Independent Process Analysis without A Priori Dimensional Information

Recently, several algorithms have been proposed for independent subspace analysis where hidden variables are i.i.d. processes. We show that these methods can be extended to certain AR, MA, ARMA and ARIMA tasks. Central to our paper is that we introduce a cascade of algorithms, which aims to solve these tasks without previous knowledge about the number and the dimensions of the hidden processes. Our claim is supported by numerical simulations. As a particular application, we search for subspaces of facial components.Comment: 9 pages, 2 figure

Bayesian Inverse Quantum Theory

A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The paper presents the basic theory, concentrating in particular on measurements of particle coordinates in quantum mechanical systems at finite temperature. The computational feasibility of the approach is demonstrated by numerical case studies. Finally, it is shown how the approach can be generalized to such many-body and few-body systems for which a mean field description is appropriate. This is done by means of a Bayesian inverse Hartree-Fock approximation.Comment: LaTex, 32 pages, 19 figure

On Approaching the Ultimate Limits of Photon-Efficient and Bandwidth-Efficient Optical Communication

It is well known that ideal free-space optical communication at the quantum limit can have unbounded photon information efficiency (PIE), measured in bits per photon. High PIE comes at a price of low dimensional information efficiency (DIE), measured in bits per spatio-temporal-polarization mode. If only temporal modes are used, then DIE translates directly to bandwidth efficiency. In this paper, the DIE vs. PIE tradeoffs for known modulations and receiver structures are compared to the ultimate quantum limit, and analytic approximations are found in the limit of high PIE. This analysis shows that known structures fall short of the maximum attainable DIE by a factor that increases linearly with PIE for high PIE. The capacity of the Dolinar receiver is derived for binary coherent-state modulations and computed for the case of on-off keying (OOK). The DIE vs. PIE tradeoff for this case is improved only slightly compared to OOK with photon counting. An adaptive rule is derived for an additive local oscillator that maximizes the mutual information between a receiver and a transmitter that selects from a set of coherent states. For binary phase-shift keying (BPSK), this is shown to be equivalent to the operation of the Dolinar receiver. The Dolinar receiver is extended to make adaptive measurements on a coded sequence of coherent state symbols. Information from previous measurements is used to adjust the a priori probabilities of the next symbols. The adaptive Dolinar receiver does not improve the DIE vs. PIE tradeoff compared to independent transmission and Dolinar reception of each symbol.Comment: 10 pages, 8 figures; corrected a typo in equation 3

Fundamental Limits of Wideband Localization - Part II: Cooperative Networks

The availability of positional information is of great importance in many commercial, governmental, and military applications. Localization is commonly accomplished through the use of radio communication between mobile devices (agents) and fixed infrastructure (anchors). However, precise determination of agent positions is a challenging task, especially in harsh environments due to radio blockage or limited anchor deployment. In these situations, cooperation among agents can significantly improve localization accuracy and reduce localization outage probabilities. A general framework of analyzing the fundamental limits of wideband localization has been developed in Part I of the paper. Here, we build on this framework and establish the fundamental limits of wideband cooperative location-aware networks. Our analysis is based on the waveforms received at the nodes, in conjunction with Fisher information inequality. We provide a geometrical interpretation of equivalent Fisher information for cooperative networks. This approach allows us to succinctly derive fundamental performance limits and their scaling behaviors, and to treat anchors and agents in a unified way from the perspective of localization accuracy. Our results yield important insights into how and when cooperation is beneficial.Comment: To appear in IEEE Transactions on Information Theor