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Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally convergent algorithm has found the globally optimal solution. When the problem is formulated in terms of maximizing the likelihood function under a statistical model for the measurements, one can construct a statistical test that a local maximum is in fact the global maximum. A one-sided test is proposed for the case that the statistical model is a member of the generalized location family of probability distributions, a condition often satisfied in imaging and other inverse problems. We propose a general method for improving the accuracy of the test by reparameterizing the likelihood function to embed its domain into a higher dimensional parameter space. We show that the proposed global maximum testing method results in improved accuracy and reduced computation for a physically-motivated joint-inverse problem arising in camera-blur estimation.

Lateral movement attacks are a serious threat to enterprise security. In these attacks, an attacker compromises a trusted user account to get a foothold into the enterprise network and uses it to attack other trusted users, increasingly gaining higher and higher privileges. Such lateral attacks are very hard to model because of the unwitting role that users play in the attack and even harder to detect and prevent because of their low and slow nature. In this paper, a theoretical framework is presented for modeling lateral movement attacks and for proposing a methodology for designing resilient cyber systems against such attacks. The enterprise is modeled as a tripartite graph capturing the interaction between users, machines, and applications, and a set of procedures is proposed to harden the network by increasing the cost of lateral movement. Strong theoretical guarantees on system resilience are established and experimentally validated for large enterprise networks., Technical report for the book chapter "Towards Cyber-Resiliency Metrics for Action Recommendations Against Lateral Movement Attacks" in the book "Industrial Control Systems Security and Resiliency: Practice and Theory" published by Springer, 2019

Objective: To develop multisensor-wearable-device sleep monitoring algorithms that are robust to health disruptions affecting sleep patterns. Methods: We develop an unsupervised transfer learning algorithm based on a multivariate hidden Markov model and Fisher's linear discriminant analysis, adaptively adjusting to sleep pattern shift by training on dynamics of sleep/wake states. The proposed algorithm operates, without requiring a priori information about true sleep/wake states, by establishing an initial training set with hidden Markov model and leveraging a taper window mechanism to learn the sleep pattern in an incremental fashion. Our domain-adaptation algorithm is applied to a dataset collected in a human viral challenge study to identify sleep/wake periods of both uninfected and infected participants. Results: The algorithm successfully detects sleep/wake sessions in subjects whose sleep patterns are disrupted by respiratory infection (H3N2 flu virus). Pre-symptomatic features based on the detected periods are found to be strongly predictive of both infection status (AUC = 0.844) and infection onset time (AUC = 0.885), indicating the effectiveness and usefulness of the algorithm. Conclusion: Our method can effectively detect sleep/wake states in the presence of sleep pattern shift. Significance: Utilizing integrated multisensor signal processing and adaptive training schemes, our algorithm is able to capture key sleep patterns in ambulatory monitoring, leading to better automated sleep assessment and prediction.

We propose a new topic modeling procedure that takes advantage of the fact that the Latent Dirichlet Allocation (LDA) log likelihood function is asymptotically equivalent to the logarithm of the volume of the topic simplex. This allows topic modeling to be reformulated as finding the probability simplex that minimizes its volume and encloses the documents that are represented as distributions over words. A convex relaxation of the minimum volume topic model optimization is proposed, and it is shown that the relaxed problem has the same global minimum as the original problem under the separability assumption and the sufficiently scattered assumption introduced by Arora et al. (2013) and Huang et al. (2016). A locally convergent alternating direction method of multipliers (ADMM) approach is introduced for solving the relaxed minimum volume problem. Numerical experiments illustrate the benefits of our approach in terms of computation time and topic recovery performance., Accepted in AISTATS 2019

Feature selection and reducing the dimensionality of data is an essential step in data analysis. In this work, we propose a new criterion for feature selection that is formulated as conditional information between features given the labeled variable. Instead of using the standard mutual information measure based on Kullback-Leibler divergence, we use our proposed criterion to filter out redundant features for the purpose of multiclass classification. This approach results in an efficient and fast non-parametric implementation of feature selection as it can be directly estimated using a geometric measure of dependency, the global Friedman-Rafsky (FR) multivariate run test statistic constructed by a global minimal spanning tree (MST). We demonstrate the advantages of our proposed feature selection approach through simulation. In addition the proposed feature selection method is applied to the MNIST data set., 5 pages, 3 Figures, 1 Table

Network data often arises via a series of structured interactions among a population of constituent elements. E-mail exchanges, for example, have a single sender followed by potentially multiple receivers. Scientific articles, on the other hand, may have multiple subject areas and multiple authors. We introduce hierarchical edge exchangeable models for the study of these structured interaction networks. In particular, we introduce the hierarchical vertex components model as a canonical example, which partially pools information via a latent, shared population-level distribution. Theoretical analysis and supporting simulations provide clear model interpretation, and establish global sparsity and power-law degree distribution. A computationally tractable Gibbs algorithm is derived. We demonstrate the model on both the Enron e-mail dataset and an ArXiv dataset, showing goodness of fit of the model via posterior predictive validation.

