Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447131
Jingjing Zhang, Felix Engelmann, P. Elia
The work explores the role of caching content at receiving users for the purpose of reducing the need for feedback in wireless communications. In the K-user broadcast channel (BC), we show how caching, when combined with a rate-splitting broadcast approach, can not only improve performance, but can also reduce the need for channel state information at the transmitter (CSIT), in the sense that the identified cache-aided optimal degrees-of-freedom performance, can in fact be achieved with reduced-quality CSIT. These CSIT savings can be traced back to an inherent relationship between caching, performance, and CSIT; caching improves performance by leveraging multicasting of common information, which automatically reduces the need for CSIT, by virtue of the fact that common information is not a cause of interference. At the same time though, too much multicasting of common information can be detrimental, as it does not utilize existing CSIT. Our caching method builds on the Maddah-Ali and Niesen coded caching scheme, by properly balancing multicast and broadcast opportunities, and by combing caching with rate-splitting communication schemes that are specifically designed to operate under imperfect-quality CSIT. The observed achievable CSIT savings here, are more pronounced for smaller values of K users and N files.
{"title":"Coded caching for reducing CSIT-feedback in wireless communications","authors":"Jingjing Zhang, Felix Engelmann, P. Elia","doi":"10.1109/ALLERTON.2015.7447131","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447131","url":null,"abstract":"The work explores the role of caching content at receiving users for the purpose of reducing the need for feedback in wireless communications. In the K-user broadcast channel (BC), we show how caching, when combined with a rate-splitting broadcast approach, can not only improve performance, but can also reduce the need for channel state information at the transmitter (CSIT), in the sense that the identified cache-aided optimal degrees-of-freedom performance, can in fact be achieved with reduced-quality CSIT. These CSIT savings can be traced back to an inherent relationship between caching, performance, and CSIT; caching improves performance by leveraging multicasting of common information, which automatically reduces the need for CSIT, by virtue of the fact that common information is not a cause of interference. At the same time though, too much multicasting of common information can be detrimental, as it does not utilize existing CSIT. Our caching method builds on the Maddah-Ali and Niesen coded caching scheme, by properly balancing multicast and broadcast opportunities, and by combing caching with rate-splitting communication schemes that are specifically designed to operate under imperfect-quality CSIT. The observed achievable CSIT savings here, are more pronounced for smaller values of K users and N files.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130600626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447165
Songbai Yan, Kamalika Chaudhuri, T. Javidi
An active learner is given an instance space, a label space and a hypothesis class, where one of the hypotheses in the class assigns ground truth labels to instances. Additionally, the learner has access to a labeling oracle, which it can interactively query for the label of any example in the instance space. The goal of the learner is to find a good estimate of the hypothesis in the hypothesis class that generates the ground truth labels while making as few interactive queries to the oracle as possible. This work considers a more general setting where the labeling oracle can abstain from providing a label in addition to returning noisy labels. We provide a model for this setting where the abstention rate and the noise rate increase as we get closer to the decision boundary of the ground truth hypothesis. We provide an algorithm and an analysis of the number of queries it makes to the labeling oracle; finally we provide matching lower bounds to demonstrate that our algorithm has near-optimal estimation accuracy.
{"title":"Active learning from noisy and abstention feedback","authors":"Songbai Yan, Kamalika Chaudhuri, T. Javidi","doi":"10.1109/ALLERTON.2015.7447165","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447165","url":null,"abstract":"An active learner is given an instance space, a label space and a hypothesis class, where one of the hypotheses in the class assigns ground truth labels to instances. Additionally, the learner has access to a labeling oracle, which it can interactively query for the label of any example in the instance space. The goal of the learner is to find a good estimate of the hypothesis in the hypothesis class that generates the ground truth labels while making as few interactive queries to the oracle as possible. This work considers a more general setting where the labeling oracle can abstain from providing a label in addition to returning noisy labels. We provide a model for this setting where the abstention rate and the noise rate increase as we get closer to the decision boundary of the ground truth hypothesis. We provide an algorithm and an analysis of the number of queries it makes to the labeling oracle; finally we provide matching lower bounds to demonstrate that our algorithm has near-optimal estimation accuracy.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130720708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447102
P. Grover, J. Weldon, S. Kelly, Praveen Venkatesh, Haewon Jeong
It is widely believed in the clinical and biosciences community that Electroencephalography (EEG) is fundamentally limited in the spatial resolution achieved using a few hundred electrodes. This belief rests on the well known decay of high-spatial frequencies as the signal passes from the brain surface to the scalp surface. These high spatial frequencies carry high spatial resolution information about the source. However, recent experimental work as well as our theoretical and numerical analyses strongly suggest that EEG's resolution could be improved significantly through increased electrode density despite this decay. Somewhat counterintuitively, instead of viewing this decay of spatial frequencies as a detriment to signal quality (which it is), in this work we propose an information-theoretic strategy to harness this decay to reduce circuit area and energy needed for high-resolution signal acquisition. This is made possible by the observation that this spatial-low-pass filtering of the signal as it passes from the brain to the scalp induces large spatial correlations that can be exploited information-theoretically. The proposed techniques are shown in idealized head models to reduce requirements on energy required for sensing by 3×. These results are being applied towards an ongoing project on developing the “Neural Web,” a 10,000 electrode portable EEG system at CMU.
