1. Introduction

Markov models, as a classical stochastic process model, play a significant role in numerous scientific and technological fields. Their applications range from particle motion simulation in physics to risk prediction in finance, and from text generation to machine translation in natural language processing. Despite their extensive applicability, Markov models encounter several problems in actual implementation, including data sparsity, model scalability, and non-linear complexities, which partly constrain their efficacy in intricate systems[1]. This paper aims to deeply analyze the current applications of Markov models and other similar models such as Hidden Markov Models across different fields and explore their specific uses in natural language processing, human resource forecasting, and personalized recommendation systems[2]. This research does a comparative analysis to elucidate the strengths and limits of Markov models in these domains and suggests appropriate enhancement tactics. The study methodologies encompass theoretical analysis and empirical case studies, intending to furnish significant references for scholars and professionals in pertinent domains. The significance of this study lies in, on one hand, providing more effective modeling methods and solutions for fields such as natural language processing, human resource management, and personalized recommendation systems, thereby enhancing system performance and user experience. On the other hand, through a thorough analysis of Markov model applications, it guides future research directions, particularly in how to integrate deep learning technology and big data resources to overcome existing challenges. This has important theoretical and practical value.

2. Markov Models

The fundamental concept of the Markov model is its memoryless property, indicating that the transition from the current state relies just on the present state, rather than on preceding states.

2.1. Markov Process

A Markov process is a stochastic process where the state evolves over time in a discrete or continuous manner. Its key feature is the Markov property, which states that:

Markov Property: The future state only depends on the current state, and not on the history of previous states. Formally, given the current state, the conditional distribution of the future state does not depend on the past states:

\( P({X_{t+1}}={x_{t+1}}∣{X_{t}}={x_{t}},{X_{t-1}}={x_{t-1}},…,{X_{0}}={x_{0}})=P({X_{t+1}}={x_{t+1}}∣{X_{t}}={x_{t}}) \) (1)

where \( {X_{t}} \) represents the state at time \( t, \) and P represents the transition probability.

2.2. Markov Chain

A Markov chain is the discrete-time variant of a Markov process, typically employed to characterize a system that shifts among various states at discrete time intervals. At each time step, the state is selected from a finite state space and alters according to a predetermined transition probability distribution.

State Space: The set of all possible states the system can be in, denoted as \( {S_{1}},{S_{2}},…,{S_{n}}. \)

Transition Probability Matrix: Describes the probability of transitioning from one state to another. If the state space has \( n \) states, the transition matrix is an \( n×n \) matrix, where the element \( {P_{ij}} \) represents the probability of transitioning from state \( {S_{i}} \) to state \( {S_{j}}, \) and satisfies:

\( {P_{ij}}=P({X_{t+1}}={S_{j}}∣{X_{t}}={S_{i}}) \) (2)

Each row sums to 1, meaning the sum of probabilities from a given state to all other states equals 1.

Initial State Distribution: The probability distribution of the system's initial state, typically represented by a probability vector \( {π_{0}}=(π_{0}^{1},π_{0}^{2},…,π_{0}^{n}), \) where \( π_{0}^{i} \) represents the probability that the system is in state \( {S_{i}} \) at the initial time.

2.3. Markov Decision Process (MDP)

MDP is an extension of the Markov process, extensively utilized in reinforcement learning and decision theory. In contrast to Markov chains, MDPs account for state transitions as well as the impact of actions made in various stages on the alterations of the system's state.

The five key elements of an MDP are:

• State Space \( S \) : The set of all possible states the system can be in.

• Action Space \( A: \) The set of all possible actions the system can take.

• Transition Probability \( P({s^{ \prime }}∣s,a): \) The probability of transitioning to state s′s′ from state ss by taking action \( a. \)

• Reward Function \( R(s,a,{s^{ \prime }}): \) The immediate reward received when transitioning from state ss to state s′s′ by acting \( a \) .

• Discount Factor \( γ: \) A factor used to discount the importance of future rewards, typically between 0 and 1.

The goal of an MDP is to choose an optimal policy \( π(s) \) (the action to take in state \( s \) ) to maximize the long-term cumulative reward, also known as the expected return.

2.4. Hidden Markov Model (HMM)

HMM is an extension of a Markov chain used to handle processes that are partially observable. In an HMM, the system's state is not directly observable (i.e., "hidden"), but can be inferred indirectly through observable outputs.

An HMM consists of the following components:

• Hidden State Space: The set of possible hidden states, which are typically not directly observable.

• Observable State Space: The set of observable outcomes that provide information about the hidden states.

