# Resilience and Resilient Systems of Artificial Intelligence: Taxonomy, Models and Methods
## 3 Background, Taxonomy and Ontology
### Vulnerabilities and Threats of AISs
In addition, the environment, in general, is not stationary, and the patterns of the observed process can change unpredictably. As a result, at certain times, the model of mapping inputs to outputs may become irrelevant. A compromised network, infected AIS software and remote access to AIS can be a source of threat to AIS in terms of the ability to acquire its data, structure and parameters, which facilitates the formation of attacks. Among AIS threats, there are three main types of disturbances: drift, adversarial attacks, and faults. Each of these types has subtypes depending on their way of formation and specifics of impact. The drift problem occurs when at a certain time point the test data begins to differ significantly from the training data in certain characteristics, which indicates the need to update the model to avoid performance degradation. Drift in machine learning is divided into real concept drift, covariance shift, and a priori probability shift. Real concept drift means a change in the distribution of a posteriori probability \(\mathrm{P_{t+w}(y|X)}\) at time \(\mathrm{t+w}\) compared to the a posteriori probability distribution \(\mathrm{P_{t}(y|X)}\) at time \(\mathrm{t}\), which is connected with principal change in the underlying target concept, that is \(\mathrm{P_{t}(y|X)\
eq P_{t+w}(y|X)}\), where X is a set of input variables, and y is target variable (Figure 3b) [35]. In the case of reinforcement learning, the real drift of concepts occurs as a result of environment context changes (environment shift). In other words, the agent functions under conditions of non-stationary rewards and/or non-stationary transition probabilities between system states. Fickle concept drift, which is a subcategory of real drift and occurs when some data samples belong to two different concepts or contexts at two different times, is considered separately. Subconcept drift or Intersect concept drift is also a subcategory of real drift and occurs when only a subset of the dataset changes its target variable or rewards feedback after drift has occurred. Full concept drift or Severe concept drift is a subcategory of real concept drift, which occurs when target variables of all data points change after the drift occurs. In the case of reinforcement learning, Full concept drift can be associated with changes in action-reward feedback and transition probabilities for all historical state-action pairs. Covariate shift, or virtual concept drift as it is commonly called in the literature, occurs when input data distribution changes without affecting the target concept (Figure 3c). In mathematical terms, \(\mathrm{P_{t}(y|x)=P_{t+w}(y|x)}\) and \(\mathrm{P_{t}(x)\
eq P_{t+w}(x)}\). Although in practice, changes in the data and the posterior probability distributions often happen simultaneously. So, covariate shift can be a component of overall drift or the initial stage of real concept drift. Out-of-distribution data can be considered one of the subcategories of Covariate shift. Out-of-distribution data may have an element of novelty and it do not ensure the reliability of the analysis. This may be related to the lack of training data in appropriate region of space, which increases epistemic uncertainty. Or it may be caused by the fact that the data is completely outside the training distribution and the model could not extrapolate effectively. It is a case of aleatoric uncertainty. Another subcategory Covariate shift is related to dynamically arising new attributes in the input space. This subcategory is also called Feature-evolution. Mathematically, this can be described as \(\mathrm{X_{t}\
eq X_{t+w}}\) and as a result \(\mathrm{P_{t}(x)\
eq P_{t+w}(x)}\). This can occur if the AIS is evolving and new data sources are added. When AIS in inference mode encounters data that falls outside the distribution on which it was trained, AIS reaction can be unpredictable and have catastrophic consequences.