R. Heusdens
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23 records found
1
In this report, we analyze privacy leakage in optimization-based decentralized federated learning, which adopts generally distributed optimization schemes such as ADMM or PDMM in federated learning. By combining local updates with global aggregations, it was proved that optimization-based approaches are more advantageous compared to the traditional average consensus-based approaches, especially in scenarios where the data at the nodes are not independent and identically distributed (non-IID).
We further extend the privacy bound in distributed optimization to the decentralized learning framework. Different from the fact in the centralized learning framework the leaked information is the local gradients of each individual participant at all rounds, we find that in decentralized cases the leaked information is the difference of the local gradients within a certain time interval. Motivated by the gradient inversion in centralized networks, we then design a homogeneous attack to iteratively optimize dummy data whose gradient differences are close to the true revealed gradient differences. Though the gradient difference information still brings privacy concerns, we show that it is more challenging for adversaries to reconstruct private data using the difference of gradients than using the gradients themselves in the centralized case.
To deal with the privacy attack, we propose several potential defense strategies such as early stopping, inexact update and quantization etc. The main advantage of these approaches is that they introduce error/noise/distortion into decentralized federated learning for protecting private information from being revealed to others without affecting the training accuracy. In addition, we also show that the larger the batchsize is, the more difficult for the adversary to reconstruct the private information. ...
In this report, we analyze privacy leakage in optimization-based decentralized federated learning, which adopts generally distributed optimization schemes such as ADMM or PDMM in federated learning. By combining local updates with global aggregations, it was proved that optimization-based approaches are more advantageous compared to the traditional average consensus-based approaches, especially in scenarios where the data at the nodes are not independent and identically distributed (non-IID).
We further extend the privacy bound in distributed optimization to the decentralized learning framework. Different from the fact in the centralized learning framework the leaked information is the local gradients of each individual participant at all rounds, we find that in decentralized cases the leaked information is the difference of the local gradients within a certain time interval. Motivated by the gradient inversion in centralized networks, we then design a homogeneous attack to iteratively optimize dummy data whose gradient differences are close to the true revealed gradient differences. Though the gradient difference information still brings privacy concerns, we show that it is more challenging for adversaries to reconstruct private data using the difference of gradients than using the gradients themselves in the centralized case.
To deal with the privacy attack, we propose several potential defense strategies such as early stopping, inexact update and quantization etc. The main advantage of these approaches is that they introduce error/noise/distortion into decentralized federated learning for protecting private information from being revealed to others without affecting the training accuracy. In addition, we also show that the larger the batchsize is, the more difficult for the adversary to reconstruct the private information.
Distributed Optimisation Using Stochastic PDMM
Convergence, transmission losses and privacy
In this study we focus on the primal-dual method of multipliers (PDMM), which is a promising dis- tributed optimisation algorithm that seems to be suitable for distributed optimisation in heterogeneous networks. Most theoretical work that can be found in existing literature focuses on synchronous ver- sions of PDMM. However, in heterogeneous networks, asynchronous algorithms are favourable over synchronous algorithms. So far, simulation results have indicated that asynchronous PDMM converges and can even converge in the presence of transmission losses.
In this work we analyse the properties of stochastic PDMM, which is a general framework that can model variations of PDMM such as asynchronous PDMM and PDMM with transmission losses. We build upon previous empirical results of PDMM and formulate theoretical proofs to substantiate these results. After defining stochastic PDMM and proving its convergence, we compare a number of PDMM variations that have been mentioned throughout the literature. Lastly, we derive a lower bound for the variance of the auxiliary variable in the context of stochastic PDMM, assuming uniform updating probabilities. This lower bound indicates that subspace based privacy preservation is applicable to certain instances of stochastic PDMM, like asynchronous PDMM.
The main result of this work is a theoretical proof that shows that stochastic PDMM converges almost surely if the updating probabilities of each auxiliary variable are nonzero. Two important conclusions that follow from this proof are the almost sure convergence of asynchronous PDMM and unicast PDMM with transmission losses. Another useful result is the fact that subspace based privacy preservation is effective when using asynchronous PDMM. ...
In this study we focus on the primal-dual method of multipliers (PDMM), which is a promising dis- tributed optimisation algorithm that seems to be suitable for distributed optimisation in heterogeneous networks. Most theoretical work that can be found in existing literature focuses on synchronous ver- sions of PDMM. However, in heterogeneous networks, asynchronous algorithms are favourable over synchronous algorithms. So far, simulation results have indicated that asynchronous PDMM converges and can even converge in the presence of transmission losses.