{"title":"An information theoretic technique for harnessing attenuation of high spatial frequencies to design ultra-high-density EEG","authors":"P. Grover, J. Weldon, S. Kelly, Praveen Venkatesh, Haewon Jeong","doi":"10.1109/ALLERTON.2015.7447102","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447102","url":null,"abstract":"It is widely believed in the clinical and biosciences community that Electroencephalography (EEG) is fundamentally limited in the spatial resolution achieved using a few hundred electrodes. This belief rests on the well known decay of high-spatial frequencies as the signal passes from the brain surface to the scalp surface. These high spatial frequencies carry high spatial resolution information about the source. However, recent experimental work as well as our theoretical and numerical analyses strongly suggest that EEG's resolution could be improved significantly through increased electrode density despite this decay. Somewhat counterintuitively, instead of viewing this decay of spatial frequencies as a detriment to signal quality (which it is), in this work we propose an information-theoretic strategy to harness this decay to reduce circuit area and energy needed for high-resolution signal acquisition. This is made possible by the observation that this spatial-low-pass filtering of the signal as it passes from the brain to the scalp induces large spatial correlations that can be exploited information-theoretically. The proposed techniques are shown in idealized head models to reduce requirements on energy required for sensing by 3×. These results are being applied towards an ongoing project on developing the “Neural Web,” a 10,000 electrode portable EEG system at CMU.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129749269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447055
Naci Saldi, S. Yüksel, T. Linder
We consider the finite-state approximation of a discrete-time constrained Markov decision process with compact state space, under the discounted cost criterion. Using the linear programming formulation of the constrained problem, we prove the convergence of the optimal value function of the finite-state model to the optimal value function of the original model. Under further continuity condition on the transition probability of the original model, we also establish a method to compute approximately optimal policies.
{"title":"Finite-state approximations to constrained Markov decision processes with Borel spaces","authors":"Naci Saldi, S. Yüksel, T. Linder","doi":"10.1109/ALLERTON.2015.7447055","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447055","url":null,"abstract":"We consider the finite-state approximation of a discrete-time constrained Markov decision process with compact state space, under the discounted cost criterion. Using the linear programming formulation of the constrained problem, we prove the convergence of the optimal value function of the finite-state model to the optimal value function of the original model. Under further continuity condition on the transition probability of the original model, we also establish a method to compute approximately optimal policies.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128061332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447072
A. Wachter-Zeh, Eitan Yaakobi
This paper studies defect memory cells and in particular partially stuck-at memory cells, which occur when charge is trapped in multi-level cells of non-volatile memories such as flash memories. If a cell can store the q levels 0, 1, ..., q - 1, we say that it is partially stuck-at level s, where 1 ≤ s ≤ q - 1, if it can only store values which are at least s. We follow the common setup where the encoder knows the positions and levels of the partially stuck-at cells whereas the decoder does not. In this paper, we study codes for masking u partially stuck-at cells. We derive lower and upper bounds on the redundancy of such codes and present code constructions. Furthermore, we analyze the dual defect model in which cells cannot reach higher levels, and show that codes for partially stuck-at cells can be used to mask this type of defects as well. Lastly, we analyze the capacity of the partially stuck-at memory channel and study how far our constructions are from the capacity.
{"title":"Masking trapped charge in flash memories","authors":"A. Wachter-Zeh, Eitan Yaakobi","doi":"10.1109/ALLERTON.2015.7447072","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447072","url":null,"abstract":"This paper studies defect memory cells and in particular partially stuck-at memory cells, which occur when charge is trapped in multi-level cells of non-volatile memories such as flash memories. If a cell can store the q levels 0, 1, ..., q - 1, we say that it is partially stuck-at level s, where 1 ≤ s ≤ q - 1, if it can only store values which are at least s. We follow the common setup where the encoder knows the positions and levels of the partially stuck-at cells whereas the decoder does not. In this paper, we study codes for masking u partially stuck-at cells. We derive lower and upper bounds on the redundancy of such codes and present code constructions. Furthermore, we analyze the dual defect model in which cells cannot reach higher levels, and show that codes for partially stuck-at cells can be used to mask this type of defects as well. Lastly, we analyze the capacity of the partially stuck-at memory channel and study how far our constructions are from the capacity.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126250315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7446994
Santhosh Kumar, Avinash Vem, K. Narayanan, H. Pfister
The focus of this article is on low-complexity capacity-achieving coding schemes for write-once memory (WOM) systems. The construction is based on spatially-coupled compound LDGM/LDPC codes. Both noiseless systems and systems with read errors are considered. Compound LDGM/LDPC codes are known to achieve capacity under MAP decoding for the closely related Gelfand-Pinsker problem and their coset decomposition provides an elegant way to encode the messages while simultaneously providing error protection. The application of compound codes to the WOM system is new. The main result is that spatial coupling enables these codes to achieve the capacity region of the 2-write WOM system with low-complexity message-passing encoding and decoding algorithms.
