Models for human choice prediction in preference learning and psychophysics often consider only binary response data, requiring many samples to accurately learn preferences or perceptual detection thresholds. The response time (RT) to make each choice captures additional information about the decision process, however existing models incorporating RTs for choice prediction do so in fully parametric settings or over discrete stimulus sets. This is in part because the de-facto standard model for choice RTs, the diffusion decision model (DDM), does not admit tractable, differentiable inference. The DDM thus cannot be easily integrated with flexible models for continuous, multivariate function approximation, particularly Gaussian process (GP) models. We propose a novel differentiable approximation to the DDM likelihood using a family of known, skewed three-parameter distributions. We then use this new likelihood to incorporate RTs into GP models for binary choices. Our RT-choice GPs enable both better latent value estimation and held-out choice prediction relative to baselines, which we demonstrate on three real-world multivariate datasets covering both human psychophysics and preference learning applications.

Multivariate analysis of fMRI data has benefited substantially from advances in machine learning. Most recently, a range of probabilistic latent variable models applied to fMRI data have been successful in a variety of tasks, including identifying similarity patterns in neural data (Representational Similarity Analysis and its empirical Bayes variant, RSA and BRSA; Intersubject Functional Connectivity, ISFC), combining multi-subject datasets (Shared Response Mapping; SRM), and mapping between brain and behavior (Joint Modeling). Although these methods share some underpinnings, they have been developed as distinct methods, with distinct algorithms and software tools. We show how the matrix-variate normal (MN) formalism can unify some of these methods into a single framework. In doing so, we gain the ability to reuse noise modeling assumptions, algorithms, and code across models. Our primary theoretical contribution shows how some of these methods can be written as instantiations of the same model, allowing us to generalize them to flexibly modeling structured noise covariances. Our formalism permits novel model variants and improved estimation strategies: in contrast to SRM, the number of parameters for MN-SRM does not scale with the number of voxels or subjects; in contrast to BRSA, the number of parameters for MN-RSA scales additively rather than multiplicatively in the number of voxels. We empirically demonstrate advantages of two new methods derived in the formalism: for MN-RSA, we show up to 10x improvement in runtime, up to 6x improvement in RMSE, and more conservative behavior under the null. For MN-SRM, our method grants a modest improvement to out-of-sample reconstruction while relaxing an orthonormality constraint of SRM. We also provide a software prototyping tool for MN models that can flexibly reuse noise covariance assumptions and algorithms across models.

The dynamics of simple decisions are well understood and modeled as a class of random walk models (e.g. Laming, 1968; Ratcliff, 1978; Busemeyer and Townsend, 1993; Usher and McClelland, 2001; Bogacz et al., 2006). However, most real-life decisions include a rich and dynamically-changing influence of additional information we call context. In this work, we describe a computational theory of decision making under dynamically shifting context. We show how the model generalizes the dominant existing model of fixed-context decision making (Ratcliff, 1978) and can be built up from a weighted combination of fixed-context decisions evolving simultaneously. We also show how the model generalizes re- cent work on the control of attention in the Flanker task (Yu et al., 2009). Finally, we show how the model recovers qualitative data patterns in another task of longstanding psychological interest, the AX Continuous Performance Test (Servan-Schreiber et al., 1996), using the same model parameters.