arXiv subjects

Greg Ver Steeg

Publications and source records attributed to Greg Ver Steeg.

114 records · Page 7Linked to original sources

arXiv2011

A Sequence of Relaxations Constraining Hidden Variable Models

Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose violation rules out some latent variable model as a "hidden variable test" for that model. Our main contribution is to introduce a sequence of relaxations which provides progressively tighter hidden variable tests. We demonstrate applicability to mixtures of sequences of i.i.d. variables, Bell inequalities, and homophily models in social networks. For the last, we demonstrate that our method provides a test that is able to rule out latent homophily as the sole explanation for correlations on a real social network that are known to be due to influence.

cs.AI↗

arXiv2011

Co-evolution of Selection and Influence in Social Networks

Many networks are complex dynamical systems, where both attributes of nodes and topology of the network (link structure) can change with time. We propose a model of co-evolving networks where both node at- tributes and network structure evolve under mutual influence. Specifically, we consider a mixed membership stochastic blockmodel, where the probability of observing a link between two nodes depends on their current membership vectors, while those membership vectors themselves evolve in the presence of a link between the nodes. Thus, the network is shaped by the interaction of stochastic processes describing the nodes, while the processes themselves are influenced by the changing network structure. We derive an efficient variational inference procedure for our model, and validate the model on both synthetic and real-world data.

cs.SI↗

arXiv2011

What Stops Social Epidemics?

Theoretical progress in understanding the dynamics of spreading processes on graphs suggests the existence of an epidemic threshold below which no epidemics form and above which epidemics spread to a significant fraction of the graph. We have observed information cascades on the social media site Digg that spread fast enough for one initial spreader to infect hundreds of people, yet end up affecting only 0.1% of the entire network. We find that two effects, previously studied in isolation, combine cooperatively to drastically limit the final size of cascades on Digg. First, because of the highly clustered structure of the Digg network, most people who are aware of a story have been exposed to it via multiple friends. This structure lowers the epidemic threshold while moderately slowing the overall growth of cascades. In addition, we find that the mechanism for social contagion on Digg points to a fundamental difference between information spread and other contagion processes: despite multiple opportunities for infection within a social group, people are less likely to become spreaders of information with repeated exposure. The consequences of this mechanism become more pronounced for more clustered graphs. Ultimately, this effect severely curtails the size of social epidemics on Digg.

cs.SI↗

arXiv2010

Community Detection with and without Prior Information

We study the problem of graph partitioning, or clustering, in sparse networks with prior information about the clusters. Specifically, we assume that for a fraction $ρ$ of the nodes their true cluster assignments are known in advance. This can be understood as a semi--supervised version of clustering, in contrast to unsupervised clustering where the only available information is the graph structure. In the unsupervised case, it is known that there is a threshold of the inter--cluster connectivity beyond which clusters cannot be detected. Here we study the impact of the prior information on the detection threshold, and show that even minute [but generic] values of $ρ>0$ shift the threshold downwards to its lowest possible value. For weighted graphs we show that a small semi--supervising can be used for a non-trivial definition of communities.

physics.soc-ph↗

arXiv2009

Relaxed uncertainty relations and information processing

We consider a range of "theories" that violate the uncertainty relation for anti-commuting observables derived in [JMP, 49, 062105 (2008)]. We first show that Tsirelson's bound for the CHSH inequality can be derived from this uncertainty relation, and that relaxing this relation allows for non-local correlations that are stronger than what can be obtained in quantum mechanics. We continue to construct a hierarchy of related non-signaling theories, and show that on one hand they admit superstrong random access encodings and exponential savings for a particular communication problem, while on the other hand it becomes much harder in these theories to learn a state. We show that the existence of these effects stems from the absence of certain constraints on the expectation values of commuting measurements from our non-signaling theories that are present in quantum theory.

quant-ph↗

arXiv2009

Entangling Power of an Expanding Universe

We show that entanglement can be used to detect spacetime curvature. Quantum fields in the Minkowski vacuum are entangled with respect to local field modes. This entanglement can be swapped to spatially separated quantum systems using standard local couplings. A single, inertial field detector in the exponentially expanding (de Sitter) vacuum responds as if it were bathed in thermal radiation in a Minkowski universe. We show that using two inertial detectors, interactions with the field in the thermal case will entangle certain detector pairs that would not become entangled in the corresponding de Sitter case. The two universes can thus be distinguished by their entangling power.

quant-ph↗