Estimating Barycenters of Measures in High Dimensions

Barycentric averaging is a principled way of summarizing populations of measures. Existing algorithms for estimating barycenters typically parametrize them as weighted sums of Diracs and optimize their weights and/or locations. However, these approaches do not scale to high-dimensional settings due to the curse of dimensionality. In this paper, we propose a scalable and general algorithm for estimating barycenters of measures in high dimensions. The key idea is to turn the optimization over measures into an optimization over generative models, introducing inductive biases that allow the method to scale while still accurately estimating barycenters. We prove local convergence under mild assumptions on the discrepancy showing that the approach is well-posed. We demonstrate that our method is fast, achieves good performance on low-dimensional problems, and scales to high-dimensional settings. In particular, our approach is the first to be used to estimate barycenters in thousands of dimensions.

Aligning Time Series on Incomparable Spaces

Dynamic time warping (DTW) is a useful method for aligning, comparing and combining time series, but it requires them to live in comparable spaces. In this work, we consider a setting in which time series live on different spaces without a sensible ground metric, causing DTW to become ill-defined. To alleviate this, we propose Gromov dynamic time warping (GDTW), a distance between time series on potentially incomparable spaces that avoids the comparability requirement by instead considering intra-relational geometry. We derive a Frank-Wolfe algorithm for computing it and demonstrate its effectiveness at aligning, combining and comparing time series living on incomparable spaces. We further propose a smoothed version of GDTW as a differentiable loss and assess its properties in a variety of settings, including barycentric averaging, generative modeling and imitation learning.

Multi-Graph Decoding for Code-Switching ASR

In the FAME! Project, a code-switching (CS) automatic speech recognition (ASR) system for Frisian-Dutch speech is developed that can accurately transcribe the local broadcaster's bilingual archives with CS speech. This archive contains recordings with monolingual Frisian and Dutch speech segments as well as Frisian-Dutch CS speech, hence the recognition performance on monolingual segments is also vital for accurate transcriptions. In this work, we propose a multi-graph decoding and rescoring strategy using bilingual and monolingual graphs together with a unified acoustic model for CS ASR. The proposed decoding scheme gives the freedom to design and employ alternative search spaces for each (monolingual or bilingual) recognition task and enables the effective use of monolingual resources of the high-resourced mixed language in low-resourced CS scenarios. In our scenario, Dutch is the high-resourced and Frisian is the low-resourced language. We therefore use additional monolingual Dutch text resources to improve the Dutch language model (LM) and compare the performance of single- and multi-graph CS ASR systems on Dutch segments using larger Dutch LMs. The ASR results show that the proposed approach outperforms baseline single-graph CS ASR systems, providing better performance on the monolingual Dutch segments without any accuracy loss on monolingual Frisian and code-mixed segments.