Gilvir Gill

Siddharth Mangalik, Johannes C. Eichstaedt, Salvatore Giorgi et al.

Compared to physical health, population mental health measurement in the U.S. is very coarse-grained. Currently, in the largest population surveys, such as those carried out by the Centers for Disease Control or Gallup, mental health is only broadly captured through "mentally unhealthy days" or "sadness", and limited to relatively infrequent state or metropolitan estimates. Through the large scale analysis of social media data, robust estimation of population mental health is feasible at much higher resolutions, up to weekly estimates for counties. In the present work, we validate a pipeline that uses a sample of 1.2 billion Tweets from 2 million geo-located users to estimate mental health changes for the two leading mental health conditions, depression and anxiety. We find moderate to large associations between the language-based mental health assessments and survey scores from Gallup for multiple levels of granularity, down to the county-week (fixed effects $β= .25$ to $1.58$; $p<.001$). Language-based assessment allows for the cost-effective and scalable monitoring of population mental health at weekly time scales. Such spatially fine-grained time series are well suited to monitor effects of societal events and policies as well as enable quasi-experimental study designs in population health and other disciplines. Beyond mental health in the U.S., this method generalizes to a broad set of psychological outcomes and allows for community measurement in under-resourced settings where no traditional survey measures - but social media data - are available.

Quinten De Man, Gilvir Gill, Michael A. Bender et al.

Dynamic connectivity is a fundamental dynamic graph problem, and recent algorithmic breakthroughs on dynamic graph sketching have reshaped what is theoretically possible: by encoding the graph as per-vertex linear sketches, these algorithms solve dynamic connectivity in only $Θ(V \log^2 V)$ space, independent of the number of edges,outperforming lossless $Θ(V+E)$-space structures that grow as the graph becomes denser. Prior to this work, no practical dynamic connectivity algorithm has been able to translate these theoretical breakthroughs into space savings on real-world graphs. The main obstacle is that per-vertex sketches cost thousands of bytes per vertex, so sketching only pays off once the graph becomes extremely dense. We observe that sparse real-world graphs are often not uniformly sparse, these graphs can contain dense cores on a small subset of vertices that account for a large fraction of edges. We exploit this structure via hybrid sketching: sketch only the dense core, and store the sparse periphery losslessly. We design new hybrid algorithms for fully-dynamic and semi-streaming connectivity with space $O(\min\{V+E, V \log V \log(2+E/V)\})$ w.h.p., simultaneously matching the lossless bound on sparse graphs, the sketching bound on dense graphs, and improving on both in an intermediate regime. A key component is BalloonSketch, a new l0-sampler reducing per-vertex sketch sizes by up to 8x. We implement HybridSCALE, a modular system treating the lossless and sketch-based components as subroutines. HybridSCALE is the first sketch-based dynamic connectivity system to save space on common real-world graphs. Compared to the state-of-the-art lossless baseline, HybridSCALE saves up to 15% space on sparse graphs (average degree < 100), up to 92% on intermediate density graphs (average degree ~ 100-1000), and up to 97% on dense graphs (average degree > 1000).