Opinion dynamics models how the publicly expressed opinions of users in a social network coevolve according to their neighbors as well as their own intrinsic opinion. Motivated by the real-world manipulation of social networks during the 2016 US elections and the 2019 Hong Kong protests, a growing body of work models the effects of a strategic actor who interferes with the network to induce disagreement or polarization. We lift the assumption of a single strategic actor by introducing a model in which any subset of network users can manipulate network outcomes. They do so by acting according to a fictitious intrinsic opinion. Strategic actors can have conflicting goals, and push competing narratives. We characterize the Nash Equilibrium of the resulting meta-game played by the strategic actors. Experiments on real-world social network datasets from Twitter, Reddit, and Political Blogs show that strategic agents can significantly increase polarization and disagreement, as well as increase the ''cost'' of the equilibrium. To this end, we give worst-case upper bounds on the Price of Misreporting (analogous to the Price of Anarchy). Finally, we give efficient learning algorithms for the platform to (i) detect whether strategic manipulation has occurred, and (ii) learn who the strategic actors are. Our algorithms are accurate on the same real-world datasets, suggesting how platforms can take steps to mitigate the effects of strategic behavior.

We study transfer learning for matrix completion in a Missing Not-at-Random (MNAR) setting that is motivated by biological problems. The target matrix $Q$ has entire rows and columns missing, making estimation impossible without side information. To address this, we use a noisy and incomplete source matrix $P$, which relates to $Q$ via a feature shift in latent space. We consider both the active and passive sampling of rows and columns. We establish minimax lower bounds for entrywise estimation error in each setting. Our computationally efficient estimation framework achieves this lower bound for the active setting, which leverages the source data to query the most informative rows and columns of $Q$. This avoids the need for incoherence assumptions required for rate optimality in the passive sampling setting. We demonstrate the effectiveness of our approach through comparisons with existing algorithms on real-world biological datasets.

We study transfer learning for estimation in latent variable network models. In our setting, the conditional edge probability matrices given the latent variables are represented by $P$ for the source and $Q$ for the target. We wish to estimate $Q$ given two kinds of data: (1) edge data from a subgraph induced by an $o(1)$ fraction of the nodes of $Q$, and (2) edge data from all of $P$. If the source $P$ has no relation to the target $Q$, the estimation error must be $\Omega(1)$. However, we show that if the latent variables are shared, then vanishing error is possible. We give an efficient algorithm that utilizes the ordering of a suitably defined graph distance. Our algorithm achieves $o(1)$ error and does not assume a parametric form on the source or target networks. Next, for the specific case of Stochastic Block Models we prove a minimax lower bound and show that a simple algorithm achieves this rate. Finally, we empirically demonstrate our algorithm's use on real-world and simulated graph transfer problems.

We construct explicit deterministic extractors for polynomial images of varieties, that is, distributions sampled by applying a low-degree polynomial map f : Fqr → Fqn to an element sampled uniformly at random from a k-dimensional variety V ⊆ Fqr. This class of sources generalizes both polynomial sources, studied by Dvir, Gabizon and Wigderson (FOCS 2007, Comput. Complex. 2009), and variety sources, studied by Dvir (CCC 2009, Comput. Complex. 2012).