Shuffled linear regression through graduated convex relaxation

The shuffled linear regression problem aims to recover linear relationships in datasets where the correspondence between input and output is unknown. This problem arises in a wide range of applications including survey data, in which one needs to decide whether the anonymity of the responses can be preserved while uncovering significant statistical connections. In this work, we propose a novel optimization algorithm for shuffled linear regression based on a posterior-maximizing objective function assuming Gaussian noise prior. We compare and contrast our approach with existing methods on synthetic and real data. We show that our approach performs competitively while achieving empirical running-time improvements. Furthermore, we demonstrate that our algorithm is able to utilize the side information in the form of seeds, which recently came to prominence in related problems

Functional Limit Theorems for Local Functionals of Dynamic Point Processes

We establish functional limit theorems for local, additive, interaction functions of temporally evolving point processes. The dynamics are those of a spatial Poisson process on the flat torus with points subject to a birth-death mechanism, and which move according to Brownian motion while alive. The results reveal the existence of a phase diagram describing at least three distinct structures for the limiting processes, depending on the extent of the local interactions and the speed of the Brownian motions. The proofs, which identify three different limits, rely heavily on Malliavin-Stein bounds on a representation of the dynamic point process via a distributionally equivalent marked point process

Coding schemes for broadcast erasure channels with feedback: the two multicast case

We consider the single hop broadcast packet erasure channel (BPEC) with two multicast sessions (each of them destined to a different group of $N$ users) and regularly available instantaneous receiver ACK/NACK feedback. Using the insight gained from recent work on BPEC with unicast and degraded messages [1], [2], we propose a virtual queue based session-mixing algorithm, which does not rely on knowledge of channel statistics and achieves capacity for $N=2$ and iid erasures. Since the optimal extension of this algorithm to $N>2$ is not straightforward, we then describe a low complexity algorithm which outperforms standard timesharing for arbitrary $N$ and is actually asymptotically better than timesharing, for any finite $N$, as the erasure probability goes to zero. We finally provide, through an information-theoretic analysis, sufficient but not necessary asymptotic conditions between $N$ and $n$ (the number of transmissions) for which the achieved sum rate, under \textit{any} coding scheme, is essentially identical to that of timesharing