Shui Yu, University of Technology Sydney
Published: 13 Nov 2019
Abstract
Current communication systems have become extraordinarily large and complex in this big data age. As a result, the traditional mathematical tools are exhaustively serving the demands from unprecedented applications. We mainly depend on artificial intelligence to address the problems. However, AI algorithms are usually black-box based, lack interpretability, and therefore cannot be used in critical and expensive cases. We are now in the middle of many unknowns. In this article, we share our belief that mathematical model guided AI is the solution for the challenges we are facing. We also present our preliminary study on a few key parts, hoping it is helpful for energetic readers to further explore the promising uncharted fields.
Introduction
Today, artificial intelligence tools are extensively used to solve the problems in communication systems. The reason behind this is twofold. On one hand, existing communication systems are dramatically big and complex, and the traditional mathematical tools sometimes cannot serve them well. For example, the available tools of graph theory cannot address the dynamic characteristics of the Internet or social networks. On the other hand, the artificial intelligence algorithms are developed significantly due to the availability of big datasets [1]. It is natural that AI methods are employed to solve problems where model based methods are awkward [2]. Moreover, researchers have realized that AI applications need the strong support of the underneath layers due to the distributed nature of big data sets [3]. In other words, the marriage between AI and communication is a natural choice.
|
Journal Name |
AI related papers |
Total number of papers |
Percentage |
|
IEEE/ACM Transactions on Networking |
2 |
30 |
6.7% |
|
IEEE Transactions On Communications |
8 |
162 |
4.9% |
|
IEEE Transactions On Wireless Communications |
6 |
125 |
4.8% |
However, AI services for communications are far from perfect. One evidence we found is that high quality publication from the AI perspective is still limited. We have collected preliminary statistics on the early access papers in the mainstream networking or communications venues (accessed on October 7,2019). The results are shown in Table 1. The data roughly demonstrates that AI based papers for communications are around 5%.
The reason behind the low percentage is mainly because of the nature of AI methodology. To date, AI based solutions are not fully trusted due to the lack of interpretability. AI methods, e.g. deep learning algorithms, are mainly black-box based, and lack interpretability. People even criticize that AI has become alchemy [4]. Moreover, a common complaint about AI algorithms is that they are hard to repeat. As a result, people dare not to apply AI based solutions in mission critical applications or expensive projects, such as nuclear reactor control, or expensive new communication infrastructure. It is time for us to seek a solution.
2. Mathematical Model Guided Artificial Intelligence
We believe the promising direction is mathematical model guided artificial intelligence. In our view, we believe mathematical models offer us the confidence of the right track, and machine learning algorithms bring an accurate solution for a specific case. In general, mathematical models are established with assumptions, e.g., some facts are ignored, some distributions are approximated, and so on. These mathematical models point to directions for us in the wilderness, although they possess discrepancies against the truth from case to case, which is termed as “All models are wrong, but some are useful” [5]. Meanwhile, AI algorithms can offer us a customized accurate answer for a given case.
In other words, we believe mathematical models offer a solution with large granularity while the solution can be elaborately tuned by artificial intelligence algorithms. At the same time, a solution from AI algorithms should be carefully examined to see whether it agrees with the related theoretical range. We show our understanding in Figure 1 below. We believe the reliable solution space should be the overlapped area between the theoretical solution space and the artificial intelligence algorithm solution space.
To date, we can see significant effort in the machine learning space, while the work on the theoretical perspective is quite limited.
In the remainder of this article, we share some of our preliminary explorations in the theoretical space.
3. Challenges from the Theortical Perspective
When we stare at the big data issues with a hat of communication, we share some problems we are facing as follows.
3.1 Big Data Modelling
It is fundamental to represent our studied objects in a theoretical way. There are many math tools used in engineering, and we list a few popular ones here.
Graph theory is a powerful tool to establish models from the perspective of geometry. For example, we can smoothly represent a social network, like Facebook, using graphs: persons are nodes, and the interactions between nodes form the edges with different weights. As a result, we have a graph of the social network.
In front of big data, graph theory faces at least two new challenges: volume and dynamics. For the volume challenge we may have two solutions: 1) taking the divide-and-conquer strategy based on ever-increasing computing power; 2) graph summary, namely making a big graph smaller and smaller by merging multiple similar nodes into one. However, the dynamic issue is a tough challenge for us today. This issue may have a strong connection with complex systems, but there are no good solutions so far to the best of our knowledge.
Tensor has been used to model big data sets. Tensor is a popular tool in modern physics. We can simply treat tensor as a high dimensional matrix, which fits the high dimension characteristics of big data sets. However, we believe there are definitely problems when we deploy tensor in big data problems.
3.2 Big Data Analysis
The theories we use to build our model do offer profound tools for analysis. We deploy these tools to obtain some conclusions based on the established models. For example, we can extract subgraphs using graph theory by some metrics; we can also conduct dimension reduction using the contraction operation of tensor.
In practice, transformation is another popular strategy. We map or transform the studied problem into another space, where we can obtain a solution. The typical example is that we can carry out noise filtering in the frequency domain while it is hard in the time domain. In the big data case, graph spectrum [6] is a good example of this kind of tool.
One challenge of big data analysis is small probability. Small probability was usually ignored in the past as it is not important. However, it is demanded now in the big data era. We recommend that readers study large deviation [7], which is a new tool for performance analysis. The basic concept is that the value of the probability is too small to calculate, then large deviation aims to offer a lower bound and an upper bound of it.
We believe there are many tools in place, and waiting to be invited and trimmed to serve our problems.
3.3 Where are the Tools
It is true that demanding from application is the motivation for new tools. In principle, there are two ways to deal with the shortage of tools in front of the big data communication age:
- Improve existing tools for new problems. It is natural that we extend the available tools to gain new capability to handle unprecedented challenges. For example, someone may extend the capability of graph theory to look after the dynamic features.
- Invent new tools. New tools may be invented when we have had essential progress in understanding the studied subjects. There are many similar examples in the history of the mathematical world, and we do not repeat them here.
4. Conclusion
We are facing the puzzle of using AI methods to address communication problems. We believe mathematical model guided machine learning is a promising direction. The theoretical conclusions guarantee the correctness of our directions while artificial intelligence algorithms offer fine granularity solutions for specific cases. The progress from the theoretical aspect requests us to extend the existing mathematical tools or invent new tools.
References
- M. Jordan and T. Mitchell, "Machine learning: trends, perspectives, and prospects," Science, vol. 349, no. 6245, pp. 255–260, 2015.
- Y. Sun et al., "Application of machine learning in wireless networks: key techniques and open issues," IEEE Commun. Surveys and Tutorials, in press, 2019.
- S. Yu et al., "Networking for Big Data: a survey," IEEE Commun. Surveys and Tutorials, vol. 19, no. 1, pp. 531-549, 2017.
- M. Hutson, "Has artificial intelligence become alchemy?," Science, vol. 360, no. 6388, 2018.
- G. Box, "Science and Statistics," J. of the American Statistical Association, vol. 71, no. 356, pp. 791-799, 1976.
- P. V. Mieghem, Graph Spectra for Complex Networks. Cambridge University Press, 2011.
- A. Shwartz, A. Weiss, and R. Vanderbei, Large Deviations for Performance Analysis. Taylor and Francis Group, 2018.
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