
Expired 10,594 (1.69%) 0 (0%)
Paying back 113,472 (18.14%) 99,085 (38.32%)
Paid 484,267 (77.43%) 157,407 (60.87%)
Ended with loss 11,143 (1.78%) 2,049 (0.79%)
Total 625,428 (100%) 258,598 (100%)
We summarize the loans on Kiva in Table 1 according their status as of December 11, 2013. The figures show that Kiva is indeed a successful microfinance platform as the proportions of expired and faulted loans are both lower than 2%. Because we will focus on the funding behavior from the lenders, we create a smaller, reduced dataset from the whole 5-year dataset with the following reduction: 1) We retain only the funding records from November 1, 2011 to October 30, 2013 where the number of loans and funding activity are relatively stable, and 2) we retain only the loans that have been fully funded, and thus loans in the fundraising and expired status are removed. This results in a reduced dataset of 258,598 fully-funded loans, which we will analyze in more details below.
amount_ecdf.png (a) Loan amount distribution ach_rate_gender.png (b) Fundraising rate for female- and male-loans ach_rate_sector.png (c) Fundraising rate for loans in different sectors
Figure 2: Summary of loan amount and fundraising rate

3.2  Loan Overview

On Kiva, a loan can be requested by an individual person or a group of people. Our dataset indicates that there are 541,937 (86.7%) individual loans and 83,491 (13.3%) group loans, where the number of borrowers associated with a group loan can be up to 50 persons. To help lenders find out the loans they are interested in, Kiva requires each loan to be associated with one of the 15 pre-defined sectors based on the expected usage of the loan.
In Figure 3, we show the proportions of borrowers' gender1 and country of origin and the sector which the loans will be used for, where the red staircase lines denote the cumulative sums of the proportions. We have made a few interesting observations. First, we observe that approximately 75% of the loans are requested by female borrowers. Second, the loans are requested for various types of purposes, among them, food (26.3%), retail (22.7%), and agriculture (22.1%) are the three main sectors the requested loans are being used for. For example, a borrower may plan to use the fund to purchase flour and baking equipments to run his own bakery or cafe (food sector); in another example, a borrower plans to buy oxen, piglets and forage for feeding the livestock (agriculture sector). Some other uses of the fund include arts, entertainment, and housing, which are much less common but not necessarily with lower desired loan amount. On the other hand, the loan applicants are from a diverse range of countries in different continents: Philippines (21.4%), Kenya (11.0%), and Peru (8.8%) together contribute 41.4% of all loans. The figures support that Kiva reaches the global needs without geographical boundaries and supports a variety of uses to improve people's lives.

4  Fairness-Aware Recommendation

The matching problem for microfinance can be modeled as a recommendation task. We want to recommend some loans to certain lenders and maximize the chances those lenders would fund the loans. In this sense, we can use the existing data to create a large matrix to represent the connections between lenders and loans. Such matrix is usually sparse as a lender is not likely to have investigated on most of the loans.
In many microfinances services such as Kiva.org, due to privacy concerns, we are only given the information about which lender has endorsed a loan, but not how much this lender contributes to the loan. Furthermore, if a lender does not endorse a loan, it is not possible to know whether it is because this lender has not yet reviewed this loan, or simply does not like it. Researchers have proposed the one-class collaborative filtering (OCCF) framework to design recommenders for such scenario. It is called one-class since only positive endorsement, where the negative and unseen behaviors are indistinguishable. Our proposed method will be developed based on BPRMF, the Bayesian Personalized Ranking (BPR) optimization criterion coupled with matrix factorization (MF), to achieve satisfactory results. Thus, we will call our method as Fairness-Aware BPRMF method.

