20 problems

Consider a MIMO multicarrier system using the multi-slot cross-domain MAMP (MS-CD-MAMP) receiver, with total transmission rate $R_{\rm{MS-CD-MAMP}}^{\rm{total}}$ and constrained ch…

Let angular synchronization be the problem of estimating vertex phases from noisy pairwise angular measurements, and suppose the noise is Gaussian. Approximate message-passing opti…

The algorithms under comparison are the two variants $\text{cycBP}_\text{e}$ and $\text{cycBP}$, trained towards the Bethe loss function $\mathcal{L}_\text{Bethe}$; their performan…

Consider the stochastic block model and compare Markov-chain Monte Carlo (MCMC) with message-passing algorithms for inference. MCMC optimality conjecture. MCMC performs as well as…

Logarithmic depth-scaling conjecture. The optimal depth satisfies

Boundary-condition diffusion conjecture. The influence of the single-node boundary conditions under Method I takes more iteration steps to diffuse messages to the bulk of the netwo…

In atomic routing games, let $x_e^*(\tau)$ denote the toll-dependent equilibrium flow on edge $e$, and let $x_e^S$ denote the flow minimizing the social cost during the upper-level…

The paper studies message-passing algorithms for MAP inference over $\mathbb{L}_2$, including standard and accelerated schemes derived from entropy regularization. Optimal-transpor…

Let $P_0$ be a signal distribution and $P_\mathrm{out}(y\mid z)$ an output likelihood satisfying the symmetry conditions that $P_0(x_1)=P_0(x_2)$ whenever $|x_1|=|x_2|$ and…

Let $J=(J_{ij})$ be the interaction matrix, and let $m_i$ and $v_i$ denote the associated magnetizations and variances. For each positive integer $p$, sum over pairwise distinct in…

The paper considers belief propagation (BP) and related message-passing algorithms for inference problems in which computationally efficient algorithms are compared with informatio…

The message-passing optimization uses binary transmitter–receiver variables $s_n\in\{0,1\}$ and link-selection variables $p_{n,m}\in[0,1]$ subject to $p_{n,m}\leq s_n(1-s_m)$ and…

Consider the message-passing algorithm on a network graph, with directed-edge messages $W^{i\to j}(t)$ and $H^{i\to j}(t)$ updated synchronously from arbitrary initial message valu…

Let $\mathcal{G}=(I,E)$ be the network graph, with $n=|I|$ nodes and $m=|E|$ edges, and let the message-passing algorithm (MPA) compute harmonic influence on this graph. The algori…

Message-passing label-recovery conjecture. A result similar to the stated error-scaling proposition should hold for label recovery using the MP algorithm.

Consider the large-system limit of the multiple-measurement vector model with jointly sparse signal vectors $\mathbf{x}_n=[x_n^{(1)},\ldots,x_n^{(J)}]$, noisy super-symbol pseudo-d…

Let $\delta$ denote the sampling ratio and let $\delta_{\rm u}$ be the spectral threshold at which the spectral approach achieves weak recovery. Fundamental-limit conjecture. The t…

Spatially coupled sparse superposition codes (SC-SS codes) are used over memoryless channels with generalized approximate message passing (GAMP) decoding. The state evolution (SE)…

Let $\Gamma$ be a positive definite matrix, and let $c_{ij}$ denote the reweighting parameters of the asynchronous algorithm. Asynchronous convergence conjecture. For every positiv…

Let $\Gamma$ be a positive definite matrix, and let the reweighted message-passing algorithm use its associated parameters. Convergence conjecture. For every positive definite…