arXiv subjects

Sanjeev R. Kulkarni

Publications and source records attributed to Sanjeev R. Kulkarni.

At least 37 records · Page 2Linked to original sources

arXiv2015

Sparse Attack Construction and State Estimation in the Smart Grid: Centralized and Distributed Models

New methods that exploit sparse structures arising in smart grid networks are proposed for the state estimation problem when data injection attacks are present. First, construction strategies for unobservable sparse data injection attacks on power grids are proposed for an attacker with access to all network information and nodes. Specifically, novel formulations for the optimization problem that provide a flexible design of the trade-off between performance and false alarm are proposed. In addition, the centralized case is extended to a distributed framework for both the estimation and attack problems. Different distributed scenarios are proposed depending on assumptions that lead to the spreading of the resources, network nodes and players. Consequently, for each of the presented frameworks a corresponding optimization problem is introduced jointly with an algorithm to solve it. The validity of the presented procedures in real settings is studied through extensive simulations in the IEEE test systems.

cs.IT↗

arXiv2013

An Upper Bound on the Convergence Time for Distributed Binary Consensus

The problem addressed in this paper is the analysis of a distributed consensus algorithm for arbitrary networks, proposed by Bénézit et al.. In the initial setting, each node in the network has one of two possible states ("yes" or "no"). Nodes can update their states by communicating with their neighbors via a 2-bit message in an asynchronous clock setting. Eventually, all nodes reach consensus on the majority states. We use the theory of electric networks, random walks, and couplings of Markov chains to derive an O(N4 logN) upper bound for the expected convergence time on an arbitrary graph of size N.

cs.PF↗

arXiv2013

Wisdom of the Crowd: Incorporating Social Influence in Recommendation Models

Recommendation systems have received considerable attention recently. However, most research has been focused on improving the performance of collaborative filtering (CF) techniques. Social networks, indispensably, provide us extra information on people's preferences, and should be considered and deployed to improve the quality of recommendations. In this paper, we propose two recommendation models, for individuals and for groups respectively, based on social contagion and social influence network theory. In the recommendation model for individuals, we improve the result of collaborative filtering prediction with social contagion outcome, which simulates the result of information cascade in the decision-making process. In the recommendation model for groups, we apply social influence network theory to take interpersonal influence into account to form a settled pattern of disagreement, and then aggregate opinions of group members. By introducing the concept of susceptibility and interpersonal influence, the settled rating results are flexible, and inclined to members whose ratings are "essential".

cs.IR↗

arXiv2013

A Random Walk Based Model Incorporating Social Information for Recommendations

Collaborative filtering (CF) is one of the most popular approaches to build a recommendation system. In this paper, we propose a hybrid collaborative filtering model based on a Makovian random walk to address the data sparsity and cold start problems in recommendation systems. More precisely, we construct a directed graph whose nodes consist of items and users, together with item content, user profile and social network information. We incorporate user's ratings into edge settings in the graph model. The model provides personalized recommendations and predictions to individuals and groups. The proposed algorithms are evaluated on MovieLens and Epinions datasets. Experimental results show that the proposed methods perform well compared with other graph-based methods, especially in the cold start case.

cs.IR↗

arXiv2013

An Upper Bound on the Convergence Time for Quantized Consensus

We analyze a class of distributed quantized consen- sus algorithms for arbitrary networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network, and then update their estimation by communicating with their neighbors in a limited capacity channel in an asynchronous clock setting. Eventually, all nodes reach consensus with quantized precision. We start the analysis with a special case of a distributed binary voting algorithm, then proceed to the expected convergence time for the general quantized consensus algorithm proposed by Kashyap et al. We use the theory of electric networks, random walks, and couplings of Markov chains to derive an O(N^3log N) upper bound for the expected convergence time on an arbitrary graph of size N, improving on the state of art bound of O(N^4logN) for binary consensus and O(N^5) for quantized consensus algorithms. Our result is not dependent on graph topology. Simulations on special graphs such as star networks, line graphs, lollipop graphs, and Erdös-Rényi random graphs are performed to validate the analysis. This work has applications to load balancing, coordination of autonomous agents, estimation and detection, decision-making networks, peer-to-peer systems, etc.

stat.AP↗

arXiv2009

Robust Fitting of Ellipses and Spheroids

Ellipse and ellipsoid fitting has been extensively researched and widely applied. Although traditional fitting methods provide accurate estimation of ellipse parameters in the low-noise case, their performance is compromised when the noise level or the ellipse eccentricity are high. A series of robust fitting algorithms are proposed that perform well in high-noise, high-eccentricity ellipse/spheroid (a special class of ellipsoid) cases. The new algorithms are based on the geometric definition of an ellipse/spheroid, and improved using global statistical properties of the data. The efficacy of the new algorithms is demonstrated through simulations.

