Homomorphic Sensing of Subspace Arrangements

Homomorphic sensing is a recent algebraic-geometric framework that studies the unique recovery of points in a linear subspace from their images under a given collection of linear maps. It has been successful in interpreting such a recovery in the case of permutations composed by coordinate projections, an important instance in applications known as unlabeled sensing, which models data that are out of order and have missing values. In this paper, we provide tighter and simpler conditions that guarantee the unique recovery for the single-subspace case, extend the result to the case of a subspace arrangement, and show that the unique recovery in a single subspace is locally stable under noise. We specialize our results to several examples of homomorphic sensing such as real phase retrieval and unlabeled sensing. In so doing, in a unified way, we obtain conditions that guarantee the unique recovery for those examples, typically known via diverse techniques in the literature, as well as novel conditions for sparse and unsigned versions of unlabeled sensing. Similarly, our noise result also implies that the unique recovery in unlabeled sensing is locally stable.Comment: 18 page

Motion-capture-based hand gesture recognition for computing and control

This dissertation focuses on the study and development of algorithms that enable the analysis and recognition of hand gestures in a motion capture environment. Central to this work is the study of unlabeled point sets in a more abstract sense. Evaluations of proposed methods focus on examining their generalization to users not encountered during system training. In an initial exploratory study, we compare various classification algorithms based upon multiple interpretations and feature transformations of point sets, including those based upon aggregate features (e.g. mean) and a pseudo-rasterization of the capture space. We find aggregate feature classifiers to be balanced across multiple users but relatively limited in maximum achievable accuracy. Certain classifiers based upon the pseudo-rasterization performed best among tested classification algorithms. We follow this study with targeted examinations of certain subproblems. For the first subproblem, we introduce the a fortiori expectation-maximization (AFEM) algorithm for computing the parameters of a distribution from which unlabeled, correlated point sets are presumed to be generated. Each unlabeled point is assumed to correspond to a target with independent probability of appearance but correlated positions. We propose replacing the expectation phase of the algorithm with a Kalman filter modified within a Bayesian framework to account for the unknown point labels which manifest as uncertain measurement matrices. We also propose a mechanism to reorder the measurements in order to improve parameter estimates. In addition, we use a state-of-the-art Markov chain Monte Carlo sampler to efficiently sample measurement matrices. In the process, we indirectly propose a constrained k-means clustering algorithm. Simulations verify the utility of AFEM against a traditional expectation-maximization algorithm in a variety of scenarios. In the second subproblem, we consider the application of positive definite kernels and the earth mover\u27s distance (END) to our work. Positive definite kernels are an important tool in machine learning that enable efficient solutions to otherwise difficult or intractable problems by implicitly linearizing the problem geometry. We develop a set-theoretic interpretation of ENID and propose earth mover\u27s intersection (EMI). a positive definite analog to ENID. We offer proof of EMD\u27s negative definiteness and provide necessary and sufficient conditions for ENID to be conditionally negative definite, including approximations that guarantee negative definiteness. In particular, we show that ENID is related to various min-like kernels. We also present a positive definite preserving transformation that can be applied to any kernel and can be used to derive positive definite EMD-based kernels, and we show that the Jaccard index is simply the result of this transformation applied to set intersection. Finally, we evaluate kernels based on EMI and the proposed transformation versus ENID in various computer vision tasks and show that END is generally inferior even with indefinite kernel techniques. Finally, we apply deep learning to our problem. We propose neural network architectures for hand posture and gesture recognition from unlabeled marker sets in a coordinate system local to the hand. As a means of ensuring data integrity, we also propose an extended Kalman filter for tracking the rigid pattern of markers on which the local coordinate system is based. We consider fixed- and variable-size architectures including convolutional and recurrent neural networks that accept unlabeled marker input. We also consider a data-driven approach to labeling markers with a neural network and a collection of Kalman filters. Experimental evaluations with posture and gesture datasets show promising results for the proposed architectures with unlabeled markers, which outperform the alternative data-driven labeling method

A Quantitative Methodology for Vetting Dark Network Intelligence Sources for Social Network Analysis

