2,307 research outputs found
An -Regularization Approach to High-Dimensional Errors-in-variables Models
Several new estimation methods have been recently proposed for the linear
regression model with observation error in the design. Different assumptions on
the data generating process have motivated different estimators and analysis.
In particular, the literature considered (1) observation errors in the design
uniformly bounded by some , and (2) zero mean independent
observation errors. Under the first assumption, the rates of convergence of the
proposed estimators depend explicitly on , while the second
assumption has been applied when an estimator for the second moment of the
observational error is available. This work proposes and studies two new
estimators which, compared to other procedures for regression models with
errors in the design, exploit an additional -norm regularization.
The first estimator is applicable when both (1) and (2) hold but does not
require an estimator for the second moment of the observational error. The
second estimator is applicable under (2) and requires an estimator for the
second moment of the observation error. Importantly, we impose no assumption on
the accuracy of this pilot estimator, in contrast to the previously known
procedures. As the recent proposals, we allow the number of covariates to be
much larger than the sample size. We establish the rates of convergence of the
estimators and compare them with the bounds obtained for related estimators in
the literature. These comparisons show interesting insights on the interplay of
the assumptions and the achievable rates of convergence
Cluster-Aided Mobility Predictions
Predicting the future location of users in wireless net- works has numerous
applications, and can help service providers to improve the quality of service
perceived by their clients. The location predictors proposed so far estimate
the next location of a specific user by inspecting the past individual
trajectories of this user. As a consequence, when the training data collected
for a given user is limited, the resulting prediction is inaccurate. In this
paper, we develop cluster-aided predictors that exploit past trajectories
collected from all users to predict the next location of a given user. These
predictors rely on clustering techniques and extract from the training data
similarities among the mobility patterns of the various users to improve the
prediction accuracy. Specifically, we present CAMP (Cluster-Aided Mobility
Predictor), a cluster-aided predictor whose design is based on recent
non-parametric bayesian statistical tools. CAMP is robust and adaptive in the
sense that it exploits similarities in users' mobility only if such
similarities are really present in the training data. We analytically prove the
consistency of the predictions provided by CAMP, and investigate its
performance using two large-scale datasets. CAMP significantly outperforms
existing predictors, and in particular those that only exploit individual past
trajectories
Erasure Codes with a Banded Structure for Hybrid Iterative-ML Decoding
This paper presents new FEC codes for the erasure channel, LDPC-Band, that
have been designed so as to optimize a hybrid iterative-Maximum Likelihood (ML)
decoding. Indeed, these codes feature simultaneously a sparse parity check
matrix, which allows an efficient use of iterative LDPC decoding, and a
generator matrix with a band structure, which allows fast ML decoding on the
erasure channel. The combination of these two decoding algorithms leads to
erasure codes achieving a very good trade-off between complexity and erasure
correction capability.Comment: 5 page
Enhanced Recursive Reed-Muller Erasure Decoding
Recent work have shown that Reed-Muller (RM) codes achieve the erasure
channel capacity. However, this performance is obtained with maximum-likelihood
decoding which can be costly for practical applications. In this paper, we
propose an encoding/decoding scheme for Reed-Muller codes on the packet erasure
channel based on Plotkin construction. We present several improvements over the
generic decoding. They allow, for a light cost, to compete with
maximum-likelihood decoding performance, especially on high-rate codes, while
significantly outperforming it in terms of speed
- …