Related papers: Knot Selection in Sparse Gaussian Processes
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…
Gaussian Processes are used in many applications to model spatial phenomena. Within this context, a key issue is to decide the set of locations where to take measurements so as to obtain a better approximation of the underlying function.…
Optimizing smooth convex functions in stochastic settings, where only noisy estimates of gradients and Hessians are available, is a fundamental problem in optimization. While first-order methods possess a low per-iteration cost, their…
We study the problem of sampling and reconstructing spectrally sparse graph signals where the objective is to select a subset of nodes of prespecified cardinality that ensures interpolation of the original signal with the lowest possible…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
Single-spin quantum sensors, for example based on nitrogen-vacancy centres in diamond, provide nanoscale mapping of magnetic fields. In applications where the magnetic field may be changing rapidly, total sensing time is crucial and must be…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…
An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…
We describe a new algorithm for Gaussian Elimination suitable for general (unsymmetric and possibly singular) sparse matrices, of any entry type, which has a natural parallel and distributed-memory formulation but degrades gracefully to…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
Bayesian optimization has become a fundamental global optimization algorithm in many problems where sample efficiency is of paramount importance. Recently, there has been proposed a large number of new applications in fields such as…
The probability of a random polygon (or a ring polymer) having a knot type $K$ should depend on the complexity of the knot $K$. Through computer simulation using knot invariants, we show that the knotting probability decreases exponentially…
A greedy algorithm is proposed for sparse-sensor selection in reduced-order sensing that contains correlated noise in measurement. The sensor selection is carried out by maximizing the determinant of the Fisher information matrix in a…
We discuss the possibility of the existence of finite algorithms that may give distinct knot classes. In particular we present two attempts for such algorithms which seem promising, one based on knot projections on a plane, the other on…
Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of…
Despite the recent success of artificial neural networks, more biologically plausible learning methods may be needed to resolve the weaknesses of backpropagation trained models such as catastrophic forgetting and adversarial attacks.…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete…
There is no known efficient method for selecting k Gaussian features from n which achieve the lowest Bayesian classification error. We show an example of how greedy algorithms faced with this task are led to give results that are not…
Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…