Venue: NAACL 2021

# Everything Has a Cause: Leveraging Causal Inference in

Legal Text Analysis

 Xiao Liu\({}^{1}\), Da Yin\({}^{2}\); Yansong Feng\({}^{1,3}\), Yuting Wu\({}^{1}\) &Dongyan Zhao\({}^{1,3}\)

\({}^{1}\)Wangxuan Institute of Computer Technology, Peking University, China

\({}^{2}\)Computer Science Department, University of California, Los Angeles

\({}^{3}\)The MOE Key Laboratory of Computational Linguistics, Peking University, China

{lxlisa,fengyansong,wyting,zhaody}@pku.edu.cn

da.ynin@cs.ucla.edu

###### Abstract

Causal inference is the process of capturing cause-effect relationship among variables. Most existing works focus on dealing with structured data, while mining causal relationship among factors from unstructured data, like text, has been less examined, but is of great importance, especially in the legal domain. In this paper, we propose a novel **G**raph-based **C**ausal **I**nference (_GCI_) framework, which builds causal graphs from fact descriptions without much human involvement and enables causal inference to facilitate legal practitioners to make proper decisions. We evaluate the framework on a challenging _similar charge disambiguation_ task. Experimental results show that _GCI_ can capture the nuance from fact descriptions among multiple confusing charges and provide explainable discrimination, especially in few-shot settings. We also observe that the causal knowledge contained in _GCI_ can be effectively injected into powerful neural networks for better performance and interpretability. Code and data are available at [https://github.com/xxxiaol/GCI/](https://github.com/xxxiaol/GCI/).

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Footnote †: Corresponding author.

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Footnote †: Corresponding author.

## 1 Introduction

Causal inference is the process of exploring how changes on variable \(T\) affect another variable \(Y\). Here we call \(T\) and \(Y\) as _treatment_ and _outcome_, respectively, and the changes on \(T\) are called _intervention_. In other words, the process of drawing a conclusion about whether and how \(Y\) changes when intervening on \(T\) is called _causal inference_.

Most research in causal inference is devoted to analyzing structured data. Take the research question _how smoking causes lung cancer_Pearl and Mackenzie (2018) as an example. _Smoking_, _lung cancer_, together with distractors like _age_ are extracted from structured data, like electronic health records, and considered as factors. Usually, such studies properly organize those factors into human-designed structures, e.g., a causal directed acyclic graph Wright (1921) with factors {_smoking_, _age_, _lung cancer_} as nodes and causal relations {_smoking_\(\rightarrow\)_lung cancer_, _age_\(\rightarrow\)_lung cancer_} as edges, and perform inference on such structures.

Recent works attempt to integrate text information into causal inference Egami et al. (2018); Veitch et al. (2019); Yao et al. (2019); Keith et al. (2020), but they mainly treat the text as a single node in the causal graph, which is relatively coarse-grained. For instance, Yao et al. (2019) investigate how the complaints from consumers affect the company's responses (admission or denial). They regard the entire text of complaint as a treatment, without looking into different aspects of the text, like the events that consumers complained about and the compensation that consumers requested.

Actually, discovering causal relationship _inside_ unstructured and high-dimensional data, like text, is also beneficial or even crucial for scenarios involving reading comprehensive text and making decisions accordingly. For instance, when a legal AI system assists judges to deal with complicated cases that involve multiple parties and complex events, causal inference could help to figure out the exact distinguishable elements that are crucial for fair and impartial judgements. As shown in Figure 1, if the system can automatically spot two

Figure 1: An example of generated causal graph for the charge fraud. Colored words are matched between the exemplified fact description and the graph.



essential key points, 1) the deceitful acts of the defendant, and 2) obtaining properties from the victim, from the unstructured fact descriptions, then the prediction fraud can be more convincing and helpful, rather than a label from a black box. In practice, we would expect a legal AI system to provide human-readable and sound explanations to help the court make the right decisions. It is worthwhile especially for underdeveloped areas, where such techniques could help the judges of rural areas with more trustworthy references from previous judgements. This would further help to maintain the principle of _treating like cases alike_ in many continental law systems. A main challenge in judicial practice is to distinguish between similar charges, we thus propose a new task _similar charge disambiguation_ as a testbed. Cases of similar charges often share similar context, and a system is expected to mine the nuance of reasoning process from the text.

However, performing causal inference on fact descriptions of criminal cases is not trivial at all. It poses the following challenges. 1) Without expert involvement, it is not easy to extract factors that are key to prediction, and organize them in a reasonable form that can both facilitate the inference process and tolerate noise. For example, automatically extracted elements may not cover all the key points in the textual descriptions, and automatically built graphs may contain unreliable edges. 2) It is not easy to benefit from both traditional causal inference models and modern neural architectures.

In this paper, we propose a novel **G**raph-based **C**ausal **I**nference (_GCI_) framework, which could effectively apply causal inference to legal text analysis. _GCI_ first recognizes key factors by extracting keywords from the fact descriptions and clustering similar ones into groups as individual nodes. Then we build causal graphs on these nodes with a causal discovery algorithm that can tolerate unobserved variables, reducing the impact of missing elements. We further estimate the causal strength of each edge, to weaken unreliable edges as much as possible, and apply the refined graph to help decision making. Experimental results show that our _GCI_ framework can induce reasonable causal graphs and capture the nuance from plain text for legal applications, especially with few training data.

