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Found 12 papers, 3 papers with code
Approximate Message Passing for the Matrix Tensor Product Model
We propose and analyze an approximate message passing (AMP) algorithm for the matrix tensor product model, which is a generalization of the standard spiked matrix models that allows for multiple types of pairwise observations over a collection of latent variables.
k-Sliced Mutual Information: A Quantitative Study of Scalability with Dimension
However, a quantitative characterization of how SMI itself and estimation rates thereof depend on the ambient dimension, which is crucial to the understanding of scalability, remain obscure.
Fundamental limits for rank-one matrix estimation with groupwise heteroskedasticity
These results are based on a novel reduction from the low-rank matrix tensor product model (with homogeneous noise) to a rank-one model with heteroskedastic noise.
Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samples
The Gaussian-smoothed optimal transport (GOT) framework, recently proposed by Goldfeld et al., scales to high dimensions in estimation and provides an alternative to entropy regularization.
The Gaussian equivalence of generative models for learning with shallow neural networks
Here, we go beyond this simple paradigm by studying the performance of neural networks trained on data drawn from pre-trained generative models.
Information-Theoretic Limits for the Matrix Tensor Product
This paper studies a high-dimensional inference problem involving the matrix tensor product of random matrices.
Information-theoretic limits of a multiview low-rank symmetric spiked matrix model
We consider a generalization of an important class of high-dimensional inference problems, namely spiked symmetric matrix models, often used as probabilistic models for principal component analysis.
Gaussian Approximation of Quantization Error for Estimation from Compressed Data
We show that the Wasserstein distance between a bitrate-$R$ compressed version of $X$ and its observation under an AWGN-channel of signal-to-noise ratio $2^{2R}-1$ is sub-linear in the problem dimension.
Mutual Information in Community Detection with Covariate Information and Correlated Networks
We study the problem of community detection when there is covariate information about the node labels and one observes multiple correlated networks.
Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation
Posterior computation for high-dimensional data with many parameters can be challenging.
Computation Methodology
Additivity of Information in Multilayer Networks via Additive Gaussian Noise Transforms
When applied to the special case of models with multivariate Gaussian channels our method is rigorous and has close connections to free probability theory for random matrices.
Classification and Reconstruction of High-Dimensional Signals from Low-Dimensional Features in the Presence of Side Information
These conditions, which are reminiscent of the well-known Slepian-Wolf and Wyner-Ziv conditions, are a function of the number of linear features extracted from the signal of interest, the number of linear features extracted from the side information signal, and the geometry of these signals and their interplay.
