# A Low-Complexity Deep Learning Model for Predicting Targeted Sequencing Depth from Probe Sequence
## 2 Materials and Methods
### Sequence Encoding Model  
In this study, the next-generation sequencing depth was predicted using a new deep learning approach. A flow chart of our new method is shown in Figure 3A. From the deep learning perspective, the process of predicting the sequencing depth from probe sequences could be regarded as a regression task. Since sequences could not be used directly as input to a neural network, they needed to be transformed into vector representations. The sequence encoding process is shown in Figure 3B. The input sequence and sequencing depth were treated as \(\left\{\mathbf{X},y^{i}\right\}_{j=1}^{n}\) using \(k\)-mer and dna2 vec, where \(\mathbf{X}^{i}\) represents the embedded probe sequences, \(y^{i}\) represents the probe sequencing depth, and \(n\) signifies the number of sequences in the dataset.  
First, the \(k\)-mer processing method, which is commonly used in sequence analysis and processing, was selected to segment the target sequence and probe sequence, where mer represents the monomer unit, and \(k\) indicates segmentation into \(k\) bases in length. Setting different step sizes (\(s\)) yielded \(k\)-mer segmentation results with different intervals. Taking a sequence as an example, the step size (\(s\)) was set as 1, and the value of \(k\) was set to 3. Therefore, a probe sequence (\(D\)) with a length of \(t\) bp could be expressed as  
\[D=n_{1}n_{2}n_{3}\ldots n_{j}\ldots n_{t},(n_{j}\in\left\{A,T,C,G\right\}), \tag{1}\]  
where \(n_{j}\) represents the nucleotide in the \(j\)-th position. The \(k\)-mer processing method was utilized to split it into \(t-2\) subsequences with a length of 3 mer. Then, these \(t-2\) subsequences were regarded as the words that made up the sentence of the DNA sequence, which was described as  
\[S=\left\{N_{1},N_{2},\ldots,N_{j},\ldots,N_{t-2}\right\}, \tag{2}\]  
where \(N_{j}\) represents the subsequence at the \(j\)-th position \(\left\{n_{j}n_{j+1}n_{j+2}\right\}\) taken from \(\left\{AAA\right\}\), \(\left\{AAC\right\}\), \(\left\{AAG\right\},\ldots,\left\{TTT\right\}\).  
Then, the dna2 vec method was applied to generate word vector representations for each 3-mer subsequence obtained through \(k\)-mer processing. The dna2 vec method is an improvement of word2 vec using skip-gram [24; 25], which predicted the occurrence probability of the target subsequence and generated its word vector based on all sequence  
Figure 2: Histograms of the frequency distribution of GC content and log sequencing depth for the three datasets. (**A**) Frequency distribution histograms of GC content for the SNP, lncRNA, and SynDNA datasets. (**B**) Histogram of the frequency distribution of the log sequencing depth for the three probe datasets.  
correlations. Each subsequence (\(N_{j}\)) was transformed into a 100-dimensional vector (\(\mathbf{x}_{j}\)). The sequence (\(D\)) was converted into a distributed representation (\(\mathbf{X}\)) as follows  
\[\mathbf{X}=\left[\mathbf{x}_{1},\mathbf{x}_{2},\ldots,\mathbf{x}_{j},\ldots, \mathbf{x}_{t-2}\right], \tag{3}\]  
and it was used as input for the RNN module.  
Figure 3: Schematic representation of the sequence-encoding phase and the sequencing depth prediction phase of the proposed model. (**A**) A flow chart demonstrating the proposed model for generating sequencing depth prediction results from probe sequences. The light gray area represents the sequence-encoding model, and the light yellow area represents the sequencing depth prediction model. (**B**) Overview of converting sequences into a feature matrix via \(k\)-mer and dna2 vec processing. (**C**) Overview of the process of using the feature matrices of probe and target sequences to generate the log sequencing depth prediction result.