# Specific-Input LIME Explanations for Tabular Data Based on Deep Learning Models
## 3 Materials and Methods
### The Disadvantages of LIME  
Tabular data represent information in the form of tables, where each row represents an instance and each column represents a feature, and there are complex relationships between tabular data, whereas LIME assumes that all features are independent, which obviously reduces the accuracy of interpretation for tabular data. Although it improves the possibility that some sample point predictions may deviate from the data points of interest, LIME samples are taken from the centre of mass of the training data rather than from the instances of interest, leading to problems of consistency, confidence, and stability of interpretation. It is easiest to describe how sampling and local model training work with Figure 1 (represented by [PERSON] [13]):  
In Figure 1, the black-box model predictions are based on x1 and x2, where x1 and x2 represent the two features or input variables used to make the predictions. The predicted classes (light) are 1 (dark) or 0 (bright). Subfigure A means that the data are sampled from a normal distribution and a point of interest (large dots) is sampled (small dots). In subfigure B, more weight is given to the points closer to the point of interest. In subfigure C, the grid marks show the classifications of the locally learned model from the weighted samples. In subfigure D, the decision boundary is marked by a white line (P(class = 1) = 0.5). It is difficult to define a meaningful neighbourhood around a point. To define the neighbourhood, LIME currently uses an exponential smoothing kernel [14]. A smoothing kernel is a function that returns a measure of the closeness of two data instances. The kernel width is a measure of the size of the neighbourhood: a minimal kernel width means that an instance must be in close proximity to affect the local model, while an extended kernel width means that instances at greater distances can also affect the model. We found that it uses an exponential smoothing kernel with a width of 0.75 times the square root of the number of columns in the training data. The main problem is that we do not have a good method for the determination of the correct kernel or width. In some cases, the adjustment of the kernel width can have a positive effect on the explanation, as shown in Figure 2 (represented by Molnar C. [13]):The predictions of the black-box model based on a single feature are shown by a thick line, while carpets represent the data distribution. Three local surrogate models are generated, each with a different kernel width. Figure 1: LIME algorithm for tabular data. Figure 2: Explanation of the example x = 1.6 prediction. In this example, there is only one feature. In a high-dimensional feature space, the situation becomes worse. It is also uncertain whether all features should be treated equally in the distance measurement. Distance measurements are arbitrary and distances in different dimensions may not be comparable. The correct definition of neighbourhoods is a huge, unresolved problem when using LIME with tabular data, which is LIME's most serious flaw and why experts recommend using it only with extreme caution. You need to experiment with different kernel settings for each application to see if the interpretation makes sense. In the existing implementation of LIME, there is room for improvement in the sampling technique. Currently, data points are generated according to a Gaussian distribution without any consideration of feature correlation. This approach can lead to the creation of unlikely data instances that can be used to learn local explanatory models despite their improbability. The complexity of the explanatory model must be determined in advance. This is a minor problem because the end user has to choose between truthfulness and sparsity. Another important issue is the instability of the interpretation. Furthermore, in our experience, results can vary when the sampling process is repeated. The uncertainty makes it difficult to accept interpretations and you should be sceptical.