arXiv subjects

Lalitha Sankar

Publications and source records attributed to Lalitha Sankar.

At least 55 records · Page 3Linked to original sources

arXiv2022

A Machine Learning Framework for Event Identification via Modal Analysis of PMU Data

Power systems are prone to a variety of events (e.g. line trips and generation loss) and real-time identification of such events is crucial in terms of situational awareness, reliability, and security. Using measurements from multiple synchrophasors, i.e., phasor measurement units (PMUs), we propose to identify events by extracting features based on modal dynamics. We combine such traditional physics-based feature extraction methods with machine learning to distinguish different event types. Including all measurement channels at each PMU allows exploiting diverse features but also requires learning classification models over a high-dimensional space. To address this issue, various feature selection methods are implemented to choose the best subset of features. Using the obtained subset of features, we investigate the performance of two well-known classification models, namely, logistic regression (LR) and support vector machines (SVM) to identify generation loss and line trip events in two datasets. The first dataset is obtained from simulated generation loss and line trip events in the Texas 2000-bus synthetic grid. The second is a proprietary dataset with labeled events obtained from a large utility in the USA involving measurements from nearly 500 PMUs. Our results indicate that the proposed framework is promising for identifying the two types of events.

eess.SY↗

arXiv2022

PMU Tracker: A Visualization Platform for Epicentric Event Propagation Analysis in the Power Grid

The electrical power grid is a critical infrastructure, with disruptions in transmission having severe repercussions on daily activities, across multiple sectors. To identify, prevent, and mitigate such events, power grids are being refurbished as 'smart' systems that include the widespread deployment of GPS-enabled phasor measurement units (PMUs). PMUs provide fast, precise, and time-synchronized measurements of voltage and current, enabling real-time wide-area monitoring and control. However, the potential benefits of PMUs, for analyzing grid events like abnormal power oscillations and load fluctuations, are hindered by the fact that these sensors produce large, concurrent volumes of noisy data. In this paper, we describe working with power grid engineers to investigate how this problem can be addressed from a visual analytics perspective. As a result, we have developed PMU Tracker, an event localization tool that supports power grid operators in visually analyzing and identifying power grid events and tracking their propagation through the power grid's network. As a part of the PMU Tracker interface, we develop a novel visualization technique which we term an epicentric cluster dendrogram, which allows operators to analyze the effects of an event as it propagates outwards from a source location. We robustly validate PMU Tracker with: (1) a usage scenario demonstrating how PMU Tracker can be used to analyze anomalous grid events, and (2) case studies with power grid operators using a real-world interconnection dataset. Our results indicate that PMU Tracker effectively supports the analysis of power grid events; we also demonstrate and discuss how PMU Tracker's visual analytics approach can be generalized to other domains composed of time-varying networks with epicentric event characteristics.

cs.HC↗

arXiv2022

The Saddle-Point Accountant for Differential Privacy

We introduce a new differential privacy (DP) accountant called the saddle-point accountant (SPA). SPA approximates privacy guarantees for the composition of DP mechanisms in an accurate and fast manner. Our approach is inspired by the saddle-point method -- a ubiquitous numerical technique in statistics. We prove rigorous performance guarantees by deriving upper and lower bounds for the approximation error offered by SPA. The crux of SPA is a combination of large-deviation methods with central limit theorems, which we derive via exponentially tilting the privacy loss random variables corresponding to the DP mechanisms. One key advantage of SPA is that it runs in constant time for the $n$-fold composition of a privacy mechanism. Numerical experiments demonstrate that SPA achieves comparable accuracy to state-of-the-art accounting methods with a faster runtime.

cs.CR↗

arXiv2022

Parameter Estimation in Ill-conditioned Low-inertia Power Systems

This paper examines model parameter estimation in dynamic power systems whose governing electro-mechanical equations are ill-conditioned or singular. This ill-conditioning is because of converter-interfaced power systems generators' zero or small inertia contribution. Consequently, the overall system inertia decreases, resulting in low-inertia power systems. We show that the standard state-space model based on least squares or subspace estimators fails to exist for these models. We overcome this challenge by considering a least-squares estimator directly on the coupled swing-equation model but not on its transformed first-order state-space form. We specifically focus on estimating inertia (mechanical and virtual) and damping constants, although our method is general enough for estimating other parameters. Our theoretical analysis highlights the role of network topology on the parameter estimates of an individual generator. For generators with greater connectivity, estimation of the associated parameters is more susceptible to variations in other generator states. Furthermore, we numerically show that estimating the parameters by ignoring their ill-conditioning aspects yields highly unreliable results.

