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The modern world contains an immense number of different and interacting systems, from the evolution of weather systems to variations in the stock market, autonomous vehicles interacting with their environment, and the spread of diseases. For society to function, it is essential to understand the behavior of the world so that informed decisions can be made that are based on likely future outcomes. For instance, consider the spread of a new disease such as COVID-19 coronavirus. It is of great importance to be able to predict the number of people that will be infected at different points in time to ensure that appropriate health-care facilities are available. It is also of interest to be able to make decisions based on accurate information to best attenuate the spread of disease. Moreover, understanding specific attributes of a disease-such as the incubation time and number of unreported cases-and how certain we are about this knowledge are also crucial.

Statistical phylogenetic analysis currently relies on complex, dedicated software packages, making it difficult for evolutionary biologists to explore new models and inference strategies. Recent years have seen more generic solutions based on probabilistic graphical models, but this formalism can only partly express phylogenetic problems. Here, we show that universal probabilistic programming languages (PPLs) solve the expressivity problem, while still supporting automated generation of efficient inference algorithms. To prove the latter point, we develop automated generation of sequential Monte Carlo (SMC) algorithms for PPL descriptions of arbitrary biological diversification (birth-death) models. SMC is a new inference strategy for these problems, supporting both parameter inference and efficient estimation of Bayes factors that are used in model testing. We take advantage of this in automatically generating SMC algorithms for several recent diversification models that have been difficult or impossible to tackle previously. Finally, applying these algorithms to 40 bird phylogenies, we show that models with slowing diversification, constant turnover and many small shifts generally explain the data best. Our work opens up several related problem domains to PPL approaches, and shows that few hurdles remain before these techniques can be effectively applied to the full range of phylogenetic models. Ronquist, Kudlicka, Senderov and colleagues present universal probabilistic programming as a powerful method for modeling and inference in statistical phylogenetics. They provide an accessible introduction to these techniques and apply them in inferring complex patterns of diversification and turnover in birds., QC 20210329Erratum: 10.1038/s42003-021-01922-8 (Scopusid: 2-s2.0-85102525244)

In this paper, we propose variations of Willems' fundamental lemma that utilize second-order moments such as correlation functions in the time domain and power spectra in the frequency domain. We believe that using a formulation with estimated correlation coefficients is suitable for data compression, and possibly can reduce noise. Also, the formulations in the frequency domain can enable modeling of a system in a frequency region of interest., Part of proceedings: ISBN 978-1-6654-3659-5QC 20220601

Deep state space models (SSMs) are an actively researched model class for temporal models developed in the deep learning community which have a close connection to classic SSMs. The use of deep SSMs as a black-box identification model can describe a wide range of dynamics due to the flexibility of deep neural networks. Additionally, the probabilistic nature of the model class allows the uncertainty of the system to be modelled. In this work a deep SSM class and its parameter learning algorithm are explained in an effort to extend the toolbox of nonlinear identification methods with a deep learning based method. Six recent deep SSMs are evaluated in a first unified implementation on nonlinear system identification benchmarks. Copyright (C) 2021 The Authors., Funding Agencies|Wallenberg AI, Autonomous Systems and Software Program (WASP) - Knut and Alice Wallenberg Foundation; Swedish Research CouncilSwedish Research CouncilEuropean Commission [2016-06079, 2019-04956]

We present an algorithm to estimate and quantify the uncertainty of the accelerometers relative geometry in an inertial sensor array. We formulate the calibration problem as a Bayesian estimation problem and propose an algorithm that samples the accelerometer positions posterior distribution using Markov chain Monte Carlo. By identifying linear substructures of the measurement model, the unknown linear motion parameters are analytically marginalized, and the remaining non-linear motion parameters are numerically marginalized. The numerical marginalization occurs in a low dimensional space where the gyroscopes give information about the motion. This combination of information from gyroscopes and analytical marginalization allows the user to make no assumptions of the motion before the calibration. It thus enables the user to estimate the accelerometer positions relative geometry by simply exposing the array to arbitrary twisting motion. We show that the calibration algorithm gives good results on both simulated and experimental data, despite sampling a high dimensional space., Funding Agencies|Wallenberg Autonomous Systems and Software Program (WASP); Swedish Foundation for Strategic Research (SSF) through the Project ASSEMBLE

