Revisiting the Boston Housing Dataset

Introduction

The Boston Housing dataset is one of the datasets currently callable in fairlearn.datasets module. In the past, it has commonly been used for benchmarking in popular machine learning libraries, including scikit-learn and OpenML. However, as the machine learning community has developed awareness about fairness issues with popular benchmarking datasets, the Boston Housing data has been phased out of many libraries. We migrated the dataset to Fairlearn after it was phased out of scikit-learn in June 2020. The dataset remains in Fairlearn as an example of how systemic racism can occur in data and to show the effects of Fairlearn’s unfairness assessment and mitigation tools on real, problematic data.

We also think this dataset provides an interesting case study of how fairness is fundamentally a socio-technical issue by exploring how societal biases manifest in data in ways that can’t simply be fixed with technical mitigation approaches (although the harms they engender may be mitigated). This article has the following goals:

• Educate users about the history of the dataset and how the variables were constructed

• Show users how socioeconomic inequities are reflected in the data in ways that can potentially lead to fairness-related harms in downstream modelling tasks

• Suggest alternative benchmarking datasets

Dataset Origin and Use

Harrison and Rubinfeld[1] developed the dataset to illustrate the issues with using housing market data to measure consumer willingness to pay for clean air. The authors use a hedonic pricing approach, which assumes that the price of a good or service can be modeled as a function of features both internal and external to the good or service. The input to this model was a dataset comprising the Boston Standard Metropolitan Statistical Area [2], with the nitric oxides concentration (NOX) serving as a proxy for air quality.

The paper sought to estimate the median value of owner-occupied homes (now MEDV), and included the remaining variables to capture other neighborhood characteristics. Further, the authors took the derivative of their housing value equation with respect to nitric oxides concentration to measure the “amount of money households were willing to pay when purchasing a home with respect to air pollution levels in their census tracts.” The variables in the dataset were collected in the early 1970s and come from a mixture of surveys, administrative records, and other research papers. While the paper does define each variable and suggest its impact on the housing value equation, it lacks reasoning for including that particular set of variables.

Modern machine learning practitioners have used the Boston Housing dataset as a benchmark to assess the performance of emerging supervised learning techniques. It’s featured in scipy lectures, indexed in the University of California-Irvine Machine Learning Repository and in Carnegie Mellon University’s StatLib, and for a time was included as one of scikit-learn’s and tensorflow’s standard toy datasets (see tf.keras.datasets.boston_housing). It has also been the benchmark of choice for many machine learning papers [3] [4] [5]. In 2020, users brought the dataset’s fairness issues to the scikit-learn development team (see scikit-learn issue #16155), after which the team decided to remove the dataset in scikit-learn version 1.2.

The dataset contains the following columns:

Column name	Description
CRIM	per capita crime rate by town
ZN	proportion of residential land zoned for lots over 25,000 sq.ft.
INDUS	proportion of non-retail business acres per town
CHAS	Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)
NOX	nitric oxides concentration (parts per 10 million)
RM	average number of rooms per dwelling
AGE	proportion of owner-occupied units built prior to 1940
DIS	weighted distances to five Boston employment centers
RAD	index of accessibility to radial highways
TAX	full-value property-tax rate per $10,000
PTRATIO	pupil-teacher ratio by town
B	1000(Bk - 0.63)^2 where Bk is the proportion of Black people by town
LSTAT	% lower status of the population
MEDV	Median value of owner-occupied homes in $1000’s

The cells below show basic summary statistics about the data, the data types of the columns, and the number of missing values.

Note that the fairlearn.datasets.fetch_boston() function warns users by default that the dataset contains fairness issues.

Setting warn=False will turn the warning off.

To return the dataset as a pandas.DataFrame, pass as_frame=True and call the data attribute.

For more information about how to use the fetch_boston function, visit fairlearn.datasets.

>>> import warnings
>>> warnings.filterwarnings('ignore')
>>> from fairlearn.datasets import fetch_boston
>>> import pandas as pd
>>> pd.set_option('display.max_columns', 20)
>>> pd.set_option('display.width', 80)
>>> X, y = fetch_boston(return_X_y=True)
>>> boston_housing=pd.concat([X, y], axis=1)
>>> with pd.option_context('expand_frame_repr', False):
...    boston_housing.head()
      CRIM    ZN  INDUS CHAS    NOX     RM   AGE     DIS RAD    TAX  PTRATIO       B  LSTAT  MEDV
0  0.00632  18.0   2.31    0  0.538  6.575  65.2  4.0900   1  296.0     15.3   396.90   4.98  24.0
1  0.02731   0.0   7.07    0  0.469  6.421  78.9  4.9671   2  242.0     17.8   396.90   9.14  21.6
2  0.02729   0.0   7.07    0  0.469  7.185  61.1  4.9671   2  242.0     17.8   392.83   4.03  34.7
3  0.03237   0.0   2.18    0  0.458  6.998  45.8  6.0622   3  222.0     18.7   394.63   2.94  33.4
4  0.06905   0.0   2.18    0  0.458  7.147  54.2  6.0622   3  222.0     18.7   396.90   5.33  36.2

Dataset Issues

While the dataset is widely used, it has significant ethical issues.

