Summarizing Bayesian Nonparametric Mixture Posterior -- Sliced Optimal Transport Metrics for Gaussian Mixtures

Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al., 2022). We propose a novel approach for summarizing posterior inference in nonparametric Bayesian mixture models, prioritizing density estimation of the mixing measure (or mixture) as an inference target. One of the key features is the model-agnostic nature of the approach, which remains valid under arbitrarily complex dependence structures in the underlying sampling model. Using a decision-theoretic framework, our method identifies a point estimate by minimizing posterior expected loss. A loss function is defined as a discrepancy between mixing measures. Estimating the mixing measure implies inference on the mixture density and the random partition. Exploiting the discrete nature of the mixing measure, we use a version of sliced Wasserstein distance. We introduce two specific variants for Gaussian mixtures. The first, mixed sliced Wasserstein, applies generalized geodesic projections on the product of the Euclidean space and the manifold of symmetric positive definite matrices. The second, sliced mixture Wasserstein, leverages the linearity of Gaussian mixture measures for efficient projection.

A cryogenic SRAM based arbitrary waveform generator in 14 nm for spin qubit control

Realization of qubit gate sequences require coherent microwave control pulses with programmable amplitude, duration, spacing and phase. We propose an SRAM based arbitrary waveform generator for cryogenic control of spin qubits. We demonstrate in this work, the cryogenic operation of a fully programmable radio frequency arbitrary waveform generator in 14 nm FinFET technology. The waveform sequence from a control processor can be stored in an SRAM memory array, which can be programmed in real time. The waveform pattern is converted to microwave pulses by a source-series-terminated digital to analog converter. The chip is operational at 4 K, capable of generating an arbitrary envelope shape at the desired carrier frequency. Total power consumption of the AWG is 40-140mW at 4 K, depending upon the baud rate. A wide signal band of 1-17 GHz is measured at 4 K, while multiple qubit control can be achieved using frequency division multiplexing at an average spurious free dynamic range of 40 dB. This work paves the way to optimal qubit control and closed loop feedback control, which is necessary to achieve low latency error mitigation

Consensus Monte Carlo for Random Subsets using Shared Anchors

We present a consensus Monte Carlo algorithm that scales existing Bayesian nonparametric models for clustering and feature allocation to big data. The algorithm is valid for any prior on random subsets such as partitions and latent feature allocation, under essentially any sampling model. Motivated by three case studies, we focus on clustering induced by a Dirichlet process mixture sampling model, inference under an Indian buffet process prior with a binomial sampling model, and with a categorical sampling model. We assess the proposed algorithm with simulation studies and show results for inference with three datasets: an MNIST image dataset, a dataset of pancreatic cancer mutations, and a large set of electronic health records (EHR). Supplementary materials for this article are available online.