Borja Peleato

Bio: Borja Peleato is an academic researcher from Purdue University. The author has contributed to research in topics: Throughput & NAND gate. The author has an hindex of 13, co-authored 33 publications receiving 15576 citations. Previous affiliations of Borja Peleato include Charles III University of Madrid & Massachusetts Institute of Technology.

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

Abstract: Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

Distance aware collision avoidance protocol for ad-hoc underwater acoustic sensor networks

Abstract: This paper proposes a channel access protocol for ad-hoc underwater acoustic networks which are characterized by long propagation delays and unequal transmit/receive power requirements. The protocol saves transmission energy by avoiding collisions while maximizing throughput. It is based on minimizing the duration of a hand-shake by taking advantage of the receiver's tolerance to interference when the two nodes are closer than the maximal transmission range. Nodes do not need to be synchronized, can move, are half-duplex, and use the same transmission power. This protocol achieves a throughput several times higher than that of the slotted FAMA, while offering similar savings in energy. Although carrier sensing ALOHA offers a higher throughput, it wastes much more power on collisions.

A MAC protocol for ad-hoc underwater acoustic sensor networks

Abstract: A medium access control (MAC) protocol is proposed that is suitable for non-synchronized ad-hoc networks, and in particular for the energy-constrained underwater acoustic networks which are characterized by long propagation delays. The protocol exploits the difference in the link lengths between the nodes instead of using waiting times proportional to the maximal link length. To do so, it relies on a receiver's ability to tolerate a certain level of interference. By minimizing the length of the hand-shake procedure preceeding the data transmission, the throughput efficiency is increased as compared to the previously proposed protocols, while collision avoidance minimizes the energy consumption.

Channel-Reconstruction-Based Hybrid Precoding for Millimeter-Wave Multi-User MIMO Systems

Abstract: The focus of this paper is on multi-user multi-input multi-output transmissions for millimeter-wave systems with a hybrid precoding architecture at the base station To enable multiuser transmissions, the base station uses a cell-specific codebook of beamforming vectors over an initial beam alignment phase Each user uses a user-specific codebook of beamforming vectors to learn the top- $P$ (where $P \geq 1$ ) beam pairs in terms of the observed signal-to-noise ratio ( ${\text{SNR}}$ ) in a single-user setting The top- $P$ beam indices along with their ${\text{SNR}}$ s are fed back from each user and the base station leverages this information to generate beam weights for simultaneous transmissions A typical method to generate the beam weights is to use only the best beam for each user and either steer energy along this beam, or to utilize this information to reduce multi-user interference The other beams are used as fall-back options to address blockage or mobility Such an approach completely discards information learned about the channel condition(s) even though each user feeds back this information With this background, this paper develops an advanced directional precoding structure for simultaneous transmissions at the cost of an additional marginal feedback overhead This construction relies on three main innovations: first, additional feedback to allow the base station to reconstruct a rank- $P$ approximation of the channel matrix between it and each user; second, a zero-forcing structure that leverages this information to combat multi-user interference by remaining agnostic of the receiver beam knowledge in the precoder design; and third, a hybrid precoding architecture that allows both amplitude and phase control at low complexity and cost to allow the implementation of the zero-forcing structure Numerical studies show that the proposed scheme results in a significant sum rate performance improvement over naive schemes even with a coarse initial beam alignment codebook

Adaptive Read Thresholds for NAND Flash

Abstract: A primary source of increased read time on nand flash comes from the fact that, in the presence of noise, the flash medium must be read several times using different read threshold voltages for the decoder to succeed. This paper proposes an algorithm that uses a limited number of rereads to characterize the noise distribution and recover the stored information. Both hard and soft decoding are considered. For hard decoding, this paper attempts to find a read threshold minimizing bit error rate (BER) and derives an expression for the resulting codeword error rate. For soft decoding, it shows that minimizing BER and minimizing codeword error rate are competing objectives in the presence of a limited number of allowed rereads, and proposes a tradeoff between the two. The proposed method does not require any prior knowledge about the noise distribution but can take advantage of such information when it is available. Each read threshold is chosen based on the results of previous reads, following an optimal policy derived through a dynamic programming backward recursion. The method and results are studied from the perspective of an SLC Flash memory with Gaussian noise, but this paper explains how the method could be extended to other scenarios.

Proximal Algorithms

Abstract: This monograph is about a class of optimization algorithms called proximal algorithms. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially well-suited to problems of substantial recent interest involving large or high-dimensional datasets. Proximal methods sit at a higher level of abstraction than classical algorithms like Newton's method: the base operation is evaluating the proximal operator of a function, which itself involves solving a small convex optimization problem. These subproblems, which generalize the problem of projecting a point onto a convex set, often admit closed-form solutions or can be solved very quickly with standard or simple specialized methods. Here, we discuss the many different interpretations of proximal operators and algorithms, describe their connections to many other topics in optimization and applied mathematics, survey some popular algorithms, and provide a large number of examples of proximal operators that commonly arise in practice.

Message-passing algorithms for compressed sensing

Abstract: Compressed sensing aims to undersample certain high-dimensional signals yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a known basis. Currently, the best known sparsity–undersampling tradeoff is achieved when reconstructing by convex optimization, which is expensive in important large-scale applications. Fast iterative thresholding algorithms have been intensively studied as alternatives to convex optimization for large-scale problems. Unfortunately known fast algorithms offer substantially worse sparsity–undersampling tradeoffs than convex optimization. We introduce a simple costless modification to iterative thresholding making the sparsity–undersampling tradeoff of the new algorithms equivalent to that of the corresponding convex optimization procedures. The new iterative-thresholding algorithms are inspired by belief propagation in graphical models. Our empirical measurements of the sparsity–undersampling tradeoff for the new algorithms agree with theoretical calculations. We show that a state evolution formalism correctly derives the true sparsity–undersampling tradeoff. There is a surprising agreement between earlier calculations based on random convex polytopes and this apparently very different theoretical formalism.

Sparse Subspace Clustering: Algorithm, Theory, and Applications

Abstract: Many real-world problems deal with collections of high-dimensional data, such as images, videos, text, and web documents, DNA microarray data, and more. Often, such high-dimensional data lie close to low-dimensional structures corresponding to several classes or categories to which the data belong. In this paper, we propose and study an algorithm, called sparse subspace clustering, to cluster data points that lie in a union of low-dimensional subspaces. The key idea is that, among the infinitely many possible representations of a data point in terms of other points, a sparse representation corresponds to selecting a few points from the same subspace. This motivates solving a sparse optimization program whose solution is used in a spectral clustering framework to infer the clustering of the data into subspaces. Since solving the sparse optimization program is in general NP-hard, we consider a convex relaxation and show that, under appropriate conditions on the arrangement of the subspaces and the distribution of the data, the proposed minimization program succeeds in recovering the desired sparse representations. The proposed algorithm is efficient and can handle data points near the intersections of subspaces. Another key advantage of the proposed algorithm with respect to the state of the art is that it can deal directly with data nuisances, such as noise, sparse outlying entries, and missing entries, by incorporating the model of the data into the sparse optimization program. We demonstrate the effectiveness of the proposed algorithm through experiments on synthetic data as well as the two real-world problems of motion segmentation and face clustering.