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mographic attributes, such as their zip code, consumption ability, or employment status, can be the proxies
for socioeconomic status. Variational autoencoder has been widely used to learn causal models with hidden
confounders, especially for approximately inferring the complex relation between the observational variables
and hidden confounders [109] . It is a computationally efficient algorithm for learning the joint distribution of
the hidden confounders and the observed ones from observational data. An alternative way to eliminate the
confounding bias in causal inference is to utilize the underlying network information that is attached to ob-
servational data (e.g., social networks) to infer the hidden confounders. For example, Guo et al. [110] proposed
the network deconfounder to infer the influence of hidden confounders by mapping the features of observa-
tional data and auxiliary network information into the hidden space. Guo et al. [111] leveraged the network
information to recognize the representation of hidden confounders. Veitch et al. [112] remarked that merely
partial information that hidden confounders contain affects both the treatment and the outcome. That is to
say, only a portion of confounders is actually used by the estimator to estimate the causal effects. Therefore,
if a good predictive model for the treatment can be built, then one may only need to plug the outputs into
a causal effect estimate directly, without any need to learn all the true confounders. Since experimental data
do not suffer from hidden confounders, another method is to combine experimental and observational data
together. For example, Kallus et al. [113] used limited experimental data to correct the hidden confounders in
causal effect models trained on larger observational data, even if the observational data do not fully overlap
with the experimental ones, which makes strictly weaker assumptions than existing approaches.

Overall, these potential outcome framework-based methods mostly rely on proxy variables. Before selecting
proxy variables for hidden confounders, we need a thorough understanding of what a hidden confounder is
supposed to represent, and whether there is any proxy variable that actually represents it. However, a suffi-
ciently clear understanding may be impossible to attain in some cases.

7.3. Comprehensive definition of fairness
The sources of unfairness in machine learning algorithms are diverse and complex, and different biases have
different degrees of impact on unfairness. Since most fairness notions, including causality-based fairness no-
tions, quantify fairness in a single dimension, when comparing the capabilities of different fairness machine
learning algorithms, using different fairness measures will often lead to different results. This means that,
whether the algorithm is fair or not is relative, which depends not only on the model and data but also on
the task requirements. There is a lack of complete and multi-dimensional causality-based fairness definition
and evaluation system for fairness, and it is not possible to effectively quantify the fairness risk faced by ma-
chine learning algorithms. Therefore, we need to further explore comprehensive causal-based fairness notions
and establish a comprehensive multi-dimensional evaluation system for the fairness of machine learning algo-
rithms. In addition, the definition of fairness needs to be combined with the laws and the concept of social
fairness of various countries to avoid narrow technical solutions. The proposition of PC-fairness and causality-
based fairness notion defined from both macro-level and individual-level [114] are useful explorations to solve
this problem.

7.4. Achieving fairness in a dynamic environment
Theexistingworksmainlyfocusonstudyingthefairnessinmachinelearninginstatic, nofeedback, short-term
impact scenarios, without examining how these decisions affect fairness in future applications over time and
failing to effectively adapt to evolutionary cycles. At present, the research on the fairness of machine learning
shows a trend of dynamic evolution, which requires the definition of fairness and algorithms to consider the
dynamic, feedback, and long-term consequences of decision-making systems. This is particularly evident in
recommendationsystems, loans, hiring, etc. Fortunately, someresearchersaremodelingthelong-termdynam-
ics of fairness in these areas [115–119] . D’Amour et al. [120] regarded dynamic long-term fair learning as a Markov
decision process (MDP) and proposed simulation studies to model fairness-enhancing learning in a dynamic
environment. They emphasized the importance of interaction between the decision system and the environ-