Online Streaming Feature Selection (OSFS) is a sequential learning problem where individual features across all samples are made available to algorithms in a streaming fashion. In this work, firstly, we assert that OSFS's main assumption of having data from all the samples available at runtime is unrealistic and introduce a new setting where features and samples are streamed concurrently called OSFS with Streaming Samples (OSFS-SS). Secondly, the primary OSFS method, SAOLA utilizes an unbounded mutual information measure and requires multiple comparison steps between the stored and incoming feature sets to evaluate a feature's importance. We introduce Geometric Online Adaption, an algorithm that requires relatively less feature comparison steps and uses a bounded conditional geometric dependency measure. Our algorithm outperforms several OSFS baselines including SAOLA on a variety of datasets. We also extend SAOLA to work in the OSFS-SS setting and show that GOA continues to achieve the best results. Thirdly, the current paradigm of the OSFS algorithm comparison is flawed. Algorithms are measured by comparing the number of features used and the accuracy obtained by the learner, two properties that are fundamentally at odds with one another. Without fixing a limit on either of these properties, the qualities of features obtained by different algorithms are incomparable. We try to rectify this inconsistency by fixing the maximum number of features available to the learner and comparing algorithms in terms of their accuracy. Additionally, we characterize the behaviour of SAOLA and GOA on feature sets derived from popular deep convolutional featurizers., Comment: 10 page, 5 figures, 4 tables

We address the problem of learning to benchmark the best achievable classifier performance. In this problem the objective is to establish statistically consistent estimates of the Bayes misclassification error rate without having to learn a Bayes-optimal classifier. Our learning to benchmark framework improves on previous work on learning bounds on Bayes misclassification rate since it learns the {\it exact} Bayes error rate instead of a bound on error rate. We propose a benchmark learner based on an ensemble of $\epsilon$-ball estimators and Chebyshev approximation. Under a smoothness assumption on the class densities we show that our estimator achieves an optimal (parametric) mean squared error (MSE) rate of $O(N^{-1})$, where $N$ is the number of samples. Experiments on both simulated and real datasets establish that our proposed benchmark learning algorithm produces estimates of the Bayes error that are more accurate than previous approaches for learning bounds on Bayes error probability., Comment: 34 pages

Consider a query-based data acquisition problem that aims to recover the values of $k$ binary variables from parity (XOR) measurements of chosen subsets of the variables. Assume the response model where only a randomly selected subset of the measurements is received. We propose a method for designing a sequence of queries so that the variables can be identified with high probability using as few ($n$) measurements as possible. We define the query difficulty $\bar{d}$ as the average size of the query subsets and the sample complexity $n$ as the minimum number of measurements required to attain a given recovery accuracy. We obtain fundamental trade-offs between recovery accuracy, query difficulty, and sample complexity. In particular, the necessary and sufficient sample complexity required for recovering all $k$ variables with high probability is $n = c_0 \max\{k, (k \log k)/\bar{d}\}$ and the sample complexity for recovering a fixed proportion $(1-\delta)k$ of the variables for $\delta=o(1)$ is $n = c_1\max\{k, (k \log(1/\delta))/\bar{d}\}$, where $c_0, c_1>0$., Comment: 26 pages, 4 figures

Scaling up robot swarms to collectives of hundreds or even thousands without sacrificing sensing, processing, and locomotion capabilities is a challenging problem. Low-cost robots are potentially scalable, but the majority of existing systems have limited capabilities, and these limitations substantially constrain the type of experiments that could be performed by robotics researchers. Instead of adding functionality by adding more components and therefore increasing the cost, we demonstrate how low-cost hardware can be used beyond its standard functionality. We systematically review 15 swarm robotic systems and analyse their sensing capabilities by applying a general sensor model from the sensing and measurement community. This work is based on the HoverBot system. A HoverBot is a levitating circuit board that manoeuvres by pulling itself towards magnetic anchors that are embedded into the robot arena. We show that HoverBot’s magnetic field readouts from its Hall-effect sensor can be associated to successful movement, robot rotation and collision measurands. We build a time series classifier based on these magnetic field readouts. We modify and apply signal processing techniques to enable the online classification of the time-variant magnetic field measurements on HoverBot’s low-cost microcontroller. We enabled HoverBot with successful movement, rotation, and collision sensing capabilities by utilising its single Hall-effect sensor. We discuss how our classification method could be applied to other sensors to increase a robot’s functionality while retaining its cost.