We also explore the potential of _GCI_ by integrating the captured causal knowledge into neural network (NN) models. We propose two approaches: 1) imposing the causal strength constraints to the NN's attention weights; 2) applying recurrent neural networks on the causal chains extracted from our causal graphs. Experiments indicate that our methods can successfully inject the extracted causal knowledge and thus enhance the NN models. We also show that integrating _GCI_ helps to mitigate the underlying bias in data towards the final prediction.

Our main contributions are as follows: 1) We propose a novel graph-based causal inference (_GCI_) framework to apply causal inference to unstructured text, without much human involvement. 2) We explore to equip popular neural network models with our _GCI_, by encouraging neural models to learn from causal knowledge derived from _GCI_. 3) We evaluate our methods on a legal text analysis task, similar charge disambiguation, and experimental results show that our _GCI_ can capture the nuance from plain fact descriptions, and further help improve neural models with interpretability.

## 2 Background

Two types of questions are typically related to causality. The first is whether there is causal relationship between a set of variables, and the second question is when two variables \(T\) and \(Y\) are causally related, how much would \(Y\) change if we change the value of \(T\). Both of them are discussed in our _GCI_ framework, and we first briefly introduce the key concepts.

### Causal Discovery

Causal discovery corresponds to the first type of questions. From the view of graph, causal discovery requires models to infer causal graphs from observational data. In our _GCI_ framework, we leverage _Greedy Fast Causal Inference_ (GFCI) algorithm [9] to implement causal discovery. GFCI combines score-based and constraint-based algorithms. It merges the best of both worlds, performing well like score-based methods, and not making too unrealistic assumptions like constraint-based ones. Specifically, GFCI does not rely on the assumption of no latent confounders, thus is suitable in our situation. More details of GFCI algorithm and its advantage is provided in Appendix A.

The output of GFCI is a graphical object called _Partial Ancestral Graph_ (PAG). PAG is a mixed graph containing the features common to all Di 

rected Acyclic Graphs (DAGs) that represent the same conditional independence relationship over the measured variables. In other words, PAG entails all the possibilities of valid DAGs concerning the original data. In causal inference settings Zhang et al. (2008), four types of edges are provided in PAG, as listed in Table 1. With PAG, we are able to consider unobserved confounders and the uncertainty in causal inference.

### Causal Strength Estimation

Causal strength estimation deals with the second type of questions. It is the very task to quantify the causal strength of each learned relation, i.e., whether the relation is strong or weak. To precisely estimate causal strength, confounders need to be kept the same. _Confounder_ is a variable causally influencing both treatment \(T\) and outcome \(Y\). Take the example of _smoking, lung cancer_ and _age_ in Section 1. Here we study if there is causal relationship between _smoking_ (\(T\)) and _lung cancer_ (\(Y\)), and _age_ is a confounder \(C\). It is straightforward to compare the proportion of _lung cancer_ among smokers and non-smokers. However, _age_ influences both _smoking_ and _lung cancer_. Older people are more likely to smoke. They also have a much higher risk of suffering from cancer. If we do not consider the value of _age_, its influence to _lung cancer_ will be regarded as _smoking_'s influence, thus wrongly amplify the causal effect of _smoking_ to _lung cancer_.

In our _GCI_ framework, we apply _Average Treatment Effect_ (ATE) Holland (1986) as a measure of causal strength. All variables are binary in our work. So given an edge \(T\to Y\), we quantify how the outcome \(Y\) is expected to change if we modify the treatment \(T\) from 0 to 1:

\[\psi_{T,Y}=E[Y~{}|~{}do(T=1)]-E[Y~{}|~{}do(T=0)], \tag{1}\]

where \(E\) means expectation, and the do-calculus \(do(T=1)\) indicates intervention on \(T\), setting its value to \(1\).

We utilize the _Propensity Score Matching_ (PSM) method to estimate ATE. PSM finds the pairs of comparable samples with the most similar propensity scores, where each pair consists of one sample in the treated group and one in the untreated. Given the great similarity between the two samples, we could make a direct comparison between them. Specifically, propensity score \(L(z)=P(T=1~{}|~{}Z=z)\) is the probability of treatment being assigned to \(1\) given a set of observed confounders \(z\). As \(T\) is binary, we have \(T\perpp Z~{}|~{}L\left(\perpp\right.\) means independence). So matching on propensity scores equals matching on the full set of confounders.

## 3 Graph-based Causal Inference Framework

Our graph-based causal inference (_GCI_) framework consists of three parts, constructing the causal graph, estimating causal strength on it, and making decisions. Figure 2 shows the overall architecture.

### Task Definition

We first define the _similar charge disambiguation_ task. Given the fact descriptions of criminal cases \(\mathbb{D}=\{d_{1},d_{2},\ldots,d_{N}\}\), a system is expected to classify each case into one charge from the similar charge set \(\mathbb{C}=\{c_{1},c_{2},\ldots,c_{M}\}\).

### Causal Graph Construction

Extracting Factors.To prepare nodes for the causal graph, we calculate the importance of word \(w_{j}\) for charge \(c_{i}\) using YAKE Campos et al. (2020). We enhance YAKE with inverse document frequency Jones (1972) to extract more discriminative words of each charge.

