Safe sets, network majority on weighted trees

Let G = (V, E) be a graph and let w : V → ℝ>0 be a positive weight function on the vertices of G. For every subset X of V, let w(X) ≔ ∑v∈Gw(v). A non-empty subset ∑ is a weighted safe set if, for every component C of the subgraph induced by S and every component D of G/S, we have w(C) ≥ w(D) whenever there is an edge between C and D. If the subgraph G(S) induced by a weighted safe set S is connected, then the set S is called a weighted connected safe set. In this article, we show that the problem of computing the minimum weight of a safe set is NP-hard for trees, even if the underlying tree is restricted to be a star, but it is polynomially solvable for paths. We also give an O(n log n) time 2-approximation algorithm for finding a weighted connected safe set with minimum weight in a weighted tree. Then, as a generalization of the concept of a minimum safe set, we define the concept of a parameterized infinite family of proper central subgraphs on weighted trees, whose polar ends are the vertex set of the tree and the centroid points. We show that each of these central subgraphs includes a centroid point. © 2017 Wiley Periodicals, Inc

Scalable secure multi-party network vulnerability analysis via symbolic optimization

Threat propagation analysis is a valuable tool in improving the cyber resilience of enterprise networks. As these networks are interconnected and threats can propagate not only within but also across networks, a holistic view of the entire network can reveal threat propagation trajectories unobservable from within a single enterprise. However, companies are reluctant to share internal vulnerability measurement data as it is highly sensitive and (if leaked) possibly damaging. Secure Multi-Party Computation (MPC) addresses this concern. MPC is a cryptographic technique that allows distrusting parties to compute analytics over their joint data while protecting its confidentiality. In this work we apply MPC to threat propagation analysis on large, federated networks. To address the prohibitively high performance cost of general-purpose MPC we develop two novel applications of optimizations that can be leveraged to execute many relevant graph algorithms under MPC more efficiently: (1) dividing the computation into separate stages such that the first stage is executed privately by each party without MPC and the second stage is an MPC computation dealing with a much smaller shared network, and (2) optimizing the second stage by treating the execution of the analysis algorithm as a symbolic expression that can be optimized to reduce the number of costly operations and subsequently executed under MPC.We evaluate the scalability of this technique by analyzing the potential for threat propagation on examples of network graphs and propose several directions along which this work can be expanded

Oversampling for Imbalanced Learning Based on K-Means and SMOTE

Learning from class-imbalanced data continues to be a common and challenging problem in supervised learning as standard classification algorithms are designed to handle balanced class distributions. While different strategies exist to tackle this problem, methods which generate artificial data to achieve a balanced class distribution are more versatile than modifications to the classification algorithm. Such techniques, called oversamplers, modify the training data, allowing any classifier to be used with class-imbalanced datasets. Many algorithms have been proposed for this task, but most are complex and tend to generate unnecessary noise. This work presents a simple and effective oversampling method based on k-means clustering and SMOTE oversampling, which avoids the generation of noise and effectively overcomes imbalances between and within classes. Empirical results of extensive experiments with 71 datasets show that training data oversampled with the proposed method improves classification results. Moreover, k-means SMOTE consistently outperforms other popular oversampling methods. An implementation is made available in the python programming language.Comment: 19 pages, 8 figure

Towards Data-Driven Autonomics in Data Centers

Continued reliance on human operators for managing data centers is a major impediment for them from ever reaching extreme dimensions. Large computer systems in general, and data centers in particular, will ultimately be managed using predictive computational and executable models obtained through data-science tools, and at that point, the intervention of humans will be limited to setting high-level goals and policies rather than performing low-level operations. Data-driven autonomics, where management and control are based on holistic predictive models that are built and updated using generated data, opens one possible path towards limiting the role of operators in data centers. In this paper, we present a data-science study of a public Google dataset collected in a 12K-node cluster with the goal of building and evaluating a predictive model for node failures. We use BigQuery, the big data SQL platform from the Google Cloud suite, to process massive amounts of data and generate a rich feature set characterizing machine state over time. We describe how an ensemble classifier can be built out of many Random Forest classifiers each trained on these features, to predict if machines will fail in a future 24-hour window. Our evaluation reveals that if we limit false positive rates to 5%, we can achieve true positive rates between 27% and 88% with precision varying between 50% and 72%. We discuss the practicality of including our predictive model as the central component of a data-driven autonomic manager and operating it on-line with live data streams (rather than off-line on data logs). All of the scripts used for BigQuery and classification analyses are publicly available from the authors' website.Comment: 12 pages, 6 figure

Coupling different methods for overcoming the class imbalance problem

Many classification problems must deal with imbalanced datasets where one class \u2013 the majority class \u2013 outnumbers the other classes. Standard classification methods do not provide accurate predictions in this setting since classification is generally biased towards the majority class. The minority classes are oftentimes the ones of interest (e.g., when they are associated with pathological conditions in patients), so methods for handling imbalanced datasets are critical. Using several different datasets, this paper evaluates the performance of state-of-the-art classification methods for handling the imbalance problem in both binary and multi-class datasets. Different strategies are considered, including the one-class and dimension reduction approaches, as well as their fusions. Moreover, some ensembles of classifiers are tested, in addition to stand-alone classifiers, to assess the effectiveness of ensembles in the presence of imbalance. Finally, a novel ensemble of ensembles is designed specifically to tackle the problem of class imbalance: the proposed ensemble does not need to be tuned separately for each dataset and outperforms all the other tested approaches. To validate our classifiers we resort to the KEEL-dataset repository, whose data partitions (training/test) are publicly available and have already been used in the open literature: as a consequence, it is possible to report a fair comparison among different approaches in the literature. Our best approach (MATLAB code and datasets not easily accessible elsewhere) will be available at https://www.dei.unipd.it/node/2357

COMET: A Recipe for Learning and Using Large Ensembles on Massive Data

COMET is a single-pass MapReduce algorithm for learning on large-scale data. It builds multiple random forest ensembles on distributed blocks of data and merges them into a mega-ensemble. This approach is appropriate when learning from massive-scale data that is too large to fit on a single machine. To get the best accuracy, IVoting should be used instead of bagging to generate the training subset for each decision tree in the random forest. Experiments with two large datasets (5GB and 50GB compressed) show that COMET compares favorably (in both accuracy and training time) to learning on a subsample of data using a serial algorithm. Finally, we propose a new Gaussian approach for lazy ensemble evaluation which dynamically decides how many ensemble members to evaluate per data point; this can reduce evaluation cost by 100X or more