We study inference in stochastic block models (SBMs) through the lens of optimal transport (OT). We first establish that maximum likelihood variational inference (MLVI) can be interpreted as a semi-relaxed Gromov-Wasserstein (srGW) projection with entropic regularization. While this formulation yields accurate clustering, the entropic regularization prevents transport plans to be sparse, hindering intrinsic model selection. Consequently, we investigate unregularized srGW estimators, and prove that they consistently recover both the SBM connectivity matrix and latent cluster assignments in the asymptotic regime. However, this asymptotic property does not translate into reliable model selection in finite samples, and calls for additional mechanisms to promote sparsity in the inferred cluster proportions. We empirically show that such a regularized formulation yields estimators that simultaneously recover model parameters and select the number of clusters in a single optimization problem, thereby avoiding costly grid search or heuristic model selection procedures.

Neural Information Processing Systems http://nips.cc/

Finally,an EEG forward model based onapre-estimated lead field matrix wasconstructed together with the ROIsource model togenerate scalp EEG observations.

We study the theory of random bipartite graph whose adjacency matrix is generated according to a connectivity matrix $M$. We consider the bipartite graph to be sparse, i.e., the entries of $M$ are upper bounded by certain sparsity parameter. We show that the performance of estimating the connectivity matrix $M$ depends on the sparsity of the graph. We focus on two measurement of performance of estimation: the error of estimating $M$ and the error of estimating the column space of $M$. In the first case, we consider the operator norm and Frobenius norm of the difference between the estimation and the true connectivity matrix. In the second case, the performance will be measured by the difference between the estimated projection matrix and the true projection matrix in operator norm and Frobenius norm. We will show that the estimators we propose achieve the minimax optimal rate.

We consider decentralized machine learning over a network where the training data is distributed across $n$ agents, each of which can compute stochastic model updates on their local data. The agent's common goal is to find a model that minimizes the average of all local loss functions. While gradient tracking (GT) algorithms can overcome a key challenge, namely accounting for differences between workers' local data distributions, the known convergence rates for GT algorithms are not optimal with respect to their dependence on the mixing parameter $p$ (related to the spectral gap of the connectivity matrix).We provide a tighter analysis of the GT method in the stochastic strongly convex, convex and non-convex settings. We improve the dependency on $p$ from $\mathcal{O}(p^{-2})$ to $\mathcal{O}(p^{-1}c^{-1})$ in the noiseless case and from $\mathcal{O}(p^{-3/2})$ to $\mathcal{O}(p^{-1/2}c^{-1})$ in the general stochastic case, where $c \geq p$ is related to the negative eigenvalues of the connectivity matrix (and is a constant in most practical applications). This improvement was possible due to a new proof technique which could be of independent interest.

Here, we apply instantaneous and lag-based measures of conditional linear dependence, based on Granger-Geweke causality (GC), to infer network connections at distinct timescales from functional magnetic resonance imaging (fMRI) data.