A report on new biology emphasizes the great potential of biosciences in the areas of health, food, energy, and environment in the 21st century [1]. The report predicts that global problems in these areas will be resolved through scientific integration. Furthermore, the report suggests that as biology develops into an information-based science, the key to successful scientific integration lies in the development of computational methods. These include support for data integration, model development for systems biology, and visualization of large masses of data. The development of these methods inevitably depends on systematic collection of large amounts of loosely connected, inherently noisy, and heterogeneous data, commonly called big data.

The volume, accumulation velocity, and complexity of biological data have grown beyond any feasible manual processing scenario, easily fulfilling all criteria for big data. This ubiquitous term is currently often used to vaguely describe almost any big data. However, the volume of the data should not be taken as the sole hallmark of big data. Modern computers can be scaled up fairly easily to automate the repeating tasks that are necessary for analyzing even the largest data collections, assuming that the structure of the data is known and sufficiently stable. Instead, the mere complexity of the data can make even moderate-sized data sets extremely challenging to analyze. For example, the human genome sequence, while quite large in size, could be easily processed computationally if its complexity allowed us to describe how exactly it needs to be analyzed. Furthermore, emerging new measurement technologies constantly feed the growth of complexity in biological data sets. For example, in the Cancer Genome Atlas (TCGA) project, the principal difficulty arises from the multitude of data types, not from the data volume per se [2].

Intelligent machine-learning and pattern recognition algorithms are needed to systematically extract information from big data. Sometimes the expectation is that algorithms more or less automatically bring forward interesting and important information out of a mass of unstructured data. However, the definitions of “interesting” and “important” are assessed on a subjective and context-dependent basis, and the computer can only recognize correlations between variables, and the meaning of these numbers is missing unless programmed explicitly. Therefore, such enthusiastic expectations are not well-founded.

Machine-learning systems, where the core of the system is deliberately detached from the reality, are called black-box approaches, and they underline the irrelevance of the deduction process. The focus of black-box approaches is correlation-based prediction. All forms of input data are equally important for this system, and the core of the system is inaccessible and uninterpretable for domain experts, such as oncologists. In a black-box approach, the contribution of the domain expert is usually focused on preprocessing data and selecting promising features for further processing.

For example, the self-organizing map (SOM) is an established black-box method of machine learning and visualization. Given the topology and convergence properties, SOM self-organizes and adapts to the input data. The entire process can be seen as execution of an optimization algorithm. It is sometimes claimed that SOM with an adaptive topology could reveal the secrets buried in the data. However, from the point of view of optimization, adaptive topology is equivalent to having more free parameters, thus adding to the problem instead of solving it. The same applies to the deep-learning approach. Unless real-life meaning is coded by manually preselecting the cost functions and the topology of the deep-learning method, the entire process is reduced into observing correlations between variables unattached from reality.

To conclude, black-box approaches can be used to make predictions by using big data. However, these approaches are limited in their capability to shed light beyond the observed data, namely gaining a system-level understanding of the mechanisms responsible for the data.

The availability of big data is sometimes expected to lead to fruitful results in data interpretation by using black-box methods. However, a leading figure of the machine-learning community warns against overeager expectations [3].

In cancer research, there is a genuine need to use the accumulated domain knowledge to cope with limited sample sizes and the ever-increasing data volumes. As the complexity of the black-box models, such as SOM or deep learning, increases, their sample requirements grow exponentially. This growth stems from the fact that the number of combinations of variables grows exponentially as the number of variables increases. Thus, a large sample size is needed to limit the probability of finding a fitting model by chance alone [3]. As a rule of thumb, thousands of samples facilitate the inferences made regarding a handful of variables in general-purpose black-box models. With millions of variables stemming from contemporary sequencing methods, even the size of the entire human population is dwarfed by the sample size requirements. However, in cancer research, the situation is typically such that the number of samples (usually number of patients) is relatively small although we have a large volume of data. Thus, it is necessary to limit the number of free variables that are inferred, leading us to consider a modeling approach that builds on the existing domain knowledge.

