Approximate Message Passing (AMP) algorithms are a class of iterative procedures for computationally-efficient estimation in high-dimensional inference and estimation tasks. Due to the presence of an ‘Onsager’ correction term in its iterates, forN×Mdesign matrices A with i.i.d. Gaussian entries, the asymptotic distribution of the estimate at any iteration of the algorithm can be exactly characterized in the large system limit asM/N→ δ ∈ (0,∞) via a scalar recursion referred to as state evolution. In this paper, we show that appropriate functionals of the iterates, in fact, concentrate around their limiting values predicted by these asymptotic distributions with rates exponentially fast inNfor a large class of AMP-style algorithms, including those that are used when high-dimensional generalized linear regression models are assumed to be the data-generating process, like the generalized AMP algorithm, or those that are used when the measurement matrix is assumed to be rotationally invariant instead of i.i.d. Gaussian, like vector AMP and generalized vector AMP. In practice, these more general AMP algorithms have many applications, for example in communications or imaging, and this work provides the first study of finite sample behavior of such algorithms.

Vector Approximate Message Passing is a computationally-efficient iterative algorithm for estimation in high-dimensional regression problems. Due to the presence of an `Onsager' correction term in its iterates, for a wide class of N × M design matrices, namely those that are right orthogonally-invariant, the asymptotic distribution of the algorithm's estimate of the signal at any iteration can be exactly characterized in the large system limit as M/N → δ ∈ (0,∞) via a scalar recursion referred to as state evolution. In this paper, we show that appropriate functionals of the iterates in fact concentrate around their limiting values predicted by these asymptotic distributions with rates exponentially fast in N.

Automatic conflict detection has grown in relevance with the advent of body-worn technology, but existing metrics such as turn-taking and overlap are poor indicators of conflict in police-public interactions. Moreover, standard techniques to compute them fall short when applied to such diversified and noisy contexts. We develop a pipeline catered to this task combining adaptive noise removal, non-speech filtering and new measures of conflict based on the repetition and intensity of phrases in speech. We demonstrate the effectiveness of our approach on body-worn audio data collected by the Los Angeles Police Department.