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Semi-analytic approximate stability selection for correlated data in generalized linear models

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2020年第9期2020卷

作者： Takahashi, Takashi Kabashima, Yoshiyuki Tokyo Inst Technol Dept Math & Comp Sci Meguro Ku 2-12-1 Ookayama Tokyo Japan Univ Tokyo Inst Phys Intelligence Bunkyo Ku 7-3-1 Hongo Tokyo 1130033 Japan Univ Tokyo Dept Phys Grad Sch Sci Bunkyo Ku 7-3-1 Hongo Tokyo 1130033 Japan

We consider the variable selection problem of generalized linear models (GLMs). Stability selection (SS) is a promising method proposed for solving this problem. Although SS provides practical variable selection criteria, it is computationally demanding because it needs to fit GLMs to many re-sampled datasets. We propose a novel approximate inference algorithm that can conduct SS without the repeated fitting. The algorithm is based on the replica method of statistical mechanics and vector approximate message passing of information theory. For datasets characterized by rotation-invariant matrix ensembles, we derive state evolution equations that macroscopically describe the dynamics of the proposed algorithm. We also show that their fixed points are consistent with the replica symmetric solution obtained by the replica method. Numerical experiments indicate that the algorithm exhibits fast convergence and high approximation accuracy for both synthetic and real-world data.

关键词： Cavity and replica method message-passing algorithms Statistical inference

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Density Evolution Analysis of Node-Based Verification-Based algorithms in Compressed Sensing

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IEEE TRANSACTIONS ON INFORMATION THEORY 2012年第10期58卷 6616-6645页

作者： Eftekhari, Yaser Heidarzadeh, Anoosheh Banihashemi, Amir H. Lambadaris, Ioannis Carleton Univ Dept Syst & Comp Engn Ottawa ON K1S 5B6 Canada

In this paper, we present a new approach for the analysis of iterative node-based verification-based (NB-VB) recovery algorithms in the context of compressed sensing. These algorithms are particularly interesting due to their low complexity (linear in the signal dimension n). The asymptotic analysis predicts the fraction of unverified signal elements at each iteration l in the asymptotic regime where n -> l. The analysis is similar in nature to the well-known density evolution technique commonly used to analyze iterative decoding algorithms. To perform the analysis, a message-passing interpretation of NB-VB algorithms is provided. This interpretation lacks the extrinsic nature of standard message-passing algorithms to which density evolution is usually applied. This requires a number of nontrivial modifications in the analysis. The analysis tracks the average performance of the recovery algorithms over the ensembles of input signals and sensing matrices as a function of l. Concentration results are devised to demonstrate that the performance of the recovery algorithms applied to any choice of the input signal over any realization of the sensing matrix follows the deterministic results of the analysis closely. Simulation results are also provided which demonstrate that the proposed asymptotic analysis matches the performance of recovery algorithms for large but finite values of n. Compared to the existing technique for the analysis of NB-VB algorithms, which is based on numerically solving a large system of coupled differential equations, the proposed method is more accurate and simpler to implement.

关键词： Asymptotic analysis channel coding compressed sensing density evolution iterative decoding algorithms iterative recovery algorithms low-complexity compressed sensing low-density parity-check (LDPC) codes message-passing algorithms sparse graphs sparse sensing matrix success threshold verification-based recovery algorithms

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Low-Complexity Dynamic Channel Estimation in Multi-Antenna Grant-Free NOMA 95

Low-Complexity Dynamic Channel Estimation in Multi-Antenna G...

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IEEE 95th Vehicular Technology Conference: (VTC-Spring)

作者： Sagheer, Fakher Lehmann, Frederic Berthet, Antoine O. SAMOVAR Inst Polytech Paris Telecom SudParis 19 Pl Marguerite Perey Palaiseau Palaiseau France Univ Paris Saclay CNRS Cent Supelec Lab Signaux & Syst F-91190 Gif Sur Yvette France

ISBN: (数字)9781665482431

ISBN: (纸本)9781665482431

In grant-free non-orthogonal multiple access, the set of active users is unknown a priori. We address the challenging problem of dynamic channel estimation in this context. Assuming that inactive users are completely muted (in order to avoid unwanted pilot/preamble interference on active users), we investigate a channel estimation method performed jointly with user activity detection, multi-user detection and decoding. Leveraging conditional independence assumptions in probabilistic modeling, we introduce a low-complexity channel estimation performing expectation propagation in parallel for the measurements over all receive antennas. The proposed channel estimation technique is evaluated under different receive antenna correlation models and shows a good performance/complexity tradeoff with respect to joint measurement processing.

关键词： Dynamic channels antenna correlation grant-free NOMA message-passing algorithms loopy belief propagation Gaussian approximation expectation propagation

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Large deviations for the perceptron model and consequences for active learning 1

Large deviations for the perceptron model and consequences f...