4.1  Fairness-Aware BPRMF

Since that we need the tuples (u,i,j) for training the model in SGD. For a given lender u and the positive loan i, we find a negative sample j from Iu and perform updating. Normally each (u,i,j) tuple is treated as equally important during updating. Our idea is that to achieve fairness, maybe we should treat the tuple with "popular" j more seriously than those with less popular j. The intuitive behind is that if j has been a popular loan liked by many lenders, it is preferable to update our model more toward a direction to reduce lenders' interests in this loan for fairness purpose. Therefore during the SGD process, we do not assign equal step size for each instance tuple, but larger step to the situation where a popular tuple has been assigned the "negative" weight adjustment. Given this idea, the next question would be how to evaluate the "popularity" of a loan j during training. Our idea is to use the model learned up to date (i.e. most recent P and Q) to predict the ratings of both i and j on all users, and the popularity of a loan j with respect to an update (u,i,j) is defined as the probability that a user likes j more than i. This popularity then becomes a weight to adjust the step size of SGD.
The detailed process goes as: first we random sample a negative example j, and then sample Nref reference lenders u1, u2,…, uNref , based on which we can generate the popularity of j, proportional to which we can determine the step size of SGD during updating:
popularity(j) : = 2 Nref

n=1 
\llbracket PunQTj > PunQTi \rrbracket / Nref
(1)
Note that our modification mainly focuses on the learning rate of SGD (Stochastic Gradient Descent), which means it can not only be applied to BPRMF, but also other BPR models that exploit SGD for updating.

4.2  Evaluation

Up to date, we have not yet seen any recommendation model that considers fairness as a key factor. Thus in the evaluation we focus on comparing the proposed item-based regularized BPRMF method and fairness-aware BPRMF approach against the original BPRMF as a baseline. Note that the goal here is not about beating the competitors in the prediction accuracy, rather we want to test whether the goal of achieving fairness can be achieved without sacrificing too much accuracy in rating prediction.
Recommender Accuracy. We choose the Area-under-ROC-curve (AUC) as the evaluation metrics for ranking accuracy, as it is one of the most popular metrics to evaluate a ranking problem such as OCCF.

AUC : = 1

Nu
Nu

u=1 
1

|E(u)|


(i,j) ∈ E(u) 
δ(
^
y
 

ui 
>
^
y
 

uj 
) ,
(2)
where the evaluation pairs E(u) per user is defined as
{ (i,j) | (u, i) ∈ Iu+ Validation , (u,j) ∉ Iu+ Training ∪Iu+ Validation }.
Recommender Fairness. Here we consider whether each loan can be fairly recommended to all of the lenders. Assuming our recommendation system suggests a constant amount of N top loans to each lender, which can be done easily in our model by choosing the loans of the top-N top2. predicted ratings for each lender. Then we can gather how many times each loan is recommended to lenders and compute the standard deviation of such count to evaluate recommender fairness. Lower standard deviation indicates higher fairness since it implies all loans have the same amount of opportunity to be recommended. Note that examining this measure itself is meaningless as one can always `enforce' fair recommendation without considering the quality of prediction. Our goal is to do so without significantly degrading the accuracy of a recommender.
Figure 3: The AUC, Std (N top =30) through learning iterations
Table 2: The best AUC and the Std under such AUC for each model
Method Best AUC Std
BPRMF 0.678 319.16
Fairness-Aware BPRMF 0.656 131.42
In the experiments, we choose different number of reference lenders Nref for Fairness-Aware BPRMF. Both methods are trained over 300 iterations, where AUC and Std are calculated over iterations for comparisons. Table 2 presents the best AUC and the Std in the iteration with the best AUC. The result shows that the Fairness-Aware BPRMF model outperforms BPRMF by reducing  ∼ 58 % in Std, while only sacrificing a small amount of AUC (  ∼ 3.2 % relative to BPRMF). Figure 3 shows the AUC and Std metric over iterations of both models, where FA stands for Fairness-Aware BPRMF. On the graph, the three FA lines overlap with each other, which indicates that FA is insensitive to |si| and Nref. It also implies that the updating rule of Fairness-Aware BPRMF can work well even with very small samples to further improve the computational efficiency. On the other hand, higher cost in Fairness-Aware BPRMF leads to lower Std but lower AUC at the same time. To sum up, our evaluation results evidence that the proposed Fairness-Aware BPRMF algorithm provides a much higher gain in terms of fairness while merely slightly sacrifices the recommendation accuracy.

