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Approximate Inference for Multiplicative Latent Force Models

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Daniel J. Tait, Bruce J. Worton

Machine Learning · Submitted 31 Dec 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We compare the performance of both methods on simulated data, and also demonstrate an application of the multiplicative latent force model on motion capture data.

how it is stated · asserted 1.00 read the record →

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arXiv ID1812.11755 (version 1)
Pith ID74BQM7DD, Pith's permanent record of this paper and its review
CitationBruce J. Worton, Daniel J. Tait. "Approximate Inference for Multiplicative Latent Force Models." arXiv:1812.11755 (2018). https://pith.science/paper/74BQM7DD
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,236 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.40 · human participants 0.14 · controlled comparison 0.13 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.69 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. An extension of this framework to include multiplicative interactions between the state and GP terms allows strong a priori control of the model geometry at the expense of tractable inference. In this paper we consider two methods of carrying out inference within this broader class of models. The first is based on an adaptive gradient matching approximation, and the second is constructed around mixtures of local approximations to the solution. We compare the performance of both methods on simulated data, and also demonstrate an application of the multiplicative latent force model on motion capture data.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. background 1.00 0.05 0.02 asserted 1.00
s1 An extension of this framework to include multiplicative interactions between the state and GP terms allows strong a priori control of the model geometry at the expense of tractable inference. background 0.81 0.14 0.05 asserted 1.00
s2 In this paper we consider two methods of carrying out inference within this broader class of models. contribution 0.94 0.77 0.04 asserted 0.96
s3 The first is based on an adaptive gradient matching approximation, and the second is constructed around mixtures of local approximations to the solution. method 0.89 0.83 0.06 asserted 0.99
s4 We compare the performance of both methods on simulated data, and also demonstrate an application of the multiplicative latent force model on motion capture data. contribution 0.75 0.95 0.16 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.99.

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  • relations to other papers
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  • P abstract
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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. An extension of this framework to include multiplicative interactions between the state and GP terms allows strong a priori control of the model geometry at the expense of tractable inference. In this paper we consider two methods of carrying out inference within this broader class of models. The first is based on an adaptive gradient matching approximation, and the second is constructed around mixtures of local approximations to the solution. We compare the performance of both methods on simulated data, and also demonstrate an application of the multiplicative latent force model on motion capture data.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 2 sentences without a confident label

Uses the method or tool of 1 paper
  • In this section we consider an alternative approach by first integrating the differential equation, and then considering fixed points of the integral operator [equation] We follow the construction in [ref] by considering an approximation to the distribution of the state variable $𝐱(t)$ conditional on dense sample paths of the coefficient matrix $𝐀(t)$.

    Multiplicative Latent Force Models · MIXTURES OF SUCCESSIVE APPROXIMATIONS · 0.80

Compares with 1 paper
  • We use the methods introduced in this paper to construct MAP estimates of the latent forces which we compare with the estimates obtained using an approximation to the true conditional density considered in [ref] .

    Multiplicative Latent Force Models · Kubo oscillator · 1.00

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