As explained in sklearn.datasets.load_boston(), Harrison and Rubenfield developed the feature B (result of the formula 1000(B_k - 0.63)^2k) under the assumption that racial self-segregation had a positive impact on house prices. B then encodes systemic racism as a factor in house pricing. Thus, any models trained using this data that do not take special care to process B will learn to use mathematically encoded racism as a factor in house price prediction.

Harrison and Rubenfield describe their projected impact of the B and LSTAT variables as follows (note that these descriptions are verbatim from their paper). However, many of the authors’ assumptions have later been found to be unsubstantiated.

• LSTAT: “Proportion of population that is lower status = 0.5 * (proportion of adults without some high school education and proportion of male workers classified as laborers). The logarithmic specification implies that socioeconomic status distinctions mean more in the upper brackets of society than in the lower classes.”

• B: “Proportion of population that is Black. At low to moderate levels of B, an increase in B should have a negative influence on housing value if Black people are regarded as undesirable neighbors by White people. However, market discrimination means that housing values are higher at very high levels of B. One expects, therefore, a parabolic relationship between proportion Black in a neighborhood and housing values.”

To describe the reasoning behind B further, the authors assume that self-segregation correlates to higher home values. However, other researchers (see [6]) did not find evidence that supports this hypothesis.

Additionally, though the authors specify a parabolic transformation for B, they do not provide evidence that the relationship between B and MEDV is parabolic. Harrison and Rubenfield set a threshold of 63% as the point in which median house prices flip from declining to increasing, but do not provide the basis for this threshold. An analysis of the dataset [7] by M. Carlisle further shows that the Boston Housing dataset suffers from serious quality and incompleteness issues, as Carlisle was unable to recover the original Census data mapping for all the points in the B variable.

The definition of the LSTAT variable is also suspect. Harrison and Rubenfield define lower status as a function of the proportion of adults without some high school education and the proportion of male workers classified as laborers. They apply a logarithmic transformation to the variable with the assumption that resulting variable distribution reflects their understanding of socioeconomic distinctions. However, the categorization of a certain level of education and job category as indicative of “lower status” is reflective of social constructs of class and not objective fact. Again, the authors provide no evidence of a proposed relationship between LSTAT and MEDV and do not sufficiently justify its inclusion in the hedonic pricing model.

Construct validity (What is construct validity?) provides a useful lens through which to analyze the construction of this dataset. Construct validity refers to the extent to which a given measurement model measures the intended construct in way that is meaningful and useful. In Harrison and Rubenfield’s analysis, the measurement model involves constructing the assumed point at which prejudice against Black people occurs and the effect that prejudice has on house values. Likewise, another measurement model also constructs membership in lower-status classes based on educational attainment and labor category. It is useful to ask whether the way the authors chose to create the measurements accurately represents the phenomenon they sought to measure. As is discussed above, the authors do not provide justification for their variable construction choices beyond the projected impacts described in the variable definitions. Both measurements fail the test of content validity, a subcategory of construct validity, as the variable definitions are subjective and thus open to being contested. The authors also do not establish convergent validity, another subcategory of construct validity, in that they do not show their measurements correlate with measurements from measurement models in which construct validity has been established. However, given the time period in which the paper was published there may have been a dearth of related measurement models.

Intersectionality also requires consideration. Intersectionality is defined as the intersection between multiple demographic groups. [8] The impacts of a technical system on intersectional groups may be different than the impacts experienced by the individual demographic groups (e.g., Black people in aggregate and women in aggregate may experience a technical system differently than Black women).

Due to the effects of discriminatory socioeconomic policies, including housing policies, in effect at the time the article was written, Black people may have been more likely to be categorized as “lower status” by the authors’ definition. Harrison and Rubenfield do not consider this intersectionality in their analysis. When using a linear model, intersectionality could be captured via an interaction variable, which combines the two fields. In the machine learning context, considering each group separately (i.e., considering impacts on B and LSTAT separately) may obscure harms. Additionally, including only one of these variables in the analysis is not sufficient in removing the signals encoded in the removed variable from the dataset. Because these columns are related, one likely can serve as a proxy for the other. Thus, we recommend great care be taken to account for intersectionality in data.

