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K. V. Rashmi

Publications and source records attributed to K. V. Rashmi.

31 records · Page 2Linked to original sources

DART: Dropouts meet Multiple Additive Regression Trees

Multiple Additive Regression Trees (MART), an ensemble model of boosted regression trees, is known to deliver high prediction accuracy for diverse tasks, and it is widely used in practice. However, it suffers an issue which we call over-specialization, wherein trees added at later iterations tend to impact the prediction of only a few instances, and make negligible contribution towards the remaining instances. This negatively affects the performance of the model on unseen data, and also makes the model over-sensitive to the contributions of the few, initially added tress. We show that the commonly used tool to address this issue, that of shrinkage, alleviates the problem only to a certain extent and the fundamental issue of over-specialization still remains. In this work, we explore a different approach to address the problem that of employing dropouts, a tool that has been recently proposed in the context of learning deep neural networks. We propose a novel way of employing dropouts in MART, resulting in the DART algorithm. We evaluate DART on ranking, regression and classification tasks, using large scale, publicly available datasets, and show that DART outperforms MART in each of the tasks, with a significant margin. We also show that DART overcomes the issue of over-specialization to a considerable extent.

cs.LG↗

Distributed Secret Dissemination Across a Network

Shamir's (n, k) threshold secret sharing is an important component of several cryptographic protocols, such as those for secure multiparty-computation and key management. These protocols typically assume the presence of direct communication links from the dealer to all participants, in which case the dealer can directly pass the shares of the secret to each participant. In this paper, we consider the problem of secret sharing when the dealer does not have direct communication links to all the participants, and instead, the dealer and the participants form a general network. Existing methods are based on secure message transmissions from the dealer to each participant requiring considerable coordination in the network. In this paper, we present a distributed algorithm for disseminating shares over a network, which we call the SNEAK algorithm, requiring each node to know only the identities of its one-hop neighbours. While SNEAK imposes a stronger condition on the network by requiring the dealer to be what we call k-propagating rather than k-connected as required by the existing solutions, we show that in addition to being distributed, SNEAK achieves significant reduction in the communication cost and the amount of randomness required.

cs.CR↗

Fundamental Limits on Communication for Oblivious Updates in Storage Networks

In distributed storage systems, storage nodes intermittently go offline for numerous reasons. On coming back online, nodes need to update their contents to reflect any modifications to the data in the interim. In this paper, we consider a setting where no information regarding modified data needs to be logged in the system. In such a setting, a 'stale' node needs to update its contents by downloading data from already updated nodes, while neither the stale node nor the updated nodes have any knowledge as to which data symbols are modified and what their value is. We investigate the fundamental limits on the amount of communication necessary for such an "oblivious" update process. We first present a generic lower bound on the amount of communication that is necessary under any storage code with a linear encoding (while allowing non-linear update protocols). This lower bound is derived under a set of extremely weak conditions, giving all updated nodes access to the entire modified data and the stale node access to the entire stale data as side information. We then present codes and update algorithms that are optimal in that they meet this lower bound. Next, we present a lower bound for an important subclass of codes, that of linear Maximum-Distance-Separable (MDS) codes. We then present an MDS code construction and an associated update algorithm that meets this lower bound. These results thus establish the capacity of oblivious updates in terms of the communication requirements under these settings.

cs.IT↗

A Solution to the Network Challenges of Data Recovery in Erasure-coded Distributed Storage Systems: A Study on the Facebook Warehouse Cluster

Erasure codes, such as Reed-Solomon (RS) codes, are being increasingly employed in data centers to combat the cost of reliably storing large amounts of data. Although these codes provide optimal storage efficiency, they require significantly high network and disk usage during recovery of missing data. In this paper, we first present a study on the impact of recovery operations of erasure-coded data on the data-center network, based on measurements from Facebook's warehouse cluster in production. To the best of our knowledge, this is the first study of its kind available in the literature. Our study reveals that recovery of RS-coded data results in a significant increase in network traffic, more than a hundred terabytes per day, in a cluster storing multiple petabytes of RS-coded data. To address this issue, we present a new storage code using our recently proposed "Piggybacking" framework, that reduces the network and disk usage during recovery by 30% in theory, while also being storage optimal and supporting arbitrary design parameters. The implementation of the proposed code in the Hadoop Distributed File System (HDFS) is underway. We use the measurements from the warehouse cluster to show that the proposed code would lead to a reduction of close to fifty terabytes of cross-rack traffic per day.