Social network analysis (SNA) is used by the DoD to describe and analyze social networks, leading to recommendations for operational decisions. However, social network models are constructed from various information sources of indeterminate reliability. Inclusion of unreliable information can lead to incorrect models resulting in flawed analysis and decisions. This research develops a methodology to assist the analyst by quantitatively identifying and categorizing information sources so that determinations on including or excluding provided data can be made. This research pursued three main thrusts. It consolidated binary similarity measures to determine social network information sources\u27 concordance and developed a methodology to select suitable measures dependent upon application considerations. A methodology was developed to assess the validity of individual sources of social network data. This methodology utilized source pairwise comparisons to measure information sources\u27 concordance and a weighting schema to account for sources\u27 unique perspectives of the underlying social network. Finally, the developed methodology was tested over a variety of generated networks with varying parameters in a design of experiments paradigm (DOE). Various factors relevant to conditions faced by SNA analysts potentially employing this methodology were examined. The DOE was comprised of a 24 full factorial design augmented with a nearly orthogonal Latin hypercube. A linear model was constructed using quantile regression to mitigate the non-normality of the error terms

An accurate analysis for guaranteed performance of multiprocessor streaming applications

Already for more than a decade, consumer electronic devices have been available for entertainment, educational, or telecommunication tasks based on multimedia streaming applications, i.e., applications that process streams of audio and video samples in digital form. Multimedia capabilities are expected to become more and more commonplace in portable devices. This leads to challenges with respect to cost efficiency and quality. This thesis contributes models and analysis techniques for improving the cost efficiency, and therefore also the quality, of multimedia devices. Portable consumer electronic devices should feature flexible functionality on the one hand and low power consumption on the other hand. Those two requirements are conflicting. Therefore, we focus on a class of hardware that represents a good trade-off between those two requirements, namely on domain-specific multiprocessor systems-on-chip (MP-SoC). Our research work contributes to dynamic (i.e., run-time) optimization of MP-SoC system metrics. The central question in this area is how to ensure that real-time constraints are satisfied and the metric of interest such as perceived multimedia quality or power consumption is optimized. In these cases, we speak of quality-of-service (QoS) and power management, respectively. In this thesis, we pursue real-time constraint satisfaction that is guaranteed by the system by construction and proven mainly based on analytical reasoning. That approach is often taken in real-time systems to ensure reliable performance. Therefore the performance analysis has to be conservative, i.e. it has to use pessimistic assumptions on the unknown conditions that can negatively influence the system performance. We adopt this hypothesis as the foundation of this work. Therefore, the subject of this thesis is the analysis of guaranteed performance for multimedia applications running on multiprocessors. It is very important to note that our conservative approach is essentially different from considering only the worst-case state of the system. Unlike the worst-case approach, our approach is dynamic, i.e. it makes use of run-time characteristics of the input data and the environment of the application. The main purpose of our performance analysis method is to guide the run-time optimization. Typically, a resource or quality manager predicts the execution time, i.e., the time it takes the system to process a certain number of input data samples. When the execution times get smaller, due to dependency of the execution time on the input data, the manager can switch the control parameter for the metric of interest such that the metric improves but the system gets slower. For power optimization, that means switching to a low-power mode. If execution times grow, the manager can set parameters so that the system gets faster. For QoS management, for example, the application can be switched to a different quality mode with some degradation in perceived quality. The real-time constraints are then never violated and the metrics of interest are kept as good as possible. Unfortunately, maintaining system metrics such as power and quality at the optimal level contradicts with our main requirement, i.e., providing performance guarantees, because for this one has to give up some quality or power consumption. Therefore, the performance analysis approach developed in this thesis is not only conservative, but also accurate, so that the optimization of the metric of interest does not suffer too much from conservativity. This is not trivial to realize when two factors are combined: parallel execution on multiple processors and dynamic variation of the data-dependent execution delays. We achieve the goal of conservative and accurate performance estimation for an important class of multiprocessor platforms and multimedia applications. Our performance analysis technique is realizable in practice in QoS or power management setups. We consider a generic MP-SoC platform that runs a dynamic set of applications, each application possibly using multiple processors. We