Variational message passing for online polynomial NARMAX identification

We propose a variational Bayesian inference procedure for online nonlinear system identification. For each output observation, a set of parameter posterior distributions is updated, which is then used to form a posterior predictive distribution for future outputs. We focus on the class of polynomial NARMAX models, which we cast into probabilistic form and represent in terms of a Forney-style factor graph. Inference in this graph is efficiently performed by a variational message passing algorithm. We show empirically that our variational Bayesian estimator outperforms an online recursive least-squares estimator, most notably in small sample size settings and low noise regimes, and performs on par with an iterative least-squares estimator trained offline.

Back to the Future -- Sequential Alignment of Text Representations

Language evolves over time in many ways relevant to natural language processing tasks. For example, recent occurrences of tokens 'BERT' and 'ELMO' in publications refer to neural network architectures rather than persons. This type of temporal signal is typically overlooked, but is important if one aims to deploy a machine learning model over an extended period of time. In particular, language evolution causes data drift between time-steps in sequential decision-making tasks. Examples of such tasks include prediction of paper acceptance for yearly conferences (regular intervals) or author stance prediction for rumours on Twitter (irregular intervals). Inspired by successes in computer vision, we tackle data drift by sequentially aligning learned representations. We evaluate on three challenging tasks varying in terms of time-scales, linguistic units, and domains. These tasks show our method outperforming several strong baselines, including using all available data. We argue that, due to its low computational expense, sequential alignment is a practical solution to dealing with language evolution.

On reducing sampling variance in covariate shift using control variates

Covariate shift classification problems can in principle be tackled by importance-weighting training samples. However, the sampling variance of the risk estimator is often scaled up dramatically by the weights. This means that during cross-validation - when the importance-weighted risk is repeatedly evaluated - suboptimal hyperparameter estimates are produced. We study the sampling variances of the importance-weighted versus the oracle estimator as a function of the relative scale of the training data. We show that introducing a control variate can reduce the variance of the importance-weighted risk estimator, which leads to superior regularization parameter estimates when the training data is much smaller in scale than the test data.