stat.ME↗

arXiv2009

Outlier Elimination for Robust Ellipse and Ellipsoid Fitting

In this paper, an outlier elimination algorithm for ellipse/ellipsoid fitting is proposed. This two-stage algorithm employs a proximity-based outlier detection algorithm (using the graph Laplacian), followed by a model-based outlier detection algorithm similar to random sample consensus (RANSAC). These two stages compensate for each other so that outliers of various types can be eliminated with reasonable computation. The outlier elimination algorithm considerably improves the robustness of ellipse/ellipsoid fitting as demonstrated by simulations.

stat.ME↗

arXiv2009

Cooperative Training for Attribute-Distributed Data: Trade-off Between Data Transmission and Performance

This paper introduces a modeling framework for distributed regression with agents/experts observing attribute-distributed data (heterogeneous data). Under this model, a new algorithm, the iterative covariance optimization algorithm (ICOA), is designed to reshape the covariance matrix of the training residuals of individual agents so that the linear combination of the individual estimators minimizes the ensemble training error. Moreover, a scheme (Minimax Protection) is designed to provide a trade-off between the number of data instances transmitted among the agents and the performance of the ensemble estimator without undermining the convergence of the algorithm. This scheme also provides an upper bound (with high probability) on the test error of the ensemble estimator. The efficacy of ICOA combined with Minimax Protection and the comparison between the upper bound and actual performance are both demonstrated by simulations.

cs.DC↗

arXiv2009

Collaborative Training in Sensor Networks: A graphical model approach

Graphical models have been widely applied in solving distributed inference problems in sensor networks. In this paper, the problem of coordinating a network of sensors to train a unique ensemble estimator under communication constraints is discussed. The information structure of graphical models with specific potential functions is employed, and this thus converts the collaborative training task into a problem of local training plus global inference. Two important classes of algorithms of graphical model inference, message-passing algorithm and sampling algorithm, are employed to tackle low-dimensional, parametrized and high-dimensional, non-parametrized problems respectively. The efficacy of this approach is demonstrated by concrete examples.

cs.DC↗

arXiv2009

Multicasting in Large Wireless Networks: Bounds on the Minimum Energy per Bit

We consider scaling laws for maximal energy efficiency of communicating a message to all the nodes in a wireless network, as the number of nodes in the network becomes large. Two cases of large wireless networks are studied -- dense random networks and constant density (extended) random networks. In addition, we also study finite size regular networks in order to understand how regularity in node placement affects energy consumption. We first establish an information-theoretic lower bound on the minimum energy per bit for multicasting in arbitrary wireless networks when the channel state information is not available at the transmitters. Upper bounds are obtained by constructing a simple flooding scheme that requires no information at the receivers about the channel states or the locations and identities of the nodes. The gap between the upper and lower bounds is only a constant factor for dense random networks and regular networks, and differs by a poly-logarithmic factor for extended random networks. Furthermore, we show that the proposed upper and lower bounds for random networks hold almost surely in the node locations as the number of nodes approaches infinity.

cs.IT↗

arXiv2008

Dimensionally Distributed Learning: Models and Algorithm

This paper introduces a framework for regression with dimensionally distributed data with a fusion center. A cooperative learning algorithm, the iterative conditional expectation algorithm (ICEA), is designed within this framework. The algorithm can effectively discover linear combinations of individual estimators trained by each agent without transferring and storing large amount of data amongst the agents and the fusion center. The convergence of ICEA is explored. Specifically, for a two agent system, each complete round of ICEA is guaranteed to be a non-expansive map on the function space of each agent. The advantages and limitations of ICEA are also discussed for data sets with various distributions and various hidden rules. Moreover, several techniques are also designed to leverage the algorithm to effectively learn more complex hidden rules that are not linearly decomposable.

cs.IT↗

arXiv2007

Regression estimation from an individual stable sequence

We consider univariate regression estimation from an individual (non-random) sequence $(x_1,y_1),(x_2,y_2), ... \in \real \times \real$, which is stable in the sense that for each interval $A \subseteq \real$, (i) the limiting relative frequency of $A$ under $x_1, x_2, ...$ is governed by an unknown probability distribution $μ$, and (ii) the limiting average of those $y_i$ with $x_i \in A$ is governed by an unknown regression function $m(\cdot)$. A computationally simple scheme for estimating $m(\cdot)$ is exhibited, and is shown to be $L_2$ consistent for stable sequences $\{(x_i,y_i)\}$ such that $\{y_i\}$ is bounded and there is a known upper bound for the variation of $m(\cdot)$ on intervals of the form $(-i,i]$, $i \geq 1$. Complementing this positive result, it is shown that there is no consistent estimation scheme for the family of stable sequences whose regression functions have finite variation, even under the restriction that $x_i \in [0,1]$ and $y_i$ is binary-valued.

math.PR↗

arXiv2007

Density estimation from an individual numerical sequence

This paper considers estimation of a univariate density from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known upper bound for the variation of the density on an increasing sequence of intervals. A simple estimation scheme is proposed, and is shown to be $L_1$ consistent when (i) and (ii) apply. In addition it is shown that there is no consistent estimation scheme for the set of individual sequences satisfying only condition (i).

