What can statisticians learn from the analysis of C.elegans data?

Speaker

Gonzalo E. Mena, University of Oxford

We live in revolutionary times for neuroscience; the recent advent of technologies for the recording of entire brains at massive scales is transforming our understanding of the mind. In this talk I argue that these developments are also shaping the way we conceive statistics; the challenges and bottlenecks that arise in these new regimes often reveal the brittleness of our current tools, dictating the need for new methods and motivating new questions.

I will focus on my contribution to NeuroPAL, a new breakthrough technology that enables the colorful imaging of every single neuron in the brain of the C.elegans worm. I will describe new statistical methods for two challenging tasks arising in these datasets; neural segmentation and identification, where classical methods fall short. Behind these new methods there is a key statistical physics principle, the so-called Schrödinger bridge, a ‘thought experiment’ that realizes the solution of an entropy-regularized optimal transport problem. This thought experiment was proposed in 1932 but has not yet percolated into the mainstream of statistics. I will show how it affords us with new rationale for the design of better statistical methods.  

First, I will comment on the statistical (sample complexity) benefits of entropic optimal transport and how a loss function based on this principle is a better optimization objective than the log-likelihood for clustering, reducing pathologies such as bad local optima and inconsistency. In consequence, a new algorithm derived from this loss, Sinkhorn EM, attains better, more robust neural segmentation performance. Then, I will comment on an alternative perspective of the Schrödinger bridge, the challenging problem of the inference of permutations: I will show how some approximate inference methods can be used for identifying neurons in C.elegans, As a result, we obtain meaningful uncertainty quantification in this hard combinatorial setup. I will further comment on how these novel methods have proven their usefulness in other contexts such as deep learning.

Finally, I will present some of my work on a recent pressing problem, the analysis of the true impact of the ongoing pandemic. This problem also raises relevant statistical questions regarding identifiability.
Gonzalo E. Mena’s website
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