Probabilistic Receiver Architecture Combining BP, MF, and EP for Multi-Signal Detection

Receiver algorithms which combine belief propagation (BP) with the mean field (MF) approximation are well-suited for inference of both continuous and discrete random variables. In wireless scenarios involving detection of multiple signals, the standard construction of the combined BP-MF framework includes the equalization or multi-user detection functions within the MF subgraph. In this paper, we show that the MF approximation is not particularly effective for multi-signal detection. We develop a new factor graph construction for application of the BP-MF framework to problems involving the detection of multiple signals. We then develop a low-complexity variant to the proposed construction in which Gaussian BP is applied to the equalization factors. In this case, the factor graph of the joint probability distribution is divided into three subgraphs: (i) a MF subgraph comprised of the observation factors and channel estimation, (ii) a Gaussian BP subgraph which is applied to multi-signal detection, and (iii) a discrete BP subgraph which is applied to demodulation and decoding. Expectation propagation is used to approximate discrete distributions with a Gaussian distribution and links the discrete BP and Gaussian BP subgraphs. The result is a probabilistic receiver architecture with strong theoretical justification which can be applied to multi-signal detection.Comment: 30 pages, 9 figure

A Spectral Framework for Anomalous Subgraph Detection

A wide variety of application domains are concerned with data consisting of entities and their relationships or connections, formally represented as graphs. Within these diverse application areas, a common problem of interest is the detection of a subset of entities whose connectivity is anomalous with respect to the rest of the data. While the detection of such anomalous subgraphs has received a substantial amount of attention, no application-agnostic framework exists for analysis of signal detectability in graph-based data. In this paper, we describe a framework that enables such analysis using the principal eigenspace of a graph's residuals matrix, commonly called the modularity matrix in community detection. Leveraging this analytical tool, we show that the framework has a natural power metric in the spectral norm of the anomalous subgraph's adjacency matrix (signal power) and of the background graph's residuals matrix (noise power). We propose several algorithms based on spectral properties of the residuals matrix, with more computationally expensive techniques providing greater detection power. Detection and identification performance are presented for a number of signal and noise models, including clusters and bipartite foregrounds embedded into simple random backgrounds as well as graphs with community structure and realistic degree distributions. The trends observed verify intuition gleaned from other signal processing areas, such as greater detection power when the signal is embedded within a less active portion of the background. We demonstrate the utility of the proposed techniques in detecting small, highly anomalous subgraphs in real graphs derived from Internet traffic and product co-purchases.Comment: In submission to the IEEE, 16 pages, 8 figure

Unsupervised Learning of Spike Patterns for Seizure Detection and Wavefront Estimation of High Resolution Micro Electrocorticographic ({\mu}ECoG) Data

For the past few years, we have developed flexible, active, multiplexed recording devices for high resolution recording over large, clinically relevant areas in the brain. While this technology has enabled a much higher-resolution view of the electrical activity of the brain, the analytical methods to process, categorize and respond to the huge volumes of seizure data produced by these devices have not yet been developed. In this work we proposed an unsupervised learning framework for spike analysis, which by itself reveals spike pattern. By applying advanced video processing techniques for separating a multi-channel recording into individual spike segments, unfolding the spike segments manifold and identifying natural clusters for spike patterns, we are able to find the common spike motion patterns. And we further explored using these patterns for more interesting and practical problems as seizure prediction and spike wavefront prediction. These methods have been applied to in-vivo feline seizure recordings and yielded promising results

Thresholds For Detecting An Anomalous Path From Noisy Environments

We consider the "searching for a trail in a maze" composite hypothesis testing problem, in which one attempts to detect an anomalous directed path in a lattice 2D box of side n based on observations on the nodes of the box. Under the signal hypothesis, one observes independent Gaussian variables of unit variance at all nodes, with zero, mean off the anomalous path and mean \mu_n on it. Under the null hypothesis, one observes i.i.d. standard Gaussians on all nodes. Arias-Castro et al. (2008) showed that if the unknown directed path under the signal hypothesis has known the initial location, then detection is possible (in the minimax sense) if \mu_n >> 1/\sqrt log n, while it is not possible if \mu_n << 1/ log n\sqrt log log n. In this paper, we show that this result continues to hold even when the initial location of the unknown path is not known. As is the case with Arias-Castro et al. (2008), the upper bound here also applies when the path is undirected. The improvement is achieved by replacing the linear detection statistic used in Arias-Castro et al. (2008) with a polynomial statistic, which is obtained by employing a multi-scale analysis on a quadratic statistic to bootstrap its performance. Our analysis is motivated by ideas developed in the context of the analysis of random polymers in Lacoin (2010)

Multiresolution Representations for Piecewise-Smooth Signals on Graphs

What is a mathematically rigorous way to describe the taxi-pickup distribution in Manhattan, or the profile information in online social networks? A deep understanding of representing those data not only provides insights to the data properties, but also benefits to many subsequent processing procedures, such as denoising, sampling, recovery and localization. In this paper, we model those complex and irregular data as piecewise-smooth graph signals and propose a graph dictionary to effectively represent those graph signals. We first propose the graph multiresolution analysis, which provides a principle to design good representations. We then propose a coarse-to-fine approach, which iteratively partitions a graph into two subgraphs until we reach individual nodes. This approach efficiently implements the graph multiresolution analysis and the induced graph dictionary promotes sparse representations piecewise-smooth graph signals. Finally, we validate the proposed graph dictionary on two tasks: approximation and localization. The empirical results show that the proposed graph dictionary outperforms eight other representation methods on six datasets, including traffic networks, social networks and point cloud meshes