5  Further Look on Lenders' Behavioral Diversity

Having shown that our recommendation algorithm, which adopts a collaborative filtering approach, can suggest appropriate loans to a lender with fairness taken into account, here, we further look at the lenders' diversity in their behaviors in order to 1) back up the need of sophisticated recommenders, and 2) explore further opportunities to enhance our proposed recommender system.
figure0.png
Figure 4: Lenders' choices over gender and sector of candidate loans

5.1  Gender-Gender Interaction

Kiva provides detailed information for each borrower, but does not do so for lenders. From the dataset, we know only the names of lenders, but their gender information are not available. Therefore, to understand what role gender plays in lenders' selection behavior, we have to infer the lenders' genders based on their first names. Based on Baby Name Statistics listed on The United States Social Security Administration Website3, we infer the lenders' genders with the following rule: If a first name is used only by women (or men), we will certainly consider the lender to be a woman (or man). If the first name is much more popular among women by an order of magnitude (i.e., ten times more popular), we consider the lender to be a woman, and vice versa; otherwise, we give up inferring the gender for this particular lender in order to ensure the quality of inference. This results in 406,414 female- and 453,392 male-lenders out of 1,160,739 individual lenders, where the first names of 300,933 (25.9%) of them cannot be confidently determined as men or women.
The gender preferences of lenders are by no means uniformly distributed, as was shown in Figure 4. With 1 referring to perfect indifferent preference, i.e., lenders contribute to a loan regardless of the borrower's gender, the values in the figure suggest a gender-homophily preference, as we find that male lenders are more likely to choose male borrowers (1.15 > 1) and likewise female lenders choose female borrowers (1.13 > 1). Moreover, group lenders also tend to select group borrowers.
The biased preferences of lenders are also found in their choices in loan sectors. While female borrowers are easier to be funded when they are engaging is arts-related business (1.38 > 1), health (1.24) and housing (1.17), male borrowers are more successful in being funded when they propose to conduct manufacturing business (1.21), construction (1.15) and transportation (1.10). The difference between males and females in loan sectors that they are more likely to be funded suggests that lenders may posses a stereotype of the kinds of business they think males and females would be good at respectively.
Evidences from the two figures show that lenders possess their own preferences of borrowers and the choices of their sponsorship are by no means uniformly distributed. Considering the fact, it is thus important that further recommendation systems should put gender into consideration in order to make correct suggestions as well as diversify the choices of loans.
figure_e1.png (a) Ratio of loans from female, top-1 sector, and top-1 country figure_e1_summary.png (b) Ratio of crowding-out-lenders
Figure 5: Loan selection behavior
      
figure_e2.png (c) Median contribution to preferred loans figure_e2_summary.png (d) Summary of median loan contributions
Figure 6: Loan contribution (i.e., lending amount) behavior

5.2  The Crowding-Out Effect in Field

We begin the analysis by observing the differences of lenders in their behavior support female- and male-loans. Below we will restrict to repetitive lenders who have supported at least 10 loans. This leaves us 57,202 (4.7%) out of all the lenders in the reduced dataset. Having shown that male and female lenders favor male and female borrowers respectively; however, how individual lenders make their funding decisions remain unanswered. To do so, we plot the graph in Figure 5(a) to observe how supportive toward female borrowers for the lenders. In the graph, the histogram shows the ratio of female-loans for each lender, where the red curve represents the cumulative sum of the proportions and the vertical dashed line stands for the proportion of female-loans out of all available loans. For example, supposing that a lender contributes to 20 loans where 10 are from male borrowers, the ratio of female-loans for this particular lender would be 0.5. While female-loans occupy approximately 75% of the loans, the graph reveals that more than 25% of lenders only contribute to female-loans and more than half of the lenders (determined by the intersection of the red curve and the vertical dashed line) show funding preferences toward female borrowers with a ratio of female-loans higher than 0.75.
We apply the same analysis to lenders' preferences toward more prevalent sectors and countries. We find that on contrary to the gender aspect, the sector and country aspects express a different phenomenon. The middle plot in Figure 5(a) shows the histogram of lenders' ratio of loans from the top-1 sector (i.e., food) in terms of number of loans. The food-related loans occupy approximately 25% of loans; thus, if all the lenders equally distribute their contributions to all types of loans, the ratios will be exactly 0.25 for all the lenders. However, this is not the case. According to the graph, nearly 60% of lenders show less interests (compared with an equal distribution) to food-related loans. The same observation applies to the country aspect (the rightmost plot in Figure 5(a)), as nearly 75% never contributed to loans from the top-1 country, Philippine, and more than 80% of lenders show less interests to these loans.
We further extend our observations to top-N sectors and countries and record the proportion of lenders who show less interests to loans from the top-N sectors/countries as ratio of crowding-out-lenders. The results are shown in Figure 5(b), respectively, and suggest that the lenders exhibit the so-called crowding out phenomenon [10,2,3,12]. In other words, lenders tend to avoid high-profile loans and support (relatively) less visible loans as lenders would feel less honored to help when realizing that their help does not count much among the many other helpers available [12]. The effect diminishes when we gradually adjust the cut-point between high-profile loans and minority loans by varying the number of top-sectors and countries on Figure 5(b). The crowding out effect applies to the top 5 (out of 15) sectors and the top 45 (out of 60) countries, which constitute 49.3% and 41.1% loan population respectively. The cause why the crowding out effect does not sustain for more prevalent sectors and countries is not clear, but we suspect that is caused by the visibility of the minority loans. Even though Kiva allows loan searches based on specific sectors and countries, most lenders may search for interested loans by browsing and therefore the least prevalent sectors/countries may be overlooked by potential lenders even if the latter tend to "crowd out" from loans with more prevalent sectors/countries.

