46,220 research outputs found
Estimation of Markov Chain via Rank-Constrained Likelihood
This paper studies the estimation of low-rank Markov chains from empirical
trajectories. We propose a non-convex estimator based on rank-constrained
likelihood maximization. Statistical upper bounds are provided for the
Kullback-Leiber divergence and the risk between the estimator and the
true transition matrix. The estimator reveals a compressed state space of the
Markov chain. We also develop a novel DC (difference of convex function)
programming algorithm to tackle the rank-constrained non-smooth optimization
problem. Convergence results are established. Experiments show that the
proposed estimator achieves better empirical performance than other popular
approaches.Comment: Accepted at ICML 201
DMFSGD: A Decentralized Matrix Factorization Algorithm for Network Distance Prediction
The knowledge of end-to-end network distances is essential to many Internet
applications. As active probing of all pairwise distances is infeasible in
large-scale networks, a natural idea is to measure a few pairs and to predict
the other ones without actually measuring them. This paper formulates the
distance prediction problem as matrix completion where unknown entries of an
incomplete matrix of pairwise distances are to be predicted. The problem is
solvable because strong correlations among network distances exist and cause
the constructed distance matrix to be low rank. The new formulation circumvents
the well-known drawbacks of existing approaches based on Euclidean embedding.
A new algorithm, so-called Decentralized Matrix Factorization by Stochastic
Gradient Descent (DMFSGD), is proposed to solve the network distance prediction
problem. By letting network nodes exchange messages with each other, the
algorithm is fully decentralized and only requires each node to collect and to
process local measurements, with neither explicit matrix constructions nor
special nodes such as landmarks and central servers. In addition, we compared
comprehensively matrix factorization and Euclidean embedding to demonstrate the
suitability of the former on network distance prediction. We further studied
the incorporation of a robust loss function and of non-negativity constraints.
Extensive experiments on various publicly-available datasets of network delays
show not only the scalability and the accuracy of our approach but also its
usability in real Internet applications.Comment: submitted to IEEE/ACM Transactions on Networking on Nov. 201
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