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System identification is a common tool for estimating (linear) plant models as a basis for model-based predictive control and optimization. The current challenges in process industry, however, ask for data-driven modelling techniques that…
Algorithms for Gaussian process, marginal likelihood methods or restricted maximum likelihood methods often require derivatives of log determinant terms. These log determinants are usually parametric with variance parameters of the…
We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…
This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned and classical Pad\'e methods shown to be…
Can linear systems be solved faster than matrix multiplication? While there has been remarkable progress for the special cases of graph structured linear systems, in the general setting, the bit complexity of solving an $n \times n$ linear…
This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via $\ell_1$-minimisation. The problem can also be seen as factorising a $\ddim \times \nsig$ matrix $Y=(y_1 >... y_\nsig),…
In unconstrained maximum a posteriori (MAP) and maximum likelihood estimation, the inverse of minus the merit-function Hessian matrix is an approximation of the estimate covariance matrix. In the Bayesian context of MAP estimation, it is…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally…
We perform a smoothed analysis of the componentwise condition numbers for determinant computation, matrix inversion, and linear equations solving for sparse n times n matrices. The bounds we obtain for the ex- pectations of the logarithm of…
We revisit the matrix problems sparse null space and matrix sparsification, and show that they are equivalent. We then proceed to seek algorithms for these problems: We prove the hardness of approximation of these problems, and also give a…
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…
Scaling problems have a rich and diverse history, and thereby have found numerous applications in several fields of science and engineering. For instance, the matrix scaling problem has had applications ranging from theoretical computer…
The paper addresses the realization and identification problem or a subclass of piecewise-affine hybrid systems. The paper provides necessary and sufficient conditions for existence of a realization, a characterization of minimality, and an…
The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…
Discovering the partial differential equations underlying spatio-temporal datasets from very limited and highly noisy observations is of paramount interest in many scientific fields. However, it remains an open question to know when model…
Anomalies and outliers are common in real-world data, and they can arise from many sources, such as sensor faults. Accordingly, anomaly detection is important both for analyzing the anomalies themselves and for cleaning the data for further…
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic…