arXiv subjects

Nikhil Karamchandani

Publications and source records attributed to Nikhil Karamchandani.

53 records · Page 3Linked to original sources

arXiv2019

Sequential Mode Estimation with Oracle Queries

We consider the problem of adaptively PAC-learning a probability distribution $\mathcal{P}$'s mode by querying an oracle for information about a sequence of i.i.d. samples $X_1, X_2, \ldots$ generated from $\mathcal{P}$. We consider two different query models: (a) each query is an index $i$ for which the oracle reveals the value of the sample $X_i$, (b) each query is comprised of two indices $i$ and $j$ for which the oracle reveals if the samples $X_i$ and $X_j$ are the same or not. For these query models, we give sequential mode-estimation algorithms which, at each time $t$, either make a query to the corresponding oracle based on past observations, or decide to stop and output an estimate for the distribution's mode, required to be correct with a specified confidence. We analyze the query complexity of these algorithms for any underlying distribution $\mathcal{P}$, and derive corresponding lower bounds on the optimal query complexity under the two querying models.

cs.LG↗

arXiv2018

Persistence of the Jordan center in Random Growing Trees

The Jordan center of a graph is defined as a vertex whose maximum distance to other nodes in the graph is minimal, and it finds applications in facility location and source detection problems. We study properties of the Jordan Center in the case of random growing trees. In particular, we consider a regular tree graph on which an infection starts from a root node and then spreads along the edges of the graph according to various random spread models. For the Independent Cascade (IC) model and the discrete Susceptible Infected (SI) model, both of which are discrete time models, we show that as the infected subgraph grows with time, the Jordan center persists on a single vertex after a finite number of timesteps. Finally, we also study the continuous time version of the SI model and bound the maximum distance between the Jordan center and the root node at any time.

cs.SI↗

arXiv2018

Effects of Storage Heterogeneity in Distributed Cache Systems

In this work, we focus on distributed cache systems with non-uniform storage capacity across caches. We compare the performance of our system with the performance of a system with the same cumulative storage distributed evenly across the caches. We characterize the extent to which the performance of the distributed cache system deteriorates due to storage heterogeneity. The key takeaway from this work is that the effects of heterogeneity in the storage capabilities depend heavily on the popularity profile of the contents being cached and delivered. We analytically show that compared to the case where contents popularity is comparable across contents, lopsided popularity profiles are more tolerant to heterogeneity in storage capabilities. We validate our theoretical results via simulations.

cs.IT↗

arXiv2018

Caching with Partial Adaptive Matching

We study the caching problem when we are allowed to match each user to one of a subset of caches after its request is revealed. We focus on non-uniformly popular content, specifically when the file popularities obey a Zipf distribution. We study two extremal schemes, one focusing on coded server transmissions while ignoring matching capabilities, and the other focusing on adaptive matching while ignoring potential coding opportunities. We derive the rates achieved by these schemes and characterize the regimes in which one outperforms the other. We also compare them to information-theoretic outer bounds, and finally propose a hybrid scheme that generalizes ideas from the two schemes and performs at least as well as either of them in most memory regimes.

cs.IT↗

arXiv2018

Learning Recommendations While Influencing Interests

Personalized recommendation systems (RS) are extensively used in many services. Many of these are based on learning algorithms where the RS uses the recommendation history and the user response to learn an optimal strategy. Further, these algorithms are based on the assumption that the user interests are rigid. Specifically, they do not account for the effect of learning strategy on the evolution of the user interests. In this paper we develop influence models for a learning algorithm that is used to optimally recommend websites to web users. We adapt the model of \cite{Ioannidis10} to include an item-dependent reward to the RS from the suggestions that are accepted by the user. For this we first develop a static optimisation scheme when all the parameters are known. Next we develop a stochastic approximation based learning scheme for the RS to learn the optimal strategy when the user profiles are not known. Finally, we describe several user-influence models for the learning algorithm and analyze their effect on the steady user interests and on the steady state optimal strategy as compared to that when the users are not influenced.

cs.IR↗

arXiv2017

Private Coded Caching

Recent work by Maddah-Ali and Niesen introduced coded caching which demonstrated the benefits of joint design of storage and transmission policies in content delivery networks. They studied a setup where a server communicates with a set of users, each equipped with a local cache, over a shared error-free link and proposed an order-optimal caching and delivery scheme. In this paper, we introduce the problem of secretive coded caching where we impose the additional constraint that a user should not be able to learn anything, from either the content stored in its cache or the server transmissions, about a file it did not request. We propose a feasible scheme for this setting and demonstrate its order-optimality with respect to information-theoretic lower bounds.