The inclusion of these columns might make sense for an econometric analysis, which seeks to understand the causal impact of various factors on a dependent variable, but these columns are problematic in the context of a predictive analysis. Predictive models will learn the patterns of systemic racism and classism encoded in the data and will reproduce those patterns in their predictions. It’s also important to note that merely excluding these variables from the dataset is not sufficient to mitigate these issues. However, through careful assessment, the negative effects of these variables can be mitigated.

The next section describes the potential risk in using this dataset in a typical machine learning prediction pipeline.

Fairness-related harms assessment

As explained above, machine learning models that use the Boston Housing dataset are at risk of generating fairness-related harms. How does that look in a typical machine learning pipeline?

We apply a column transformation to the target feature to turn this problem into a classification problem. The code below maps LSTAT and MEDV to binary values where values greater than the median of the column map to TRUE, and otherwise the values are FALSE. This methodology follows scikit-lego’s [9] exploration of the Boston Housing data. We also transform B into a binary variable where TRUE values are above the value 136.9. Observations below this point correspond to the “true” proportion of Black people above 63%, at which point the authors assumed that house prices would begin to be affected by the racism of others in the community.

>>> import sklearn.metrics as skm
>>> import fairlearn.metrics as fm
>>> from sklearn.linear_model import LogisticRegression
>>> from sklearn.model_selection import train_test_split
>>> import numpy as np
>>> X_clf = X.assign(B=lambda d: d['B'] > 136.9,
...                  LSTAT=lambda d: d['LSTAT'] > np.median(d['LSTAT']))
>>> y_clf = y > np.median(y)
>>> X_train, X_test, y_train, y_test = train_test_split(X_clf, y_clf)
>>> model = LogisticRegression(random_state=123, solver = 'liblinear')
>>> model.fit(X_train, y_train)
LogisticRegression(random_state=123, solver='liblinear')
>>> predicted = model.predict(X_test)
>>> DP_B = fm.demographic_parity_difference(y_true = y_test,
...                                      y_pred = predicted,
...                                      sensitive_features = X_test["B"])
>>> DP_LSTAT = fm.demographic_parity_difference(y_true = y_test,
...                                          y_pred = predicted,
...                                          sensitive_features = X_test["LSTAT"])
>>> print(f"Demographic parity difference:\nB: {DP_B}\nLSTAT: {DP_LSTAT}")  
Demographic parity difference for:
B: 0.5470085470085471
LSTAT: 0.8583829365079365
>>> metrics = {'accuracy': skm.accuracy_score,
...            'precision': skm.precision_score,
...            'recall': skm.recall_score,
...            'false positive rate': fm.false_positive_rate,
...            'true positive rate': fm.true_positive_rate,
...            'selection rate': fm.selection_rate,
...            'count': fm.count}
>>> grouped_metric = fm.MetricFrame(metrics=metrics,
...                                 y_true=y_test,
...                                 y_pred=predicted,
...                                 sensitive_features=X_test["B"])
>>> print(grouped_metric.by_group)  
    accuracy     precision       recall   false positive rate   true positive rate    selection rate  count
B
False       1.0           0.0          0.0                   0.0                  0.0               0.0     10
True   0.837607       0.84375     0.857143              0.185185             0.857143          0.547009    117

[2 rows x 7 columns]
>>> grouped_metric = fm.MetricFrame(metrics=metrics,
...                                 y_true=y_test,
...                                 y_pred=predicted,
...                                 sensitive_features=X_test["LSTAT"])
>>> print(grouped_metric.by_group)  
    accuracy     precision       recall   false positive rate   true positive rate    selection rate  count
LSTAT
False   0.84127      0.864407     0.962264                   0.8             0.962264          0.936508     63
True   0.859375           0.6          0.3              0.037037                  0.3          0.078125     64

[2 rows x 7 columns]

The demographic parity differences shows that neither variable has a demographic parity at zero, which implies different selection rates across groups. The vast majority of observations of B fall above the cutoff. For the B variable, observations below the cutoff have zero precision and recall, but the model has a higher accuracy for this group than records where B > 136.9. The precision, recall, and selection rate when LSTAT is True all are lower than when LSTAT is False. These results indicate that our simple model is worse at predicting an outcome for individuals in the “lower status” category.