In contrast to black-box approaches, a mathematical model has better potential to integrate the existing domain knowledge to the desired extent. Mathematical models are often used as computational models—an obvious example being a mathematically defined group of differential equations for which solutions can be derived computationally through simulation. A mathematical model is used in science for a two-fold purpose: first, to understand and convey understanding of observed phenomena, and second, to predict the state of a system given initial conditions [4]. In addition to the prediction capability, the modeling approach facilitates an incremental understanding of the domain area through interpretation of the model parameters. Needless to say, black-box approaches are usually much more easily implemented for complex systems because very little domain knowledge can be implemented into them.

If we accept the view that machine learning is a special case of mathematical modeling, both can be easily defined in similar terms. A machine-learning system includes an internal representation that directly corresponds to a mathematical model. The processes of machine learning and mathematical modeling include parameter fitting (technically, optimization). Finally, the goals of machine learning and mathematical modeling coincide. Both aim to predict outcome based on measurement data, e.g., patient survival may be predicted based on clinical observations. Just as importantly, the goal of machine learning and mathematical modeling is to gain a broad-level understanding of the subject area by observing how well different models fit the data. However, a mathematical model facilitates the accumulation of knowledge into its structure and parameter values. Instead, a black-box approach has a more predetermined structure, detached from reality, and its knowledge accumulation capacity is restricted to preprocessing of input data and preselection of promising features.

In the following section, we illustrate the differences between black-box and modeling approaches using an example from everyday life.

In cancer research, the situation is typically such that we have a large volume of data, for example, from genome-wide expression, copy number, or methylation measurements, but the number of samples is relatively small. This situation prevents the use of many datum-mining algorithms, and we end up in a familiar situation, where genome-wide measurements result in the identification of one gene or of another feature, such as a mutation, instead of giving a deeper understanding of what is occurring in the gene regulatory network of cancerous cells. Thus, we argue that the inclusion of domain knowledge is necessary in limiting the degrees of freedom to a level where machine learning and big data can be fully used in cancer research.

One particularly successful way of introducing domain knowledge to genome-wide data is by using gene regulatory, signaling, metabolic, or context-specific pathways. These pathways contain information on genes, in relation to each other, that often work in concert towards a phenotypic action, such as cell movement, or something more intangible, such as growth signaling, giving the cell’s interaction a biological context. If we refer to the previous example, measurements of genes are much like measurements of the radio’s components or other properties. They are ambiguous without context and do not offer much help in understanding how the entire system works or why it does not work the way it should. Continuing with the analogy, pathways give genes a context whereby they influence the system, much like circuit diagrams show connections of the components in the radio, an inarguably valuable tool in understanding and fixing the device.

Pathway activities or inactivity are often more interesting than individual genes or mutations. This is not only because different aberrations can bring similar cancer phenotypes, for example the mouse double minute 2 homolog (MDM2)-p53 interaction, but also because pathways are closer to the phenotype that is often the context of interest in cancer research, such as “are the cells dividing after the treatment or not?” Computationally, the appealing feature in pathways is that they can reduce the dimensionality of gene expression data from tens of thousands of genes to hundreds of pathways. This reduction also makes genome-wide data much more digestible for researchers. Therefore, in many applications, researchers rather work on the pathway level than on the gene level, and many different pathway analyses have been implemented to date.

Recent genomic and molecular characterizations of cancer, especially the findings reported by the TCGA project, have shed light on cancer heterogeneity and potential targeted therapeutics, for example by recognizing new subtypes of gastric cancer [6]. In general, targeted computational methods, which make effective use of the available multimodal biological information, can significantly improve our ability to identify candidate biomarkers and targets and to conduct functional analyses [7]. For example, reducing the redundancy in enrichment analysis helps to reveal gene ontology modules efficiently and systematically [8].