To discriminate the similar charges, we select \(p\) words with the highest importance scores for each charge, cluster them into \(q\) classes to merge similar keywords. The \(q\) classes together with the \(M\) charges form the nodes of the causal graph. All these factors are binary. When the graph is applied to a case, each factor is of value \(1\) if it exists in this case, and \(0\) if not. Unlike factors extracted by experts, automatically extracted keywords may be incomplete, resulting in unobserved confounders in causal discovery.

Learning Causal Relationship.The next step is to build edges for the graph, in other words, discover the causal relationship between different factors. To learn causal relations and tackle the unobserved confounder problem, we use GFCI Ogarrio et al. (2016), which does not rely on the assumption

\begin{table}
\begin{tabular}{r|l} \hline \hline
**Edge** & **Meaning** \\ \hline A \(\rightarrow\) B & A causes B. \\ A \(\leftrightarrow\) B & There is an unobserved confounder of A and B. \\ A \(\leftrightarrow\)B & Either A causes B, or unobserved confounder. \\ A \(\leftrightarrow\)B & Either A causes B, or B causes A, or unobserved confounder. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of edge types in PAG.

 

of no unobserved confounders. As mentioned in Section 2, the output of GFCI is a PAG. Appendix C gives an example of a generated PAG in detail.

We further introduce constraints to filter noisy edges. First, as the judgement is made based on the fact description, we do not allow edges from charge nodes to other ones, e.g., an edge from fraud to _lie_ is prohibited. Second, given that causes usually appear before effects in time Black (1956), and fact descriptions in legal text are often written in the temporal order of events, we thus consider the chronological order of descriptions as temporal constraints to filter noisy edges. If factor \(A\) appears after \(B\) in most cases, we will not allow the edge from \(A\) to \(B\). Note that this constraint does not imply there is an edge from \(B\) to \(A\), as chronological order is not a sufficient condition of causality.

Sampling Causal Graphs.PAG contains uncertain relations shown in Table 1, which leaves challenges for quantification and further application. So we sample \(Q\) causal graphs from PAG. Among the four edge types, \(\rightarrow\) and \(\leftrightarrow\) are clear: in each sampled graph, \(\rightarrow\) edges are retained and \(\leftrightarrow\) edges are removed (because they do not indicate causal relations between the two nodes). For \(\circ\rightarrow\) edges, they have two possible choices: being kept (cause) and being removed (unobserved confounder). In the absence of true possibility, we simply keep an edge with \(1/2\) probability, and remove it with another \(1/2\). And for \(\circ\!\!-\!\!\circ\) edges, we give \(1/3\) probability for \(\rightarrow\), \(\leftarrow\), and no edge, respectively. The quality of each sampled graph \(G_{q}\) is measured by its fitness with data **X**, where we use the Bayesian information criterion \(\mathrm{BIC}(G_{q},\textbf{X})\) to estimate Schwarz et al. (1978).

### Strength Estimation on Causal Graphs

As the resulting graphs are noisy in nature, we estimate the strength of the learned causal relations to refine a sampled causal graph. We assign high strength to edges with strong causal effect, and near-zero strength to edges that do not indicate causal relations or with weak effect. We regard the Average Treatment Effect \(\psi^{G}_{T,Y}\) (ATE, Section 2.2) as the strength of \(T\to Y\) in graph \(G\), and utilize the Propensity Score Matching (PSM, Section 2.2) to measure it:

\[\hat{\psi}^{G}_{T,Y}=[\sum_{i:t_{i}=1}(y_{i}-y_{j})+\sum_{i:t_{i}=0}(y_{j}-y_{ i})]/N, \tag{2}\]

where \( j=\underset{k:t_{k}\neq t_{i}}{\operatorname*{argmin}}|L(z_{i})-L(z_{k})|\) means the most similar instance in the opposite group of \(i\), and \(t_{i},y_{i},z_{i}\) are the value of treatment, outcome and confounders of instance \(i\), respectively.

### Making Decisions

When applying the sampled causal graphs to the similar charge disambiguation task, we simply extract factors and map the case description with the graph accordingly, and decide which charge in \(\mathbb{C}\) is more appropriate to this case. Firstly, we compute the overall causal strength of each factor \(T_{j}\) to \(Y_{i}\) among the \(Q\) sampled causal graphs, where \(Y_{i}\) represents whether charge \(c_{i}\) is committed:

\[\tilde{\psi}_{T_{j},Y_{i}}=\sum_{q=1}^{Q}\mathrm{BIC}(G_{q},\mathbf{X})\times \hat{\psi}^{G_{q}}_{T_{j},Y_{i}},\] (3) 

where \(\hat{\psi}_{T_{j},Y_{i}}^{G_{q}}\) is the measured causal strength in \(G_{q}\), and is \(0\) if edge \(T_{j}\to Y_{i}\) does not exist in \(G_{q}\).

For each case, we then map the text with the graphs, and calculate scores for each charge:

\[S(Y_{i})=\sum_{T_{j}\in Tr(Y_{i})}\tilde{\psi}_{T_{j},Y_{i}}\times\tau(T_{j}), i\in\{1,\ldots,M\}, \tag{4}\]

where \(\tau(T_{j})\) is a dummy variable indicating the presence of \(T_{j}\) in this case, and \(Tr(Y_{i})\) is the set of treatments of \(Y_{i}\) (from the view of graph, the nodes pointing to \(Y_{i}\)). The calculated scores are fed into a random forest classifier [Ho, 1995] to learn thresholds between the charges. More advanced classifiers can also be used.

