Publications

Optimization and Analysis of Distributed Averaging With Short Node Memory
Boris Oreshkin
Mark Coates
Michael Rabbat
Distributed averaging describes a class of network algorithms for the decentralized computation of aggregate statistics. Initially, each nod… (see more)e has a scalar data value, and the goal is to compute the average of these values at every node (the so-called average consensus problem). Nodes iteratively exchange information with their neighbors and perform local updates until the value at every node converges to the initial network average. Much previous work has focused on algorithms where each node maintains and updates a single value; every time an update is performed, the previous value is forgotten. Convergence to the average consensus is achieved asymptotically. The convergence rate is fundamentally limited by network connectivity, and it can be prohibitively slow on topologies such as grids and random geometric graphs, even if the update rules are optimized. In this paper, we provide the first theoretical demonstration that adding a local prediction component to the update rule can significantly improve the convergence rate of distributed averaging algorithms. We focus on the case where the local predictor is a linear combination of the node's current and previous values (i.e., two memory taps), and our update rule computes a combination of the predictor and the usual weighted linear combination of values received from neighboring nodes. We derive the optimal mixing parameter for combining the predictor with the neighbors' values, and conduct a theoretical analysis of the improvement in convergence rate that can be achieved using this acceleration methodology. For a chain topology on N nodes, this leads to a factor of N improvement over standard consensus, and for a two-dimensional grid, our approach achieves a factor of ¿N improvement.
2010-05-01
IEEE Transactions on Signal Processing (published)
doi.org
arxiv.org
Theano: A CPU and GPU Math Compiler in Python
James Bergstra
Olivier Breuleux
Frédéric Bastien
Pascal Lamblin
Razvan Pascanu
Guillaume Desjardins
Joseph Turian
David Warde-Farley
Yoshua Bengio
2010-01-01
Proceedings of the Python in Science Conference (published)
doi.org
Theano: A CPU and GPU Math Compiler in Python
James Bergstra
Olivier Breuleux
Frédéric Bastien
Pascal Lamblin
Razvan Pascanu
Guillaume Desjardins
Joseph P. Turian
David Warde-Farley
Yoshua Bengio
Theano is a compiler for mathematical expressions in Python that combines the convenience of NumPy's syntax with the speed of optimized nati… (see more)ve machine language. The user composes mathematical expressions in a high-level description that mimics NumPy's syntax and semantics, while being statically typed and functional (as opposed to imperative). These expressions allow Theano to provide symbolic differentiation. Before performing computation, Theano optimizes the choice of expressions, translates them into C++ (or CUDA for GPU), compiles them into dynamically loaded Python modules, all automatically. Common machine learn- ing algorithms implemented with Theano are from 1:6 to 7:5 faster than competitive alternatives (including those implemented with C/C++, NumPy/SciPy and MATLAB) when compiled for the CPU and between 6:5 and 44 faster when compiled for the GPU. This paper illustrates how to use Theano, outlines the scope of the compiler, provides benchmarks on both CPU and GPU processors, and explains its overall design.
2010-01-01
SciPy (published)
doi.org
Optimization and Analysis of Distributed Averaging With Short Node Memory
Boris Oreshkin
Mark Coates
Michael Rabbat
Distributed averaging describes a class of network algorithms for the decentralized computation of aggregate statistics. Initially, each nod… (see more)e has a scalar data value, and the goal is to compute the average of these values at every node (the so-called average consensus problem). Nodes iteratively exchange information with their neighbors and perform local updates until the value at every node converges to the initial network average. Much previous work has focused on algorithms where each node maintains and updates a single value; every time an update is performed, the previous value is forgotten. Convergence to the average consensus is achieved asymptotically. The convergence rate is fundamentally limited by network connectivity, and it can be prohibitively slow on topologies such as grids and random geometric graphs, even if the update rules are optimized. In this paper, we provide the first theoretical demonstration that adding a local prediction component to the update rule can significantly improve the convergence rate of distributed averaging algorithms. We focus on the case where the local predictor is a linear combination of the node's current and previous values (i.e., two memory taps), and our update rule computes a combination of the predictor and the usual weighted linear combination of values received from neighboring nodes. We derive the optimal mixing parameter for combining the predictor with the neighbors' values, and conduct a theoretical analysis of the improvement in convergence rate that can be achieved using this acceleration methodology. For a chain topology on N nodes, this leads to a factor of N improvement over standard consensus, and for a two-dimensional grid, our approach achieves a factor of ¿N improvement.
2009-03-20
ArXiv (preprint)
doi.org
arxiv.org
Fully Parallel Stochastic LDPC Decoders
S. Tehrani
Shie Mannor
Warren Gross
Stochastic decoding is a new approach to iterative decoding on graphs. This paper presents a hardware architecture for fully parallel stocha… (see more)stic low-density parity-check (LDPC) decoders. To obtain the characteristics of the proposed architecture, we apply this architecture to decode an irregular state-of-the-art (1056,528) LDPC code on a Xilinx Virtex-4 LX200 field-programmable gate-array (FPGA) device. The implemented decoder achieves a clock frequency of 222 MHz and a throughput of about 1.66 Gb/s at Eb/N0=4.25 dB (a bit error rate of 10-8). It provides decoding performance within 0.5 and 0.25 dB of the floating-point sum-product algorithm with 32 and 16 iterations, respectively, and similar error-floor behavior. The decoder uses less than 40% of the lookup tables, flip-flops, and IO ports available on the FPGA device. The results provided in this paper validate the potential of stochastic LDPC decoding as a practical and competitive fully parallel decoding approach.