In this work we analyse the properties of stochastic PDMM, which is a general framework that can model variations of PDMM such as asynchronous PDMM and PDMM with transmission losses. We build upon previous empirical results of PDMM and formulate theoretical proofs to substantiate these results. After defining stochastic PDMM and proving its convergence, we compare a number of PDMM variations that have been mentioned throughout the literature. Lastly, we derive a lower bound for the variance of the auxiliary variable in the context of stochastic PDMM, assuming uniform updating probabilities. This lower bound indicates that subspace based privacy preservation is applicable to certain instances of stochastic PDMM, like asynchronous PDMM.
The main result of this work is a theoretical proof that shows that stochastic PDMM converges almost surely if the updating probabilities of each auxiliary variable are nonzero. Two important conclusions that follow from this proof are the almost sure convergence of asynchronous PDMM and unicast PDMM with transmission losses. Another useful result is the fact that subspace based privacy preservation is effective when using asynchronous PDMM.
Our FCN is designed to extract spectral and temporal patterns from stereo recordings, aggregate the temporal information over time-frames, and predict the likelihood of virtual sources corresponding to reflective surfaces at specific locations. Whereas most source localization algorithms are limited to direction-of-arrival (DOA) estimation, the proposed method jointly estimates distances and DOAs. Numerical experiments confirm that the network is able to generalize to mismatched microphone array sizes, sensor directivity patterns, or audio signal types, while highlighting front-back ambiguity as a prominent source of uncertainty. When a single reflective surface is present, up to 80% of the sources are detected, while this figure approaches 50% in rectangular rooms.
Further tests on real-world recordings report similar accuracy as with artificially reverberated speech signals, validating the generalization capabilities of the framework. ...
Our FCN is designed to extract spectral and temporal patterns from stereo recordings, aggregate the temporal information over time-frames, and predict the likelihood of virtual sources corresponding to reflective surfaces at specific locations. Whereas most source localization algorithms are limited to direction-of-arrival (DOA) estimation, the proposed method jointly estimates distances and DOAs. Numerical experiments confirm that the network is able to generalize to mismatched microphone array sizes, sensor directivity patterns, or audio signal types, while highlighting front-back ambiguity as a prominent source of uncertainty. When a single reflective surface is present, up to 80% of the sources are detected, while this figure approaches 50% in rectangular rooms.
Further tests on real-world recordings report similar accuracy as with artificially reverberated speech signals, validating the generalization capabilities of the framework.
Inferring the location of reflecting surfaces from acoustic measurements
Using a compact microphone array collocated with a loudspeaker
Distributed Convex Optimization
Based on Monotone Operator Theory
In parallel to the improvements in computer to computer communication, the emergence of new paradigms such as the Internet of Things (IoT), Big Data processing and cloud computing in recent years has placed an increasing importance on networked systems in many facets of the modern world. From power grid management, to autonomous vehicle navigation, to even our basic means of interaction through social media, these networks are a pervasive presence in our day to day lives. The vast amounts of data generated by these networks and their ever increasing sizes makes it impractical if not impossible to resort to traditional centralized processing and therefore necessitates the search for new methods of signal processing within networked systems.
In this thesis we approach the task of distributed signal processing by exploiting the synergy between such tasks and equivalent convex optimization problems. Specifically, we focus on the task of distributed convex optimization, that of solving optimization problems involving groups of computers in a collaborative manner and the development of distributed solvers for such tasks. Such solvers distinguish themselves by only allowing local computations at each computer in a network and the exchange of information between connected computers. In this way, distributed solvers naturally respect the structure of the underlying network in which they are deployed.
In the pursuit of our goal, we approach the task of distributed solver design via the lens of monotone operator theory. Providing a well known platform for the derivation of many first order convex solvers, herein we demonstrate the use of this theory as a means of constructing and analyzing a number of algorithms for distributed optimization. The first major contribution of this thesis lies in the analysis and understanding of an existing algorithm for distributed optimization within the literature termed the primal dual method of multipliers (PDMM). In particular, by demonstrating a novel interpretation of PDMM from the perspective of monotone operator theory we are able to better understand its convergent characteristics and highlight sufficient conditions for which PDMM will converge at a geometric rate. Furthermore we quantify the impact that network topology has on these convergence rates, drawing a direct connection between spectral characteristics of networks and distributed optimization.
