# A Survey of Graphene-to-Phoneme Conversion Methods
## 2 Grapheme-to-Phoneme Methods
### Traditional Methods
#### 2.1.2 Statistical Machine Learning-Based Methods  
Statistical machine learning-based methods utilize probabilistic statistics and machine learning algorithms to build a speech model with sufficient training data and employ decoding algorithms to label each word. This type of task can be summarized as follows: given a sequence of letters \(L\), find the phoneme sequence \(P^{*}\) that maximizes \(\Pr(P|L)\),  
\[P^{*}=\operatorname*{arg\,max}_{P}\Pr(P\mid L)=\operatorname*{arg\,max}_{P} \Pr(L,P) \tag{2}\]  
Selecting either the conditional distribution \(\Pr(P|L)\) or the joint distribution \(\Pr(L,P)\) can accomplish this task; both frameworks have seen extensive work on grapheme-to-phoneme conversion. N-gram models have been successfully used in speech recognition and other data sequence statistical modeling applications, offering flexibility, compactness, and fast decoding capabilities. Joint models do not require pre-aligned data for training and are a natural way to generate the alignment needed for conditional models. Additionally, joint models are typically symmetric, allowing them to be used directly for both grapheme-to-phoneme and phoneme-to-grapheme conversion. In the literature [5], the Expectation Maximization (EM) Algorithm is utilized to infer the minimal correspondence between the graphemes and phonemes; the G2P converter is constructed by a joint N-gram model. Experimental results also show that adding accent information and word frequency information to the training data can improve the model's accuracy. Formally, within the context of a joint sequence model, consider a word \(w\) with its spelling represented as \(\gamma(w)=l_{1}l_{2}\ldots l_{n}\), where \(l_{i}\) denotes a letter, and its pronunciation represented as \(\pi(w)=p_{1}p_{2}\ldots p_{m}\), where \(p_{i}\) denotes a phoneme. The joint probability \(P(Y(w),\pi(w))\)is pertinent in this scenario. The task can be articulated as identifying the most probable transcription \(\pi^{*}\) for the given input \(\gamma\):  
\[\pi^{*}=\arg\max P(\gamma,\pi) \tag{3}\]  
Here, \(P(\gamma,\pi)\) signifies the joint probability of the spelling \(\gamma\) and the pronunciation \(\pi\). Ref. [6] combined the joint \(n\)-gram model with a decision tree model to measure the impact of improved G2P models on LVCSR performance in challenging ASR tasks, proposing the use of \(N\) best pronunciation variants instead of a single best pronunciation. Ref. [7] first applied Weighted Finite State Transducers (WFST) to the G2P conversion task, using EM for alignment. This effectively reduced storage space and accelerated decoding speed, significantly shortening training time compared to [8] without degrading performance. Ref. [9] introduced a new open-source WFST-driven G2P conversion toolkit that supports a range of features, including EM-driven many-to-many alignment algorithms and three novel decoding techniques. The training process involves first converting aligned sequence pairs into aligned joint label pairs, \((g1:p1,g2:p2,...,gn:pn)\), training a joint N-gram model, and then using the mitm tool to convert the N-gram model into a WFST. Ref. [10] improved joint sequence modeling by enhancing the alignment algorithm and using an RNN LM alongside the standard n-gram LM for N-best rescoring. Ref. [11] investigated two related issues in the WFST-based G2P conversion domain. The first was the impact of the method used to convert target words into equivalent finite-state machines on downstream decoding efficiency. The second issue was the impact of the method used to represent the joint n-gram model within the WFST framework on system speed and accuracy. Ref. [12] applied Hidden Markov Models (HMMs) to G2P transformation, and [13] modeled context at HMMs' observations with discrete observations and discrete probability distributions. Ref. [14] proposed a new many-to-many alignment training technique.