cs.NI↗

A Piggybacking Design Framework for Read-and Download-efficient Distributed Storage Codes

We present a new 'piggybacking' framework for designing distributed storage codes that are efficient in data-read and download required during node-repair. We illustrate the power of this framework by constructing classes of explicit codes that entail the smallest data-read and download for repair among all existing solutions for three important settings: (a) codes meeting the constraints of being Maximum-Distance-Separable (MDS), high-rate and having a small number of substripes, arising out of practical considerations for implementation in data centers, (b) binary MDS codes for all parameters where binary MDS codes exist, (c) MDS codes with the smallest repair-locality. In addition, we employ this framework to enable efficient repair of parity nodes in existing codes that were originally constructed to address the repair of only the systematic nodes. The basic idea behind our framework is to take multiple instances of existing codes and add carefully designed functions of the data of one instance to the other. Typical savings in data-read during repair is 25% to 50% depending on the choice of the code parameters.

cs.IT↗

Regenerating Codes for Errors and Erasures in Distributed Storage

Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during the data-reconstruction and node-repair operations. We provide explicit regenerating codes that are resilient to errors and erasures, and show that these codes are optimal with respect to storage and bandwidth requirements. As a special case, we also establish the capacity of a class of distributed storage systems in the presence of malicious adversaries. While our code constructions are based on previously constructed Product-Matrix codes, we also provide necessary and sufficient conditions for introducing resilience in any regenerating code.

cs.IT↗

Information-theoretically Secure Regenerating Codes for Distributed Storage

Regenerating codes are a class of codes for distributed storage networks that provide reliability and availability of data, and also perform efficient node repair. Another important aspect of a distributed storage network is its security. In this paper, we consider a threat model where an eavesdropper may gain access to the data stored in a subset of the storage nodes, and possibly also, to the data downloaded during repair of some nodes. We provide explicit constructions of regenerating codes that achieve information-theoretic secrecy capacity in this setting.

cs.IT↗

Enabling Node Repair in Any Erasure Code for Distributed Storage

Erasure codes are an efficient means of storing data across a network in comparison to data replication, as they tend to reduce the amount of data stored in the network and offer increased resilience in the presence of node failures. The codes perform poorly though, when repair of a failed node is called for, as they typically require the entire file to be downloaded to repair a failed node. A new class of erasure codes, termed as regenerating codes were recently introduced, that do much better in this respect. However, given the variety of efficient erasure codes available in the literature, there is considerable interest in the construction of coding schemes that would enable traditional erasure codes to be used, while retaining the feature that only a fraction of the data need be downloaded for node repair. In this paper, we present a simple, yet powerful, framework that does precisely this. Under this framework, the nodes are partitioned into two 'types' and encoded using two codes in a manner that reduces the problem of node-repair to that of erasure-decoding of the constituent codes. Depending upon the choice of the two codes, the framework can be used to avail one or more of the following advantages: simultaneous minimization of storage space and repair-bandwidth, low complexity of operation, fewer disk reads at helper nodes during repair, and error detection and correction.

cs.IT↗

Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction

Regenerating codes are a class of distributed storage codes that optimally trade the bandwidth needed for repair of a failed node with the amount of data stored per node of the network. Minimum Storage Regenerating (MSR) codes minimize first, the amount of data stored per node, and then the repair bandwidth, while Minimum Bandwidth Regenerating (MBR) codes carry out the minimization in the reverse order. An [n, k, d] regenerating code permits the data to be recovered by connecting to any k of the n nodes in the network, while requiring that repair of a failed node be made possible by connecting (using links of lesser capacity) to any d nodes. Previous, explicit and general constructions of exact-regenerating codes have been confined to the case n=d+1. In this paper, we present optimal, explicit constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all [n, k, d >= 2k-2], using a product-matrix framework. The particular product-matrix nature of the constructions is shown to significantly simplify system operation. To the best of our knowledge, these are the first constructions of exact-regenerating codes that allow the number n of nodes in the distributed storage network, to be chosen independent of the other parameters. The paper also contains a simpler description, in the product-matrix framework, of a previously constructed MSR code in which the parameter d satisfies [n=d+1, k, d >= 2k-1].

