Balanced model truncation has been considered by many authors, since it is a simple and, nevertheless, efficient model reduction technique. In many cases the approximation error may be bounded by a function of the neglected singular values. In this paper the performance of balanced truncation of state space models for ARMA processes is analysed, where the goodness of fit is measured by the asym...

Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent progress in proving various non-convex algorithms converge from a good initial point, it remains unclear why random or arbitrary initialization suffices in ...

It is well known that performing gradient descent on fixed surfaces may result in poor travel through getting stuck in local minima and other surface features. Subgoal chaining in supervised learning is a method to improve travel for neural networks by directing local variation in the surface during training. This paper shows however that linear subgoal chains such as those used in ERA are not ...

There are many local and greedy algorithms for energy minimization over Markov Random Field (MRF) such as iterated condition mode (ICM) and various gradient descent methods. Local minima solutions can be obtained with simple implementations and usually require smaller computational time than global algorithms. Also, methods such as ICM can be readily implemented in a various difficult problems ...

In this paper the existence of two positive solutions for a Dirichlet problem having a critical growth, and depending on a real parameter, is established. The approach is based on methods which are totally variational, unlike the fundamental result of Ambrosetti, Brezis and Cerami where a clever combination of topological and variational methods is used in order to obtain the same conclusion. I...

We study the problem of computing a minimum cut in a simple, undirected graph and give a deterministic O(m log n log log n) time algorithm. This improves both on the best previously known deterministic running time of O(m log n) (Kawarabayashi and Thorup [12]) and the best previously known randomized running time of O(m log n) (Karger [11]) for this problem, though Karger’s algorithm can be fur...