RT @sbi_devs: 🚀 Join the 4th SBI Hackathon! 🚀. The last hackathon was a fantastic milestone in forming a collaborative open-source communit….

RT @KadhimKyra: Looking forward to the #Bernsteinconference tomorrow where I'll be presenting work developing a preliminary model of the mo….

Join millions who have switched to Grok.

Thrilled to be at #BernsteinConference next week to present my most recent work⬇️ on how probabilistic numerical methods can help with parameter inference in Hodgkin-Huxley models. If you’re curious or want to chat about fitting biophysical models, come by Poster 10 on Tue 2:15.

We built a simulator for biophysical neuron models that is.- all python.- accelerated.- fully differentiable.- capable of morphological detail.- scalable to >1M params. Very proud to be part of this! Much respect to @deismic_, who put most of it together. See what it can do ⬇️.

RT @lappalainenjk: Biggest joy and honour leading this project at the intersection of visual neuroscience and ML to a successful finish! Pa….

RT @sbi_devs: We just released a new version of `sbi`, and this one has _a ton_ of new features! Many of these features are thanks to more….

RT @mackelab: @gloecklermanuel and @deismic_ are at ICML to present our work on `All-in-one simulation-based inference`. Join us at ORAL 6F….

RT @alfcnz: It’s 2020. @samgreydanus pushes on @arXiv a remarkable unpublished paper. 4 years later, @hippopedoid helps getting it publishe….

RT @mackelab: After long and exhausting travels, the MackeLab has arrived in Vienna for ICML.

If you want to find out more, check out our code and paper or come say hi at #ICML2024 (Hall C 4-9 #1313 Tuesday 11:30) if you want to talk PN or ML + Neuro. @deismic_ and I will be there. 12/12.

Hence, you can do inference on ODEs now where the original method (top) previously struggled, like for a pretty complex HH model with 6 free parameters. 11/n

This improves the reliability of parameter estimates on a variety of ODEs, like the Lottka-Volterra system or Hodgkin-Huxley models of various complexities and only comes at a small cost-overhead compared to the original probabilistic ODE solver with a few tweaks (OURS+). 10/n

We show that for a 1D pendulum this controlled 'smoothing' effectively avoids local minima during optimization, i.e. a pendulum w. infinite period (green) and reliably seeks out the global optimum (dashed) thanks to successively better initializations (C). 9/n

By iteratively reducing the diffusion parameter along a predetermined schedule and initializing with the previous parameter estimate at every step, we force the optimizer to find good parameter estimates at a given level of decreasing uncertainty. 8/n.

We therefore propose diffusion tempering, a novel regularization technique for probabilistic numerical methods which dramatically increases the robustness of the optimization. 7/n.

In practice this increasing of (k^2) amounts to 'smoothing out' the loss surface, making the joint optimization very vulnerable to local minima. 6/n.

Namely, the optimizer can increase the likelihood that a bad ODE solution (grey) could have generated the data (black) by increasing the calibration/diffusion parameter (k^2), rather than by finding better parameters for the ODE. 5/n

We find that this is because the uncertainty of the probabilistic integrator is calibrated at the same time that the ODE parameters are being optimized, and this leads to undesirable behaviour. 4/n.

This approach has been shown to outperform classical RK least squares regression. However, in practice these methods still struggle in more complex nonlinear dynamical systems, like the Hodgkin-Huxley model. 3/n

Inferring parameters of an IVP from noisy measurements is often challenging due to uncertainty about both the ODE solution and the data. Probabilistic ODE solvers therefore re-cast the solution of IVPs as Bayesian inference. 2/n.