Invertible Generative Modeling using Linear Rational Splines

Dolatabadi, Hadi M.; Erfani, Sarah M.

doi:10.48550/arxiv.2001.05168

Cited by 3 publications

(7 citation statements)

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“…We constrain age a variable with lower bound (exponential transform) and rescale it with fixed affine transform for normalization. Spline θ transformation refers to the linear neural spline flows [7]. The ConditionalTransform θ (•) can be conditional affine or conditional spline transform, which reparameterizes the noise distribution into another Gaussian distribution.…”

Section: Discussionmentioning

confidence: 99%

“…The ConditionalTransform θ (•) can be conditional affine or conditional spline transform, which reparameterizes the noise distribution into another Gaussian distribution. We use linear [7] and quadratic [10] autoregressive neural spline flows for the conditional spline transform, which are more expressive compared to the affine flows. The transformation parameters of the ConditionalTransform θ (•) are predicted by a context neural network taking • as input.…”

Section: Discussionmentioning

confidence: 99%

“…will have the additional benefit that we will be able to use normalizing flows to efficiently the abduction and prediction steps above and obtain an efficient method for counterfactual inference. Normalizing flows model a complex probability density as the result of a transformation applied to some simple probability density [23,24,7,10]; these transformations are learned using samples from the target. Formally, given observed variables x and base density ∼ p( ), we want to find an invertible and differentiable transformation x = f ( ).…”

Section: Building Blocksmentioning

confidence: 99%

“…Implementation We implement three variants of flow-based SCM with different flow types (affine, linear and quadratic autoregressive splines [7,10]) using Py-Torch [25] and Pyro [4]. To construct each flow-based SCM, we predict logits for sex and site variables and fit normalizing flows for other structural assignments.…”

Section: Setupmentioning

confidence: 99%

“…We quantitatively compare the associative capabilities of affine, linear autoregressive spline [7], and quadratic autoregressive spline [10] normalizing flow models by evaluating their total log-likelihood as shown in the Appendix. For both iSTAGING and ADNI datasets, the performance improves consistently with the while quadratic-spline model shows slightly higher log-likelihood than the linearspline model in iSTAGING dataset.…”

Section: Density Estimationmentioning

confidence: 99%

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Harmonization with Flow-based Causal Inference

Wang

Chaudhari

Davatzikos

2021

Preprint

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Heterogeneity in medical data, e.g., from data collected at different sites and with different protocols in a clinical study, is a fundamental hurdle for accurate prediction using machine learning models, as such models often fail to generalize well. This paper presents a normalizing-flow-based method to perform counterfactual inference upon a structural causal model (SCM) to harmonize such data. We formulate a causal model for observed effects (brain magnetic resonance imaging data) that result from known confounders (site, gender and age) and exogenous noise variables. Our method exploits the bijection induced by flow for harmonization. We can infer the posterior of exogenous variables, intervene on observations, and draw samples from the resultant SCM to obtain counterfactuals. We evaluate on multiple, large, real-world medical datasets to observe that this method leads to better cross-domain generalization compared to state-of-the-art algorithms. Further experiments that evaluate the quality of confounder-independent data generated by our model using regression and classification tasks are provided.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Building Blocksmentioning

confidence: 99%

Section: Setupmentioning

confidence: 99%

Section: Density Estimationmentioning

confidence: 99%

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Harmonization with Flow-based Causal Inference

Wang

Chaudhari

Davatzikos

2021

Preprint

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New angles on fast calorimeter shower simulation

Diefenbacher,

Eren,

Gaede

et al. 2023

Mach. Learn.: Sci. Technol.

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The demands placed on computational resources by the simulation requirements of high energy physics experiments motivate the development of novel simulation tools. Machine learning based generative models offer a solution that is both fast and accurate. In this work we extend the Bounded Information Bottleneck Autoencoder (BIB-AE) architecture, designed for the simulation of particle showers in highly granular calorimeters, in two key directions. First, we generalise the model to a multi-parameter conditioning scenario, while retaining a high degree of physics fidelity. In a second step, we perform a detailed study of the effect of applying a state-of-the-art particle flow-based reconstruction procedure to the generated showers. We demonstrate that the performance of the model remains high after reconstruction. These results are an important step towards creating a more general simulation tool, where maintaining physics performance after reconstruction is the ultimate target.

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Can We Constrain Warm Dark Matter Masses with Individual Galaxies?

Lin 林,

Villaescusa-Navarro,

Rose

et al. 2024

ApJ

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We study the impact of warm dark matter (WDM) mass on the internal properties of individual galaxies using a large suite of 1024 state-of-the-art cosmological hydrodynamic simulations from the DREAMS project. We take individual galaxies’ properties from the simulations, which have different cosmologies, astrophysics, and WDM masses, and train normalizing flows to learn the posterior of the parameters. We find that our models cannot infer the value of the WDM mass, even when the values of the cosmological and astrophysical parameters are given explicitly. This result holds for galaxies with stellar mass larger than 2 × 108 M ⊙ h −1 at both low and high redshifts. We calculate the mutual information and find no significant dependence between the WDM mass and galaxy properties. On the other hand, our models can infer the value of Ωm with a ∼10% accuracy from the properties of individual galaxies while marginalizing astrophysics and WDM masses.

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Invertible Generative Modeling using Linear Rational Splines

Cited by 3 publications

References 0 publications

Harmonization with Flow-based Causal Inference

Harmonization with Flow-based Causal Inference

New angles on fast calorimeter shower simulation

Can We Constrain Warm Dark Matter Masses with Individual Galaxies?

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