{"title":"Spatially-coupled codes for write-once memories","authors":"Santhosh Kumar, Avinash Vem, K. Narayanan, H. Pfister","doi":"10.1109/ALLERTON.2015.7446994","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7446994","url":null,"abstract":"The focus of this article is on low-complexity capacity-achieving coding schemes for write-once memory (WOM) systems. The construction is based on spatially-coupled compound LDGM/LDPC codes. Both noiseless systems and systems with read errors are considered. Compound LDGM/LDPC codes are known to achieve capacity under MAP decoding for the closely related Gelfand-Pinsker problem and their coset decomposition provides an elegant way to encode the messages while simultaneously providing error protection. The application of compound codes to the WOM system is new. The main result is that spatial coupling enables these codes to achieve the capacity region of the 2-write WOM system with low-complexity message-passing encoding and decoding algorithms.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127203978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447020
P. Babaheidarian, Somayeh Salimi, Panos Papadimitratos
In this work, we consider a K-user Gaussian wiretap multiple-access channel (GW-MAC) in which each transmitter has an independent confidential message for the receiver. There is also an external eavesdropper who intercepts the communications. The goal is to transmit the messages reliably while keeping them confidential from the eavesdropper. To accomplish this goal, two different approaches have been proposed in prior works, namely, i.i.d. Gaussian random coding and real alignment. However, the former approach fails at moderate and high SNR regimes as its achievable result does not grow with SNR. On the other hand, while the latter approach gives a promising result at the infinite SNR regime, its extension to the finite-SNR regime is a challenging task. To fill the gap between the performance of the existing approaches, in this work, we establish a new scheme in which, at the receiver's side, it utilizes an extension of the compute-and-forward decoding strategy and at the transmitters' side it exploits lattice alignment, cooperative jamming, and i.i.d. random codes. For the proposed scheme, we derive a new achievable bound on sum secure rate which scales with log(SNR) and hence it outperforms the i.i.d. Gaussian codes in moderate and high SNR regimes. We evaluate the performance of our scheme, both theoretically and numerically. Furthermore, we show that our sum secure rate achieves the optimal sum secure degrees of freedom in the infinite-SNR regime.
{"title":"Finite-SNR regime analysis of the Gaussian wiretap multiple-access channel","authors":"P. Babaheidarian, Somayeh Salimi, Panos Papadimitratos","doi":"10.1109/ALLERTON.2015.7447020","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447020","url":null,"abstract":"In this work, we consider a K-user Gaussian wiretap multiple-access channel (GW-MAC) in which each transmitter has an independent confidential message for the receiver. There is also an external eavesdropper who intercepts the communications. The goal is to transmit the messages reliably while keeping them confidential from the eavesdropper. To accomplish this goal, two different approaches have been proposed in prior works, namely, i.i.d. Gaussian random coding and real alignment. However, the former approach fails at moderate and high SNR regimes as its achievable result does not grow with SNR. On the other hand, while the latter approach gives a promising result at the infinite SNR regime, its extension to the finite-SNR regime is a challenging task. To fill the gap between the performance of the existing approaches, in this work, we establish a new scheme in which, at the receiver's side, it utilizes an extension of the compute-and-forward decoding strategy and at the transmitters' side it exploits lattice alignment, cooperative jamming, and i.i.d. random codes. For the proposed scheme, we derive a new achievable bound on sum secure rate which scales with log(SNR) and hence it outperforms the i.i.d. Gaussian codes in moderate and high SNR regimes. We evaluate the performance of our scheme, both theoretically and numerically. Furthermore, we show that our sum secure rate achieves the optimal sum secure degrees of freedom in the infinite-SNR regime.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127319777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447118
Abhishek K. Gupta, R. Jain, R. Rajagopal
A market comprising a scheduler with a renewable generator and a pumped water storage system, a certain number of flexible and inflexible loads, and a non-renewable generator is considered. At the beginning of activity, the scheduler receives the following three information from each of the loads - consumption (in MW), duration (in hours) and start window. The start window of a load is the time interval in which the load must be started. A load is inflexible if its start window is singleton. The loads are assumed to be non-preemptive, that is, after a load is started, it cannot be interrupted or paused, and it must be served for its duration. The goal of the scheduler is to develop a scheduling policy that minimizes the aggregate cost of buying electricity from the non-renewable generator. We develop an understanding of the nature of optimal solutions to such an optimization problem and propose an approximately optimal scheduling policy for a sufficiently wide class of scheduling problems.