eess.SY↗

arXiv2022

Generation of Synthetic Multi-Resolution Time Series Load Data

The availability of large datasets is crucial for the development of new power system applications and tools; unfortunately, very few are publicly and freely available. We designed an end-to-end generative framework for the creation of synthetic bus-level time-series load data for transmission networks. The model is trained on a real dataset of over 70 Terabytes of synchrophasor measurements spanning multiple years. Leveraging a combination of principal component analysis and conditional generative adversarial network models, the scheme we developed allows for the generation of data at varying sampling rates (up to a maximum of 30 samples per second) and ranging in length from seconds to years. The generative models are tested extensively to verify that they correctly capture the diverse characteristics of real loads. Finally, we develop an open-source tool called LoadGAN which gives researchers access to the fully trained generative models via a graphical interface.

eess.SY↗

arXiv2022

Lower Bounds for the MMSE via Neural Network Estimation and Their Applications to Privacy

The minimum mean-square error (MMSE) achievable by optimal estimation of a random variable $Y\in\mathbb{R}$ given another random variable $X\in\mathbb{R}^{d}$ is of much interest in a variety of statistical settings. In the context of estimation-theoretic privacy, the MMSE has been proposed as an information leakage measure that captures the ability of an adversary in estimating $Y$ upon observing $X$. In this paper we establish provable lower bounds for the MMSE based on a two-layer neural network estimator of the MMSE and the Barron constant of an appropriate function of the conditional expectation of $Y$ given $X$. Furthermore, we derive a general upper bound for the Barron constant that, when $X\in\mathbb{R}$ is post-processed by the additive Gaussian mechanism and $Y$ is binary, produces order optimal estimates in the large noise regime. In order to obtain numerical lower bounds for the MMSE in some concrete applications, we introduce an efficient optimization process that approximates the value of the proposed neural network estimator. Overall, we provide an effective machinery to obtain provable lower bounds for the MMSE.

cs.IT↗

arXiv2022

Cactus Mechanisms: Optimal Differential Privacy Mechanisms in the Large-Composition Regime

Most differential privacy mechanisms are applied (i.e., composed) numerous times on sensitive data. We study the design of optimal differential privacy mechanisms in the limit of a large number of compositions. As a consequence of the law of large numbers, in this regime the best privacy mechanism is the one that minimizes the Kullback-Leibler divergence between the conditional output distributions of the mechanism given two different inputs. We formulate an optimization problem to minimize this divergence subject to a cost constraint on the noise. We first prove that additive mechanisms are optimal. Since the optimization problem is infinite dimensional, it cannot be solved directly; nevertheless, we quantize the problem to derive near-optimal additive mechanisms that we call "cactus mechanisms" due to their shape. We show that our quantization approach can be arbitrarily close to an optimal mechanism. Surprisingly, for quadratic cost, the Gaussian mechanism is strictly sub-optimal compared to this cactus mechanism. Finally, we provide numerical results which indicate that cactus mechanism outperforms the Gaussian mechanism for a finite number of compositions.

cs.CR↗

arXiv2022

Generating Fair Universal Representations using Adversarial Models

We present a data-driven framework for learning fair universal representations (FUR) that guarantee statistical fairness for any learning task that may not be known a priori. Our framework leverages recent advances in adversarial learning to allow a data holder to learn representations in which a set of sensitive attributes are decoupled from the rest of the dataset. We formulate this as a constrained minimax game between an encoder and an adversary where the constraint ensures a measure of usefulness (utility) of the representation. The resulting problem is that of censoring, i.e., finding a representation that is least informative about the sensitive attributes given a utility constraint. For appropriately chosen adversarial loss functions, our censoring framework precisely clarifies the optimal adversarial strategy against strong information-theoretic adversaries; it also achieves the fairness measure of demographic parity for the resulting constrained representations. We evaluate the performance of our proposed framework on both synthetic and publicly available datasets. For these datasets, we use two tradeoff measures: censoring vs. representation fidelity and fairness vs. utility for downstream tasks, to amply demonstrate that multiple sensitive features can be effectively censored even as the resulting fair representations ensure accuracy for multiple downstream tasks.