5.3  Higher Contributions to Favored Loans

So far we have looked closely lenders' diversity in choosing loans to contribute, we further inspect the contribution amount from a lender. We conjecture that a lender would contribute more to loans she favored and less to loans less favored. Unfortunately, Kiva does not provide the amount for individual funding activity, thus we have to infer the contribution amount made by each lender. To do so, we assume that it is unlikely that lenders who contributed to a particular loan are all more generous than average or all less generous than average. Based on this assumption, we can calculate each lender's median contribution to a set of loans by taking the median of the expected contributions to each of the loans in the set assuming the lender contributed equally with other lenders to the same loan (i.e., dividing the loan amount by the number of lenders contributed).
We first examine the median loan contributions made by each lenders according to her own preferences over genders, as shown in the leftmost plot in Figure 6(a). Here we define the preferences (i.e., favor) by comparing the overall contributions to loans from each gender; the more contributions to borrowers of a certain gender, we say the lender favors more on the gender. As can be seen in the CDF plot, regardless whether a lender favors female- or male-loans, lenders generally made larger contributions to each loan from her own favored gender, though the difference is not large. Furthermore, we find that the gaps between the most favored and the rest sectors/countries are much more prominent, as shown in the middle and rightmost plots in Figure 6(a). For example, generally, 25% lenders contributed more than $45 to loans from the favorite sector and more than $65 to loans from the favorite country, while most lenders contributed less than $30 (Kiva requires each loan contribute to be no lower than $25) to loans from less favored sectors/countries. We extend the definition of favor to include the top-N favored sectors and countries and draw the median loan amounts to the loans from top-N favored sectors/countries vs. those to the rest loans of the "median lender", i.e., the lender with 50% ranking position in terms of median loan amount among all the lenders. As shown in Figure 6(b), lenders tend to contribute more in loans from favored sectors and countries, where the effect of countries is more significant. For example, a lender tends to contribute 1.24 times more to loans from the most favorite sector (compared with loans from the rest sectors); meanwhile, the loans from the most favored countries can receive up to 1.53 times contribution from lenders compared with less favored countries.

5.4  Implications

To sum up, we confirm that the crowding-out effect exists in the lenders' choice toward loans and that lenders tend to contribute more to loans they favor. These observations strongly supports the need for recommender systems for the following reasons: 1) Since some lenders tend to crowd out from more prevalent loans, a good recommender would save them much time searching for relatively less prevalent loans and make them feel more fulfilled [12]; 2) the least prevalent loans should be recommended to pursue higher equality in loan distribution; and 3) strong individual preferences also decide how much lenders would contribute to each loan, thus suggesting loans which a lender favors is also important in order to maximize the overall contribution. However, as described in Section 1, the goals (maximizing the contributions and pursuing the equality over loans and loan attributes such as sectors and countries) may be in conflict with each other, so sophisticated recommender systems are more than demanded in order to address all the goals and issues we report here.

