120 research outputs found
Distributionally robust L1-estimation in multiple linear regression
Linear regression is one of the most important and widely used techniques in data analysis, for which a key step is the estimation of the unknown parameters. However, it is often carried out under the assumption that the full information of the error distribution is available. This is clearly unrealistic in practice. In this paper, we propose a distributionally robust formulation of L1-estimation (or the least absolute value estimation) problem, where the only knowledge on the error distribution is that it belongs to a well-defined ambiguity set. We then reformulate the estimation problem as a computationally tractable conic optimization problem by using duality theory. Finally, a numerical example is solved as a conic optimization problem to demonstrate the effectiveness of the proposed approach
Small-Sample Inferred Adaptive Recoding for Batched Network Coding
Batched network coding is a low-complexity network coding solution to
feedbackless multi-hop wireless packet network transmission with packet loss.
The data to be transmitted is encoded into batches where each of which consists
of a few coded packets. Unlike the traditional forwarding strategy, the
intermediate network nodes have to perform recoding, which generates recoded
packets by network coding operations restricted within the same batch. Adaptive
recoding is a technique to adapt the fluctuation of packet loss by optimizing
the number of recoded packets per batch to enhance the throughput. The input
rank distribution, which is a piece of information regarding the batches
arriving at the node, is required to apply adaptive recoding. However, this
distribution is not known in advance in practice as the incoming link's channel
condition may change from time to time. On the other hand, to fully utilize the
potential of adaptive recoding, we need to have a good estimation of this
distribution. In other words, we need to guess this distribution from a few
samples so that we can apply adaptive recoding as soon as possible. In this
paper, we propose a distributionally robust optimization for adaptive recoding
with a small-sample inferred prediction of the input rank distribution. We
develop an algorithm to efficiently solve this optimization with the support of
theoretical guarantees that our optimization's performance would constitute as
a confidence lower bound of the optimal throughput with high probability.Comment: 7 pages, 2 figures, accepted in ISIT-21, appendix adde
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