2008-11-01
IEEE Transactions on Signal Processing (published)
doi.org
Fully Parallel Stochastic LDPC Decoders
Saeed Sharifi Tehrani
Shie Mannor
Warren Gross
Stochastic decoding is a new approach to iterative decoding on graphs. This paper presents a hardware architecture for fully parallel stocha… (see more)stic low-density parity-check (LDPC) decoders. To obtain the characteristics of the proposed architecture, we apply this architecture to decode an irregular state-of-the-art (1056,528) LDPC code on a Xilinx Virtex-4 LX200 field-programmable gate-array (FPGA) device. The implemented decoder achieves a clock frequency of 222 MHz and a throughput of about 1.66 Gb/s at
2008-11-01
IEEE Transactions on Signal Processing (published)
doi.org
Stochastic Decoding of Linear Block Codes With High-Density Parity-Check Matrices
Saeed Sharifi Tehrani
Christophe Jego
Bo Zhu
Warren Gross
This correspondence extends the application of the recently proposed stochastic decoding approach to decode linear block codes with high-den… (see more)sity parity-check matrices and discusses its hardware complexity. Results demonstrate decoding performance close to floating-point iterative soft-input soft-output (SISO) decoding while offering nodes with considerably lower complexity compared to fixed-point SISO decoding.
2008-11-01
IEEE Transactions on Signal Processing (published)
doi.org
Stochastic Decoding of Linear Block Codes With High-Density Parity-Check Matrices
S. Tehrani
Christophe Jego
Bo Zhu
Warren Gross
This correspondence extends the application of the recently proposed stochastic decoding approach to decode linear block codes with high-den… (see more)sity parity-check matrices and discusses its hardware complexity. Results demonstrate decoding performance close to floating-point iterative soft-input soft-output (SISO) decoding while offering nodes with considerably lower complexity compared to fixed-point SISO decoding.
2008-11-01
IEEE Transactions on Signal Processing (published)
doi.org
Distributed Average Consensus With Dithered Quantization
Tuncer Can Aysal
Mark Coates
Michael Rabbat
In this paper, we develop algorithms for distributed computation of averages of the node data over networks with bandwidth/power constraints… (see more) or large volumes of data. Distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted. We propose a distributed algorithm in which the nodes utilize probabilistically quantized information, i.e., dithered quantization, to communicate with each other. The algorithm we develop is a dynamical system that generates sequences achieving a consensus at one of the quantization values almost surely. In addition, we show that the expected value of the consensus is equal to the average of the original sensor data. We derive an upper bound on the mean-square-error performance of the probabilistically quantized distributed averaging (PQDA). Moreover, we show that the convergence of the PQDA is monotonic by studying the evolution of the minimum-length interval containing the node values. We reveal that the length of this interval is a monotonically nonincreasing function with limit zero. We also demonstrate that all the node values, in the worst case, converge to the final two quantization bins at the same rate as standard unquantized consensus. Finally, we report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios.
2008-10-01
IEEE Transactions on Signal Processing (published)
doi.org
Distributed Average Consensus With Dithered Quantization
T. C. Aysal
Mark Coates
Michael Rabbat
In this paper, we develop algorithms for distributed computation of averages of the node data over networks with bandwidth/power constraints… (see more) or large volumes of data. Distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted. We propose a distributed algorithm in which the nodes utilize probabilistically quantized information, i.e., dithered quantization, to communicate with each other. The algorithm we develop is a dynamical system that generates sequences achieving a consensus at one of the quantization values almost surely. In addition, we show that the expected value of the consensus is equal to the average of the original sensor data. We derive an upper bound on the mean-square-error performance of the probabilistically quantized distributed averaging (PQDA). Moreover, we show that the convergence of the PQDA is monotonic by studying the evolution of the minimum-length interval containing the node values. We reveal that the length of this interval is a monotonically nonincreasing function with limit zero. We also demonstrate that all the node values, in the worst case, converge to the final two quantization bins at the same rate as standard unquantized consensus. Finally, we report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios.
2008-10-01
IEEE Transactions on Signal Processing (published)
doi.org
Greedy Gossip With Eavesdropping
Deniz Ustebay
Boris Oreshkin
Mark Coates
Michael Rabbat
This paper presents greedy gossip with eavesdropping (GGE), a novel randomized gossip algorithm for distributed computation of the average c… (see more)onsensus problem. In gossip algorithms, nodes in the network randomly communicate with their neighbors and exchange information iteratively. The algorithms are simple and decentralized, making them attractive for wireless network applications. In general, gossip algorithms are robust to unreliable wireless conditions and time varying network topologies. In this paper, we introduce GGE and demonstrate that greedy updates lead to rapid convergence. We do not require nodes to have any location information. Instead, greedy updates are made possible by exploiting the broadcast nature of wireless communications. During the operation of GGE, when a node decides to gossip, instead of choosing one of its neighbors at random, it makes a greedy selection, choosing the node which has the value most different from its own. In order to make this selection, nodes need to know their neighbors' values. Therefore, we assume that all transmissions are wireless broadcasts and nodes keep track of their neighbors' values by eavesdropping on their communications. We show that the convergence of GGE is guaranteed for connected network topologies. We also study the rates of convergence and illustrate, through theoretical bounds and numerical simulations, that GGE consistently outperforms randomized gossip and performs comparably to geographic gossip on moderate-sized random geometric graph topologies.
2008-05-07
ArXiv (preprint)
doi.org
arxiv.org
Recent Advances in Reinforcement Learning
Joelle Pineau
2008-01-01
Lecture Notes in Computer Science (published)
doi.org