## 4 Integration of Causal Analysis and Neural Networks

Neural networks (NN) are considered to be good at exploring large volumes of textual data. This motivates us to integrate the causal framework with NN, to benefit each other. Here we propose two integration methods as shown in Figure 3.

### Imposing Strength Constraint

First, we inject the estimated causal strength to constrain the attention weights of a Bi-LSTM with attention model [Zhou et al., 2016]. A Bi-LSTM layer is first applied to the fact descriptions to obtain contextual embeddings \(\mathbf{H}=\{\mathbf{h}_{1},\mathbf{h}_{2},\dots,\mathbf{h}_{n}\},\mathbf{h} _{i}\in\mathbb{R}^{b_{0}}\), where \(b_{0}\) is the dimension of embeddings. Then, an attention layer assigns different weights \(\{a_{1},a_{2},\dots,a_{n}\}\) to each word, and sums the words up according to the weights to build a text embedding \(\mathbf{v}\):

\[a_{i}=\frac{\exp(\mathbf{q}^{T}\cdot\mathbf{h}_{i})}{\sum_{k=1}^{n}\exp( \mathbf{q}^{T}\cdot\mathbf{h}_{k})},\mathbf{v}=\sum_{i=1}^{n}a_{i}\times \mathbf{h}_{i}, \tag{5}\]

where \(\mathbf{q}\in\mathbb{R}^{b_{0}}\) is a learnable query vector. Finally, we apply two fully connected layers to the text embedding \(\mathbf{v}\), and form the prediction vector \(\mathbf{r}_{cons}\).

Besides a cross-entropy loss \(L_{cross}\) on \(\mathbf{r}_{cons}\), we introduce an auxiliary loss \(L_{cons}\) to guide the attention module with the causal strength learned from _GCI_. Given the golden label \(c_{j}\), for each word \(w_{i}\) which belongs to the factor \(f\), \(\tilde{\psi}_{T_{j},Y_{j}}\) is the corresponding causal strength, and \(g_{i}\) is the normalized strength over the whole sequence. \(L_{cons}\) is set to make the attention weights close to the normalized strength:

\[\begin{split}& L_{cons}=\sum_{i=1}^{n}(a_{i}-g_{i})^{2},\\ & L=L_{cross}+\alpha L_{cons}.\end{split} \tag{6}\]

Note that in the validation and testing stages, the inputs do not contain any strength constraint and golden charge information. Therefore, we select the epoch with the least cross-entropy loss in the validation stage to evaluate on the test set.

### Leveraging Causal Chains

Causal chains are another type of knowledge that can be captured from causal graphs. In the legal scenario, causal chains depict the process of committing crimes. They can also be treated as the summarization of cases or behavioural patterns for each charge. Therefore, the second approach is to leverage the causal chains directly, as the chains may contain valuable information for judgement. For a given text, we extract factors and traverse all causal chains composed by the factors from the sampled causal graphs, \(Chains=\{chain_{1},chain_{2},\dots,chain_{m}\}\). In this task, we only consider chains ending up with treatments of charges, as they are more relevant with the judgement. An LSTM layer is applied to each chain, and all the chains are pooled to build case representation \(\mathbf{c}\in\mathbb{R}^{b_{0}}\):

\[\begin{split}&\mathbf{ch}_{i}=\sum_{j=1}^{l_{i}}(\mathrm{LSTM}(chain_{i})_{ j}),\\ &\mathbf{c}=\mathrm{MaxPooling}(\mathrm{BIC}(G_{q},\mathbf{X}) \times\mathbf{ch}_{i}),\\ &\qquad\quad 1\leq i\leq m,~{}~{}chain_{i}\in G_{q},\end{split} \tag{7}\]

where \(l_{i}\) indicates the length of \(chain_{i}\). The case representation \(\mathbf{c}\) is then fed to two fully connected layers to make the prediction \(\mathbf{r}_{chain}\), and a cross-entropy loss is used to optimize the model.

Figure 3: Two ways of integrating causal analysis and neural networks.

 



## 5 Experiments and Evaluation

### Experimental Setup

Dataset.For the similar charge disambiguation task, we pick five similar charge sets from the _Criminal Law of the People's Republic of China_(Congress, 2017), which are hard to discriminate in practice (Ouyang et al., 1999), and select the corresponding fact descriptions from the Chinese AI and Law Challenge (CAIL2018) (Xiao et al., 2018). Detailed statistics of the charge sets are given in Table 2. Note we filter out the cases whose judgements include multiple charges from one charge set. The fact descriptions in our dataset are in Chinese.

Our Models.We evaluate our graph-based causal inference (_GCI_) framework as described in Section 3, and two models integrating _GCI_ with NN (_Bi-LSTM+Att+Cons_ and _CausalChain_) as described in Section 4.