Sparsity Learning Based Multiuser Detection in Grant-Free Massive-Device Multiple Access

In this work, we study the multiuser detection (MUD) problem for a grant-free massive-device multiple access (MaDMA) system, where a large number of single-antenna user devices transmit sporadic data to a multi-antenna base station (BS). Specifically, we put forth two MUD schemes, termed random sparsity learning multiuser detection (RSL-MUD) and structured sparsity learning multiuser detection (SSL-MUD) for the time-slotted and non-time-slotted grant-free MaDMA systems, respectively. In the time-slotted RSL-MUD scheme, active users generate and transmit data packets with random sparsity. In the non-time-slotted SSL-MUD scheme, we introduce a sliding-window-based detection framework, and the user signals in each observation window naturally exhibit structured sparsity. We show that by exploiting the sparsity embedded in the user signals, we can recover the user activity state, the channel, and the user data in a single phase, without using pilot signals for channel estimation and/or active user identification. To this end, we develop a message-passing based statistical inference framework for the BS to blindly detect the user data without any prior knowledge of the identities and the channel state information (CSI) of the active users. Simulation results show that our RSL-MUD and SSL-MUD schemes significantly outperform their counterpart schemes in both reducing the transmission overhead and improving the error behavior of the system.Comment: 12 pages, 9 figures, 3 table

Catching Loosely Synchronized Behavior in Face of Camouflage

Fraud has severely detrimental impacts on the business of social networks and other online applications. A user can become a fake celebrity by purchasing "zombie followers" on Twitter. A merchant can boost his reputation through fake reviews on Amazon. This phenomenon also conspicuously exists on Facebook, Yelp and TripAdvisor, etc. In all the cases, fraudsters try to manipulate the platform's ranking mechanism by faking interactions between the fake accounts they control and the target customers.Comment: Submitted to WWW 2019, Oct.201

SliceNDice: Mining Suspicious Multi-attribute Entity Groups with Multi-view Graphs

Given the reach of web platforms, bad actors have considerable incentives to manipulate and defraud users at the expense of platform integrity. This has spurred research in numerous suspicious behavior detection tasks, including detection of sybil accounts, false information, and payment scams/fraud. In this paper, we draw the insight that many such initiatives can be tackled in a common framework by posing a detection task which seeks to find groups of entities which share too many properties with one another across multiple attributes (sybil accounts created at the same time and location, propaganda spreaders broadcasting articles with the same rhetoric and with similar reshares, etc.) Our work makes four core contributions: Firstly, we posit a novel formulation of this task as a multi-view graph mining problem, in which distinct views reflect distinct attribute similarities across entities, and contextual similarity and attribute importance are respected. Secondly, we propose a novel suspiciousness metric for scoring entity groups given the abnormality of their synchronicity across multiple views, which obeys intuitive desiderata that existing metrics do not. Finally, we propose the SliceNDice algorithm which enables efficient extraction of highly suspicious entity groups, and demonstrate its practicality in production, in terms of strong detection performance and discoveries on Snapchat's large advertiser ecosystem (89% precision and numerous discoveries of real fraud rings), marked outperformance of baselines (over 97% precision/recall in simulated settings) and linear scalability.Comment: Published in Proceedings of 2019 IEEE 6th International Conference on Data Science and Advanced Analytics (DSAA

Signal Representations on Graphs: Tools and Applications

We present a framework for representing and modeling data on graphs. Based on this framework, we study three typical classes of graph signals: smooth graph signals, piecewise-constant graph signals, and piecewise-smooth graph signals. For each class, we provide an explicit definition of the graph signals and construct a corresponding graph dictionary with desirable properties. We then study how such graph dictionary works in two standard tasks: approximation and sampling followed with recovery, both from theoretical as well as algorithmic perspectives. Finally, for each class, we present a case study of a real-world problem by using the proposed methodology

Statistical Evaluation of Spectral Methods for Anomaly Detection in Networks

Monitoring of networks for anomaly detection has attracted a lot of attention in recent years especially with the rise of connected devices and social networks. This is of importance as anomaly detection could span a wide range of application, from detecting terrorist cells in counter-terrorism efforts to phishing attacks in social network circles. For this reason, numerous techniques for anomaly detection have been introduced. However, application of these techniques to more complex network models is hindered by various challenges such as the size of the network being investigated, how much apriori information is needed, the size of the anomalous graph, among others. A recent technique introduced by Miller et al, which relies on a spectral framework for anomaly detection, has the potential to address many of these challenges. In their discussion of the spectral framework, three algorithms were proposed that relied on the eigenvalues and eigenvectors of the residual matrix of a binary network. The authors demonstrated the ability to detect anomalous subgraphs that were less than 1% of the network size. However, to date, there is little work that has been done to evaluate the statistical performance of these algorithms. This study investigates the statistical properties of the spectral methods, specifically the Chi-square and L1 norm algorithm proposed by Miller. We will analyze the performance of the algorithm using simulated networks and also extend the method's application to count networks. Finally we will make some methodological improvements and recommendations to both algorithms.Comment: 39 pages, 17 figure