Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a framework for metric MSTs that first (1) finds a forest of trees using practical heuristics, and then (2) finds a small weight set of edges to connect disjoint components in the forest into a spanning tree. We prove that optimally solving step (2) still takes $\Omega(n^2)$ time, but we provide a subquadratic 2.62-approximation algorithm. In the spirit of learning-augmented algorithms, we then show that if the heuristic forest found in step (1) overlaps with an optimal MST, we can approximate the original MST problem in subquadratic time, where the approximation factor depends on a measure of overlap. In practice, we find nearly optimal spanning trees for a wide range of metrics, while being orders of magnitude faster than exact algorithms.

YGM is a general-purpose asynchronous distributed computing library for C++/MPI, designed to handle the irregular data access patterns and small messages of graph algorithms and data science applications. It uses data serialization to give an easily usable active message interface and message aggregation to maximize application throughput. Our design philosophy makes a tradeoff that increases network bandwidth utilization at the cost of added latency. We provide a suite of benchmarks showcasing YGM's performance. Compared to similar distributed active message benchmark implementations that do not provide message buffering, we are able to achieve over 10x throughput on thousands of cores at a latency cost that can be as small as 2x or as large as 100x, depending on the machine being used. For applications that can be written to be latency-tolerant, this represents a significant potential performance improvement through using YGM.

Understanding the higher-order interactions within network data is a key objective of network science. Surveys of metadata triangles (or patterned 3-cycles in metadata-enriched graphs) are often of interest in this pursuit. In this work, we develop TriPoll, a prototype distributed HPC system capable of surveying triangles in massive graphs containing metadata on their edges and vertices. We contrast our approach with much of the prior effort on triangle analysis, which often focuses on simple triangle counting, usually in simple graphs with no metadata. We assess the scalability of TriPoll when surveying triangles involving metadata on real and synthetic graphs with up to hundreds of billions of edges. We utilize communication-reducing optimizations to demonstrate a triangle counting task on a 224 billion edge web graph in approximately half of the time of competing approaches, while additionally supporting metadata-aware capabilities.

While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex non-linear embeddings, but do not naturally quantify uncertainty and are often data-inefficient to train. GPs infer posterior distributions over functions, but popular kernels exhibit limited expressivity on complex and high-dimensional data. Fortunately, recently discovered conjugate and neural tangent kernel functions encode the behavior of overparameterized neural networks in the kernel domain. We demonstrate that these kernels can be efficiently applied to regression and reinforcement learning problems by analyzing a baseline case study.We apply GPs with neural network dual kernels to solve reinforcement learning tasks for the first time. We demonstrate, using the well understood mountain-car problem, that GPs empowered with dual kernels perform at least as well as those using the conventional radial basis function kernel. We conjecture that by inheriting the probabilistic rigor of GPs and the powerful embedding properties of DNNs, GPs using NN dual kernels will empower future reinforcement learning models on difficult domains.

Enterprise computer networks are filled with users performing a variety of tasks, ranging from business-critical tasks to personal interest browsing. Due to this multi-modal distribution of behaviors, it is non-trivial to automatically discern which behaviors are business-relevant and which are not. Additionally, it is difficult to infer communities of interest within the enterprise, even given an organizational mapping. In this work, we present a two-step framework for classifying user behavior within an enterprise in a data-driven way. As a first step, we use a latent topic model on active search queries to identify types of behaviors and topics of interest associated with a given user. We then leverage the information about user's assigned role within the organization to extract relevant topics which are most reflective of self-organizing communities of interest. We demonstrate that our framework is able to identify rich communities of interest that are better representations of how users interact and assemble in an enterprise setting.