Efficient Sequential Monte-Carlo Samplers for Bayesian Inference

In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such inference problems. However, in the presence of a high-dimensional and/or multimodal posterior distribution, it is widely documented that standard Monte-Carlo techniques could lead to poor performance. In this paper, the study is focused on a Sequential Monte-Carlo (SMC) sampler framework, a more robust and efficient Monte Carlo algorithm. Although this approach presents many advantages over traditional Monte-Carlo methods, the potential of this emergent technique is however largely underexploited in signal processing. In this work, we aim at proposing some novel strategies that will improve the efficiency and facilitate practical implementation of the SMC sampler specifically for signal processing applications. Firstly, we propose an automatic and adaptive strategy that selects the sequence of distributions within the SMC sampler that minimizes the asymptotic variance of the estimator of the posterior normalization constant. This is critical for performing model selection in modelling applications in Bayesian signal processing. The second original contribution we present improves the global efficiency of the SMC sampler by introducing a novel correction mechanism that allows the use of the particles generated through all the iterations of the algorithm (instead of only particles from the last iteration). This is a significant contribution as it removes the need to discard a large portion of the samples obtained, as is standard in standard SMC methods. This will improve estimation performance in practical settings where computational budget is important to consider.Comment: arXiv admin note: text overlap with arXiv:1303.3123 by other author

Choice and information in the public sector: a Higher Education case study

Successive governments have encouraged the view of users of public services as consumers, choosing between different providers on the basis of information about the quality of service. As part of this approach, prospective students are expected to make their decisions about which universities to apply to with reference to the consumer evaluations provided by the National Student Survey. However, a case study of a post-1992 university showed that not all students made genuine choices and those who did tended to be in stronger social and economic positions. Where choices were made, they were infrequently based on external evaluations of quality

Global Carbon Budget: Ocean carbon sink.

CO2 emissions from human activities, the main contributor to global climate change, are set to rise again in 2014 reaching 40 billion tonnes CO2 The natural carbon ‘sinks’ on land and in the ocean absorb on average 55% of the total CO2 emissions, thus slowing the rate of global climate change Increasing CO2 in the oceans is causing ocean acidificatio

Accelerating Motion Planning via Optimal Transport

Motion planning is still an open problem for many disciplines, e.g., robotics, autonomous driving, due to their need for high computational resources that hinder real-time, efficient decision-making. A class of methods striving to provide smooth solutions is gradient-based trajectory optimization. However, those methods usually suffer from bad local minima, while for many settings, they may be inapplicable due to the absence of easy-to-access gradients of the optimization objectives. In response to these issues, we introduce Motion Planning via Optimal Transport (MPOT) -- a \textit{gradient-free} method that optimizes a batch of smooth trajectories over highly nonlinear costs, even for high-dimensional tasks, while imposing smoothness through a Gaussian Process dynamics prior via the planning-as-inference perspective. To facilitate batch trajectory optimization, we introduce an original zero-order and highly-parallelizable update rule: the Sinkhorn Step, which uses the regular polytope family for its search directions. Each regular polytope, centered on trajectory waypoints, serves as a local cost-probing neighborhood, acting as a \textit{trust region} where the Sinkhorn Step "transports" local waypoints toward low-cost regions. We theoretically show that Sinkhorn Step guides the optimizing parameters toward local minima regions of non-convex objective functions. We then show the efficiency of MPOT in a range of problems from low-dimensional point-mass navigation to high-dimensional whole-body robot motion planning, evincing its superiority compared to popular motion planners, paving the way for new applications of optimal transport in motion planning.Comment: Published as a conference paper at NeurIPS 2023. Project website: https://sites.google.com/view/sinkhorn-step

A Carleman-Picard approach for reconstructing zero-order coefficients in parabolic equations with limited data

We propose a globally convergent computational technique for the nonlinear inverse problem of reconstructing the zero-order coefficient in a parabolic equation using partial boundary data. This technique is called the "reduced dimensional method". Initially, we use the polynomial-exponential basis to approximate the inverse problem as a system of 1D nonlinear equations. We then employ a Picard iteration based on the quasi-reversibility method and a Carleman weight function. We will rigorously prove that the sequence derived from this iteration converges to the accurate solution for that 1D system without requesting a good initial guess of the true solution. The key tool for the proof is a Carleman estimate. We will also show some numerical examples

Reconstruction of Short-Lived Particles using Graph-Hypergraph Representation Learning

In collider experiments, the kinematic reconstruction of heavy, short-lived particles is vital for precision tests of the Standard Model and in searches for physics beyond it. Performing kinematic reconstruction in collider events with many final-state jets, such as the all-hadronic decay of topantitop quark pairs, is challenging. We present HyPER, a graph neural network that uses blended graph-hypergraph representation learning to reconstruct parent particles from sets of final-state objects. HyPER is tested on simulation and shown to perform favorably when compared to existing state-of-the-art reconstruction techniques, while demonstrating superior parameter efficiency. The novel hypergraph approach allows the method to be applied to particle reconstruction in a multitude of different physics processes

Reaching peak emissions

Rapid growth in global CO2 emissions from fossil fuels and industry ceased in the past two years, despite continued economic growth. Decreased coal use in China was largely responsible, coupled with slower global growth in petroleum and faster growth in renewables