cs.IT↗

arXiv2016

Randomized Kaczmarz for Rank Aggregation from Pairwise Comparisons

We revisit the problem of inferring the overall ranking among entities in the framework of Bradley-Terry-Luce (BTL) model, based on available empirical data on pairwise preferences. By a simple transformation, we can cast the problem as that of solving a noisy linear system, for which a ready algorithm is available in the form of the randomized Kaczmarz method. This scheme is provably convergent, has excellent empirical performance, and is amenable to on-line, distributed and asynchronous variants. Convergence, convergence rate, and error analysis of the proposed algorithm are presented and several numerical experiments are conducted whose results validate our theoretical findings.

cs.LG↗

arXiv2016

Content Replication in Large Distributed Caches

In this paper, we consider the algorithmic task of content replication and request routing in a distributed caching system consisting of a central server and a large number of caches, each with limited storage and service capabilities. We study a time-slotted system where in each time-slot, a large batch of requests has to be matched to a large number of caches, where each request can be served by any cache which stores the requested content. All requests which cannot be served by the caches are served by fetching the requested content from the central server. The goal is to minimize the transmission rate from the central server. We use a novel mapping between our content replication problem and the Knapsack problem to prove a lower bound on the transmission rate for any content replication policy. Using insights obtained from the mapping, we propose a content replication policy - Knapsack Storage - which achieves this lower bound. While it intuitively makes sense to replicate the more popular contents on a larger number of caches, surprisingly, in certain cases, the Knapsack Storage policy chooses not to replicate the most popular contents on the caches at all.

cs.NI↗

arXiv2015

Coded Caching for Multi-level Popularity and Access

To address the exponentially rising demand for wireless content, use of caching is emerging as a potential solution. It has been recently established that joint design of content delivery and storage (coded caching) can significantly improve performance over conventional caching. Coded caching is well suited to emerging heterogeneous wireless architectures which consist of a dense deployment of local-coverage wireless access points (APs) with high data rates, along with sparsely-distributed, large-coverage macro-cell base stations (BS). This enables design of coded caching-and-delivery schemes that equip APs with storage, and place content in them in a way that creates coded-multicast opportunities for combining with macro-cell broadcast to satisfy users even with different demands. Such coded-caching schemes have been shown to be order-optimal with respect to the BS transmission rate, for a system with single-level content, i.e., one where all content is uniformly popular. In this work, we consider a system with non-uniform popularity content which is divided into multiple levels, based on varying degrees of popularity. The main contribution of this work is the derivation of an order-optimal scheme which judiciously shares cache memory among files with different popularities. To show order-optimality we derive new information-theoretic lower bounds, which use a sliding-window entropy inequality, effectively creating a non-cutset bound. We also extend the ideas to when users can access multiple caches along with the broadcast. Finally we consider two extreme cases of user distribution across caches for the multi-level popularity model: a single user per cache (single-user setup) versus a large number of users per cache (multi-user setup), and demonstrate a dichotomy in the order-optimal strategies for these two extreme cases.

cs.IT↗

arXiv2015

Secure State Estimation against Sensor Attacks in the Presence of Noise

We consider the problem of estimating the state of a noisy linear dynamical system when an unknown subset of sensors is arbitrarily corrupted by an adversary. We propose a secure state estimation algorithm, and derive (optimal) bounds on the achievable state estimation error given an upper bound on the number of attacked sensors. The proposed state estimator involves Kalman filters operating over subsets of sensors to search for a sensor subset which is reliable for state estimation. To further improve the subset search time, we propose Satisfiability Modulo Theory based techniques to exploit the combinatorial nature of searching over sensor subsets. Finally, as a result of independent interest, we give a coding theoretic view of attack detection and state estimation against sensor attacks in a noiseless dynamical system.

math.OC↗

arXiv2015

Secure State Estimation: Optimal Guarantees against Sensor Attacks in the Presence of Noise

Motivated by the need to secure cyber-physical systems against attacks, we consider the problem of estimating the state of a noisy linear dynamical system when a subset of sensors is arbitrarily corrupted by an adversary. We propose a secure state estimation algorithm and derive (optimal) bounds on the achievable state estimation error. In addition, as a result of independent interest, we give a coding theoretic interpretation for prior work on secure state estimation against sensor attacks in a noiseless dynamical system.