Comparison Models.To study the effect of causal relationship captured by _GCI_, we implement a variant called _GCI-co_, which is built upon a correlation-based graph rather than our discovered causal graph. In detail, we compute the Pearson correlation coefficient \(\phi\) for every two factors, and draw an edge if \(\phi>0.5\). The direction of the edge is from the factor that appears earlier in the text more often, to the other. Then we compare _GCI_ and two integration methods with NN baselines, including _LSTM_, _Bi-LSTM_ and _Bi-LSTM+Att_. _Bi-LSTM+Att_ is a common backbone of legal judgement prediction models, while we do not add multi-task learning (Luo et al., 2017) and expert knowledge (Xu et al., 2020) for simplicity. Since the prior knowledge learned from pre-trained models may result in unfair comparison, we do not choose the models such as BERT (Devlin et al., 2018) as baselines and backbones to eliminate the influence. Previous works integrating text into causal inference are not able to find causal relationships inside text, so we do not take them into comparison.

We select a set of training ratios, 1%, 5%, 10%, 30%, and 50%, to study how the performance gap changes along with different training data available. For each setting, we run the experiments on three random seeds and report the average accuracy (Acc) and macro-F1 (F1). More details about baselines, parameter selection, and training process are in Appendix B.

### Main Results

Table 3 reports the charge disambiguation performance of our models and comparison models.

Causal Graph vs. Correlation-based Graph._GCI_ outperforms _GCI-co_ by 4.5% on average Acc, and 9.8% on average F1, indicating the graph constructed by mining causal relations better captures the relationship between charges and factors.

Causal Inference vs. Neural Networks.Comparing _GCI_ with NN baselines _LSTM_, _Bi-LSTM_ and _Bi-LSTM+Att_, we observe in few-shot settings (1%, 5%), _GCI_ outperforms NNs by about 10% on average, since NNs tend to underfit in few-shot settings. However, with the increase of training data, the performance gap becomes narrower and consequently, NNs outperform _GCI_ in several cases. Compared with _GCI_, NNs have the advantage of learning from large amounts of unstructured data.

Adding Strength Constraints.We can see that _Bi-LSTM+Att+Cons_ outperforms _Bi-LSTM+Att_ by around 1-5%. The performance gap is much larger in few-shot settings. This suggests that our estimated causal strength is helpful for attention-based models to capture the key information in the text.

Causal Chains vs. Whole Text.Both _CausalChain_ and _LSTM_ are a straightforward application of unidirectional LSTM, but over different texts, one for our extracted causal chains and the other for the whole fact description. We find _CausalChain_ outperforms _LSTM_ by 8.2% on average Acc and 11.7% on average F1. The difference shows that causal chains contain condensed key information that contributes to the judgement, while the whole description may contain far more irrelevant information that may disturb the prediction. We also conduct experiments on combining causal chains and the

\begin{table}
\begin{tabular}{l|c|c} \hline \hline
**Charge Sets** & **Charges** & **\#Class** \\ \hline Perronal Injury & \begin{tabular}{c} Intentional Injury \& Murder \& 6377/ 2282/ / \\ Involuntary Manslaughter \\ \end{tabular} \\ \hline Violent Acquisition & Robry \& Seitzer \& 5020/ 2113/ \\  & Kidapplying & 622 \\ \hline FAE & Fraud \& Extortion & 3536/ 2149 \\ \hline EEMPF & \begin{tabular}{c} Enbenzzlement \& \\ Misappropriation of Public Funds \\ \end{tabular} & 2931/ 1998 \\ \hline APRDD & 
\begin{tabular}{c} Abuse of Power \& \\ Derclion of Duty \\ \end{tabular} & 1950/ 1938 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of the similar charge sets.



whole plain text, but simply concatenating them does not work well since the whole text may introduce noise, and better integration methods are needed, which we leave for future work.

## 6 Analysis

### Quality of Causal Graphs

To analyze the robustness of the causal discovery process, we apply sensitivity analysis on the causal graphs. In detail, we make disturbance to the original causal relations, and examine the sensitivity of causal effect towards the violations. Following Kiciman and Sharma (2018), we use three features for examination: 1) _Random Confounder_, a new confounder with random value is added to the graph, and ideally, the causal strength should remain the same as before. 2) _Placebo Treatment_, the value of a treatment is replaced by a random value, so the treatment becomes a placebo, and the strength should be zero. 3) _Subset of Data_, we use a subset of cases to recalculate the strength. Ideally, the strength estimation will not vary significantly.

We take a sampled causal graph of F&E (Fraud & Extortion) as an example, and exhibit the refuters on the treatments of charge extortion in Figure 4. Causal strength is almost the same as before after _Random Confounder_ and _Subset of Data_ refutation; and turns to nearly zero after _Placebo Treatment_. The results show that our graph construction method is robust against disturbance.

### Causal Chains in Graph

Causal chains manifest how effective _GCI_ is in terms of inducing common patterns of suspect's

Figure 4: An example of sensitivity analysis for treatments of extortion in the causal graph of F&E.

 

behaviors. It is helpful for people to better understand the core part of legal cases. Here we select the causal graph of Personal Injury (Intentional Injury & Murder & Involuntary Manslaughter) and showcase several causal chains underlying the text. As shown in Figure 5, the chains depict common patterns of these charges, from the initial causes, to the final criminal behaviour. More examples are provided in Appendix D.

