Traditional methods for black box optimization require a considerable number of evaluations which can be time consuming, unpractical, and often unfeasible for many engineering applications that rely on accurate representations and expensive models to evaluate. Bayesian Optimization (BO) methods search for the global optimum by progressively (actively) learning a surrogate model of the objective function along the search path. Bayesian optimization can be accelerated through multifidelity approaches which leverage multiple black-box approximations of the objective functions that can be computationally cheaper to evaluate, but still provide relevant information to the search task. Further computational benefits are offered by the availability of parallel and distributed computing architectures whose optimal usage is an open opportunity within the context of active learning. This paper introduces the Resource Aware Active Learning (RAAL) strategy, a multifidelity Bayesian scheme to accelerate the optimization of black box functions. At each optimization step, the RAAL procedure computes the set of best sample locations and the associated fidelity sources that maximize the information gain to acquire during the parallel/distributed evaluation of the objective function, while accounting for the limited computational budget. The scheme is demonstrated for a variety of benchmark problems and results are discussed for both single fidelity and multifidelity settings. In particular we observe that the RAAL strategy optimally seeds multiple points at each iteration allowing for a major speed up of the optimization task.

We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank SVD for matrices and multi-linear SVD for tensors. Then, building on this novel decomposition we construct a general class of convex optimization problems for approximately solving low-rank tensor inverse problems, such as tensor Robust PCA. The whole framework is named as 'Multilinear Low-rank tensors on Graphs (MLRTG)'. Our theoretical analysis shows: 1) MLRTG stands on the notion of approximate stationarity of multi-dimensional signals on graphs and 2) the approximation error depends on the eigen gaps of the graphs. We demonstrate applications for a wide variety of 4 artificial and 12 real tensor datasets, such as EEG, FMRI, BCI, surveillance videos and hyperspectral images. Generalization of the tensor concepts to non-euclidean domain, orders of magnitude speed-up, low-memory requirement and significantly enhanced performance at low SNR are the key aspects of our framework.

Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods for signal processing on graphs ignore the dimension of time, treating successive graph signals independently or taking a global average. To address this shortcoming, this paper considers the statistical analysis of time-varying graph signals. We introduce a novel definition of joint (time-vertex) stationarity, which generalizes the classical definition of time stationarity and the more recent definition appropriate for graphs. Joint stationarity gives rise to a scalable Wiener optimization framework for joint denoising, semi-supervised learning, or more generally inversing a linear operator, that is provably optimal. Experimental results on real weather data demonstrate that taking into account graph and time dimensions jointly can yield significant accuracy improvements in the reconstruction effort.