cs.IT↗

Distributed Storage Codes with Repair-by-Transfer and Non-achievability of Interior Points on the Storage-Bandwidth Tradeoff

Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any subset of k nodes within the n-node network. However, regenerating codes possess in addition, the ability to repair a failed node by connecting to an arbitrary subset of d nodes. It has been shown that for the case of functional-repair, there is a tradeoff between the amount of data stored per node and the bandwidth required to repair a failed node. A special case of functional-repair is exact-repair where the replacement node is required to store data identical to that in the failed node. Exact-repair is of interest as it greatly simplifies system implementation. The first result of the paper is an explicit, exact-repair code for the point on the storage-bandwidth tradeoff corresponding to the minimum possible repair bandwidth, for the case when d=n-1. This code has a particularly simple graphical description and most interestingly, has the ability to carry out exact-repair through mere transfer of data and without any need to perform arithmetic operations. Hence the term `repair-by-transfer'. The second result of this paper shows that the interior points on the storage-bandwidth tradeoff cannot be achieved under exact-repair, thus pointing to the existence of a separate tradeoff under exact-repair. Specifically, we identify a set of scenarios, termed `helper node pooling', and show that it is the necessity to satisfy such scenarios that over-constrains the system.

cs.IT↗

Interference Alignment in Regenerating Codes for Distributed Storage: Necessity and Code Constructions

Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary k of n nodes. However regenerating codes possess in addition, the ability to repair a failed node by connecting to any arbitrary d nodes and downloading an amount of data that is typically far less than the size of the data file. This amount of download is termed the repair bandwidth. Minimum storage regenerating (MSR) codes are a subclass of regenerating codes that require the least amount of network storage; every such code is a maximum distance separable (MDS) code. Further, when a replacement node stores data identical to that in the failed node, the repair is termed as exact. The four principal results of the paper are (a) the explicit construction of a class of MDS codes for d = n-1 >= 2k-1 termed the MISER code, that achieves the cut-set bound on the repair bandwidth for the exact-repair of systematic nodes, (b) proof of the necessity of interference alignment in exact-repair MSR codes, (c) a proof showing the impossibility of constructing linear, exact-repair MSR codes for d < 2k-3 in the absence of symbol extension, and (d) the construction, also explicit, of MSR codes for d = k+1. Interference alignment (IA) is a theme that runs throughout the paper: the MISER code is built on the principles of IA and IA is also a crucial component to the non-existence proof for d < 2k-3. To the best of our knowledge, the constructions presented in this paper are the first, explicit constructions of regenerating codes that achieve the cut-set bound.

cs.IT↗

Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A subspace based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.

cs.IT↗

Explicit Codes Minimizing Repair Bandwidth for Distributed Storage

We consider the setting of data storage across n nodes in a distributed manner. A data collector (DC) should be able to reconstruct the entire data by connecting to any k out of the n nodes and downloading all the data stored in them. When a node fails, it has to be regenerated back using the existing nodes. In a recent paper, Wu et al. have obtained an information theoretic lower bound for the repair bandwidth. Also, there has been additional interest in storing data in systematic form as no post processing is required when DC connects to k systematic nodes. Because of their preferred status there is a need to regenerate back any systematic node quickly and exactly. Replacement of a failed node by an exact replica is termed Exact Regeneration.In this paper, we consider the problem of minimizing the repair bandwidth for exact regeneration of the systematic nodes. The file to be stored is of size B and each node can store alpha = B/k units of data. A failed systematic node is regenerated by downloading beta units of data each from d existing nodes. We give a lower bound for the repair bandwidth for exact regeneration of the systematic nodes which matches with the bound given by Wu et al. For d >= 2k-1 we give an explicit code construction which minimizes the repair bandwidth when the existing k-1 systematic nodes participate in the regeneration. We show the existence and construction of codes that achieve the bound for d >= 2k-3. Here we also establish the necessity of interference alignment. We prove that the bound is not achievable for d <= 2k-4 when beta=1. We also give a coding scheme which can be used for any d and k, which is optimal for d >= 2k-1.

cs.IT↗