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In this paper we suggest a moment matching method for quadratic-bilinear dynamical systems. Most system-theoretic reduction methods for nonlinear systems rely on multivariate frequency representations. Our approach instead uses univariate…
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…
We present a method that allows efficient and safe approximation of model predictive controllers using kernel interpolation. Since the computational complexity of the approximating function scales linearly with the number of data points, we…
Recent breakthroughs in 3D generation have enabled the synthesis of high-fidelity individual assets. However, generating 3D compositional objects from single images--particularly under occlusions--remains challenging. Existing methods often…
Decomposing discrete signals such as images into components is vital in many applications, and this paper propose a framework to produce filtering banks to accomplish this task. The framework is an equation set which is ill-posed, and thus…
We present in this work a new methodology to design kernels on data which is structured with smaller components, such as text, images or sequences. This methodology is a template procedure which can be applied on most kernels on measures…
We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…
Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…
We present significant improvements to our previous work on noise reduction in {\sl Herschel} observation maps by defining sparse filtering tools capable of handling, in a unified formalism, a significantly improved noise reduction as well…
Several techniques were proposed to model the Piecewise linear (PWL) functions, including convex combination, incremental and multiple choice methods. Although the incremental method was proved to be very efficient, the attention of the…
Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…
No matter the expressive power and sophistication of supervised learning algorithms, their effectiveness is restricted by the features describing the data. This is not a new insight in ML and many methods for feature selection,…
Interest point detection is a common task in various computer vision applications. Although a big variety of detector are developed so far computational efficiency of interest point based image analysis remains to be the problem. Current…
We consider Lagrange interpolation on the set of finitely many intervals. This problem is closely related to the least deviating polynomial from zero on such sets. We will obtain lower and upper estimates for the corresponding Lebesgue…
Symbolic models have recently spurred the interest of the research community because they offer a correct-by-design approach to the control of embedded and cyber-physical systems. In this paper we address construction of symbolic models for…
Growth in both size and complexity of modern data challenges the applicability of traditional likelihood-based inference. Composite likelihood (CL) methods address the difficulties related to model selection and computational intractability…
Hierarchies allow feature sharing between objects at multiple levels of representation, can code exponential variability in a very compact way and enable fast inference. This makes them potentially suitable for learning and recognizing a…
We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is…
High-dimensional datasets depict a challenge for learning tasks in data mining and machine learning. Feature selection is an effective technique in dealing with dimensionality reduction. It is often an essential data processing step prior…
A rule for constructing interpolation nodes for $n$th degree polynomials on the simplex is presented. These nodes are simple to define recursively from families of 1D node sets, such as the Lobatto-Gauss-Legendre (LGL) nodes. The resulting…