math.OC↗

arXiv2015

Effect of Number of Users in Multi-level Coded Caching

It has been recently established that joint design of content delivery and storage (coded caching) can significantly improve performance over conventional caching. This has also been extended to the case when content has non-uniform popularity through several models. In this paper we focus on a multi-level popularity model, where content is divided into levels based on popularity. We consider two extreme cases of user distribution across caches for the multi-level popularity model: a single user per cache (single-user setup) versus a large number of users per cache (multi-user setup). When the capacity approximation is universal (independent of number of popularity levels as well as number of users, files and caches), we demonstrate a dichotomy in the order-optimal strategies for these two extreme cases. In the multi-user case, sharing memory among the levels is order-optimal, whereas for the single-user case clustering popularity levels and allocating all the memory to them is the order-optimal scheme. In proving these results, we develop new information-theoretic lower bounds for the problem.

cs.IT↗

arXiv2015

Content Caching and Delivery over Heterogeneous Wireless Networks

Emerging heterogeneous wireless architectures consist of a dense deployment of local-coverage wireless access points (APs) with high data rates, along with sparsely-distributed, large-coverage macro-cell base stations (BS). We design a coded caching-and-delivery scheme for such architectures that equips APs with storage, enabling content pre-fetching prior to knowing user demands. Users requesting content are served by connecting to local APs with cached content, as well as by listening to a BS broadcast transmission. For any given content popularity profile, the goal is to design the caching-and-delivery scheme so as to optimally trade off the transmission cost at the BS against the storage cost at the APs and the user cost of connecting to multiple APs. We design a coded caching scheme for non-uniform content popularity that dynamically allocates user access to APs based on requested content. We demonstrate the approximate optimality of our scheme with respect to information-theoretic bounds. We numerically evaluate it on a YouTube dataset and quantify the trade-off between transmission rate, storage, and access cost. Our numerical results also suggest the intriguing possibility that, to gain most of the benefits of coded caching, it suffices to divide the content into a small number of popularity classes.

cs.IT↗

arXiv2014

Hierarchical Coded Caching

Caching of popular content during off-peak hours is a strategy to reduce network loads during peak hours. Recent work has shown significant benefits of designing such caching strategies not only to deliver part of the content locally, but also to provide coded multicasting opportunities even among users with different demands. Exploiting both of these gains was shown to be approximately optimal for caching systems with a single layer of caches. Motivated by practical scenarios, we consider in this work a hierarchical content delivery network with two layers of caches. We propose a new caching scheme that combines two basic approaches. The first approach provides coded multicasting opportunities within each layer; the second approach provides coded multicasting opportunities across multiple layers. By striking the right balance between these two approaches, we show that the proposed scheme achieves the optimal communication rates to within a constant multiplicative and additive gap. We further show that there is no tension between the rates in each of the two layers up to the aforementioned gap. Thus, both layers can simultaneously operate at approximately the minimum rate.

cs.IT↗

arXiv2013

Computation over Mismatched Channels

We consider the problem of distributed computation of a target function over a multiple-access channel. If the target and channel functions are matched (i.e., compute the same function), significant performance gains can be obtained by jointly designing the computation and communication tasks. However, in most situations there is mismatch between these two functions. In this work, we analyze the impact of this mismatch on the performance gains achievable with joint computation and communication designs over separation-based designs. We show that for most pairs of target and channel functions there is no such gain, and separation of computation and communication is optimal.

cs.IT↗

arXiv2011

Linear Codes, Target Function Classes, and Network Computing Capacity

We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, injective, semi-injective, and linear target functions over finite fields. Computing capacity bounds and achievability are given with respect to these target function classes for network codes that use routing, linear coding, or nonlinear coding.

cs.IT↗

arXiv2010

Network Coding for Computing: Cut-Set Bounds

The following \textit{network computing} problem is considered. Source nodes in a directed acyclic network generate independent messages and a single receiver node computes a target function $f$ of the messages. The objective is to maximize the average number of times $f$ can be computed per network usage, i.e., the ``computing capacity''. The \textit{network coding} problem for a single-receiver network is a special case of the network computing problem in which all of the source messages must be reproduced at the receiver. For network coding with a single receiver, routing is known to achieve the capacity by achieving the network \textit{min-cut} upper bound. We extend the definition of min-cut to the network computing problem and show that the min-cut is still an upper bound on the maximum achievable rate and is tight for computing (using coding) any target function in multi-edge tree networks and for computing linear target functions in any network. We also study the bound's tightness for different classes of target functions. In particular, we give a lower bound on the computing capacity in terms of the Steiner tree packing number and a different bound for symmetric functions. We also show that for certain networks and target functions, the computing capacity can be less than an arbitrarily small fraction of the min-cut bound.

cs.IT↗