Elias B. Khalil

Scalable diffusion-aware optimization of network topology

How can we optimize the topology of a networked system to bring a flu under control, propel a video to popularity, or stifle a network malware in its infancy? Previous work on information diffusion has focused on modeling the diffusion dynamics and selecting nodes to maximize/minimize influence. Only a paucity of recent studies have attempted to address the network modification problems, where the goal is to either facilitate desirable spreads or curtail undesirable ones by adding or deleting a small subset of network nodes or edges. In this paper, we focus on the widely studied linear threshold diffusion model, and prove, for the first time, that the network modification problems under this model have supermodular objective functions. This surprising property allows us to design efficient data structures and scalable algorithms with provable approximation guarantees, despite the hardness of the problems in question. Both the time and space complexities of our algorithms are linear in the size of the network, which allows us to experiment with millions of nodes and edges. We show that our algorithms outperform an array of heuristics in terms of their effectiveness in controlling diffusion processes, often beating the next best by a significant margin.

Generating Graph Snapshots from Streaming Edge Data

We study the problem of determining the proper aggregation granularity for a stream of time-stamped edges. Such streams are used to build time-evolving networks, which are subsequently used to study topics such as network growth. Currently, aggregation lengths are chosen arbitrarily, based on intuition or convenience. We describe ADAGE, which detects the appropriate aggregation intervals from streaming edges and outputs a sequence of structurally mature graphs. We demonstrate the value of ADAGE in automatically finding the appropriate aggregation intervals on edge streams for belief propagation to detect malicious files and machines.

Large-scale insider trading analysis: patterns and discoveries

How do company insiders trade? Do their trading behaviors differ based on their roles (e.g., chief executive officer vs. chief financial officer)? Do those behaviors change over time (e.g., impacted by the 2008 market crash)? Can we identify insiders who have similar trading behaviors? And what does that tell us? This work presents the first academic, large-scale exploratory study of insider filings and related data, based on the complete Form 4 fillings from the U.S. Securities and Exchange Commission. We analyze 12 million transactions by 370 thousand insiders spanning 1986–2012, the largest reported in academia. We explore the temporal and network-based aspects of the trading behaviors of insiders, and make surprising and counterintuitive discoveries. We study how the trading behaviors of insiders differ based on their roles in their companies, the types of their transactions, their companies’ sectors, and their relationships with other insiders. Our work raises exciting research questions and opens up many opportunities for future studies. Most importantly, we believe our work could form the basis of novel tools for financial regulators and policymakers to detect illegal insider trading, help them understand the dynamics of the trades, and enable them to adapt their detection strategies toward these dynamics.

Learning to Run Heuristics in Tree Search

“Primal heuristics” are a key contributor to the improved performance of exact branch-and-bound solvers for combinatorial optimization and integer programming. Perhaps the most crucial question concerning primal heuristics is that of at which nodes they should run, to which the typical answer is via hard-coded rules or fixed solver parameters tuned, offline, by trial-and-error. Alternatively, a heuristic should be run when it is most likely to succeed, based on the problem instance’s characteristics, the state of the search, etc. In this work, we study the problem of deciding at which node a heuristic should be run, such that the overall (primal) performance of the solver is optimized. To our knowledge, this is the first attempt at formalizing and systematically addressing this problem. Central to our approach is the use of Machine Learning (ML) for predicting whether a heuristic will succeed at a given node. We give a theoretical framework for analyzing this decision-making process in a simplified setting, propose a ML approach for modeling heuristic success likelihood, and design practical rules that leverage the ML models to dynamically decide whether to run a heuristic at each node of the search tree. Experimentally, our approach improves the primal performance of a stateof-the-art Mixed Integer Programming solver by up to 6% on a set of benchmark instances, and by up to 60% on a family of hard Independent Set instances.

Learning feature engineering for classification

Feature engineering is the task of improving predictive modelling performance on a dataset by transforming its feature space. Existing approaches to automate this process rely on either transformed feature space exploration through evaluation-guided search, or explicit expansion of datasets with all transformed features followed by feature selection. Such approaches incur high computational costs in runtime and/or memory. We present a novel technique, called Learning Feature Engineering (LFE), for automating feature engineering in classification tasks. LFE is based on learning the effectiveness of applying a transformation (e.g., arithmetic or aggregate operators) on numerical features, from past feature engineering experiences. Given a new dataset, LFE recommends a set of useful transformations to be applied on features without relying on model evaluation or explicit feature expansion and selection. Using a collection of datasets, we train a set of neural networks, which aim at predicting the transformation that impacts classification performance positively. Our empirical results show that LFE outperforms other feature engineering approaches for an overwhelming majority (89%) of the datasets from various sources while incurring a substantially lower computational cost.

CP-ORTHO: An Orthogonal Tensor Factorization Framework for Spatio-Temporal Data

Extracting patterns and deriving insights from spatio-temporal data finds many target applications in various domains, such as in urban planning and computational sustainability. Due to their inherent capability of simultaneously modeling the spatial and temporal aspects of multiple instances, tensors have been successfully used to analyze such spatio-temporal data. However, standard tensor factorization approaches often result in components that are highly overlapping, which hinders the practitioners ability to interpret them without advanced domain knowledge. In this work, we tackle this challenge by proposing a tensor factorization framework, called CP-ORTHO, to discover distinct and easily-interpretable patterns from multi-modal, spatio-temporal data. We evaluate our approach on real data reflecting taxi drop-off activity. CP-ORTHO provides more distinct and interpretable patterns than prior art, as measured via relevant quantitative metrics, without compromising the solutions accuracy. We observe that CP-ORTHO is fast, in that it achieves this result in 5x less time than the most accurate competing approach.