46 problems

Consider the belief propagation equations for the matrix factorization model and their fixed points. Bayes-optimal inference refers to inference under the true generative distribut…

Robust reconstruction independence conjecture. The robust reconstruction accuracy is independent of $\delta$ for any parameters, and the same conclusion holds for more general tree…

Let a US-LDPC code be a code from the ensemble under consideration, and let its weight enumerator function (WEF) be calculated using belief propagation (BP) at a fixed point. Asymp…

Belief propagation (BP) is understood through its fixed points, and PCS-style analysis concerns the study of instanton spectra using an accelerated method. BP analysis conjecture.…

Alternative-gauge cancellation conjecture. For some other classes of graphical models, such as those naturally defined on regular lattices, similar cancellations can take place for…

Consider linear-programming (LP) decoding as a large-signal-to-noise-ratio limit of belief-propagation decoding, and suppose that an LP modification is required to preserve the lin…

Let an instanton noise configuration cause a failure of the bare belief-propagation (BP) decoder, and consider the loop-calculus expansion of the partition function, whose zero-ord…

Finite-termination conjecture. If $\pi^*$ is unique, then the min-sum auction I algorithm terminates after finitely many iterations when this condition is removed from step (4).

Consider the sufficient convergence bounds for loopy belief propagation (LBP) in graphical models with discrete variables and nonnegative factors, including Corollary … is stronger…

Square-root saturation exponent conjecture. Away from the critical window, the exponent $\ell/3$ in the below-threshold bound can be improved to $\ell/2$, but not beyond; equivalen…

Exact-BP dichotomy conjecture. Exact BP should obey the same Kesten–Stigum dichotomy as the pairwise rule, with, below the threshold, a strictly faster saturation exponent than the…

Let $\mathbf{H}$ be the parity-check matrix of a BCH code, and compare its row density with that of parity-check matrices used for LDPC codes. Density conjecture. The root cause of…

In the setting of quantitative group testing with a non-binary alphabet, let BP denote belief-propagation decoding and let spatial coupling refer to a spatially coupled code or gra…

Consider the belief-propagation operator for the symmetric Potts broadcasting model, with reconstruction threshold and Kesten–Stigum threshold given by $d\lambda^2=1$. Let BP uniqu…

Marginal-velocity conjecture. In line with previous results, the selected value of $\theta$ is the one for which

Consider a finite sample for which the critical temperatures $T_\text{\tiny KS}$ and $T_d$ are estimated by belief-propagation stability analyses. For each paired sample estimate,…

Angelini et al.'s Kesten–Stigum threshold conjecture. The condition $(q-1)\mu_2^2>d$ marks the phase transition for the performance of belief-propagation algorithms.

Belief Propagation entropy conjecture. In the limit or regime $n\to\infty$, the entropy of those partitions is given by the results of Belief Propagation.

Let $\mathrm{M}$ be a model with unstable fixed point $\overline{m}$, and let $\mathrm{M}^{\times}$ denote its null model. Belief-propagation detection conjecture. BP should succes…

Let $\mathrm{M}$ be a model with fixed point $\overline{m}$. The fixed point is unstable when arbitrarily small perturbations of $\overline{m}$ lead BP iteration away from it. Beli…

Let $\mathrm{M}$ be a statistical model with canonical initialization $\overline{m}$ for belief propagation. The initialization $\overline{m}$ is stable when there is a neighborhoo…

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

Condensation-threshold conjecture. The condensation threshold $\alpha_c$ should be the threshold up to which belief-propagation-inspired algorithms are effective.

Consider the asymmetric stochastic block model in which the information about community memberships carried by the vertex labels tends to zero: a fraction $\beta$ of vertices revea…

Let $G(\alpha)$ be the function governing the belief-propagation recursion in the labeled stochastic block model, let $p$ denote the community-balance parameter, and let $\lambda$…