Simon Barthelmé

Expectation propagation for likelihood-free inference

Many models of interest in the natural and social sciences have no closed-form likelihood function, which means that they cannot be treated using the usual techniques of statistical inference. In the case where such models can be efficiently simulated, Bayesian inference is still possible thanks to the approximate Bayesian computation (ABC) algorithm. Although many refinements have been suggested, ABC inference is still far from routine. ABC is often excruciatingly slow due to very low acceptance rates. In addition, ABC requires introducing a vector of “summary statistics” s(y), the choice of which is relatively arbitrary, and often require some trial and error, making the whole process laborious for the user. We introduce in this work the EP-ABC algorithm, which is an adaptation to the likelihood-free context of the variational approximation algorithm known as expectation propagation. The main advantage of EP-ABC is that it is faster by a few orders of magnitude than standard algorithms, while producing an overall approximation error that is typically negligible. A second advantage of EP-ABC is that it replaces the usual global ABC constraint ‖s(y) − s(y⋆)‖ ⩽ ϵ, where s(y⋆) is the vector of summary statistics computed on the whole dataset, by n local constraints of the form ‖si(yi) − si(y⋆i)‖ ⩽ ϵ that apply separately to each data point. In particular, it is often possible to take si(yi) = yi, making it possible to do away with summary statistics entirely. In that case, EP-ABC makes it possible to approximate directly the evidence (marginal likelihood) of the model. Comparisons are performed in three real-world applications that are typical of likelihood-free inference, including one application in neuroscience that is novel, and possibly too challenging for standard ABC techniques.

Spatial statistics and attentional dynamics in scene viewing

In humans and in foveated animals visual acuity is highly concentrated at the center of gaze, so that choosing where to look next is an important example of online, rapid decision-making. Computational neuroscientists have developed biologically-inspired models of visual attention, termed saliency maps, which successfully predict where people fixate on average. Using point process theory for spatial statistics, we show that scanpaths contain, however, important statistical structure, such as spatial clustering on top of distributions of gaze positions. Here, we develop a dynamical model of saccadic selection that accurately predicts the distribution of gaze positions as well as spatial clustering along individual scanpaths. Our model relies on activation dynamics via spatially-limited (foveated) access to saliency information, and, second, a leaky memory process controlling the re-inspection of target regions. This theoretical framework models a form of context-dependent decision-making, linking neural dynamics of attention to behavioral gaze data.

The Poisson transform for unnormalised statistical models

Contrary to standard statistical models, unnormalised statistical models only specify the likelihood function up to a constant. While such models are natural and popular, the lack of normalisation makes inference much more difficult. Extending classical results on the multinomial-Poisson transform (Baker In: J Royal Stat Soc 43(4):495–504, 1994), we show that inferring the parameters of a unnormalised model on a space

Visualizing the effects of a changing distance on data using continuous embeddings

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Expectation propagation in the large data limit

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Divide and conquer in ABC: Expectation-Progagation algorithms for likelihood-free inference

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