assume that the applications are independent, although it is possible to relax this requirement in the future. To support real-time constraints, we require that the platform can provide guaranteed computation, communication and memory budgets for applications. Following important trends in system-on-chip communication, we support both global buses and networks-on-chip. We represent every application as a homogeneous synchronous dataflow (HSDF) graph, where the application tasks are modeled as graph nodes, called actors. We allow dynamic datadependent actor execution delays, which makes HSDF graphs very useful to express modern streaming applications. Our reason to consider HSDF graphs is that they provide a good basic foundation for analytical performance estimation. In this setup, this thesis provides three major contributions: 1. Given an application mapped to an MP-SoC platform, given the performance guarantees for the individual computation units (the processors) and the communication unit (the network-on-chip), and given constant actor execution delays, we derive the throughput and the execution time of the system as a whole. 2. Given a mapped application and platform performance guarantees as in the previous item, we extend our approach for constant actor execution delays to dynamic datadependent actor delays. 3. We propose a global implementation trajectory that starts from the application specification and goes through design-time and run-time phases. It uses an extension of the HSDF model of computation to reflect the design decisions made along the trajectory. We present our model and trajectory not only to put the first two contributions into the right context, but also to present our vision on different parts of the trajectory, to make a complete and consistent story. Our first contribution uses the idea of so-called IPC (inter-processor communication) graphs known from the literature, whereby a single model of computation (i.e., HSDF graphs) are used to model not only the computation units, but also the communication unit (the global bus or the network-on-chip) and the FIFO (first-in-first-out) buffers that form a ‘glue’ between the computation and communication units. We were the first to propose HSDF graph structures for modeling bounded FIFO buffers and guaranteed throughput network connections for the network-on-chip communication in MP-SoCs. As a result, our HSDF models enable the formalization of the on-chip FIFO buffer capacity minimization problem under a throughput constraint as a graph-theoretic problem. Using HSDF graphs to formalize that problem helps to find the performance bottlenecks in a given solution to this problem and to improve this solution. To demonstrate this, we use the JPEG decoder application case study. Also, we show that, assuming constant – worst-case for the given JPEG image – actor delays, we can predict execution times of JPEG decoding on two processors with an accuracy of 21%. Our second contribution is based on an extension of the scenario approach. This approach is based on the observation that the dynamic behavior of an application is typically composed of a limited number of sub-behaviors, i.e., scenarios, that have similar resource requirements, i.e., similar actor execution delays in the context of this thesis. The previous work on scenarios treats only single-processor applications or multiprocessor applications that do not exploit all the flexibility of the HSDF model of computation. We develop new scenario-based techniques in the context of HSDF graphs, to derive the timing overlap between different scenarios, which is very important to achieve good accuracy for general HSDF graphs executing on multiprocessors. We exploit this idea in an application case study – the MPEG-4 arbitrarily-shaped video decoder, and demonstrate execution time prediction with an average accuracy of 11%. To the best of our knowledge, for the given setup, no other existing performance technique can provide a comparable accuracy and at the same time performance guarantees

Bayesian inference for stable differential equation models with applications in computational neuroscience

Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations. The dynamics in these models are approximately linear around a stable fixed point of the system. We exploit this property to develop fast approximate methods for posterior inference. We first illustrate our approach using simulated EEG data on the Liley et al model, a mechanistic neural population model. Then we apply our methods to experimental EEG data from rats to estimate how parameters in the Liley et al model vary with level of isoflurane anaesthesia. More generally, stable differential equation models and the corresponding inference methods are useful for analysis of stationary time-series data. Compared to the existing state-of-the art, our methods are several orders of magnitude faster, and are particularly suited to analysis of long time-series (>10,000 time-points) and models of moderate dimension (10-50 state variables and 10-50 parameters.

CLADAG 2021 BOOK OF ABSTRACTS AND SHORT PAPERS

The book collects the short papers presented at the 13th Scientific Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society (SIS). The meeting has been organized by the Department of Statistics, Computer Science and Applications of the University of Florence, under the auspices of the Italian Statistical Society and the International Federation of Classification Societies (IFCS). CLADAG is a member of the IFCS, a federation of national, regional, and linguistically-based classification societies. It is a non-profit, non-political scientific organization, whose aims are to further classification research