The Vital Role of Stochastic Processes in Data Science and AI

Data from a specific study could be categorized as collected under a deterministic or a stochastic process. Some are also provided data from unknown processes. On the other hand, most grand challenges from data relate to probabilistic or statistical problems. Alongside fundamental technologies, effective processes to address these challenges based on advanced data science techniques could establish a bridge to create a new science. In the field of AI, generative models thereof attempt to create a wide range of AI applications, including new transdisciplinary applications. Data collected under various stochastic process assumptions can also have a teaching character, thereby forming invaluable data science tools. This review emphasizes the importance of taking stochastic process assumptions into account during data study, specifically in the context of later AI application. In particular, we summarize probability models and their formulation for AI categories, which have primary applications in various other fields as basic patterns for observed data. (Sarker, 2021)(Wang et al., 2022)(Xie et al., 2020)(Gervet et al.2020)(Leik & Leik, 2021)

Data science now plays a vital role in various fields of research and industry, not only because the capabilities of AI have been greatly expanded by data science techniques, but also because it can be a new framework for non-AI research to create a bridge to AI applications. Location-based services, economic and social behavior analyses, medical image analyses, and scientific studies based on observed data have directly supported individuals, industries, and academic disciplines. These have been applied to study and obtain knowledge or create new services via intelligence. Through this broad outreach, interpretable data science approaches are crucial to further develop AI and any relevant industry. (Xu et al.2021)(Raschka et al., 2020)

Definition of Stochastic Processes

For AI, the framework of stochastic calculus and stochastic differential equations is particularly powerful in approximating normalizing constants, probability distributions, and expected values. Using sequential Monte Carlo, also called particle filter, and related methods are equally powerful in approximating these probabilities and expectations. We shall, however, save these methods for much later in the book. We shall first work through fundamental computational techniques in the context of Gaussian processes, on which a more general class of stochastic processes depends heavily. Recall that a stochastic process X indexes elements of a probability space. An outcome is defined as a function of X to a real number. These real-valued random variables trace out paths indexed by the set of possible timesteps. These paths are samples from the stochastic process.

A set of data collected or being collected is inherently a realization of a random experiment. The fundamentals of the probability theory, onto which stochastic processes are built, provide powerful tools to reason about uncertainty. In simple terms, these tools are very lacking if better theory does not endow us with the right models. In the area of large-scale machine learning and AI, handling uncertainty via stochastic processes is still an underappreciated field. In the data-sparse regime of AI, Monte Carlo simulation plays an important role in helping machines make wiser choices under uncertainty. In this chapter, we illustrate how to use stochastic processes to detect and (partially) remedy these pathologies in the applied field of improving sensor fusion, a fundamental algorithm of AI. (Mozaffar et al.2022)(Cao et al.2021)(Gawlikowski et al.2023)

Relevance in Data Science and AI

All the analysis work carried out by these areas should be qualified, based on decision-making oriented to the solution of business problems, an approach and mindset more than technique. There is a wide variety of AI techniques available for use, and one of them, which is increasingly popular, is machine learning (ML). Data professionals in general, and data scientists and AI professionals in particular, utilize a broad range of deterministic and non-deterministic machine learning techniques to assist them in solving real problems with real data. In addition to the typical mathematical and/or algorithmic techniques of AI, there are also other methodologies frequently employed, such as Monte Carlo simulation and bootstrap simulation. These approaches enhance the overall effectiveness of AI modeling. However, it is important to note that there is a crucial aspect in the field of AI that has not received adequate attention, despite being increasingly well-documented: the consideration of stochastic processes. These processes are formed by data in their natural state of minimum order, where each datum is associated with its own timestamp and possesses correlated characteristics such as volume, arrival rate, and variation order. Moreover, the arrival of these data points is based on distinct inter-events times and follows various probability distributions, each characterized by its own descriptive statistics and inflection points. The generation of events within these stochastic processes can be understood through the use of sequences such as Bernoulli, Poisson, Markov, or other different processes. It is crucial for AI professionals to explore and understand these stochastic processes thoroughly, as they can provide valuable insights and solutions to a wide range of business problems. (Abdar et al.2021)(Sarker, 2022)(Zhang et al.2021)

