Paulo Shakarian

A Scalable Framework for Modeling Competitive Diffusion in Social Networks

Multiple phenomena often diffuse through a social network, sometimes in competition with one another. Product adoption and political elections are two examples where network diffusion is inherently competitive in nature. For example, individuals may choose to only select one product from a set of competing products (i.e. most people will need only one cell-phone provider) or can only vote for one person in a slate of political candidate (in most electoral systems). We introduce the weighted generalized annotated program (wGAP) framework for expressing competitive diffusion models. Applications are interested in the eventual results from multiple competing diffusion models (e.g. what is the likely number of sales of a given product, or how many people will support a particular candidate). We define the “most probable interpretation” (MPI) problem which technically formalizes this need. We develop algorithms to efficiently solve MPI and show experimentally that our algorithms work on graphs with millions of vertices.

Annotated probabilistic temporal logic

The semantics of most logics of time and probability is given via a probability distribution over threads, where a thread is a structure specifying what will be true at different points in time (in the future). When assessing the probabilities of statements such as “Event a will occur within 5 units of time of event b,” there are many different semantics possible, even when assessing the truth of this statement within a single thread. We introduce the syntax of annotated probabilistic temporal (APT) logic programs and axiomatically introduce the key notion of a frequency function (for the first time) to capture different types of intrathread reasoning, and then provide a semantics for intrathread and interthread reasoning in APT logic programs parameterized by such frequency functions. We develop a comprehensive set of complexity results for consistency checking and entailment in APT logic programs, together with sound and complete algorithms to check consistency and entailment. The basic algorithms use linear programming, but we then show how to substantially and correctly reduce the sizes of these linear programs to yield better computational properties. We describe a real world application we are developing using APT logic programs.

GAPs: Geospatial Abduction Problems

There are many applications where we observe various phenomena in space (e.g., locations of victims of a serial killer), and where we want to infer “partner” locations (e.g., the location where the killer lives) that are geospatially related to the observed phenomena. In this article, we define geospatial abduction problems (GAPs for short). We analyze the complexity of GAPs, develop exact and approximate algorithms (often with approximation guarantees) for these problems together with analyses of these algorithms, and develop a prototype implementation of our GAP framework. We demonstrate accuracy of our algorithms on a real world data set consisting of insurgent IED (improvised explosive device) attacks against U.S. forces in Iraq (the observations were the locations of the attacks, while the “partner” locations we were trying to infer were the locations of IED weapons caches).

Darknet and deepnet mining for proactive cybersecurity threat intelligence

In this paper, we present an operational system for cyber threat intelligence gathering from various social platforms on the Internet particularly sites on the darknet and deepnet. We focus our attention to collecting information from hacker forum discussions and marketplaces offering products and services focusing on malicious hacking. We have developed an operational system for obtaining information from these sites for the purposes of identifying emerging cyber threats. Currently, this system collects on average 305 high-quality cyber threat warnings each week. These threat warnings include information on newly developed malware and exploits that have not yet been deployed in a cyber-attack. This provides a significant service to cyber-defenders. The system is significantly augmented through the use of various data mining and machine learning techniques. With the use of machine learning models, we are able to recall 92% of products in marketplaces and 80% of discussions on forums relating to malicious hacking with high precision. We perform preliminary analysis on the data collected, demonstrating its application to aid a security expert for better threat analysis.

Fast and Deterministic Computation of Fixation Probability in Evolutionary Graphs

Abstract : In evolutionary graph theory biologists study the problem of determining the probability that a small number of mutants overtake a population that is structured on a weighted, possibly directed graph. Currently Monte Carlo simulations are used for estimating such fixation probabilities on directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic algorithm for computing fixation probabilities for strongly connected directed, weighted evolutionary graphs under the case of neutral drift, which we show to be a lower bound for the case where the mutant is more fit than the rest of the population (previously, this was only observed from simulation). We also show that, in neutral drift, fixation probability is additive under the weighted, directed case. We implement our algorithm and show experimentally that it consistently outperforms Monte Carlo simulations by several orders of magnitude, which can allow researchers to study fixation probability on much larger graphs.

A novel analytical method for evolutionary graph theory problems.

Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are used for estimating such fixation probabilities on general directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic framework for computing fixation probabilities for strongly connected, directed, weighted evolutionary graphs under neutral drift. We show how this framework can also be used to calculate the expected number of mutants at a given time step (even if we relax the assumption that the graph is strongly connected), how it can extend to other related models (e.g. voter model), how our framework can provide non-trivial bounds for fixation probability in the case of an advantageous mutant, and how it can be used to find a non-trivial lower bound on the mean time to fixation. We provide various experimental results determining fixation probabilities and expected number of mutants on different graphs. Among these, we show that our method consistently outperforms Monte Carlo simulations in speed by several orders of magnitude. Finally we show how our approach can provide insight into synaptic competition in neurology.