cs.LG↗

arXiv2022

$α$-GAN: Convergence and Estimation Guarantees

We prove a two-way correspondence between the min-max optimization of general CPE loss function GANs and the minimization of associated $f$-divergences. We then focus on $α$-GAN, defined via the $α$-loss, which interpolates several GANs (Hellinger, vanilla, Total Variation) and corresponds to the minimization of the Arimoto divergence. We show that the Arimoto divergences induced by $α$-GAN equivalently converge, for all $α\in \mathbb{R}_{>0}\cup\{\infty\}$. However, under restricted learning models and finite samples, we provide estimation bounds which indicate diverse GAN behavior as a function of $α$. Finally, we present empirical results on a toy dataset that highlight the practical utility of tuning the $α$ hyperparameter.

cs.LG↗

arXiv2022

A Variational Formula for Infinity-Rényi Divergence with Applications to Information Leakage

We present a variational characterization for the Rényi divergence of order infinity. Our characterization is related to guessing: the objective functional is a ratio of maximal expected values of a gain function applied to the probability of correctly guessing an unknown random variable. An important aspect of our variational characterization is that it remains agnostic to the particular gain function considered, as long as it satisfies some regularity conditions. Also, we define two variants of a tunable measure of information leakage, the maximal $α$-leakage, and obtain closed-form expressions for these information measures by leveraging our variational characterization.

cs.IT↗

arXiv2022

Being Properly Improper

Properness for supervised losses stipulates that the loss function shapes the learning algorithm towards the true posterior of the data generating distribution. Unfortunately, data in modern machine learning can be corrupted or twisted in many ways. Hence, optimizing a proper loss function on twisted data could perilously lead the learning algorithm towards the twisted posterior, rather than to the desired clean posterior. Many papers cope with specific twists (e.g., label/feature/adversarial noise), but there is a growing need for a unified and actionable understanding atop properness. Our chief theoretical contribution is a generalization of the properness framework with a notion called twist-properness, which delineates loss functions with the ability to "untwist" the twisted posterior into the clean posterior. Notably, we show that a nontrivial extension of a loss function called $α$-loss, which was first introduced in information theory, is twist-proper. We study the twist-proper $α$-loss under a novel boosting algorithm, called PILBoost, and provide formal and experimental results for this algorithm. Our overarching practical conclusion is that the twist-proper $α$-loss outperforms the proper $\log$-loss on several variants of twisted data.

cs.LG↗

arXiv2022

Localization and Estimation of Unknown Forced Inputs: A Group LASSO Approach

We model and study the problem of localizing a set of sparse forcing inputs for linear dynamical systems from noisy measurements when the initial state is unknown. This problem is of particular relevance to detecting forced oscillations in electric power networks. We express measurements as an additive model comprising the initial state and inputs grouped over time, both expanded in terms of the basis functions (i.e., impulse response coefficients). Using this model, with probabilistic guarantees, we recover the locations and simultaneously estimate the initial state and forcing inputs using a variant of the group LASSO (linear absolute shrinkage and selection operator) method. Specifically, we provide a tight upper bound on: (i) the probability that the group LASSO estimator wrongly identifies the source locations, and (ii) the $\ell_2$-norm of the estimation error. Our bounds explicitly depend upon the length of the measurement horizon, the noise statistics, the number of inputs and sensors, and the singular values of impulse response matrices. Our theoretical analysis is one of the first to provide a complete treatment for the group LASSO estimator for linear dynamical systems under input-to-output delay assumptions. Finally, we validate our results on synthetic models and the IEEE 68-bus, 16-machine system.

math.OC↗

arXiv2022

A Complex-LASSO Approach for Localizing Forced Oscillations in Power Systems

We study the problem of localizing multiple sources of forced oscillations (FOs) and estimating their characteristics, such as frequency, phase, and amplitude, using noisy PMU measurements. For each source location, we model the input oscillation as a sum of unknown sinusoidal terms. This allows us to obtain a linear relationship between measurements and the inputs at the unknown sinusoids' frequencies in the frequency domain. We determine these frequencies by thresholding the empirical spectrum of the noisy measurements. Assuming sparsity in the number of FOs' locations and the number of sinusoids at each location, we cast the location recovery problem as an $\ell_1$-regularized least squares problem in the complex domain -- i.e., complex-LASSO (linear shrinkage and selection operator). We numerically solve this optimization problem using the complex-valued coordinate descent method, and show its efficiency on the IEEE 68-bus, 16 machine and WECC 179-bus, 29-machine systems.