QC 20210111

Deep learning is a topic of considerable interest today. Since it deals with estimating - or learning - models, there are connections to the area of System Identification developed in the Automatic Control community. Such connections are explored and exploited in this contribution. It is stressed that common deep nets such as feedforward and cascadeforward nets are nonlinear ARX (NARX) models, and can thus be easily incorporated in System Identification code and practice. The case of LSTM nets is an example of NonLinear State-Space (NLSS) models. Copyright (C) 2020 The Authors., Funding Agencies|Swedish Foundation for Strategic Research (SSF) via the project ASSEMBLE [RIT15-0012]; Swedish Research CouncilSwedish Research CouncilEuropean Commission [2017-03807, 621-2016-06079]; Vinnovas Competence Center LinkSicVinnova

We consider the combined use of resampling and partial rejection control in sequential Monte Carlo methods, also known as particle filters. While the variance reducing properties of rejection control are known, there has not been (to the best of our knowledge) any work on unbiased estimation of the marginal likelihood (also known as the model evidence or the normalizing constant) in this type of particle filter. Being able to estimate the marginal likelihood without bias is highly relevant for model comparison, computation of interpretable and reliable confidence intervals, and in exact approximation methods, such as particle Markov chain Monte Carlo. In the paper we present a particle filter with rejection control that enables unbiased estimation of the marginal likelihood., Funding Agencies|Swedish Foundation for Strategic Research via the project ASSEMBLESwedish Foundation for Strategic Research [RIT15-0012]; Swedish Research CouncilSwedish Research CouncilEuropean Commission [2013-4853, 2017-03807]

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as expectations with respect to the posterior distribution. The key challenge is to approximate these intractable expectations. In this tutorial, we review sequential Monte Carlo (SMC), a random-sampling-based class of methods for approximate inference. First, we explain the basics of SMC, discuss practical issues, and review theoretical results. We then examine two of the main user design choices: the proposal distributions and the so called intermediate target distributions. We review recent results on how variational inference and amortization can be used to learn efficient proposals and target distributions. Next, we discuss the SMC estimate of the normalizing constant, how this can be used for pseudo-marginal inference and inference evaluation. Throughout the tutorial we illustrate the use of SMC on various models commonly used in machine learning, such as stochastic recurrent neural networks, probabilistic graphical models, and probabilistic programs.

Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without a good proposal distribution can perform poorly, in particular in high dimensions. We propose nested sequential Monte Carlo, a methodology that generalizes the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correctSMCalgorithm. This way, we can compute an "exact approximation" of, e. g., the locally optimal proposal, and extend the class of models forwhichwe can perform efficient inference using SMC. We showimproved accuracy over other state-of-the-art methods on several spatio-temporal state-space models., Funding Agencies|Swedish Research Council [2016-04278, 621-2016-06079]; Swedish Foundation for Strategic Research [RIT15-0012, ICA16-0015]

In this paper, we present an approach to combine measurements from inertial sensors (accelerometers and gyroscopes) with time-of-arrival measurements from an ultrawideband (UWB) system for indoor positioning. Our algorithm uses a tightly coupled sensor fusion approach, where we formulate the problem as a maximum a posteriori (MAP) problem that is solved using an optimization approach. It is shown to lead to accurate 6-D position and orientation estimates when compared to reference data from an independent optical tracking system. To be able to obtain position information from the UWB measurements, it is imperative that accurate estimates of the UWB receivers positions and their clock offsets are available. Hence, we also present an easy-to-use algorithm to calibrate the UWB system using a maximum-likelihood (ML) formulation. Throughout this work, the UWB measurements are modeled by a tailored heavy-tailed asymmetric distribution to account for measurement outliers. The heavy-tailed asymmetric distribution works well on experimental data, as shown by analyzing the position estimates obtained using the UWB measurements via a novel multilateration approach., Funding Agencies|Control, Autonomy, and Decision-making In Complex Systems (CADICS): a Linnaeus Center - Swedish Research Council (VR); BALANCE: a European Commission FP7 Research Project; Swedish Research Council (VR) [621-2013-5524]