Structured filtering

Abstract

A major challenge facing existing sequential Monte Carlo methods for parameter estimation in physics stems from the inability of existing approaches to robustly deal with experiments that have different mechanisms that yield the results with equivalent probability. We address this problem here by proposing a form of particle filtering that clusters the particles that comprise the sequential Monte Carlo approximation to the posterior before applying a resampler. Through a new graphical approach to thinking about such models, we are able to devise an artificial-intelligence based strategy that automatically learns the shape and number of the clusters in the support of the posterior. We demonstrate the power of our approach by applying it to randomized gap estimation and a form of low circuit-depth phase estimation where existing methods from the physics literature either exhibit much worse performance or even fail completely.

Learning Quantum Systems

“…A practical difficulty is that post-processing the Bayesian distribution requires to evaluate it on a grid of φ values, which can be problematic for broad distributions and in multiparameter scenarios. An efficient Bayesian inference for the estimation of multiple parameters [51,266,267] thus requires using approximate methods, such as particle-filtering and Sequential Monte Carlo methods [60,265,268], or structured filtering [269] when dealing with multiple, equivalent optima.…”

Learning models of quantum systems from experiments

“…Inheritance rules can be seen as an extreme pruning rule for all the other nodes in µ (Fig. 1d), similarly to what adopted for a graphical model exploration in [52]. Therefore, another way to mitigate the greediness of the approach is to discard only those particularly unsuccessful models Ĥr , that have: B rj < b , ∀j in the same layer and b a user-defined threshold.…”

“…The reason to adopt a logarithmic likelihood is here that likelihoods are prone to numerical instabilities as the number of sample measurement grows [50], so that adopting a log-difference instead of a ratio can help reducing artefacts. BFs are known to be a statistically robust measure for comparing the predictive power of different models, whilst favourably weighting less structure to limit overfitting [34], and have been successfully used in the context of resolving multi-modal distributions in [52]. The resulting B ij are stored as a comparative Directed Acyclic Graph (cDAG) representation across the same nodes, where the edges' directionality maps the sign of B ij − 1, pointing towards the model favoured by statistical evidence (Fig.…”

“…Degeneracies in the likelihood function are known to mislead sequential Monte-Carlo algorithms, such as that exploited by CLE, which are implicitly based on assumptions of unimodality [51]. This problem was recently addressed in [52].…”

Bayesian ACRONYM Tuning

“…In practice, we use a method proposed by Liu and West [29] to move the particles but other methods exist and we recommend reviewing [28,30,31] for more details. Here, we will use the implementation of particle filtering and Liu-West resampling provided by the QInfer package [32].…”