• Transition Probability \( P({s_{t}}∣{s_{t-1}}): \) The probability of transitioning from state \( {s_{t-1}} \) to state \( {s_{t}} \)

• Observation Probability \( P({o_{t}}∣{s_{t}}) \) : The probability of observing a particular observable outcome \( {o_{t}} \) given the hidden state \( {s_{t}} \) .

• Initial State Distribution: The probability distribution of the system's hidden state at the initial time.

HMMs are extensively utilized in domains including speech recognition, natural language processing, and genomic sequence analysis.

3. Applications of Markov Models in Natural Language Processing

The Markov model is a prevalent technique in natural language processing within machine learning. Markov chains and hidden Markov models are stochastic methods employed to represent dynamical systems in which the subsequent state is contingent upon the present state. Markov chains, which formulate whole sentences by producing a sequence of words, are frequently employed to generate natural language. The hidden Markov model is employed for recognizing certain speech objects, aiming to forecast concealed labels based on the observed words.

3.1. Applications

Part-of-Speech (POS) tagging is a fundamental activity in Natural Language Processing (NLP) that involves assigning a grammatical category, such as noun, verb, or adjective, to each word in a phrase. Hidden Markov Models (HMMs) have been effectively employed for this task, leveraging the sequential structure of language to forecast the most probable sequence of tags. As Phil Blunsom discusses in his work, "HMMs have been applied with great success to problems such as part-of-speech tagging and noun-phrase chunking"[1]. The model's efficacy is from its ability to capture the statistical regularities in the data, learning the transition probabilities between different POS tags.

In the field of text generation, Markov chains are used to generate natural language text by predicting the next word in a sequence based on the previous context. This approach is particularly useful for tasks such as chatbot development and content generation.

Machine translation represents another significant application of Markov models, where two-language databases are used to train a translation model. The statistical nature of Markov models allows for the modeling of the probability of a sentence in one language given a sentence in another, facilitating the generation of translations that are not only correct in grammar but also appropriate in context. This approach is supported by the idea of Sudha Morwal et al., which states that "Named Entity Recognition (NER) is the subtask of NLP that has many applications mainly in machine translation, text-to-speech synthesis, natural language understanding, etc."[3] Although their paper focuses on NER, the underlying principle of utilizing probabilistic models like HMMs for language translation is well-established.

3.2. Research Progress

The application of Natural Language Processing (NLP) in engineering education and management focuses on a machine learning model that uses a Hidden Markov Model (HMM) integrated with a named entity model for categorizing variables in text documents. The proposed HMMNE model employs probability states and an n-gram classifier to achieve high precision in identifying location, name, and organization entities, with precision values reaching 99% for location and 98% for name and organization. The research underscores the difficulties of Named Entity Recognition in morphologically complex languages such as Telugu and stresses the necessity of annotated corpora for the progression of statistical Natural Language Processing research. The HMMNE model's effectiveness is demonstrated through comparative analysis, showcasing its superiority in classification and identification tasks[4]. In another research, the researchers investigate the use of Pairwise Markov Chains (PMC) for efficient text segmentation tasks such as POS tagging, Named Entity Recognition, and Chunking. PMC achieves comparable performance to Conditional Random Fields (CRF) but with significantly faster training and execution times, making it suitable for low-resource environments. The study demonstrates PMC's effectiveness in handling known and unknown words by incorporating word features, highlighting its potential as a lightweight alternative for NLP tasks[1].

4. Applications in HR Forecasting

Forecasting workforce supply is crucial for strategic planning in human resource management. The Markov chain model is very useful for predicting staff turnover, promotions, and other organizational moves through a probabilistic approach[4].

The application of Markov chains in academic staffing is exemplified by the work of Ezugwu and Ologun, who utilized the Markov chain model to forecast the academic staff structure at the University of Uyo in Nigeria[5]. Their research indicated future trends in staff composition, such as increases in Graduate Assistants and Senior Lecturers, and decreases in Assistant Lecturers and Professors. Enhancing HR deployment strategies is another area where Markov chains have been effectively applied. Bányai et al. expanded the use of Markov-chain simulations to analyze human resource deployment in manufacturing[6]. They proposed models that consider different HR strategies, including promotions and demotions, and their impact on the future workforce structure.

Integrating Markov Chain in HR Forecasting, Markov chain models emerge as a robust tool for anticipating employee transitions and shaping HR strategies. They help in aligning current workforce optimization with long-term organizational goals, promoting sustainable HR management. These models can identify discrepancies between current and desired workforce structures, as demonstrated in a case study of the Slovenian Armed Forces[7]. The researchers offer a Markov-chain simulation model to assess human resource deployment processes in manufacturing firms, taking into account aspects such as promotion and recruiting rates. The research illustrates the model's implementation via scenarios, highlighting its capacity to enhance human resource strategies for sustainable management. Organizations might examine policy modifications to enhance and maintain their workforce by simulating diverse scenarios. Markov chain models enhance sustainable HR management by connecting current workforce conditions with future organizational requirements.

