Neural Information Processing Systems http://nips.cc/

Stimulus-drivenbrain-computer interfaces (BCIs), such astheP300 speller,rely onusing asequence ofsensory stimuli toelicit specific neural responses ascontrol signals, while a user attends to relevant target stimuli that occur within the sequence. In current BCIs, the stimulus presentation schedule is typically generated in a pseudo-random fashion. Given the non-stationarity of brain electrical signals, a better strategy could be to adapt the stimulus presentation schedule in real-time by selecting the optimal stimuli that will maximize the signal-to-noise ratios of the elicited neural responses and provide the most information about the user's intent based on the uncertainties of the data being measured. However, the high-dimensional stimulus space limits the development of algorithms with tractable solutions for optimized stimulus selection to allow for real-time decision-making within the stringent time requirements of BCI processing.

We prove its consistency and show that the asymptotic variance ofitssolution canattaintheequality oftheefficiencybound undermild regularity conditions.

Such feedback can be stochastic, e.g. the

Sampling and inference algorithms behave poorly as the number of modes increases, andthisproblem isonlyexacerbated inthiscontextsinceincreasing thenumber ofcomponents in the mixture model leads to a super-exponential increase in the number of modes of the posterior.

The classic Mallows model is a widely-used tool to realize distributions on permutations.

Tuning scientific and probabilistic machine learning models - for example, partial differential equations, Gaussian processes, or Bayesian neural networks - often relies on evaluating functions of matrices whose size grows with the data set or the number of parameters. While the state-of-the-art for evaluating these quantities is almost always based on Lanczos and Arnoldi iterations, the present work is the first to explain how to differentiate these workhorses of numerical linear algebra efficiently. To get there, we derive previously unknown ad-joint systems for Lanczos and Arnoldi iterations, implement them in JAX, and show that the resulting code can compete with Diffrax when it comes to differentiating PDEs, GPyTorch for selecting Gaussian process models and beats standard factorisation methods for calibrating Bayesian neural networks. All this is achieved without any problem-specific code optimisation.

Finally, we apply our method to training deep convolutional neural networks, and the experimental results show that the proposed method achievesfasterconvergence,lowermemoryconsumption,andbettergeneralization errorthancomparedmethods.