Discussion

The Boston housing dataset presents many ethical issues, and in general, we strongly discourage using it in predictive modelling analyses. We’ve kept it in Fairlearn because of its potential as a teaching tool for how to deal with ethical issues in a dataset. There are ways to remove correlations between sensitive features and the remaining columns [9], but that is by no means a guarantee that fairness-related harms won’t occur. Besides, other benchmark datasets exist that do not present these issues.

It’s important to keep the differences between the way Harrison and Rubenfield used the dataset and the way modern machine learning practitioners have used it in focus. Harrison and Rubenfield conducted an empirical study, the goal of which was to determine the causal impacts of these variables on median home value. Interpretation of causal models involves looking at model coefficients to ascertain the effect of one variable on the dependent variable, holding all other factors constant. This use case is different than the typical supervised learning analysis. A machine learning model will pick up on the patterns encoded in the data and use those patterns to predict an outcome. In the Boston housing dataset, the patterns the authors encoded through the B and LSTAT variables include systemic racism and class inequalities, respectively. Using the Boston housing dataset as a benchmark for a new supervised learning model means that the model’s performance is in part due to how well it learns and replicates these patterns.

The Boston Housing dataset raises the more general issue of whether it’s valid to port datasets constructed for one specific use case to different use cases (see The Portability Trap). Using a dataset without considering the context and purposes for which it was created can be risky even if the dataset does not carry the possibility of generating fairness-related harms. Any machine learning model developed using a dataset with an opaque data-generating process runs the risk of generating spurious or non-meaningful results. Construct validity is also relevant here; a dataset may not maintain construct validity across different types of statistical analyses and different predicted outcomes.

If you are searching for a house pricing dataset to use for benchmarking purposes or to create a hedonic pricing model, scikit-learn recommends the California housing dataset (sklearn.datasets.fetch_california_housing()) or the Ames housing dataset [10] in place of the Boston housing dataset, as using these datasets should not generate the same fairness-related harms. We strongly discourage using the Boston Housing dataset for machine learning benchmarking purposes, and hope this article gives you pause about using it in the future.

References

[1]

David Harrison, Jr and Daniel L Rubinfeld. Hedonic housing prices and the demand for clean air. Journal of environmental economics and management, 5(1):81–102, 1978. URL: https://deepblue.lib.umich.edu/bitstream/handle/2027.42/22636/0000186.pdf?sequence=1&isAllowed=y.

[2]

United States Census Bureau. Metropolitan areas. URL: https://www.census.gov/history/www/programs/geography/metropolitan_areas.html.

[3]

Ali Al Bataineh and Devinder Kaur. A comparative study of different curve fitting algorithms in artificial neural network using housing dataset. In Naecon 2018-ieee national aerospace and electronics conference, 174–178. IEEE, 2018. URL: https://ieeexplore.ieee.org/abstract/document/8556738.

[4]

Mohsen Shahhosseini, Guiping Hu, and Hieu Pham. Optimizing ensemble weights for machine learning models: a case study for housing price prediction. In Smart Service Systems, Operations Management, and Analytics: Proceedings of the 2019 INFORMS International Conference on Service Science, 87–97. Springer, 2020. URL: https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1187&context=imse_conf.

[5]

Michael Tipping. The relevance vector machine. Advances in neural information processing systems, 1999. URL: https://proceedings.neurips.cc/paper/1999/file/f3144cefe89a60d6a1afaf7859c5076b-Paper.pdf.

[6]

John F. Kain and John M. Quigley. Housing markets and racial discrimination: a microeconomic analysis. 1975. URL: https://www.nber.org/books-and-chapters/housing-markets-and-racial-discrimination-microeconomic-analysis.

[7]

M Carlisle. Racist data destruction? 2019. URL: https://medium.com/@docintangible/racist-data-destruction-113e3eff54a8.

[8]

Kimberlé Crenshaw. Mapping the margins: intersectionality, identity politics, and violence against women of color. Stanford Law Review, 43(6):1241–1299, 1991. URL: https://www.jstor.org/stable/1229039, arXiv:https://www.jstor.org/stable/1229039, doi:https://doi.org/10.2307/1229039.

[9] (1,2)

Vincent Warmerdam, Matthijs Brouns, and Scikit-Lego contributors. Fairness. 2019. URL: https://scikit-lego.netlify.app/fairness.html.

[10]

Scikit-Learn developers. The ames housing dataset. 2022. URL: https://inria.github.io/scikit-learn-mooc/python_scripts/datasets_ames_housing.html.