Now the question is how the graph structures help to discriminate similar charges. Here we analyze the nuance between the causal chains of two similar charges E&MPF (Embezzlement & Misapppriation of Public Funds). For both charges, the cases often first give the background that someone held a certain position of authority, thus had power. Then both kinds of cases describe that the person illegally obtained a large amount of money by utilizing his power. While the cases in E&MPF share very similar context, there exists nuance between them: embezzlement emphasizes that someone privately and illegally possesses the bulk of money, while misappropriation of public funds emphasizes that someone would temporally use the money for a certain purpose. By observing the causal chains of two charges, _GCI_ could capture the slight difference well: for embezzlement, the causal chains tend to be _work / take charge of \(\rightarrow\) take advantage of (position/power)_; for misappropriation of public funds, the causal chains tend to be _take charge of \(\rightarrow\) take advantage of (position/power) \(\rightarrow\) misappropriate \(\rightarrow\) profit_. The difference between the former and latter chains is whether the person had subsequent behaviour (e.g., using the money for purposes like making profits). We could observe that the difference in causal chains accords with the definitions of the two charges.

### Effect of Integrating Causal Strength with Attention

Following Lei et al. (2017), we conduct human evaluation on words accorded with high attention weights and compare the evaluation results of standard (_Bi-LSTM+Att_) and constraint-based attention models (_Bi-LSTM+Att+Cons_).

For each set of charges, we train both models with 10% data, and randomly select 30 cases that both models predict correctly. For the total 150 cases, we showcase content, charge names, attention weights above 0.05, and corresponding words. Each participant is asked to score from 1 to 5 for the extent of how beneficial the extracted keywords are to disambiguation. A higher score means that the attention weights indeed capture the keywords. Each case is assigned to at least four participants. Results are shown in Table 4. We observe that the constraint-based model is better at explanation than normal attention-based models on all five charge groups. Take Violent Acquisition as an example. Although the cases are predicted correctly by _Bi-LSTM+Att_, the model tends to attend to words _bag_, _RMB_ and _value_, which frequently occur but cannot be treated as clues for judgement. Instead, _Bi-LSTM+Att+Cons_ values factors such as _grab_, _rob_ and _hold_, which are more helpful for judgement.

## 7 Related Works

Causal Inference with Text.Recently, a few works try to take text into account when performing causal inference. Landeiro and Culotta (2016) introduce causal inference to text classification, and manage to remove bias from certain out-of-text confounders. Wood-Doughty et al. (2018) use text as a supplement of missing data and measurement error for the causal graphs constructed by structured data. Egami et al. (2018) focus on mapping text to a low-dimensional representation of the treatment or outcome. Veitch et al. (2019) and Yao et al. (2019) treat text as confounder and covariate, which help to make causal estimation more accurate. These works all build causal graphs manually, and regard text as a whole to be one of the factors. In contrast, we set our sights on text containing rich causal information in itself. Paul (2017) looks into text by computing propensity score for each word, but only

Figure 5: Causal chains in Personal Injury’s graph.

 

focuses on causal relationship between words and sentiment. We instead take a causal graph perspective, discover and utilize causal relationship inside text to perform reasoning.

Neural Networks for Causal Discovery.Recently, researchers attempt to apply neural networks to causal discovery (Ponti and Korhonen, 2017; Alvarez-Melis and Jaakkola, 2017; Ning et al., 2018; Gao et al., 2019; Weber et al., 2020). However, Alvarez-Melis and Jaakkola (2017) model causal relationship by correlation, which may introduce bias into causal inference; Ning et al. (2018) and Gao et al. (2019) merely focus on capturing causality by explicit textual features or supervision from labeled causal pairs. There are also a line of works focusing on how to use neural networks to summarize confounders and estimate treatment effects Louizos et al. (2017); Yao et al. (2018); Kunzel et al. (2018), which are parts of the whole causal inference process. Weber et al. (2020) show how to formalize causal relationships in script learning, but it is limited to pairwise learning of events and cannot be generalized to sequential and compositional events.

Legal Judgement Prediction.Previous works in legal text analysis focus on the task of legal judgement prediction (LJP). Luo et al. (2017) and Zhong et al. (2018) exploit neural networks to solve LJP tasks. Zhong et al. (2020) provide interpretable judgements by iteratively questioning and answering. Another line pays attention to confusing charges: Hu et al. (2018) manually design discriminative attributes, and Xu et al. (2020) use attention mechanisms to highlight differences between similar charges. Using knowledge derived from causal graphs, _GCI_ exhibits a different and interpretable discrimination process.

## 8 Discussion

Although _GCI_ is effective on its own and when working with powerful neural network models, there is still room for further improvement.

More Precise Causal Inference Models.The causal estimation results of _GCI_ is based on the constructed causal graphs in former stages, and the automated construction process may bring imprecise factors and even omissions. As clustering algorithms try to summarize the general characteristics of text, descriptions with subtle differences may be clustered into one factor, but the differences matter in legal judgement. For example, in Personal Injury's graph, different ways of killing are summarized as the factor _kill_, therefore lose valuable information. Specifically, beaten to death might occur in cases of involuntary manslaughter, while shooting cases are more likely to be associated with murder. Also, factors with low frequency may be omitted in clustering, but are actually useful for discrimination. Overall, under the circumstance without much expert effort, it is worthwhile to explore how to construct a more reliable causal graph.