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Conference on Mathematical and Scientific Machine Learning

作者： Cui, Hugo Saglietti, Luca Zdeborova, Lenka PSL Univ Ecole Normale Super Paris France CNRS Lab Phys Stat Paris France PSL Univ Sorbonnes Univ Ecole Normale Super Paris France CNRS Inst Phys Theor Saclay France CEA Saclay France Univ Paris Saclay Saclay France

Active learning is a branch of machine learning that deals with problems where unlabeled data is abundant yet obtaining labels is expensive. The learning algorithm has the possibility of querying a limited number of samples to obtain the corresponding labels, subsequently used for supervised learning. In this work, we consider the task of choosing the subset of samples to be labeled from a fixed finite pool of samples. We assume the pool of samples to be a random matrix and the ground truth labels to be generated by a single-layer teacher random neural network. We employ replica methods to analyze the large deviations for the accuracy achieved after supervised learning on a subset of the original pool. These large deviations then provide optimal achievable performance boundaries for any active learning algorithm. We show that the optimal learning performance can be efficiently approached by simple message-passing active learning algorithms. We also provide a comparison with the performance of some other popular active learning strategies.

关键词： Active learning Large Deviations perceptron Model message-passing algorithms

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Universally-Optimal Distributed Exact Min-Cut 22

Universally-Optimal Distributed Exact Min-Cut

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ACM Symposium on Principles of Distributed Computing (PODC)

作者： Ghaffari, Mohsen Zuzic, Goran MIT Cambridge MA 02139 USA Swiss Fed Inst Technol Zurich Switzerland

ISBN: (纸本)9781450392624

We present a universally-optimal distributed algorithm for the exact weighted min-cut. The algorithm is guaranteed to complete in (O) over tilde (D + root n) rounds on every graph, recovering the recent result of Dory, Efron, Mukhopadhyay, and Nanongkai [STOC'21], but runs much faster on structured graphs. Specifically, the algorithm completes in (O) over tilde (D) rounds on (weighted) planar graphs or, more generally, any (weighted) excluded-minor family. We obtain this result by designing an aggregation-based algorithm: each node receives only an aggregate of the messages sent to it. While somewhat restrictive, recent work shows any such black-box algorithm can be simulated on any minor of the communication network. Furthermore, we observe this also allows for the addition of (a small number of) arbitrarily-connected virtual nodes to the network. We leverage these capabilities to design a min-cut algorithm that is significantly simpler compared to prior distributed work. We hope this paper showcases how working within this paradigm yields simple-to-design and ultra-efficient distributed algorithms for global problems. Our main technical contribution is a distributed algorithm that, given any tree T, computes the minimum cut that 2-respects T (i.e., cuts at most 2 edges of T) in universally near-optimal time. Moreover, our algorithm gives a deterministic (O) over tilde (D)-round 2-respecting cut solution for excluded-minor families and a deterministic (O) over tilde (D + root n)-round solution for general graphs, the latter resolving a question of Dory, et al. [STOC'21]

关键词： exact minimum cut distributed algorithms message-passing algorithms CONGEST model minor-aggregation model low-congestion shortcuts universal optimality

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Construction of optimal spectral methods in phase retrieval 2

Construction of optimal spectral methods in phase retrieval

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2nd Annual Conference on Mathematical and Scientific Machine Learning

作者： Maillard, Antoine Krzakala, Florent Lu, Yue M. Zdeborova, Lenka Sorbonne Univ PSL Univ CNRS Lab PhysENS Paris France Ecole Polytech Fed Lausanne IdePHICS Lab Lausanne Switzerland Harvard Univ John A Paulson Sch Engn & Appl Sci Cambridge MA 02138 USA Ecole Polytech Fed Lausanne SPOC Lab Lausanne Switzerland

We consider the phase retrieval problem, in which the observer wishes to recover a n-dimensional real or complex signal X-star from the (possibly noisy) observation of vertical bar Phi X-star vertical bar, in which Phi is a matrix of size m x n. We consider a high-dimensional setting where n, m -> infinity with m/n = O(1), and a large class of (possibly correlated) random matrices Phi and observation channels. Spectral methods are a powerful tool to obtain approximate observations of the signal X-star which can be then used as initialization for a subsequent algorithm, at a low computational cost. In this paper, we extend and unify previous results and approaches on spectral methods for the phase retrieval problem. More precisely, we combine the linearization of message-passing algorithms and the analysis of the Bethe Hessian, a classical tool of statistical physics. Using this toolbox, we show how to derive optimal spectral methods for arbitrary channel noise and right-unitarily invariant matrix Phi, in an automated manner (i.e. with no optimization over any hyperparameter or preprocessing function).

关键词： Phase retrieval spectral methods message-passing algorithms

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Robust message-passing for statistical inference in sensor networks

Robust message-passing for statistical inference in sensor n...