Secondly, we explored the space of solver design by proposing novel algorithms for distributed networks. For the family of separable optimization problems, those with separable objectives and constraints, we demonstrated a distributed solver design using a specific lifted dual form. Based on monotone operator theory, the convergence analysis of the proposed method followed naturally from well known results and broadened the class of distributable problems compared to the likes of PDMM. Furthermore, in the case of time-varying consensus problems, we again proposed a new algorithm by combining a network dependent metric choice with classic operator splitting methods. Again the monotone basis of this algorithm facilitated the convergence analysis of this method which empirically was also shown to converge for general closed, convex and proper functions.
Finally, we demonstrated how these methods could be used for practical distributed signal processing in networks by considering the case of multichannel speech enhancement in wireless acoustic sensor networks. By combining a particular modeling of the acoustic scene with the algorithms mentioned above, the proposed method was not only distributable but also offered increased resilience to steering vector mismatch than other standard approaches. This example also highlights the importance of understanding both the target application and the distributed solvers themselves in developing effective solutions.
Overall, this thesis provides a first foray into the world of distributed optimization via the lens of monotone operator theory. We feel that this perspective provides an ideal reference for the analysis of such algorithms while also providing a general framework for convex optimization solver design in turn. While this thesis is not the end of this branch of research, it indicates the potential of the monotone operator theory as a unifying method for the development and analysis of distributed optimization solutions. ...
In parallel to the improvements in computer to computer communication, the emergence of new paradigms such as the Internet of Things (IoT), Big Data processing and cloud computing in recent years has placed an increasing importance on networked systems in many facets of the modern world. From power grid management, to autonomous vehicle navigation, to even our basic means of interaction through social media, these networks are a pervasive presence in our day to day lives. The vast amounts of data generated by these networks and their ever increasing sizes makes it impractical if not impossible to resort to traditional centralized processing and therefore necessitates the search for new methods of signal processing within networked systems.
In this thesis we approach the task of distributed signal processing by exploiting the synergy between such tasks and equivalent convex optimization problems. Specifically, we focus on the task of distributed convex optimization, that of solving optimization problems involving groups of computers in a collaborative manner and the development of distributed solvers for such tasks. Such solvers distinguish themselves by only allowing local computations at each computer in a network and the exchange of information between connected computers. In this way, distributed solvers naturally respect the structure of the underlying network in which they are deployed.
In the pursuit of our goal, we approach the task of distributed solver design via the lens of monotone operator theory. Providing a well known platform for the derivation of many first order convex solvers, herein we demonstrate the use of this theory as a means of constructing and analyzing a number of algorithms for distributed optimization. The first major contribution of this thesis lies in the analysis and understanding of an existing algorithm for distributed optimization within the literature termed the primal dual method of multipliers (PDMM). In particular, by demonstrating a novel interpretation of PDMM from the perspective of monotone operator theory we are able to better understand its convergent characteristics and highlight sufficient conditions for which PDMM will converge at a geometric rate. Furthermore we quantify the impact that network topology has on these convergence rates, drawing a direct connection between spectral characteristics of networks and distributed optimization.
Secondly, we explored the space of solver design by proposing novel algorithms for distributed networks. For the family of separable optimization problems, those with separable objectives and constraints, we demonstrated a distributed solver design using a specific lifted dual form. Based on monotone operator theory, the convergence analysis of the proposed method followed naturally from well known results and broadened the class of distributable problems compared to the likes of PDMM. Furthermore, in the case of time-varying consensus problems, we again proposed a new algorithm by combining a network dependent metric choice with classic operator splitting methods. Again the monotone basis of this algorithm facilitated the convergence analysis of this method which empirically was also shown to converge for general closed, convex and proper functions.
Finally, we demonstrated how these methods could be used for practical distributed signal processing in networks by considering the case of multichannel speech enhancement in wireless acoustic sensor networks. By combining a particular modeling of the acoustic scene with the algorithms mentioned above, the proposed method was not only distributable but also offered increased resilience to steering vector mismatch than other standard approaches. This example also highlights the importance of understanding both the target application and the distributed solvers themselves in developing effective solutions.
Overall, this thesis provides a first foray into the world of distributed optimization via the lens of monotone operator theory. We feel that this perspective provides an ideal reference for the analysis of such algorithms while also providing a general framework for convex optimization solver design in turn. While this thesis is not the end of this branch of research, it indicates the potential of the monotone operator theory as a unifying method for the development and analysis of distributed optimization solutions.
Snoring Sound Production and Modelling
Acoustic Tube Modelling
As of today, analog consumption meters are still widely used to measure the consumption of gas, electricity and water. Often, smart home appliance use a simple reflective photosensor located on a rotating part of the meter to obtain information about the state of the consumption meter. The algorithm presented in this thesis accurately estimates the phase of the repeating pattern that occurs in the sensor observation when the meter rotates. Using this estimate, the signal of the photosensor can be converted to an estimate of the total resource consumption and consumption rate.