Using Generalized Annotated Programs to Solve Social Network Diffusion Optimization Problems

There has been extensive work in many different fields on how phenomena of interest (e.g., diseases, innovation, product adoption) “diffuse” through a social network. As social networks increasingly become a fabric of society, there is a need to make “optimal” decisions with respect to an observed model of diffusion. For example, in epidemiology, officials want to find a set of k individuals in a social network which, if treated, would minimize spread of a disease. In marketing, campaign managers try to identify a set of k customers that, if given a free sample, would generate maximal “buzz” about the product. In this article, we first show that the well-known Generalized Annotated Program (GAP) paradigm can be used to express many existing diffusion models. We then define a class of problems called Social Network Diffusion Optimization Problems (SNDOPs). SNDOPs have four parts: (i) a diffusion model expressed as a GAP, (ii) an objective function we want to optimize with respect to a given diffusion model, (iii) an integer k > 0 describing resources (e.g., medication) that can be placed at nodes, (iv) a logical condition VC that governs which nodes can have a resource (e.g., only children above the age of 5 can be treated with a given medication). We study the computational complexity of SNDOPs and show both NP-completeness results as well as results on complexity of approximation. We then develop an exact and a heuristic algorithm to solve a large class of SNDOPproblems and show that our GREEDY-SNDOPs algorithm achieves the best possible approximation ratio that a polynomial algorithm can achieve (unless P = NP). We conclude with a prototype experimental implementation to solve SNDOPs that looks at a real-world Wikipedia dataset consisting of over 103,000 edges.

Diffusion in Social Networks

This book presents the leading models of social network diffusion that are used to demonstrate the spread of disease, ideas, and behavior. It introduces diffusion models from the fields of computer science (independent cascade and linear threshold), sociology (tipping models), physics (voter models), biology (evolutionary models), and epidemiology (SIR/SIS and related models). A variety of properties and problems related to these models are discussed including identifying seeds sets to initiate diffusion, game theoretic problems, predicting diffusion events, and more. The book explores numerous connections between social network diffusion research and artificial intelligence through topics such as agent-based modeling, logic programming, game theory, learning, and data mining. The book also surveys key empirical results in social network diffusion, and reviews the classic and cutting-edge research with a focus on open problems.

Annotated Probabilistic Temporal Logic: Approximate Fixpoint Implementation

Annotated Probabilistic Temporal (APT) logic programs support building applications where we wish to reason about statements of the form “Formula G becomes true with a probability in the range [L, U] within (or in exactly) Δt time units after formula F became true.” In this paper, we present a sound, but incomplete fixpoint operator that can be used to check consistency and entailment in APT logic programs. We present the first implementation of APT-logic programs and evaluate both its compute time and convergence on a suite of 23 ground APT-logic programs that were automatically learned from two real-world data sets. In both cases, the APT-logic programs contained up to 1,000 ground rules. In one data set, entailment problems were solved on average in under 0.1 seconds per ground rule, while in the other, it took up to 1.3 seconds per ground rule. Consistency was also checked in a reasonable amount of time. When discussing entailment of APT-logic formulas, convergence of the fixpoint operator refers to (U − L) being below a certain threshold. We show that on virtually all of the 23 automatically generated APT-logic programs, convergence was quick---often in just 2-3 iterations of the fixpoint operator. Thus, our implementation is a practical first step towards checking consistency and entailment in temporal probabilistic logics without independence or Markovian assumptions.

Mining for geographically disperse communities in social networks by leveraging distance modularity

Social networks where the actors occupy geospatial locations are prevalent in military, intelligence, and policing operations such as counter-terrorism, counter-insurgency, and combating organized crime. These networks are often derived from a variety of intelligence sources. The discovery of communities that are geographically disperse stems from the requirement to identify higher-level organizational structures, such as a logistics group that provides support to various geographically disperse terrorist cells. We apply a variant of Newman-Girvan modularity to this problem known as distance modularity. To address the problem of finding geographically disperse communities, we modify the well-known Louvain algorithm to find partitions of networks that provide near-optimal solutions to this quantity. We apply this algorithm to numerous samples from two real-world social networks and a terrorism network data set whose nodes have associated geospatial locations. Our experiments show this to be an effective approach and highlight various practical considerations when applying the algorithm to distance modularity maximization. Several military, intelligence, and law-enforcement organizations are working with us to further test and field software for this emerging application.