math.PR↗

arXiv2007

A Better Good-Turing Estimator for Sequence Probabilities

We consider the problem of estimating the probability of an observed string drawn i.i.d. from an unknown distribution. The key feature of our study is that the length of the observed string is assumed to be of the same order as the size of the underlying alphabet. In this setting, many letters are unseen and the empirical distribution tends to overestimate the probability of the observed letters. To overcome this problem, the traditional approach to probability estimation is to use the classical Good-Turing estimator. We introduce a natural scaling model and use it to show that the Good-Turing sequence probability estimator is not consistent. We then introduce a novel sequence probability estimator that is indeed consistent under the natural scaling model.

cs.IT↗

arXiv2006

Finite-Dimensional Bounds on Zm and Binary LDPC Codes with Belief Propagation Decoders

This paper focuses on finite-dimensional upper and lower bounds on decodable thresholds of Zm and binary low-density parity-check (LDPC) codes, assuming belief propagation decoding on memoryless channels. A concrete framework is presented, admitting systematic searches for new bounds. Two noise measures are considered: the Bhattacharyya noise parameter and the soft bit value for a maximum a posteriori probability (MAP) decoder on the uncoded channel. For Zm LDPC codes, an iterative m-dimensional bound is derived for m-ary-input/symmetric-output channels, which gives a sufficient stability condition for Zm LDPC codes and is complemented by a matched necessary stability condition introduced herein. Applications to coded modulation and to codes with non-equiprobable distributed codewords are also discussed. For binary codes, two new lower bounds are provided for symmetric channels, including a two-dimensional iterative bound and a one-dimensional non-iterative bound, the latter of which is the best known bound that is tight for binary symmetric channels (BSCs), and is a strict improvement over the bound derived by the channel degradation argument. By adopting the reverse channel perspective, upper and lower bounds on the decodable Bhattacharyya noise parameter are derived for non-symmetric channels, which coincides with the existing bound for symmetric channels.

cs.IT↗

arXiv2006

Exhausting Error-Prone Patterns in LDPC Codes

It is proved in this work that exhaustively determining bad patterns in arbitrary, finite low-density parity-check (LDPC) codes, including stopping sets for binary erasure channels (BECs) and trapping sets (also known as near-codewords) for general memoryless symmetric channels, is an NP-complete problem, and efficient algorithms are provided for codes of practical short lengths n~=500. By exploiting the sparse connectivity of LDPC codes, the stopping sets of size <=13 and the trapping sets of size <=11 can be efficiently exhaustively determined for the first time, and the resulting exhaustive list is of great importance for code analysis and finite code optimization. The featured tree-based narrowing search distinguishes this algorithm from existing ones for which inexhaustive methods are employed. One important byproduct is a pair of upper bounds on the bit-error rate (BER) & frame-error rate (FER) iterative decoding performance of arbitrary codes over BECs that can be evaluated for any value of the erasure probability, including both the waterfall and the error floor regions. The tightness of these upper bounds and the exhaustion capability of the proposed algorithm are proved when combining an optimal leaf-finding module with the tree-based search. These upper bounds also provide a worst-case-performance guarantee which is crucial to optimizing LDPC codes for extremely low error rate applications, e.g., optical/satellite communications. Extensive numerical experiments are conducted that include both randomly and algebraically constructed LDPC codes, the results of which demonstrate the superior efficiency of the exhaustion algorithm and its significant value for finite length code optimization.

cs.IT↗

arXiv2006

Strong Consistency of the Good-Turing Estimator

We consider the problem of estimating the total probability of all symbols that appear with a given frequency in a string of i.i.d. random variables with unknown distribution. We focus on the regime in which the block length is large yet no symbol appears frequently in the string. This is accomplished by allowing the distribution to change with the block length. Under a natural convergence assumption on the sequence of underlying distributions, we show that the total probabilities converge to a deterministic limit, which we characterize. We then show that the Good-Turing total probability estimator is strongly consistent.

cs.IT↗

arXiv2006

Upper Bounding the Performance of Arbitrary Finite LDPC Codes on Binary Erasure Channels

Assuming iterative decoding for binary erasure channels (BECs), a novel tree-based technique for upper bounding the bit error rates (BERs) of arbitrary, finite low-density parity-check (LDPC) codes is provided and the resulting bound can be evaluated for all operating erasure probabilities, including both the waterfall and the error floor regions. This upper bound can also be viewed as a narrowing search of stopping sets, which is an approach different from the stopping set enumeration used for lower bounding the error floor. When combined with optimal leaf-finding modules, this upper bound is guaranteed to be tight in terms of the asymptotic order. The Boolean framework proposed herein further admits a composite search for even tighter results. For comparison, a refinement of the algorithm is capable of exhausting all stopping sets of size <14 for irregular LDPC codes of length n=500, which requires approximately 1.67*10^25 trials if a brute force approach is taken. These experiments indicate that this upper bound can be used both as an analytical tool and as a deterministic worst-performance (error floor) guarantee, the latter of which is crucial to optimizing LDPC codes for extremely low BER applications, e.g., optical/satellite communications.

cs.IT↗