# Interpretability Study of Gradient Information in Individual Travel Prediction
## 2 Related Work
### Transparent Interpretability Models Framework  
The core advantage of the transparent model interpretability framework lies in the mathematical interpretability that the model itself can provide [12]. Through structured decision logic and explicit feature interaction relationships, researchers can directly trace the transformation process from input to output. In the field of individual travel analysis, decision tree models [13] achieve this goal through a recursive feature space partitioning mechanism: each internal node in the tree structure selects the splitting feature based on the information gain maximization criterion, which is specifically quantified as follows:  
\[IG(D,f)=H(D)-\sum_{v=1}^{V}\frac{|D_{v}|}{D}H(D_{v}) \tag{1}\]  
where \(H(D)=-\sum p_{k}\log p_{k}\) represents the entropy of the parent node, and \(D_{v}\) is the subset of data where feature \(f\) takes value \(v\). The prediction process of the decision tree can be formalized as an explicit rule combination:  
\[f(x)=\sum_{i=1}^{K}v_{i}\cdot I(x\in R_{i}) \tag{2}\]  
where \(x\) represents the input features, \(R_{i}\) represents the feature space region corresponding to the \(i\)th leaf node, \(v_{i}\) represents the predicted value of the \(i\)th leaf node, and \(I\) is the indicator function. When \(x\in R_{i}\), it takes the value of 1, otherwise, it is 0, and \(K\) represents the total number of leaf nodes. This formula implies that, for an input \(x\), the prediction result is based on the feature space region \(R_{i}\) it belongs to, and the corresponding leaf node prediction value \(v_{i}\) is taken as the output, allowing users to clearly identify the decision-making process based on the features in the model [14]. The interpretability of decision trees can also be transferred to more complex models through rule extraction techniques [15], thus constructing an interpretable travel behavior prediction framework [16].  
Compared with the visualization of static rules by decision trees, Markov models provide interpretability for temporal behavior modeling through dynamic probability transfer mechanisms [17]. The core assumption is the memoryless property of state transitions, meaning that the future state of the system depends only on the current state, not on the  
Figure 2: A visual comparison of interpretability frameworks.  
history. If the system is in state \(s_{i}\) at time \(s_{t}\), the probability of transitioning to state \(s_{j}\) at the next time step depends only on the current state \(s_{i}\), which can be represented by the transition probability matrix:  
\[A=[P(s_{t+1}=s_{j}|s_{t}=s_{i})] \tag{3}\]  
This property gives [PERSON] models unique value in dynamic scenarios such as short-term traffic flow forecasting and user movement trajectory modeling [18]. Furthermore, the hidden Markov model (HMM) infers the transition and generation processes of hidden states from observed data, making it more suitable for handling complex temporal problems with underlying patterns. For example, by analyzing historical GPS trajectory data to construct a transition probability matrix, it can predict an individual's next visited location [19; 20]. Transparent interpretability models, through simplified logic and clear decision-making processes, provide users and decision-makers with easily understandable predictions. However, this approach is limited by the transparent structure of the model, making it difficult to extend to deep learning models.