Stochastic bounds with a low rank decomposition

نویسندگان

  • Ana Bušić
  • Jean-Michel Fourneau
  • Mouad Ben Mamoun
چکیده

We investigate how we can bound a Discrete Time Markov Chain (DTMC) by a stochastic matrix with a low rank decomposition. In the first part of the paper we show the links with previous results for matrices with a decomposition of size 1 or 2. Then we show how the complexity of the analysis for steady-state and transient distributions can be simplified when we take into account the decomposition. Finally, we show how we can obtain a monotone stochastic upper bound with a low rank decomposition.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Cramer-Rao lower bounds for low-rank decomposition of multidimensional arrays

Unlike low-rank matrix decomposition, which is generically nonunique for rank greater than one, low-rank threeand higher dimensional array decomposition is unique, provided that the array rank is lower than a certain bound, and the correct number of components (equal to array rank) is sought in the decomposition. Parallel factor (PARAFAC) analysis is a common name for low-rank decomposition of ...

متن کامل

Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation X of the sum of an (approximately) low rank matrix Θ⋆ with a second matrix Γ⋆ endowed with a complementary form of low-dimensional structure; this set-up includes many statistical models of interest, including ...

متن کامل

Noisy Matrix Decomposition via Convex Relaxation: Optimal Rates in High Dimensions1 by Alekh Agarwal2, Sahand Negahban3 And

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation X of the sum of an (approximately) low rank matrix with a second matrix endowed with a complementary form of low-dimensional structure; this set-up includes many statistical models of interest, including factor...

متن کامل

Clustered low rank approximation of graphs in information science applications

In this paper we present a fast and accurate procedure called clustered low rank matrix approximation for massive graphs. The procedure involves a fast clustering of the graph and then approximates each cluster separately using existing methods, e.g. the singular value decomposition, or stochastic algorithms. The cluster-wise approximations are then extended to approximate the entire graph. Thi...

متن کامل

Fast and Accurate Low Rank Approximation of Massive Graphs

In this paper we present a fast and accurate procedure called clustered low rank matrix approximation for massive graphs. The procedure involves a fast clustering of the graph and then approximating each cluster separately using existing methods, e.g. the singular value decomposition, or stochastic algorithms. The cluster-wise approximations are then extended to approximate the entire graph. Th...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014