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Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…
An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work…
Solving inverse problems is central to geosciences and remote sensing. Radiative transfer models (RTMs) represent mathematically the physical laws which govern the phenomena in remote sensing applications (forward models). The numerical…
Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both…
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…
Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a…
Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample…
Strictly Positive Real (SPR) transfer functions arise in many areas of engineering like passivity theory in circuit analysis and adaptive control to name a few. In many physical systems, it is possible to conclude that the system is…
Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
Matched Field Processing (MFP) locates the underwater sources by matching the received data with the replica vectors, which could be regarded as a generalized beamformer. In this paper, the MFP method is combined with a recently developed…
Statistical shape models (SSMs) represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional…
A new technique is presented to solve a class of linear boundary value problems (BVP). Technique is primarily based on an operational matrix developed from a set of modified Bernoulli polynomials. The new set of polynomials is an…
Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it…
Obstacle-aware trajectory navigation is crucial for many systems. For example, in real-world navigation tasks, an agent must avoid obstacles, such as furniture in a room, while planning a trajectory. Gaussian Process (GP) regression, in its…
Genetic Programming (GP) has been primarily used to tackle optimization, classification, and feature selection related tasks. The widespread use of GP is due to its flexible and comprehensible tree-type structure. Similarly, research is…
We propose a principled convolutional neural pyramid (CNP) framework for general low-level vision and image processing tasks. It is based on the essential finding that many applications require large receptive fields for structure…
Graph signal processing (GSP) studies signals that live on irregular data kernels described by graphs. One fundamental problem in GSP is sampling---from which subset of graph nodes to collect samples in order to reconstruct a bandlimited…
This paper addresses the positive semi-definite procrustes problem (PSDP). The PSDP corresponds to a least squares problem over the set of symmetric and semi-definite positive matrices. These kinds of problems appear in many applications…
The $G^{+}$ method is a new method, a powerful one, for the study of (homogeneous and nonhomogeneous) products of nonnegative matrices -- for problems on the products of nonnegative matrices. To study such products, new classes of matrices…