Archive for eclipse
watching the eclipse
Posted in Kids, pictures, Running, Travel with tags 20h17, eclipse, ghost image, jatp, Parc de Sceaux, Sceaux, solar eclipse, sunset on August 21, 2026 by xi'an
information maximising neural networks summaries
Posted in pictures, Statistics with tags ABC, eclipse, fiducial inference, Fisher information, IAP, moon, neural network, Observatoire de Paris, summary statistics on February 6, 2019 by xi'an
After missing the blood moon eclipse last night, I had a meeting today at the Paris observatory (IAP), where we discussed an ABC proposal made by Tom Charnock, Guilhem Lavaux, and Benjamin Wandelt from this institute.
“We introduce a simulation-based machine learning technique that trains artificial neural networks to find non-linear functionals of data that maximise Fisher information : information maximising neural networks.” T. Charnock et al., 2018
The paper is centred on the determination of “optimal” summary statistics. With the goal of finding “transformation which maps the data to compressed summaries whilst conserving Fisher information [of the original data]”. Which sounds like looking for an efficient summary and hence impossible in non-exponential cases. As seen from the description in (2.1), the assumed distribution of the summary is Normal, with mean μ(θ) and covariance matrix C(θ) that are implicit transforms of the parameter θ. In that respect, the approach looks similar to the synthetic likelihood proposal of Wood (2010). From which an unusual form of Fisher information can be derived, as μ(θ)’C(θ)⁻¹μ(θ)… A neural net is trained to optimise this information criterion at a given (so-called fiducial) value of θ, in terms of a set of summaries of the same dimension as the data. Which means the information contained in the whole data (likelihood) is not necessarily recovered, linking with this comment from Edward Ionides (in a set of lectures at Wharton).
“Even summary statistics derived by careful scientific or statistical reasoning have been found surprisingly uninformative compared to the whole data likelihood in both scientific investigations (Shrestha et al., 2011) and simulation experiments (Fasiolo et al., 2016)” E. Ionides, slides, 2017
The maximal Fisher information obtained in this manner is then used in a subsequent ABC step as the natural metric for the distance between the observed and simulated data. (Begging the question as to why being maximal is necessarily optimal.) Another question is about the choice of the fiducial parameter, which choice should be tested by for instance iterating the algorithm a few steps. But having to run simulations for a single value of the parameter is certainly a great selling point!
it’s only an eclipse, for heavens sake!
Posted in Statistics with tags astronomy, eclipse, rationalism, religions, secularism, solar system on September 2, 2017 by xi'anI have been amazed and utterly baffled by the number of commentaries about the solar eclipse of last week that involved metaphysics and religious aspects. An eclipse is a most natural [and beautiful] phenomenon of one astronomical object getting in front of another one in a very predictable way: no reason to invoke deities or spirits in the process! 