The algorithm improves in accuracy over conventional methods based on peak detection, and is shown to work in cases where the peak detection methods fails. Examples of this are signals where there is no distinctive peak in the signal or a signal where the recurring pattern is reversed. Furthermore, a template compression scheme is proposed that is used to decrease the computational complexity of the algorithm. Different time series compression methods are applied to the algorithm and evaluated on their performance.
...
As of today, analog consumption meters are still widely used to measure the consumption of gas, electricity and water. Often, smart home appliance use a simple reflective photosensor located on a rotating part of the meter to obtain information about the state of the consumption meter. The algorithm presented in this thesis accurately estimates the phase of the repeating pattern that occurs in the sensor observation when the meter rotates. Using this estimate, the signal of the photosensor can be converted to an estimate of the total resource consumption and consumption rate.
The algorithm improves in accuracy over conventional methods based on peak detection, and is shown to work in cases where the peak detection methods fails. Examples of this are signals where there is no distinctive peak in the signal or a signal where the recurring pattern is reversed. Furthermore, a template compression scheme is proposed that is used to decrease the computational complexity of the algorithm. Different time series compression methods are applied to the algorithm and evaluated on their performance.
The choice of algorithm that was used for the estimation is covered in the in the state of the art analysis of the current internal delay estimation techniques. The subsystem receives pre-determined times between units and uses these to estimate the internal delays. This estimation is done with a random initialization of the delays (within reasonable margins for the delays). After which this estimation converges towards the real values by minimizing a Frobenius norm between the rank three approximation and the received times. This is elaborated on in the Estimating Internal Delays section. The algorithm can also make use of a regularization term which decreases the time required for the estimation of the delays. The results of the algorithm are discussed in the Implementation section, which consists of a number of MATLAB simulations using the implemented algorithm. Using the results, a conclusion is drawn for the viability of the solution after which a recommendation of future work is given. ...
The choice of algorithm that was used for the estimation is covered in the in the state of the art analysis of the current internal delay estimation techniques. The subsystem receives pre-determined times between units and uses these to estimate the internal delays. This estimation is done with a random initialization of the delays (within reasonable margins for the delays). After which this estimation converges towards the real values by minimizing a Frobenius norm between the rank three approximation and the received times. This is elaborated on in the Estimating Internal Delays section. The algorithm can also make use of a regularization term which decreases the time required for the estimation of the delays. The results of the algorithm are discussed in the Implementation section, which consists of a number of MATLAB simulations using the implemented algorithm. Using the results, a conclusion is drawn for the viability of the solution after which a recommendation of future work is given.
The design choice for the type of localization method implemented is based on the gathered information from an initial literature study, the hardware specifications of the Bosch DICENTIS system and the demands for the localization system that were imposed by Bosch. The subsystem will function by transmitting a set of pseudo-random codes, modulated using a type of Frequency Shift Keying (FSK), where two On Off Keying (OOK) signals, modulated at different frequencies, are superimposed. The received and demodulated pseudo-random codes are then correlated with multiple different peak detectors that will correlate with multiple different sets of the transmitted string of pseudo-random codes to gain a higher robustness for the estimated propagation times and a higher accuracy for these estimates. Results show that the the use of multiple different sets of transmitted codes indeed improves the propagation time estimation. The overall system as presented, concerning accuracy and robustness, meets the requirements made by Bosch. However, in future work, optimalization of the system with regard to computation time is required. ...
The design choice for the type of localization method implemented is based on the gathered information from an initial literature study, the hardware specifications of the Bosch DICENTIS system and the demands for the localization system that were imposed by Bosch. The subsystem will function by transmitting a set of pseudo-random codes, modulated using a type of Frequency Shift Keying (FSK), where two On Off Keying (OOK) signals, modulated at different frequencies, are superimposed. The received and demodulated pseudo-random codes are then correlated with multiple different peak detectors that will correlate with multiple different sets of the transmitted string of pseudo-random codes to gain a higher robustness for the estimated propagation times and a higher accuracy for these estimates. Results show that the the use of multiple different sets of transmitted codes indeed improves the propagation time estimation. The overall system as presented, concerning accuracy and robustness, meets the requirements made by Bosch. However, in future work, optimalization of the system with regard to computation time is required.
