Search Results for author:
Found 8 papers, 0 papers with code
Is it easier to count communities than find them?
In particular, we consider certain hypothesis testing problems between models with different community structures, and we show (in the low-degree polynomial framework) that testing between two options is as hard as finding the communities.
The planted matching problem: Sharp threshold and infinite-order phase transition
Conversely, if $\sqrt{d} B(\mathcal{P},\mathcal{Q}) \ge 1+\epsilon$ for an arbitrarily small constant $\epsilon>0$, the reconstruction error for any estimator is shown to be bounded away from $0$ under both the sparse and dense model, resolving the conjecture in [Moharrami et al. 2019, Semerjian et al. 2020].
Learner-Private Convex Optimization
Convex optimization with feedback is a framework where a learner relies on iterative queries and feedback to arrive at the minimizer of a convex function.
Consistent recovery threshold of hidden nearest neighbor graphs
Motivated by applications such as discovering strong ties in social networks and assembling genome subsequences in biology, we study the problem of recovering a hidden $2k$-nearest neighbor (NN) graph in an $n$-vertex complete graph, whose edge weights are independent and distributed according to $P_n$ for edges in the hidden $2k$-NN graph and $Q_n$ otherwise.
Optimal query complexity for private sequential learning against eavesdropping
We study the query complexity of a learner-private sequential learning problem, motivated by the privacy and security concerns due to eavesdropping that arise in practical applications such as pricing and Federated Learning.
The cost-free nature of optimally tuning Tikhonov regularizers and other ordered smoothers
Our theory reveals that if the Tikhonov regularizers share the same penalty matrix with different tuning parameters, a convex procedure based on $Q$-aggregation achieves the mean square error of the best estimator, up to a small error term no larger than $C\sigma^2$, where $\sigma^2$ is the noise level and $C>0$ is an absolute constant.
Estimating the Coefficients of a Mixture of Two Linear Regressions by Expectation Maximization
We also show that the population EM operator for mixtures of two regressions is anti-contractive from the target parameter vector if the cosine angle between the input vector and the target parameter vector is too small, thereby establishing the necessity of our conic condition.
