Tensor Decomposition With Generalized Lasso Penalties

Online Function Tracking with Generalized Penalties

We attend to the classic setting where an observer needs to inform a tracker about an arbitrary time varying function f : N0 → Z. This is an optimization problem, where both wrong values at the tracker and sending updates entail a certain cost. We consider an online variant of this problem, i.e., at time t, the observer only knows f(t′) for all t′ ≤ t. In this paper, we generalize existing cost...

Tensor Decomposition with Smoothness

Tensor Decomposition with Smoothness

Real data tensors are typically high dimensional; however, their intrinsic information is preserved in low-dimensional space, which motivates the use of tensor decompositions such as Tucker decomposition. Frequently, real data tensors smooth in addition to being low dimensional, which implies that adjacent elements are similar or continuously changing. These elements typically appear as spatial...

Generalized Higher-Order Orthogonal Iteration for Tensor Decomposition and Completion

Low-rank tensor estimation has been frequently applied in many real-world problems. Despite successful applications, existing Schatten 1-norm minimization (SNM) methods may become very slow or even not applicable for large-scale problems. To address this difficulty, we therefore propose an efficient and scalable core tensor Schatten 1-norm minimization method for simultaneous tensor decompositi...

Network Exploration via the Adaptive Lasso and Scad Penalties.

Graphical models are frequently used to explore networks, such as genetic networks, among a set of variables. This is usually carried out via exploring the sparsity of the precision matrix of the variables under consideration. Penalized likelihood methods are often used in such explorations. Yet, positive-definiteness constraints of precision matrices make the optimization problem challenging. ...