Online Non-linear Topology Identification from Graph-connected Time Series

Sparse Online Learning with Kernels using Random Features for Estimating Nonlinear Dynamic Graphs

“…However, notice that the estimates of LMS are prone to observation noise and can be unstable in practice. To avoid this problem, we formulate (16) in a recursive least square (RLS) sense, which further provides necessary stability in addition to faster convergence:…”

“…The above discussion motivates the need for algorithms that can learn nonlinear and dynamic topologies. Kernels are an ideal choice in this regard due to their interpretability and capability to learn functions online [14]- [16]. In kernel frameworks, the data points are transformed to a function space, where a linear relationship exists between them.…”

“…Second, the number of parameters required to express the function increases with the number of data samples, and the computational complexity becomes prohibitive at some point, which is typically known as the curse of dimensionality [17]. This dimensionality growth is circumvented in [16] by discarding the past data samples using a forgetting window. However, such an approach can lead to suboptimal function learning because it discards data samples without assessing their significance in representing the functions to be learned.…”

Sparse Online Learning with Kernels using Random Features for Estimating Nonlinear Dynamic Graphs

“…The above discussion motivates the need for algorithms that can learn nonlinear and non-stationary topologies. Kernels are an ideal choice in this regard due to their interpretability and capability to learn functions online [20]- [22]. However, a major drawback associated with the kernel-based algorithms is the curse of dimensionality [23], i.e., the number of parameters required to express the function increases with number of data samples, and the computational complexity becomes prohibitive at some point.…”

Scalable and Privacy-Aware Online Learning of Nonlinear Structural Equation Models

“…The nonlinearity is tackled using kernel methods, and the curse of dimensionality of kernels is mitigated through random feature (RF) approximation. Kernel techniques are conventionally used for nonlinear topology estimation [14]- [16] and help transform the problem into an amenable form. Instead, RF is typically used to reduce the complexity of nonlinear models as well as to ensure that connectivity is inferred without revealing nodal attributes [17]- [22].…”