12 problems

Let $\theta\in\mathbb{R}^d$ be an $s$-sparse mean vector in the horizontal-split distributed mean-estimation model, where each of $K$ machines holds a subset of $m$ independent sam…

Global convergence conjecture. Such self-confidence adaptation dynamics globally converge to one of the equivalent strict Nash equilibria of the game.

Let $A$ be the system matrix, let $C^i$ be the observation matrix at node $i$, let $\mathcal{S}$ index the sensors, and let $\mathcal{N}$ index the network nodes. Assume: (A1) $A$…

Consider an algorithm indexed by $k$ for nonparametric estimation, with $r$ denoting the number of interactions and with the optimal risk given by (erpb4). Diverging-interaction co…

Unimodality conjecture. The function $\bar{J}_{i}(u_i,u_j)$ is unimodal.

Consider estimating correlations between remotely observed jointly Gaussian random vectors under one-way communication constraints, with unlimited local samples. Let the communicat…

All-time proportionality conjecture. The estimator is proportional to the BLUE and can be written as

In generalized distributed compressive sensing, partial common information may occur among multiple signals, and the proposed sequential correlation search attempts to identify the…

Let $V$ be the finite set of agents, let $X_v(t)$ be the estimator of agent $v$ at time $t$ in the model where agents retain their previous values, and let $X(\infty)$ denote the l…

Let $X(\infty)$ be the limiting estimator produced by the memoryless iterative process on an interval graph of length $n$, and let $Z(\infty)$ be the benchmark estimator used in th…

Gaussian-profile conjecture. The coefficients $A_k$ approach a Gaussian profile centered at the midpoint, in the sense that

Let $V$ be the finite set of agents, let $X_v(t)$ denote the estimator held by agent $v\in V$ at iteration $t$, and let $X(\infty)$ be a common limiting estimator. Convergence conj…