Machine Learning Methods for Attack Detection in the Smart Grid

Attack detection problems in the smart grid are posed as statistical learning problems for different attack scenarios in which the measurements are observed in batch or online settings. In this approach, machine learning algorithms are used to classify measurements as being either secure or attacked. An attack detection framework is provided to exploit any available prior knowledge about the system and surmount constraints arising from the sparse structure of the problem in the proposed approach. Well-known batch and online learning algorithms (supervised and semi-supervised) are employed with decision and feature level fusion to model the attack detection problem. The relationships between statistical and geometric properties of attack vectors employed in the attack scenarios and learning algorithms are analyzed to detect unobservable attacks using statistical learning methods. The proposed algorithms are examined on various IEEE test systems. Experimental analyses show that machine learning algorithms can detect attacks with performances higher than the attack detection algorithms which employ state vector estimation methods in the proposed attack detection framework.Comment: 14 pages, 11 Figure

Communication-Efficient Algorithms For Distributed Optimization

This thesis is concerned with the design of distributed algorithms for solving optimization problems. We consider networks where each node has exclusive access to a cost function, and design algorithms that make all nodes cooperate to find the minimum of the sum of all the cost functions. Several problems in signal processing, control, and machine learning can be posed as such optimization problems. Given that communication is often the most energy-consuming operation in networks, it is important to design communication-efficient algorithms. The main contributions of this thesis are a classification scheme for distributed optimization and a set of corresponding communication-efficient algorithms. The class of optimization problems we consider is quite general, since each function may depend on arbitrary components of the optimization variable, and not necessarily on all of them. In doing so, we go beyond the common assumption in distributed optimization and create additional structure that can be used to reduce the number of communications. This structure is captured by our classification scheme, which identifies easier instances of the problem, for example the standard distributed optimization problem, where all functions depend on all the components of the variable. In our algorithms, no central node coordinates the network, all the communications occur between neighboring nodes, and the data associated with each node is processed locally. We show several applications including average consensus, support vector machines, network flows, and several distributed scenarios for compressed sensing. We also propose a new framework for distributed model predictive control. Through extensive numerical experiments, we show that our algorithms outperform prior distributed algorithms in terms of communication-efficiency, even some that were specifically designed for a particular application.Comment: Thesis defended on October 10, 2013. Dual PhD degree from Carnegie Mellon University, PA, and Instituto Superior T\'ecnico, Lisbon, Portuga

Distributed stochastic optimization and learning

Abstract—We consider the problem of distributed stochastic optimization, where each of several machines has access to samples from the same source distribution, and the goal is to jointly optimize the expected objective w.r.t. the source distribution, minimizing: (1) overall runtime; (2) communi-cation costs; (3) number of samples used. We study this problem systematically, highlighting fundamental limitations, and differences versus distributed consensus problems where each machine has a different, independent, objective. We show how the best known guarantees are obtained by an accelerated mini-batched SGD approach, and contrast the runtime and sample costs of the approach with those of other distributed optimization algorithms. I

Hybrid-Parallel Parameter Estimation for Frequentist and Bayesian Models

Distributed algorithms in machine learning follow two main flavors: horizontal partitioning, where the data is distributed across multiple slaves and vertical partitioning, where the model parameters are partitioned across multiple machines. The main drawback of the former strategy is that the model parameters need to be replicated on every machine. This is problematic when the number of parameters is very large, and hence cannot fit in a single machine. This drawback of the latter strategy is that the data needs to be replicated on each machine, thus failing to scale to massive datasets.The goal of this thesis is to achieve the best of both worlds by partitioning both - the data as well as the model parameters, thus enabling the training of more sophisticated models on massive datasets. In order to do so, we exploit a structure that is observed in several machine learning models, which we term as \textit{Double-Separability}. Double-Separability basically means that the objective function of the model can be decomposed into independent sub-functions which can be computed independently. For distributed machine learning, this implies that both data and model parameters can partitioned across machines and stochastic updates for parameters can be carried out independently and without any locking. Furthermore, double-separability naturally lends itself to developing efficient asynchronous algorithms which enable computation and communication to happen in parallel, offering further speedup. Some machine learning models such as Matrix Factorization directly exhibit double-separability in their objective function, however the majority of models do not. My work explores techniques to reformulate the objective function of such models to cast them into double-separable form. Often this involves introducing additional auxiliary variables that have nice interpretations. In this direction, I have developed Hybrid Parallel algorithms for machine learning tasks that include {\it Latent Collaborative Retrieval}, {\it Multinomial Logistic Regression}, {\it Variational Inference for Mixture of Exponential Families} and {\it Factorization Machines}. The software resulting from this work are available for public use under an open-source license

Distributed Classification of Localization Attacks in Sensor Networks Using Exchange-Based Feature Extraction and Classifier

Secure localization under different forms of attack has become an essential task in wireless sensor networks. Despite the significant research efforts in detecting the malicious nodes, the problem of localization attack type recognition has not yet been well addressed. Motivated by this concern, we propose a novel exchange-based attack classification algorithm. This is achieved by a distributed expectation maximization extractor integrated with the PECPR-MKSVM classifier. First, the mixed distribution features based on the probabilistic modeling are extracted using a distributed expectation maximization algorithm. After feature extraction, by introducing the theory from support vector machine, an extensive contractive Peaceman-Rachford splitting method is derived to build the distributed classifier that diffuses the iteration calculation among neighbor sensors. To verify the efficiency of the distributed recognition scheme, four groups of experiments were carried out under various conditions. The average success rate of the proposed classification algorithm obtained in the presented experiments for external attacks is excellent and has achieved about 93.9% in some cases. These testing results demonstrate that the proposed algorithm can produce much greater recognition rate, and it can be also more robust and efficient even in the presence of excessive malicious scenario