This research introduces a state-of-the-art Persian spelling correction system that seamlessly integrates deep learning techniques with phonetic analysis, significantly enhancing the accuracy and efficiency of natural language processing (NLP) for Persian. Utilizing a fine-tuned language representation model, our methodology effectively combines deep contextual analysis with phonetic insights, adeptly correcting both non-word and real-word spelling errors. This strategy proves particularly effective in tackling the unique complexities of Persian spelling, including its elaborate morphology and the challenge of homophony. A thorough evaluation on a wide-ranging dataset confirms our system's superior performance compared to existing methods, with impressive F1-Scores of 0.890 for detecting real-word errors and 0.905 for correcting them. Additionally, the system demonstrates a strong capability in non-word error correction, achieving an F1-Score of 0.891. These results illustrate the significant benefits of incorporating phonetic insights into deep learning models for spelling correction. Our contributions not only advance Persian language processing by providing a versatile solution for a variety of NLP applications but also pave the way for future research in the field, emphasizing the critical role of phonetic analysis in developing effective spelling correction system.

Automatic spelling correction stands as a pivotal challenge within the ambit of natural language processing (NLP), demanding nuanced solutions. Traditional spelling correction techniques are typically only capable of detecting and correcting non-word errors, such as typos and misspellings. However, context-sensitive errors, also known as real-word errors, are more challenging to detect because they are valid words that are used incorrectly in a given context. The Persian language, characterized by its rich morphology and complex syntax, presents formidable challenges to automatic spelling correction systems. Furthermore, the limited availability of Persian language resources makes it difficult to train effective spelling correction models. This paper introduces a cutting-edge approach for precise and efficient real-word error correction in Persian text. Our methodology adopts a structured, multi-tiered approach, employing semantic analysis, feature selection, and advanced classifiers to enhance error detection and correction efficacy. The innovative architecture discovers and stores semantic similarities between words and phrases in Persian text. The classifiers accurately identify real-word errors, while the semantic ranking algorithm determines the most probable corrections for real-word errors, taking into account specific spelling correction and context properties such as context, semantic similarity, and edit-distance measures. Evaluations have demonstrated that our proposed method surpasses previous Persian real-word error correction models. Our method achieves an impressive F-measure of 96.6% in the detection phase and an accuracy of 99.1% in the correction phase. These results clearly indicate that our approach is a highly promising solution for automatic real-word error correction in Persian text.

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error distributions are assumed to be convolutions of a Gaussian density. We construct uniformly consistent estimators under general conditions while simultaneously highlighting several pain points in extending existing pointwise consistency results to uniform results. The resulting analysis turns out to be nontrivial, and several novel technical tools are developed along the way. In the case of mixed regression, we prove $L^1$ convergence of the regression functions while allowing for the component regression functions to intersect arbitrarily often, which presents additional technical challenges. We also consider generalizations to general (i.e. non-convolutional) nonparametric mixtures.