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We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…
In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces,…
Randomized iterative methods, such as the randomized Kaczmarz method, have gained significant attention for solving large-scale linear systems due to their simplicity and efficiency. Meanwhile, Krylov subspace methods have emerged as a…
Design of printed circuit board (PCB) stack-up requires the consideration of characteristic impedance, insertion loss and crosstalk. As there are many parameters in a PCB stack-up design, the optimization of these parameters needs to be…
Bilinear dynamical systems are commonly used in science and engineering because they form a bridge between linear and non-linear systems. However, simulating them is still a challenge because of their large size. Hence, a lot of research is…
Standard Gibbs sampling applied to a multivariate normal distribution with a specified precision matrix is equivalent in fundamental ways to the Gauss-Seidel iterative solution of linear equations in the precision matrix. Specifically, the…
Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…
In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system…
Science and engineering problems frequently require solving a sequence of dual linear systems. Besides having to store only few Lanczos vectors, using the BiConjugate Gradient method (BiCG) to solve dual linear systems has advantages for…
Successful applications of sparse models in computer vision and machine learning imply that in many real-world applications, high dimensional data is distributed in a union of low dimensional subspaces. Nevertheless, the underlying…
In this paper, we modify the adaptive cubic regularization method for large-scale unconstrained optimization problem by using a real positive definite scalar matrix to approximate the exact Hessian. Combining with the nonmonotone technique,…
Entity alignment has always had significant uses within a multitude of diverse scientific fields. In particular, the concept of matching entities across networks has grown in significance in the world of social science as communicative…
Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. In this paper, we introduce a method that simultaneously learns an embedding space along…
Nowadays, analysing data from different classes or over a temporal grid has attracted a great deal of interest. As a result, various multiple graphical models for learning a collection of graphical models simultaneously have been derived by…
We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo approaches, the proposed method is derived from an approximation of…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We introduce BriskStream, an in-memory data stream processing system (DSPSs) specifically designed for modern shared-memory multicore architectures. BriskStream's key contribution is an execution plan optimization paradigm, namely RLAS,…
Eulerian nonlinear uncertainty propagation methods often suffer from finite domain limitations and computational inefficiencies. A recent approach to this class of algorithm, Grid-based Bayesian Estimation Exploiting Sparsity, addresses the…