arXiv subjects

Yingying Xu

Publications and source records attributed to Yingying Xu.

21 records · Page 2Linked to original sources

arXiv2014

Bayesian signal reconstruction for 1-bit compressed sensing

The 1-bit compressed sensing framework enables the recovery of a sparse vector x from the sign information of each entry of its linear transformation. Discarding the amplitude information can significantly reduce the amount of data, which is highly beneficial in practical applications. In this paper, we present a Bayesian approach to signal reconstruction for 1-bit compressed sensing, and analyze its typical performance using statistical mechanics. Utilizing the replica method, we show that the Bayesian approach enables better reconstruction than the L1-norm minimization approach, asymptotically saturating the performance obtained when the non-zero entries positions of the signal are known. We also test a message passing algorithm for signal reconstruction on the basis of belief propagation. The results of numerical experiments are consistent with those of the theoretical analysis.

physics.data-an↗

arXiv2014

Statistical inference with probabilistic graphical models

These are notes from the lecture of Devavrat Shah given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithms", that took place in Les Houches, France from Monday September 30th, 2013, till Friday October 11th, 2013. The school was organized by Florent Krzakala from UPMC & ENS Paris, Federico Ricci-Tersenghi from La Sapienza Roma, Lenka Zdeborova from CEA Saclay & CNRS, and Riccardo Zecchina from Politecnico Torino. This lecture of Devavrat Shah (MIT) covers the basics of inference and learning. It explains how inference problems are represented within structures known as graphical models. The theoretical basis of the belief propagation algorithm is then explained and derived. This lecture sets the stage for generalizations and applications of message passing algorithms.

cs.LG↗

arXiv2014

Statistical mechanics approach to 1-bit compressed sensing

Compressed sensing is a technique for recovering a high-dimensional signal from lower-dimensional data, whose components represent partial information about the signal, utilizing prior knowledge on the sparsity of the signal. For further reducing the data size of the compressed expression, a scheme to recover the original signal utilizing only the sign of each entry of the linearly transformed vector was recently proposed. This approach is often termed the 1-bit compressed sensing. Here we analyze the typical performance of an L1-norm based signal recovery scheme for the 1-bit compressed sensing using statistical mechanics methods. We show that the signal recovery performance predicted by the replica method under the replica symmetric ansatz, which turns out to be locally unstable for modes breaking the replica symmetry, is in a good consistency with experimental results of an approximate recovery algorithm developed earlier. This suggests that the L1-based recovery problem typically has many local optima of a similar recovery accuracy, which can be achieved by the approximate algorithm. We also develop another approximate recovery algorithm inspired by the cavity method. Numerical experiments show that when the density of nonzero entries in the original signal is relatively large the new algorithm offers better performance than the abovementioned scheme and does so with a lower computational cost.

cs.IT↗