Inexact distributed optimization schemes
A convergence analysis using monotone operator theory
extensively studied field for years. Recent developments in the area of sensors makes it possible to create networks consisting of a large number of nodes. The focus of this thesis will be optimizing distributed problems over a decentralized network. These distributed optimization schemes operate in an iterative matter as follows. First each node performs some local computations, after which the data is transmitted to its neighbours. The purpose of this study is to investigate the effects of approximating these local computations inexactly on the convergence of distributed optimization schemes. Although we consider many optimization schemes in general, the primal-dual method of multipliers (PDMM) is used during the simulations. Therefore we start off by deriving the inexact iteration for PDMM which shows how the inexactness propagates through the iterates. This derivation also suggests that the inexactness depends on the optimization constant, which was verified during the simulations. After that, the convergence of distributed optimization schemes is analyzed by making use of monotone operator theory to investigate under
which conditions convergence will be reached. This convergence analysis has two main results. It firstly shows that distributed optimization schemes converge to a fixed point if the error is summable and secondly
that an error has less influence as iterations pass. Thereafter simulations are presented that suggest that the inexactness affects how far the algorithm converges, thus what the remaining error is when convergence is
reached. Decreasing the error when convergence is reached causes the inexact PDMM iteration to resume converging at the rate of the standard PDMM algorithm. These observations holds in synchronous as well as asynchronous operation. Introducing packet loss only influences the convergence rate of the inexact PDMM iteration. ...
extensively studied field for years. Recent developments in the area of sensors makes it possible to create networks consisting of a large number of nodes. The focus of this thesis will be optimizing distributed problems over a decentralized network. These distributed optimization schemes operate in an iterative matter as follows. First each node performs some local computations, after which the data is transmitted to its neighbours. The purpose of this study is to investigate the effects of approximating these local computations inexactly on the convergence of distributed optimization schemes. Although we consider many optimization schemes in general, the primal-dual method of multipliers (PDMM) is used during the simulations. Therefore we start off by deriving the inexact iteration for PDMM which shows how the inexactness propagates through the iterates. This derivation also suggests that the inexactness depends on the optimization constant, which was verified during the simulations. After that, the convergence of distributed optimization schemes is analyzed by making use of monotone operator theory to investigate under
which conditions convergence will be reached. This convergence analysis has two main results. It firstly shows that distributed optimization schemes converge to a fixed point if the error is summable and secondly
that an error has less influence as iterations pass. Thereafter simulations are presented that suggest that the inexactness affects how far the algorithm converges, thus what the remaining error is when convergence is
reached. Decreasing the error when convergence is reached causes the inexact PDMM iteration to resume converging at the rate of the standard PDMM algorithm. These observations holds in synchronous as well as asynchronous operation. Introducing packet loss only influences the convergence rate of the inexact PDMM iteration.
For the data collection phase, two experiments were conducted in the working environment of imec. 40 participants were recruited and were asked to participate in the Controlled and Free-Living Study. The subjects wore two imec wearables, a wrist-worn and chest-worn accelerometer sensor and performed everyday activities. These activities include sitting, dynamic sitting, lying with face up and face down, lying to the left and right, standing, dynamic standing, walking upstairs, walking downstairs, walking, running, and cycling. The Controlled Study showed that most of these activities could be detected accurately using accelerometer data from both sensors with 91.83% F1-score. Similarly, the combination of these two sensors achieved the best performance for the Free-Living Study with 86.98% F1-score. Finally, this work proved that between the two environments a correlation could be possible only for the activity cycling. Consequently, this research concludes that the activity recognition should be explicitly investigated in free-living environments, focusing on real-time activity detection.
...
For the data collection phase, two experiments were conducted in the working environment of imec. 40 participants were recruited and were asked to participate in the Controlled and Free-Living Study. The subjects wore two imec wearables, a wrist-worn and chest-worn accelerometer sensor and performed everyday activities. These activities include sitting, dynamic sitting, lying with face up and face down, lying to the left and right, standing, dynamic standing, walking upstairs, walking downstairs, walking, running, and cycling. The Controlled Study showed that most of these activities could be detected accurately using accelerometer data from both sensors with 91.83% F1-score. Similarly, the combination of these two sensors achieved the best performance for the Free-Living Study with 86.98% F1-score. Finally, this work proved that between the two environments a correlation could be possible only for the activity cycling. Consequently, this research concludes that the activity recognition should be explicitly investigated in free-living environments, focusing on real-time activity detection.
Clock-Offset Invariant Beamforming in Wireless Acoustic Sensor Networks
A Generalized Eigenvalue Decomposition Approach