The Hitchhiker’s guide to nonlinear filtering

Kutschireiter, Anna; Surace, Simone Carlo; Pfister, Jean-Pascal

doi:10.1016/j.jmp.2019.102307

Cited by 13 publications

(13 citation statements)

References 54 publications

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“…The objective of CAI is to obtain the optimal posterior ppa t:T |s t:T , O t:T q over a full trajectory. There are many ways to approximate this desired posterior, ranging from variational inference (Beal et al, 2003;Wainwright & Jordan, 2008), message passing algorithms (Weiss & Freeman, 2000;Yedidia, 2011), and importance sampling (Kappen & Ruiz, 2016;Kutschireiter, Surace, & Pfister, 2020). Each of these approaches can be seen to correspond to a family of RL algorithms in the literature.…”

Section: Control As Inferencementioning

confidence: 99%

Reinforcement Learning as Iterative and Amortised Inference

Millidge,

Tschantz,

Seth

et al. 2020

Preprint

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There are several ways to categorise reinforcement learning (RL) algorithms, such as either modelbased or model-free, policy-based or planning-based, on-policy or off-policy, and online or offline. Broad classification schemes such as these help provide a unified perspective on disparate techniques and can contextualise and guide the development of new algorithms. In this paper, we utilise the control as inference framework to outline a novel classification scheme based on amortised and iterative inference. We demonstrate that a wide range of algorithms can be classified in this manner providing a fresh perspective and highlighting a range of existing similarities. Moreover, we show that taking this perspective allows us to identify parts of the algorithmic design space which have been relatively unexplored, suggesting new routes to innovative RL algorithms 1 .

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Section: Control As Inferencementioning

confidence: 99%

Reinforcement Learning as Iterative and Amortised Inference

Millidge,

Tschantz,

Seth

et al. 2020

Preprint

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“…As an important feature of the Nelson-Siegel-Svensson specification is the ability to parsimoniously capture nonlinear curvatures in the term structure, one may be concerned whether the linearization in the extended Kalman filter may compromise this feature. As this issue appears to be little explored in the literature, I consider two alternative nonlinear filtering methods [21,22]: the unscented filter and the Rao-Blackwellized particle filter.…”

Section: Filtering and Estimationmentioning

confidence: 99%

Recovering Yield Curves from Dynamic Term Structure Models with Time-Varying Factors

Kawakatsu

2020

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A dynamic version of the Nelson-Siegel-Svensson term structure model with time-varying factors is considered for predicting out-of-sample maturity yields. Simple linear interpolation cannot be applied to recover yields at the very short- and long- end of the term structure where data are often missing. This motivates the use of dynamic parametric term structure models that exploit both time series and cross-sectional variation in yield data to predict missing data at the extreme ends of the term structure. Although the dynamic Nelson–Siegel–Svensson model is weakly identified when the two decay factors become close to each other, their predictions may be more accurate than those from more restricted models depending on data and maturity.

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“…Below, they will be presented within a broader framework, but see e.g. [2], section 8.6, and the tutorials [7,15] for more detailed surveys of the PFs.…”

Section: Formal Solutionmentioning

confidence: 99%

“…Here we present its continuous-time formulation (see e.g. [2], chapter 9, or [15], section 6.1). The particles in this filter move with the same law as the hidden process, thereby being distributed according to the prior.…”

Section: Formal Solutionmentioning

confidence: 99%

A Unification of Weighted and Unweighted Particle Filters

Abedi,

Surace,

Pfister

2020

Preprint

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Particle filters (PFs), which are successful methods for approximating the solution of the filtering problem, can be divided into two types: weighted and unweighted PFs. It is wellknown that weighted PFs suffer from the weight degeneracy and curse of dimensionality. To sidestep these issues, unweighted PFs have been gaining attention, though they have their own challenges. The existing literature on these types of PFs is based on distinct approaches. In order to establish a connection, we put forward a framework that unifies weighted and unweighted PFs in the continuoustime filtering problem. We show that the stochastic dynamics of a particle system described by a pair process, representing particles and their importance weights, should satisfy two necessary conditions in order for its distribution to match the solution of the Kushner-Stratonovich equation.In particular, we demonstrate that the bootstrap particle filter (BPF), which relies on importance sampling, and the feedback particle filter (FPF), which is an unweighted PF based on optimal control, arise as special cases from a broad class, and that there is a smooth transition between the two. The freedom in designing the PF dynamics opens up potential ways to address the existing issues in the aforementioned algorithms, namely weight degeneracy in the BPF and gain estimation in the FPF.

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The Hitchhiker’s guide to nonlinear filtering

Cited by 13 publications

References 54 publications

Reinforcement Learning as Iterative and Amortised Inference

Reinforcement Learning as Iterative and Amortised Inference

Recovering Yield Curves from Dynamic Term Structure Models with Time-Varying Factors

A Unification of Weighted and Unweighted Particle Filters

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