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6th International Symposium on Information Processing Sensor Networks

作者： Schiff, Jeremy Antonelli, Dominic Dimakis, Alexandros G. Chu, David Wainwright, Martin J. Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94704 USA

ISBN: (纸本)9781595936387

Large-scale sensor network applications require in-network processing and data fusion to compute statistically relevant summaries of the sensed measurements. This paper studies distributed message-passing algorithms, in which neighboring nodes in the network pass local information relevant to a global computation, for performing statistical inference. We focus on the class of reweighted belief propagation (RBP) algorithms, which includes as special cases the standard sum-product and max-product algorithms for general networks with cycles, but in contrast to standard algorithms has attractive theoretical properties (uniqueness of fixed points, convergence, and robustness). Our main contribution is to design and implement a practical and modular architecture for implementing RBP algorithms in real networks. In addition, we show how intelligent scheduling of RBP messages can be used to minimize communication between motes and prolong the lifetime of the network. Our simulation and Mica2 mote deployment indicate that the proposed algorithms achieve accurate results despite real-world problems such as dying motes, dead and asymmetric links, and dropped messages. Overall, the class of RBP provides provides an ideal fit for sensor networks due to their distributed nature, requiring only local knowledge and coordination, and little requirements on other services such as reliable transmission.

关键词： message-passing algorithms sensor networks statistical inference reweighted belief propagation

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message Scheduling for Performant, Many-Core Belief Propagation

Message Scheduling for Performant, Many-Core Belief Propagat...

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IEEE High Performance Extreme Computing Conference (HPEC)

作者： Van der Merwe, Mark Joseph, Vinu Gopalakrishnan, Ganesh Univ Utah Sch Comp Salt Lake City UT 84112 USA

ISBN: (纸本)9781728150208

Belief Propagation (BP) is a message-passing algorithm for approximate inference over Probabilistic Graphical Models (PGMs), finding many applications such as computer vision, error-correcting codes, and protein-folding. While general, the convergence and speed of the algorithm has limited its practical use on difficult inference problems. As an algorithm that is highly amenable to parallelization, many-core Graphical Processing Units (GPUs) could significantly improve BP performance. Improving BP through many-core systems is non-trivial: the scheduling of messages in the algorithm strongly affects performance. We present a study of message scheduling for BP on GPUs. We demonstrate that BP exhibits a tradeoff between speed and convergence based on parallelism and show that existing message schedulings are not able to utilize this tradeoff. To this end, we present a novel randomized message scheduling approach, Randomized BP (RnBP), which outperforms existing methods on the GPU.

关键词： General Purpose GPU Computing Randomized algorithms message-passing algorithms

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Reliability-based schedule for decoding low-density parity-check codes

Reliability-based schedule for decoding low-density parity-c...

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IEEE International Conference on Communications (ICC 2004)

作者： Nouh, A Banihashemi, AH Carleton Univ Dept Syst & Comp Engn BCWS Ctr Ottawa ON K1S 5B6 Canada

ISBN: (纸本)0780385330

A reliability-based message-passing schedule for iterative decoding of low-density parity-check codes is proposed. Simulation results for bit-flipping algorithms (with binary messages) show that reliability-based schedule can provide considerable improvement in performance and decoding speed over the so-called flooding (parallel) schedule as well as the existing graph-based schedules. The cost associated with this improvement is negligible and is equivalent to having a 2-bit representation for initial messages, instead of the standard 1-bit for hard-decision algorithms, only at the first iteration (all the exchanged messages are still binary).

关键词： schedules for iterative decoding message-passing schedule reliability-based schedule iterative decoding low-density party-check (LDPC) codes message-passing algorithms bit-flipping algorithms hard-decision algorithms

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Graph algorithms for Preventing Cascading Failures in Networks 52

Graph Algorithms for Preventing Cascading Failures in Networ...

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52nd Annual Conference on Information Sciences and Systems (CISS)

作者： Yu, Pei Duo Tan, Chee Wei Fu, Hung-Lin City Univ Hong Kong Hong Kong Hong Kong Peoples R China Natl Chiao Tung Univ Hsinchu Taiwan

ISBN: (纸本)9781538605790

Cascading failures in critical networked infrastructures that result even from a single source of failure often lead to rapidly widespread outages as witnessed in the 2013 Northeast blackout in northern America. This paper examines the problem of minimizing the outage when a cascading failure from a single source occurs. An optimization problem is formulated where a limited number of protection nodes, when placed strategically in the network to mitigate systemic risk, can minimize the spread of cascading failure. Computationally fast distributed message-passing algorithms are developed to solve this problem. Global convergence and the optimality of the algorithm are proved using graph theoretic analysis. In particular, we illustrate how the poset-constrained graph algorithms can be designed to address the trade-off between complexity and optimality.

关键词： Cascading failure viral spreading graph theory large-scale optimization message-passing algorithms

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