6  Conclusion and Future Work

In this work, we argue that a recommendation system for social welfare, optimizing accuracy and fairness altogether is more preferable, and further design a mechanism to achieve such purpose. We hope this paper can serve as an initiation to de-congest the congestible altruists using algorithms and attract more attention on designing fairness-aware recommendation systems for the good of society. On the other hand, in this paper, we merely focus on designing a CF-based recommender to achieve such purpose, while in the future we will focus on bringing the content information into consideration, as have been shown in some of our analysis that certain attributes of loans and lenders can significantly affect the acceptance rate of the proposal. By analyzing the content of the loan proposal, it is possible to gain more understanding about lenders' taste and further improve the quality of the recommendation systems.

References

[1] R. Agrawal, S. Gollapudi, A. Halverson, and S. Ieong. Diversifying search results. In Proceedings of ACM WSDM 2009, pages 5-14, New York, NY, USA, 2009. ACM.
[2] J. Andreoni. An experimental test of the public-goods crowding-out hypothesis. The American Economic Review, pages 1317-1327, 1993.
[3] J. Andreoni and A. A. Payne. Do government grants to private charities crowd out giving or fund-raising? American Economic Review, pages 792-812, 2003.
[4] D. Anthony. Cooperation in microcredit borrowing groups: identity, sanctions, and reciprocity in the production of collective goods. American Sociological Review, 70(3):496-515, 2005.
[5] J. Choo, C. Lee, D. Lee, H. Zha, and H. Park. A better world for all: Understanding and promoting micro-finance activities in Kiva.org. In WSDM'14: Proceedings of the 7th ACM International Conference on Web Search and Data Mining. ACM, 2014.
[6] J. Choo, D. Lee, B. Dilkina, H. Zha, and H. Park. To gather together for a better world: Understanding and leveraging communities in micro-lending recommendation. In Proceedings of WWW 2014. ACM, 2014.
[7] J. S. Coleman et al. Social capital in the creation of human capital. University of Chicago Press, 1989.
[8] M. Granovetter. Economic action and social structure: the problem of embeddedness. American journal of sociology, pages 481-510, 1985.
[9] M. Hechter. Principles of group solidarity, volume 11. Univ of California Press, 1988.
[10] G. Marwell and R. E. Ames. Experiments on the provision of public goods. I. resources, interest, group size, and the free-rider problem. American Journal of sociology, pages 1335-1360, 1979.
[11] R. Pan, Y. Zhou, B. Cao, N. N. Liu, R. M. Lukose, M. Scholz, and Q. Yang. One-class collaborative filtering. In IEEE International Conference on Data Mining (ICDM 2008), pages 502-511, 2008.
[12] A. J. Van de Kragt, J. M. Orbell, and R. M. Dawes. The minimal contributing set as a solution to public goods problems. The American political science review, pages 112-122, 1983.
[13] M. Yunus. Building social business: The new kind of capitalism that serves humanity's most pressing needs. PublicAffairs, 2011.
[14] M. Yunus and A. J. M. Yusus. Banker to the Poor. Penguin Books India, 1998.
[15] M. Zhang and N. Hurley. Avoiding monotony: improving the diversity of recommendation lists. In P. Pu, D. G. Bridge, B. Mobasher, and F. Ricci, editors, RecSys, pages 123-130. ACM, 2008.
[16] C.-N. Ziegler, S. M. McNee, J. A. Konstan, and G. Lausen. Improving recommendation lists through topic diversification. In Proceedings of ACM WWW 2005, pages 22-32, New York, NY, USA, 2005. ACM Press.

Footnotes:

1. Only the individual loans are considered as a group loan may comprise borrowers of both genders.
2. We tried Ntop=10,20, and 30, and found that the three settings yield similar results; thus, we will only report the results with N top = 30
3. http://www.ssa.gov/oact/babynames/limits.html


Sheng-Wei Chen (also known as Kuan-Ta Chen)
http://www.iis.sinica.edu.tw/~swc 
Last Update September 19, 2017