Deep understanding on legal documents.Although _GCI_ to some extent tackles the challenges of incapability of causal inference methods on unstructured text, it may make mistakes when facing complex fact descriptions. _Negation semantics_ is a typical example. It is occasional to see negation word usage in fact descriptions, which usually indicates that someone did _not_ have a certain behaviour. However, _GCI_ has not considered this aspect, and may be awry in cases containing negation usage. Besides, _pronoun resolution_ is also an important aspect that may confuse models. For example, certain behaviour is done by the victim and the subject of the behaviour is a pronoun. If the model was unaware of the subject of the behaviour, it would be counted as criminal's behaviour and introduces noise to later inference stage. Moreover, _intent_ could be a decisive factor when discriminating charges, for example, murder and involuntary manslaughter. But it may not be mentioned explicitly in the fact descriptions. It should be better to recover the complete course of fact and recognize the implicit intents between the lines with deep understanding of the context and relevant common sense knowledge.

## 9 Conclusions

We propose _GCI_, a graph-based causal inference framework to discover causal information in text, and design approaches to integrate causal models and neural networks. In the similar charge disambiguation task, we show our approaches capture important evidence for judgement and nuance among charges. Further analysis demonstrates the quality of causal graphs, value of causal chains, and interpretability of computed causal strength 

Ethical Considerations

### Intended Use

We aim to facilitate legal service with our proposed _GCI_, providing valuable evidence instead of directly making judgements. We hope that legal AI models could assist legal workers in underdeveloped areas, helping them to explore key points in cases, discriminate from similar crimes, and make better decisions. By treating like cases alike in different regions of the country, influences of judges' intellectual flaws and arbitrariness are weakened, and rights of people, both the defendants and the victims, are protected.

Failure Mode.The model may give wrong evidence in some cases, but this will not cause significantly bad impact. The process of GCI is transparent. Extracted factors, the causal relations between them, and causal chains that lead to the final decision are all shown to users. By checking these "rationales" of model reasoning, users can clearly find where goes wrong, and not adopt the outputs, or intervene and correct the model.

Misuse Potential.We emphasize that such a model cannot be used individually, as the trial process is seriously conducted and regulated by the judicial system. In the actual judicial process, the prosecutors, judges, and lawyers are under strict supervision. We do not think there is a possibility for them to misuse computer models.

### Bias Analysis

Criminal behaviour is very unbalanced in gender. Take the three charges in our Personal Injury charge set as an example. Lin and Zou (2020) counted gender ratio in criminal cases from 2013 to 2017 in China, and the ratios of male defendant are 94.70% (Intentional Injury), 87.72% (Murder), and 93.97% (Involuntary Manslaughter). The disparity in defendants of male and female leads to the small proportion of female cases in training corpus. Therefore, female cases may be inadequately trained. If this results in more incorrect predictions for female cases, women's rights are violated.

Following Dixon et al. (2018) and Park et al. (2018), we use False Positive Equality Difference (FPED) and False Negative Equality Difference (FNED) to examine the performance difference in two genders. They are defined as:

\[{\rm FPED}=\sum_{t\in T}|{\rm FPR-FPR}_{t}|, \tag{8}\] \[{\rm FNED}=\sum_{t\in T}|{\rm FNR-FNR}_{t}|,\]

where FPR is false positive rate of classification, FNR is false negative rate, and \(T=\{male,female\}\). The two metrics quantify the extent of variation between the performances of two genders.

Applying them to _Bi-LSTM+Att_ and _Bi-LSTM+Att+Cons_ models in Personal Injury charge set, the results are shown in Table 5. The model with causal constraints achieves smaller variance measured by both metrics, which reduce between \(1/4\) to \(1/3\) of the unfairness in performance of _Bi-LSTM+Att_. This shows the superiority of our model with causal knowledge. Compared with normal neural networks, our constraint-based model utilizes causal relations, which are more stable to the number of occurrences.

Though adding causal knowledge narrows the equality difference, it still exists in _Bi-LSTM+Att+Cons_ (the metrics are greater than zero). Other types of bias may also exist in our model, given that the training corpora contain decisions of humans and systemic bias of humans may be preserved. Further debiasing method is needed if the model is put into real use.

In general, we believe that adding causal knowledge to decision making will help debiasing, and the transparent exhibition of causal graphs and chains will enable people to find biases in time and correct them.

## Acknowledgments

This work is supported in part by National Hi-Tech R&D Program of China (2018YFC0831900). We would like to thank the anonymous reviewers for the helpful discussions and suggestions. Also, we would thank Yuxuan Lai, Liunian Harold Li, Jieyu Zhao, Chen Wu and Xingchen Lan for advice about

\begin{table}
\begin{tabular}{l|c|c} \hline \hline
**Metrics** & _Bi-LSTM+An_ & _Bi-LSTM+Att+Cons_ \\ \hline FPED & 0.048 & **0.032** \\ FNED & 0.065 & **0.049** \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results of equality difference. Better results are in bold.

 

experiments and writing. For any correspondence, please contact Yansong Feng.

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GFCI Algorithm

GFCI (Ogarrio et al., 2016) is a combination of a constraint-based causal discovery algorithm FCI (Spirtes et al., 2013) and a score-based algorithm FGES (Ramsey et al., 2016). Based on the skeleton of FCI, it uses initialization from FGES to improve accuracy and efficiency.

