arXiv subjects

Vassilis N. Ioannidis

Publications and source records attributed to Vassilis N. Ioannidis.

40 records · Page 3Linked to original sources

arXiv2018

Semi-Blind Inference of Topologies and Dynamical Processes over Graphs

Network science provides valuable insights across numerous disciplines including sociology, biology, neuroscience and engineering. A task of major practical importance in these application domains is inferring the network structure from noisy observations at a subset of nodes. Available methods for topology inference typically assume that the process over the network is observed at all nodes. However, application-specific constraints may prevent acquiring network-wide observations. Alleviating the limited flexibility of existing approaches, this work advocates structural models for graph processes and develops novel algorithms for joint inference of the network topology and processes from partial nodal observations. Structural equation models (SEMs) and structural vector autoregressive models (SVARMs) have well-documented merits in identifying even directed topologies of complex graphs; while SEMs capture contemporaneous causal dependencies among nodes, SVARMs further account for time-lagged influences. This paper develops algorithms that iterate between inferring directed graphs that "best" fit the data, and estimating the network processes at reduced computational complexity by leveraging tools related to Kalman smoothing. To further accommodate delay-sensitive applications, an online joint inference approach is put forth that even tracks time-evolving topologies. Furthermore, conditions for identifying the network topology given partial observations are specified. It is proved that the required number of observations for unique identification reduces significantly when the network structure is sparse. Numerical tests with synthetic as well as real datasets corroborate the effectiveness of the novel approach.

cs.LG↗

arXiv2018

Kernel-based Inference of Functions over Graphs

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and generalizes the reconstruction approaches put forth recently by the signal processing on graphs community. Both the static and the dynamic settings are considered along with effective modeling approaches for addressing real-world problems. The herein analytical discussion is complemented by a set of numerical examples, which showcase the effectiveness of the presented techniques, as well as their merits related to state-of-the-art methods.

stat.ML↗

arXiv2017

Inference of Spatio-Temporal Functions over Graphs via Multi-Kernel Kriged Kalman Filtering

Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filter that accounts for the spatio-temporal variations, and offers efficient online reconstruction, even for dynamically evolving network topologies. The kernel-based learning framework bypasses the need for statistical information by capitalizing on the smoothness that graph signals exhibit with respect to the underlying graph. To address the challenge of selecting the appropriate kernel, the proposed filter is combined with a multi-kernel selection module. Such a data-driven method selects a kernel attuned to the signal dynamics on-the-fly within the linear span of a pre-selected dictionary. The novel multi-kernel learning algorithm exploits the eigenstructure of Laplacian kernel matrices to reduce computational complexity. Numerical tests with synthetic and real data demonstrate the superior reconstruction performance of the novel approach relative to state-of-the-art alternatives.

cs.LG↗

arXiv2017

Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly different time instants. Leveraging spatiotemporal dynamics can drastically reduce the number of observed vertices, and hence the cost of sampling. Alleviating the limited flexibility of existing approaches, the present paper broadens the existing kernel-based graph function reconstruction framework to accommodate time-evolving functions over possibly time-evolving topologies. This approach inherits the versatility and generality of kernel-based methods, for which no knowledge on distributions or second-order statistics is required. Systematic guidelines are provided to construct two families of space-time kernels with complementary strengths. The first facilitates judicious control of regularization on a space-time frequency plane, whereas the second can afford time-varying topologies. Batch and online estimators are also put forth, and a novel kernel Kalman filter is developed to obtain these estimates at affordable computational cost. Numerical tests with real data sets corroborate the merits of the proposed methods relative to competing alternatives.

cs.LG↗