In the beginning of the 21st century, data and information have become a pervasive and indispensable global commodity resource, surpassing all boundaries and limitations. This exponential growth has reached such a critical mass that it now overwhelms the very foundations of data processing within teams and extends far beyond the confines of traditional systems, equipment, and techniques. In order to effectively navigate this vast ocean of data, organizations and entities are now required to meticulously analyze information with varying degrees of intricacy and scrutiny, across an extensive range of formats including text, images, videos, and more. These diverse data sources possess distinct characteristics such as volume, speed, and variety, which further complicates the process. Nonetheless, organizations have answered this challenge with a myriad of specialized services, often accompanied by a diverse array of Business Intelligence and Data Science capabilities, each exhibiting their own unique shades and nuances. Consequently, they possess an innate ability to understand, adapt, and aid in the transformation of raw data into valuable insights. Data Science (DS) and artificial intelligence (AI) lie at the crux of this data-driven revolution. They propel themselves through the rigorous examination of data, uncovering concealed patterns, correlations, and relationships, thereby empowering companies to make accurate predictions, recognize untapped opportunities, and mitigate potential risks. These innovative domains have emerged as pivotal players within the realm of business analysis and strategic decision-making, consequently attracting substantial investments across a multitude of sectors. Simultaneously, there has been an unabating surge in demand across the labor market for skilled professionals proficient in these disciplines. (Soni et al., 2020)(Medeiros et al., 2020)(Bharadiya, 2023).

References

Sarker, I. H. (2021). Data science and analytics: an overview from data-driven smart computing, decision-making and applications perspective. SN Computer Science. springer.com

Wang, J., Xu, C., Zhang, J., & Zhong, R. (2022). Big data analytics for intelligent manufacturing systems: A review. Journal of Manufacturing Systems. researchgate.net

Xie, J., Fang, J., Liu, C., & Li, X. (2020). Deep learning-based spectrum sensing in cognitive radio: A CNN-LSTM approach. IEEE Communications Letters. [HTML]

Gervet, T., Koedinger, K., Schneider, J., & Mitchell, T. (2020). When is deep learning the best approach to knowledge tracing?. Journal of Educational Data Mining, 12(3), 31-54. educationaldatamining.org

Leik, R. K. & Leik, S. A. (2021). Transition to interpersonal commitment. Behavioral theory in sociology. [HTML]

Xu, Y., Liu, X., Cao, X., Huang, C., Liu, E., Qian, S., ... & Zhang, J. (2021). Artificial intelligence: A powerful paradigm for scientific research. The Innovation, 2(4). cell.com

Raschka, S., Patterson, J., & Nolet, C. (2020). Machine learning in python: Main developments and technology trends in data science, machine learning, and artificial intelligence. Information. mdpi.com

Mozaffar, M., Liao, S., Xie, X., Saha, S., Park, C., Cao, J., ... & Gan, Z. (2022). Mechanistic artificial intelligence (mechanistic-AI) for modeling, design, and control of advanced manufacturing processes: Current state and perspectives. Journal of Materials Processing Technology, 302, 117485. sciencedirect.com

Cao, L., Yang, Q., & Yu, P. S. (2021). Data science and AI in FinTech: An overview. International Journal of Data Science and Analytics, 12(2), 81-99. springer.com

Gawlikowski, J., Tassi, C. R. N., Ali, M., Lee, J., Humt, M., Feng, J., ... & Zhu, X. X. (2023). A survey of uncertainty in deep neural networks. Artificial Intelligence Review, 56(Suppl 1), 1513-1589. springer.com

Abdar, M., Pourpanah, F., Hussain, S., Rezazadegan, D., Liu, L., Ghavamzadeh, M., ... & Nahavandi, S. (2021). A review of uncertainty quantification in deep learning: Techniques, applications and challenges. Information fusion, 76, 243-297. sciencedirect.com

Sarker, I. H. (2022). AI-based modeling: techniques, applications and research issues towards automation, intelligent and smart systems. SN Computer Science. springer.com

Zhang, Z., Li, W., & Yang, J. (2021). Analysis of stochastic process to model safety risk in construction industry. Journal of Civil Engineering and Management, 27(2), 87-99. vilniustech.lt

Soni, N., Sharma, E. K., Singh, N., & Kapoor, A. (2020). Artificial intelligence in business: from research and innovation to market deployment. Procedia Computer Science. sciencedirect.com

Medeiros, M. M., Hoppen, N., & Ma?ada, A. C. G. (2020). Data science for business: benefits, challenges and opportunities. The Bottom Line. researchgate.net