stat.AP↗

arXiv2021

Realizing GANs via a Tunable Loss Function

We introduce a tunable GAN, called $α$-GAN, parameterized by $α\in (0,\infty]$, which interpolates between various $f$-GANs and Integral Probability Metric based GANs (under constrained discriminator set). We construct $α$-GAN using a supervised loss function, namely, $α$-loss, which is a tunable loss function capturing several canonical losses. We show that $α$-GAN is intimately related to the Arimoto divergence, which was first proposed by Österriecher (1996), and later studied by Liese and Vajda (2006). We also study the convergence properties of $α$-GAN. We posit that the holistic understanding that $α$-GAN introduces will have practical benefits of addressing both the issues of vanishing gradients and mode collapse.

cs.LG↗

arXiv2021

Evaluating Multiple Guesses by an Adversary via a Tunable Loss Function

We consider a problem of guessing, wherein an adversary is interested in knowing the value of the realization of a discrete random variable $X$ on observing another correlated random variable $Y$. The adversary can make multiple (say, $k$) guesses. The adversary's guessing strategy is assumed to minimize $α$-loss, a class of tunable loss functions parameterized by $α$. It has been shown before that this loss function captures well known loss functions including the exponential loss ($α=1/2$), the log-loss ($α=1$) and the $0$-$1$ loss ($α=\infty$). We completely characterize the optimal adversarial strategy and the resulting expected $α$-loss, thereby recovering known results for $α=\infty$. We define an information leakage measure from the $k$-guesses setup and derive a condition under which the leakage is unchanged from a single guess.

cs.IT↗

arXiv2021

Synthetic Time-Series Load Data via Conditional Generative Adversarial Networks

A framework for the generation of synthetic time-series transmission-level load data is presented. Conditional generative adversarial networks are used to learn the patterns of a real dataset of hourly-sampled week-long load profiles and generate unique synthetic profiles on demand, based on the season and type of load required. Extensive testing of the generative model is performed to verify that the synthetic data fully captures the characteristics of real loads and that it can be used for downstream power system and/or machine learning applications.

eess.SY↗

arXiv2021

A Verifiable Framework for Cyber-Physical Attacks and Countermeasures in a Resilient Electric Power Grid

In this paper, we investigate the feasibility and physical consequences of cyber attacks against energy management systems (EMS). Within this framework, we have designed a complete simulation platform to emulate realistic EMS operations: it includes state estimation (SE), real-time contingency analysis (RTCA), and security constrained economic dispatch (SCED). This software platform allowed us to achieve two main objectives: 1) to study the cyber vulnerabilities of an EMS and understand their consequences on the system, and 2) to formulate and implement countermeasures against cyber-attacks exploiting these vulnerabilities. Our results show that the false data injection attacks against state estimation described in the literature do not easily cause base-case overflows because of the conservatism introduced by RTCA. For a successful attack, a more sophisticated model that includes all of the EMS blocks is needed; even in this scenario, only post-contingency violations can be achieved. Nonetheless, we propose several countermeasures that can detect changes due to cyber-attacks and limit their impact on the system.

eess.SY↗

arXiv2021

Three Variants of Differential Privacy: Lossless Conversion and Applications

We consider three different variants of differential privacy (DP), namely approximate DP, Rényi DP (RDP), and hypothesis test DP. In the first part, we develop a machinery for optimally relating approximate DP to RDP based on the joint range of two $f$-divergences that underlie the approximate DP and RDP. In particular, this enables us to derive the optimal approximate DP parameters of a mechanism that satisfies a given level of RDP. As an application, we apply our result to the moments accountant framework for characterizing privacy guarantees of noisy stochastic gradient descent (SGD). When compared to the state-of-the-art, our bounds may lead to about 100 more stochastic gradient descent iterations for training deep learning models for the same privacy budget. In the second part, we establish a relationship between RDP and hypothesis test DP which allows us to translate the RDP constraint into a tradeoff between type I and type II error probabilities of a certain binary hypothesis test. We then demonstrate that for noisy SGD our result leads to tighter privacy guarantees compared to the recently proposed $f$-DP framework for some range of parameters.

cs.IT↗