(𝑥,𝑦)∈𝑋𝐿

𝑝𝜃 (𝑦 𝑗, 𝑥𝑖) log 𝑝𝜃 (𝑦 𝑗, 𝑥𝑖)

(29)

where 𝑝𝜃 (𝑦 𝑗|𝑥𝑖) is the predicted probability of the 𝑗-th label for the unlabelled data point 𝑥𝑖. Finally
the overall objective function for semi-supervised learning can be expressed as L = L𝑠𝑢𝑝 +𝛼L𝑢𝑛𝑠𝑢𝑝,
𝛼 is a hyperparameter that controls the weight of the unsupervised loss term. The goal is to find
the optimal parameters 𝜃 that minimize this objective function. Semi-supervised learning involves
learning a model from both labelled and unlabelled data by minimizing a combination of supervised
and unsupervised loss terms. By leveraging the additional unlabelled data, semi-supervised learning
can improve the generalization and performance of the model in downstream tasks.
AReviewofDeepLearningTechniquesforSpeechProcessing