Related papers: Scale Invariant Power Iteration
While scale-invariant modeling has substantially boosted the performance of visual recognition tasks, it remains largely under-explored in deep networks based image restoration. Naively applying those scale-invariant techniques (e.g.…
In a Bayesian approach for solving linear inverse problems one needs to specify the prior laws for calculation of the posterior law. A cost function can also be defined in order to have a common tool for various Bayesian estimators which…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
H{\infty} control of nonlinear continuous-time system depends on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which has been proved impossible to obtain a closed-form solution due to the nonlinearity of HJI equation. In order…
Motivated by the previously developed multilevel aggregation method for solving structural analysis problems a novel two-level aggregation approach for efficient iterative solution of Principal Component Analysis (PCA) problems is proposed.…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
Recently, Stochastic Variational Inference (SVI) has been increasingly attractive thanks to its ability to find good posterior approximations of probabilistic models. It optimizes the variational objective with stochastic optimization,…
One key challenge for solving a general stochastic optimization problem with expectations in the objective and constraint functions using ordinary stochastic iterative methods lies in the infeasibility issue caused by the randomness over…
The existing inverse power ($\mathbf{IP}$) method for solving the balanced graph cut lacks local convergence and its inner subproblem requires a nonsmooth convex solver. To address these issues, we develop a simple inverse power…
Tackling large approximate dynamic programming or reinforcement learning problems requires methods that can exploit regularities, or intrinsic structure, of the problem in hand. Most current methods are geared towards exploiting the…
There has been a recent focus in reinforcement learning on addressing continuous state and action problems by optimizing parameterized policies. PI2 is a recent example of this approach. It combines a derivation from first principles of…
In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework…
Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power…
Motivated by multi-user optimization problems and non-cooperative Nash games in uncertain regimes, we consider stochastic Cartesian variational inequalities (SCVI) where the set is given as the Cartesian product of a collection of component…
How can we compute the pseudoinverse of a sparse feature matrix efficiently and accurately for solving optimization problems? A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized as a fundamental…
Semidefinite programs (SDPs) are powerful theoretical tools that have been studied for over two decades, but their practical use remains limited due to computational difficulties in solving large-scale, realistic-sized problems. In this…