{"title":"Scheduling, pricing, and efficiency of non-preemptive flexible loads under direct load control","authors":"Abhishek K. Gupta, R. Jain, R. Rajagopal","doi":"10.1109/ALLERTON.2015.7447118","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447118","url":null,"abstract":"A market comprising a scheduler with a renewable generator and a pumped water storage system, a certain number of flexible and inflexible loads, and a non-renewable generator is considered. At the beginning of activity, the scheduler receives the following three information from each of the loads - consumption (in MW), duration (in hours) and start window. The start window of a load is the time interval in which the load must be started. A load is inflexible if its start window is singleton. The loads are assumed to be non-preemptive, that is, after a load is started, it cannot be interrupted or paused, and it must be served for its duration. The goal of the scheduler is to develop a scheduling policy that minimizes the aggregate cost of buying electricity from the non-renewable generator. We develop an understanding of the nature of optimal solutions to such an optimization problem and propose an approximately optimal scheduling policy for a sufficiently wide class of scheduling problems.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126331852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447035
Georg Pichler, P. Piantanida, G. Matz
A novel multi-terminal source coding problem motivated by biclustering applications is investigated. In this setting, two separate encoders observe two dependent memoryless processes Xn and Zn, respectively. The encoders' goal is to find rate-limited functions f(Xn) and g(Zn) that maximize asymptotically the mutual information I(f(Xn); g(Zn)) ≥ nμ. We derive non-trivial inner and outer bounds on the optimal characterization of the achievable rates for this problem. Applications also arise in the context of distributed hypothesis testing against independence under communication constraints.
{"title":"Distributed information-theoretic biclustering of two memoryless sources","authors":"Georg Pichler, P. Piantanida, G. Matz","doi":"10.1109/ALLERTON.2015.7447035","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447035","url":null,"abstract":"A novel multi-terminal source coding problem motivated by biclustering applications is investigated. In this setting, two separate encoders observe two dependent memoryless processes X<sup>n</sup> and Z<sup>n</sup>, respectively. The encoders' goal is to find rate-limited functions f(X<sup>n</sup>) and g(Z<sup>n</sup>) that maximize asymptotically the mutual information I(f(X<sup>n</sup>); g(Z<sup>n</sup>)) ≥ nμ. We derive non-trivial inner and outer bounds on the optimal characterization of the achievable rates for this problem. Applications also arise in the context of distributed hypothesis testing against independence under communication constraints.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126695529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447147
Dionysios S. Kalogerias, A. Petropulu
We present a theoretical comparison of the state-of-the-art sufficient conditions required for pathwise (almost sure type of) convergence between grid based and particle approximate filters, as well as discuss the implications of these conditions on the specific mode of convergence achieved. Focusing on general Markov processes observed in conditionally Gaussian noise, we have recently shown that a sufficient condition for pathwise convergence of grid based filters is conditional regularity of stochastic kernels. The respective condition for almost sure convergence of particle filters is the well known Feller property. While our analysis shows that the comparison between the afore-mentioned conditions may be indeed inconclusive, we identify a large class of systems for which conditional regularity may hold true, whereas the Feller property cannot. This is achieved through a structural analysis of both sufficient conditions. This work can be summarized in that there provably exist system classes supported by either grid based or particle filtering approximations, but not necessarily by both; for systems supported by both, grid based filters exhibit a theoretical advantage in terms of convergence robustness.
{"title":"On pathwise convergence of particle & grid based nonlinear filters: Feller vs conditional regularity","authors":"Dionysios S. Kalogerias, A. Petropulu","doi":"10.1109/ALLERTON.2015.7447147","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447147","url":null,"abstract":"We present a theoretical comparison of the state-of-the-art sufficient conditions required for pathwise (almost sure type of) convergence between grid based and particle approximate filters, as well as discuss the implications of these conditions on the specific mode of convergence achieved. Focusing on general Markov processes observed in conditionally Gaussian noise, we have recently shown that a sufficient condition for pathwise convergence of grid based filters is conditional regularity of stochastic kernels. The respective condition for almost sure convergence of particle filters is the well known Feller property. While our analysis shows that the comparison between the afore-mentioned conditions may be indeed inconclusive, we identify a large class of systems for which conditional regularity may hold true, whereas the Feller property cannot. This is achieved through a structural analysis of both sufficient conditions. This work can be summarized in that there provably exist system classes supported by either grid based or particle filtering approximations, but not necessarily by both; for systems supported by both, grid based filters exhibit a theoretical advantage in terms of convergence robustness.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128628738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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