FCI takes sample data and optional background knowledge as input, and guarantees to represent the Markov equivalence class of the true causal DAG. It has two phases: adjacency and orientation. It does not rely on no latent confounder assumption, but it performs relatively poorly, especially on real data.

On the other hand, FGES greedily searches over potential DAGs, and outputs the highest scoring graph it finds. It is fast and accurate when its assumptions are satisfied, but it relies on the condition that there are no latent confounders.

GFCI takes the output of FGES as an initialized graph, and the graph is further augmented by FCI's adjacency phase, in which some adjacencies are removed by conditional independence tests. A similar process happens in the orientation phase. Orientations of FGES are provided as initialization, and further orientations from FCI are applied. Proof in Ogarrio et al. (2016) guarantees the GFCI algorithm outputs a PAG that represents the true causal DAG.

Figure 6 shows the advantage of GFCI. When factor \(A\) is unobserved, score-based algorithms like GES (Chickering, 2002) will wrongly discover edge \(B\to D\), while GFCI correctly recognizes the relation between factors \(B\) and \(D\): there is an unobserved confounder of \(B\) and \(D\).

## Appendix B Implementation Details

When the training set ratio is 1%, we select \(p=15\) keywords for each charge, and cluster the keywords of both charges into \(q=20\) factors; for the training set ratio 5% and 10%, \(p=25\) and \(q=30\); for the training set ratio 30% and 50%, \(p=40\) and \(q=60\). We use K-means (MacQueen et al., 1967) for clustering. When learning causal relationship, besides cases in the training set, we also use some unlabeled cases of other charges to improve the interpretability of the causal graph. Note that removing these cases will not hurt the performance. We sample \(Q=5\) causal graphs for each PAG.

For the neural network based models (both the baselines and our proposed models), 10% of the training set is used as the validation set. The models are trained for 30 epochs, and the early stopping mechanism takes effect when the validation loss does not drop for more than 1000 batches. We use Adam optimizer with learning rate 0.001, and the dropout rate is 0.5. We use Tencent Allab Chinese Word Embedding (Song et al., 2018) as word embeddings, and the dimension of each word is 200. The hidden sizes are \(b_{0}=128\) and \(b_{1}=64\). The batchsize is selected from \(\{4,8,16,32,64,128\}\) considering the dataset size and training set ratio. For _Bi-LSTM+Att+Cons_, \(\alpha\) is manually tuned within \(\{0.1,0.25,0.5,1\}\), selecting the one with best validation F1. All the hyperparameters are empirically selected and kept the same for different models in the same dataset and the same training set ratio.

To reduce the impact of data imbalance between charges, we apply data augmentation to smaller charges whose cases are 3 times fewer than the biggest charge in that set, regardless of the training ratio. We did not keep them 1:1, in order to reflect their distributions in the real world.

The models are trained on Intel Xeon CPU. It takes about one hour to construct the causal graphs, and a few minutes to perform inference.

## Appendix C Example of Generated PAG

In this section, we further show part of a Partial Ancestor Graph (PAG) generated by our _GCI_ framework. The example is shown in Figure 7.

For the edge between _Hold People_ and _Hostage_, the arrow is \(\rightarrow\), indicating there is a causal relationship between the factors _Hold People_ and _Hostage_ (the person who was held might become a hostage).

For the edge between _Hold Knife_ and _Hold People_, the arrow is \(\circ\rightarrow\), which means there _might_ be an unobserved confounder which causes the two factors, and there _might_ exist causal relationship

Figure 6: Comparison between the output of GES and GFCI. \(A\) is a latent variable, which is also an unobserved confounder of \(B\) and \(D\). This implies that in fact there is no causal relationship between \(B\) and \(D\) but without the consideration of unobserved confounders, GES tends to be awry in this situation.

 

between the two factors. In the first possible situation, the confounder could be _Latent1_, the intent to commit a crime. A person who intends to commit a crime may hold a knife and hold people. And in the second possible situation, the person who holds a knife is likely to hold people. Therefore, there is uncertainty in predicting the causal relationship.

For the edge between _Hostage_ and _Family_, the arrow is \(\longleftrightarrow\), which means there _is_ an unobserved confounder which causes the two factors, and there _does not_ exist causal relationship between them. For example, the confounder could be _Latent2_, the intent to obtain properties from the hostage. The intent could not only make the suspect grab the hostage's money, but also contact families to ask for ransom.

## Appendix D Exhibition of More Causal Chains

Table 6 showcases three chains for each charge set. They depict common patterns of behaviours of defendants that are charged with the crime at the tail of the chains. Note that each chain merely describes one possibility and one aspect of the criminal behaviour, and the chain itself may not be sufficient to initiate such a lawsuit. For example, the chain _complete understand_\(\rightarrow\)_violate_\(\rightarrow\) abuse of power of charge set AP&DD shows that the litigant deliberately violated the rules, but he/she will be charged with abuse of power only when his/her action results in major loss of public property.

Figure 7: An example of part of the generated PAG of charge kidnapping in charge set Violent Acquisition. _Latent1_ and _Latent2_ are unobserved variables that do not exist in the generated PAG. Detailedly, _Latent1_ may denote the suspect’s intent to commit a crime; and _Latent2_ may denote the suspect’s intent to obtain properties from the hostage.