In the realm of personalized recommendation systems, the application of Markov chains to forecast user behavior and generate customized suggestions is a very useful tool. This explanation will draw on two significant studies to elucidate how these methods function. Adapting to Shifting Preferences with HMM, the first paper addresses a common flaw in recommendation systems: the assumption that user preferences remain constant. However, it's evident that our interests can evolve over time. To address this, the authors propose a Hidden Markov Model (HMM), which tracks changes in user preferences by treating them as a sequence of hidden states. Each state represents a distinct preference, allowing the model to adapt recommendations as user tastes shift[8].

Enhancing Personalization with FPMC, the second paper introduces an innovative approach by integrating matrix factorization with Markov chains, resulting in Factorized Personalized Markov Chains (FPMC). This approach allocates a distinct transition matrix to each user, encapsulating their overall preferences and the order of their selections. It's akin to having a tailored recommendation system that not only knows your general likes but also how they progress over time[9]. The FPMC model addresses the issue of sparse data by distributing information across similar users and items, thus enhancing the model's predictive power[10].

5. Discussion

Markov Models are increasingly used in machine learning and artificial intelligence for tasks like natural language processing and image recognition. Their ability to model sequential data makes them valuable for predicting future events in dynamic systems. As computational power grows, Markov Models will likely become more sophisticated, enabling more accurate predictions and broader applications in various industries. However, in terms of Markov model applications, several challenges and issues are frequently encountered:

Data Sparsity: Markov models frequently meet the challenge of data sparsity, which can significantly reduce the models' predictive accuracy and effectiveness. As discussed by Zhu and Xing, this issue is addressed by leveraging the principles of ℓ1-norm regularization. This approach is helpful in achieving primal sparsity, which is crucial for selecting significant features and reducing the risk of overfitting[11]. The authors further contribute to the field by introducing the concept of ℓ1-norm max-margin Markov networks (ℓ1-M3N), which not only attains primal sparsity but also achieves dual sparsity, a property that is particularly beneficial in high-dimensional learning scenarios. The development of a robust EM-style algorithm for learning ℓ1-M3Ns, as presented by Zhu and Xing, offers a practical solution for enhancing the performance of Markov models in the presence of sparse data.

Model Scalability and Complexity: In complicated systems, the Markov model may encompass an extensive state space, resulting in significant processing costs. As the quantity of states increases, the model's complexity escalates, rendering it more challenging to handle regarding computational resources and interpretability.

Non-linearity: Many real-world problems exhibit non-linear characteristics, yet Markov models take linear state transitions. This limitation can be a significant drawback when dealing with systems where the relationship between states is not linear or the impact of one state on another is not immediately apparent.

Looking ahead to future research, there are several promising directions:

Integration of Deep Learning and Markov Models: Combining deep learning techniques, such as Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM) networks, with Markov models could help overcome some of the limitations of traditional Markov models. These deep learning architectures can catch complex patterns that are not well-captured by Markov models alone.

Big Data and Markov Models: With the advance of big data technologies, there is an opportunity to enhance the performance of Markov models by taking advantage of large datasets. This is especially relevant in applications like natural language processing and recommendation systems, where the availability of vast amounts of data can help in estimating transition probabilities more accurately and in dealing with the sparsity issue.

6. Conclusion

Markov models are applied in natural language processing for tasks like part-of-speech tagging, text generation, and machine translation. In HR forecasting, they predict staffing changes and optimize workforce alignment. To provide tailored recommendations, they monitor the progression of user preferences and improve forecast precision. In conclusion, although Markov models have shown beneficial in numerous applications, it is essential to tackle the issues of data sparsity, model complexity, and non-linearity to ensure their ongoing relevance and efficacy. The amalgamation of deep learning and the application of big data presents great opportunities for future study and development in this domain. The paper's use of research literature has some shortcomings: it uses older works and lacks comprehensive coverage of other application areas. For future research, the focus should be on integrating deep learning with Markov models to overcome limitations and provide effective solutions for complex tasks in various fields. Another direction is using big data to enhance Markov model performance, improving model robustness and prediction accuracy. Lastly, exploring applications in emerging fields like IoT, intelligent transportation, and medical health will expand the application scope and provide new solutions for practical problems.