As mainly applied, pure and operations research mathematicians we elucidate mathematical modelling as the process of converting a real-world problem to mathematical formulation. It is the description of a system using mathematical concepts and language. This transfer process is a precondition for approaching and solving the real world problem. It incorporates the main features and characteristics of the system while leaving out less important features that have little impact on the system.
Also known as the science of better decision making, Operations Research is often considered a subfield of applied mathematics. It focuses on finding efficient solutions to operational problems and arriving at a maximum or minimum quantity keeping in mind constraints on the system. It draws on a range of methods from the fields of:
- Mathematical Programming (linear, integer, nonlinear and dynamic programming)
- Simulation (statistical, Markovian)
- Graph Theory (combinatorial optimization)
In our work, we are often faced with complex problems that can only be solved combining multiple methods. This may be a combination of different methods used in Operations Research, but may also include methods from an entirely different field altogether. For example, we often combine Predictive Analytics and operational research methods, whereby the predictive models deliver the necessary knowledge regarding how the variables of interest are connected.
The term Business Analytics incorporates the areas of Business Intelligence, Predictive Analytics, and Data Mining.
Business Intelligence focusses on:
- Transforming data into meaningful measures that summarize any chosen level of business processes
- Mapping how the business is running at the moment
- Visualizing and reporting past data as well as real-time data.
We believe confidence intervals and hypothesis tests ideally complement visualization and reporting of summary measures because they help you tell whether a difference between two groups is “real” or if it might just have happened by chance.
Predictive Analytics builds on Business Intelligence Data in order to draw valid conclusions that are crucial for business decision making. For example:
- How individual business processes or management decisions affect each other
- How changes in business policy or national policies affect the company’s performance
- Which historic decisions led to a present situation
- Which factors influence customer behavior such as purchases
Predictive Analytics draws on a wide array of statistical, econometric and machine learning models, whereby a specific focus lies on being able to predict the effect of hypothetical scenarios as well as forecasting.
In contrast to Predictive Analytics, Data Mining focuses on pattern recognition and data reduction. Data Mining therefore also plays a role in Business Intelligence when it comes to creating meaningful indicator variables that summarize large amounts of data. This can also be useful for prediction, for example, if no “model” of reality is known. Data reduction is also an integral part of many Natural Language Processing tasks.
Big Data Architectures
As datasets become very large, the normal ways of handling and processing data become inadequate. In order to process vast amounts of data, distributed systems, systems that can coordinate tens to thousands of servers easily, are key when it comes to:
- Moving data from one place to another in real-time
- Fast computation
- Storing unstructured data for fast and easy retrieval
- Collecting data from the worldwide web
Artificial Intelligence applications draw on a wide array of predictive methods from the fields of statistics, data mining, machine learning and aim to simulate human abilities. Each of these fields enhances a system’s ability to learn from experience/external data. We distinguish between three types of “learning”:
- Supervised: Here an algorithm is pre-trained using labeled example data before being used
- Unsupervised: Here the algorithm can be used immediately without pre-training. Predictions are made based on similarity to labeled example data
- Reinforced: Here the algorithm learns the best action based on the rewards it receives
The term Software Engineering describes a process of
- Analyzing client needs and developing an appropriate software methodology
- Designing algorithms, data models, and databases
- Development and testing of the application itself
- Ensuring the client’s needs continue to be met through support, including patches and updates