Related papers: Statistical and computational thresholds for the p…
We study nonconvex optimization in high dimensions through Langevin dynamics, focusing on the multi-spiked tensor PCA problem. This tensor estimation problem involves recovering $r$ hidden signal vectors (spikes) from noisy Gaussian tensor…
We study the high-dimensional dynamics of online stochastic gradient descent (SGD) for the multi-spiked tensor model. This multi-index model arises from the tensor principal component analysis (PCA) problem with multiple spikes, where the…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still…
We study the computational properties of two canonical planted average-case problems -- noisy planted $k$-XOR and Tensor PCA -- by formally unifying them into a family of planted problems parametrized by tensor order $k$, number of entries…
In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by the smallest signal strength that it can…
We study the problem of community recovery and detection in multi-layer stochastic block models, focusing on the critical network density threshold for consistent community structure inference. Using a prototypical two-block model, we…
We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…
We formulate and analyze a heterogeneous random hypergraph model, and we provide an achieveability result for recovery of hyperedges from the observed projected graph. We observe a projected graph which combines random hyperedges across all…
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…
The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…
We note the significance of hypergraphic planted clique (HPC) detection in the investigation of computational hardness for a range of tensor problems. We ask if more evidence for the computational hardness of HPC detection can be developed.…
We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of…
The typical complexity of Constraint Satisfaction Problems (CSPs) can be investigated by means of random ensembles of instances. The latter exhibit many threshold phenomena besides their satisfiability phase transition, in particular a…
For two correlated graphs which are independently sub-sampled from a common Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}.…
Given a weighted hypergraph $\mathcal{H}(V, \mathcal{E} \subseteq 2^V, w)$, the approximate $k$-cover problem seeks for a size-$k$ subset of $V$ that has the maximum weighted coverage by \emph{sampling only a few hyperedges} in…
In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…
We study the problem of community detection in hypergraphs under a stochastic block model. Similarly to how the stochastic block model in graphs suggests studying spiked random matrices, our model motivates investigating statistical and…
In this paper, we consider the planted partition model, in which $n = ks$ vertices of a random graph are partitioned into $k$ "clusters," each of size $s$. Edges between vertices in the same cluster and different clusters are included with…
Detection of a planted dense subgraph in a random graph is a fundamental statistical and computational problem that has been extensively studied in recent years. We study a hypergraph version of the problem. Let $G^r(n,p)$ denote the…