The Reasonable Effectiveness of Randomness in Scalable and Integrative Gene Regulatory Network Inference and Beyond

Gene regulation is orchestrated by a vast number of molecules, including transcription factors and co-factors, chromatin regulators, as well as epigenetic mechanisms, and it has been shown that transcriptional misregulation, e.g., caused by mutations in regulatory sequences, is responsible for a plethora of diseases, including cancer, developmental or neurological disorders. As a consequence, decoding the architecture of gene regulatory networks has become one of the most important tasks in modern (computational) biology. However, to advance our understanding of the mechanisms involved in the transcriptional apparatus, we need scalable approaches that can deal with the increasing number of large-scale, high-resolution, biological datasets. In particular, such approaches need to be capable of efficiently integrating and exploiting the biological and technological heterogeneity of such datasets in order to best infer the underlying, highly dynamic regulatory networks, often in the absence of sufficient ground truth data for model training or testing. With respect to scalability, randomized approaches have proven to be a promising alternative to deterministic methods in computational biology. As an example, one of the top performing algorithms in a community challenge on gene regulatory network inference from transcriptomic data is based on a random forest regression model. In this concise survey, we aim to highlight how randomized methods may serve as a highly valuable tool, in particular, with increasing amounts of large-scale, biological experiments and datasets being collected. Given the complexity and interdisciplinary nature of the gene regulatory network inference problem, we hope our survey maybe helpful to both computational and biological scientists. It is our aim to provide a starting point for a dialogue about the concepts, benefits, and caveats of the toolbox of randomized methods, since unravelling the intricate web of highly dynamic, regulatory events will be one fundamental step in understanding the mechanisms of life and eventually developing efficient therapies to treat and cure diseases.

Golub–Kahan vs. Monte Carlo: a comparison of bidiagonlization and a randomized SVD method for the solution of linear discrete ill-posed problems

Randomized methods can be competitive for the solution of problems with a large matrix of low rank. They also have been applied successfully to the solution of large-scale linear discrete ill-posed problems by Tikhonov regularization (Xiang and Zou in Inverse Probl 29:085008, 2013). This entails the computation of an approximation of a partial singular value decomposition of a large matrix A that is of numerical low rank. The present paper compares a randomized method to a Krylov subspace method based on Golub–Kahan bidiagonalization with respect to accuracy and computing time and discusses characteristics of linear discrete ill-posed problems that make them well suited for solution by a randomized method.

Randomized approximation numbers on Besov classes with mixed smoothness

We study the Kolmogorov and the linear approximation numbers of the Besov classes [Formula: see text] with mixed smoothness in the norm of [Formula: see text] in the randomized setting. We first establish two discretization theorems. Then based on them, we determine the exact asymptotic orders of the Kolmogorov and the linear approximation numbers for certain values of the parameters [Formula: see text]. Our results show that the linear randomized methods lead to considerably better rates than those of the deterministic ones for [Formula: see text].

Derivative-free optimization methods

In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.