Counterexample-Guided Learning of Monotonic Neural Networks

Sivaraman, Aishwarya; Farnadi, Golnoosh; Millstein, Todd; Broeck, Guy Van den

doi:10.48550/arxiv.2006.08852

Cited by 3 publications

(2 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One approach is to specify a loss function penalising the network for outputs that violate the constraints, as done in Sill and Abu-Mostafa [1997]. Alternatively, counterexample-guided learning Sivaraman et al [2020] can be employed, to ensure the trained network does not produce any of these outputs when given the corresponding input. Lastly, as Theorem B equates counterfactual ordering with monotonicity, a recent method uses "look-up tables" Gupta et al [2016] to enforce monotonicity, and has been implemented in TensorFlow Lattice.…”

Section: : End Formentioning

confidence: 99%

Estimating categorical counterfactuals via deep twin networks

2023

View full text Add to dashboard Cite

Counterfactual inference is a powerful tool, capable of solving challenging problems in high-profile sectors. To perform counterfactual inference, one requires knowledge of the underlying causal mechanisms. However, causal mechanisms cannot be uniquely determined from observations and interventions alone. This raises the question of how to choose the causal mechanisms so that resulting counterfactual inference is trustworthy in a given domain. This question has been addressed in causal models with binary variables, but the case of categorical variables remains unanswered. We address this challenge by introducing for causal models with categorical variables the notion of counterfactual ordering, a principle that posits desirable properties causal mechanisms should posses, and prove that it is equivalent to specific functional constraints on the causal mechanisms. To learn causal mechanisms satisfying these constraints, and perform counterfactual inference with them, we introduce deep twin networks. These are deep neural networks that, when trained, are capable of twin network counterfactual inference-an alternative to the abduction, action, & prediction method. We empirically test our approach on diverse real-world and semi-synthetic data from medicine, epidemiology, and finance, reporting accurate estimation of counterfactual probabilities while demonstrating the issues that arise with counterfactual reasoning when counterfactual ordering is not enforced.

show abstract

Section: : End Formentioning

confidence: 99%

Estimating categorical counterfactuals via deep twin networks

2023

View full text Add to dashboard Cite

show abstract

“…In this case it can still be shown that the corresponding PDE operator is strongly monotone and the Browder-Minty theorem can be applied. Let us also point out that there are ways to enforce monotonicity during training [13,25,29] via a sufficiently good derivative approximation (Sobolev training) [12].…”

mentioning

confidence: 99%

First-order conditions for the optimal control of learning-informed nonsmooth PDEs

Dong¹,

Hintermüller²,

Papafitsoros³

et al. 2022

Preprint

View full text Add to dashboard Cite

In this paper we study the optimal control of a class of semilinear elliptic partial differential equations which have nonlinear constituents that are only accessible by data and are approximated by nonsmooth ReLU neural networks. The optimal control problem is studied in detail. In particular, the existence and uniqueness of the state equation are shown, and continuity as well as directional differentiability properties of the corresponding control-to-state map are established. Based on approximation capabilities of the pertinent networks, we address fundamental questions regarding approximating properties of the learning-informed control-to-state map and the solution of the corresponding optimal control problem. Finally, several stationarity conditions are derived based on different notions of generalized differentiability.

show abstract

Estimating Categorical Counterfactuals via Deep Twin Networks

Vlontzos

Kainz

Gilligan-Lee

2022

Preprint

View full text Add to dashboard Cite

Counterfactual inference is a powerful tool, capable of solving challenging problems in high-profile sectors. To perform counterfactual inference, one requires knowledge of the underlying causal mechanisms. However, causal mechanisms cannot be uniquely determined from observations and interventions alone. This raises the question of how to choose the causal mechanisms so that resulting counterfactual inference is trustworthy in a given domain. This question has been addressed in causal models with binary variables, but the case of categorical variables remains unanswered. We address this challenge by introducing for causal models with categorical variables the notion of counterfactual ordering, a principle that posits desirable properties causal mechanisms should posses, and prove that it is equivalent to specific functional constraints on the causal mechanisms. To learn causal mechanisms satisfying these constraints, and perform counterfactual inference with them, we introduce deep twin networks. These are deep neural networks that, when trained, are capable of twin network counterfactual inference---an alternative to the abduction, action, & prediction method. We empirically test our approach on diverse real-world and semi-synthetic data from medicine, epidemiology, and finance, reporting accurate estimation of counterfactual probabilities while demonstrating the issues that arise with counterfactual reasoning when counterfactual ordering is not enforced.

show abstract

Counterexample-Guided Learning of Monotonic Neural Networks

Cited by 3 publications

References 28 publications

Estimating categorical counterfactuals via deep twin networks

Estimating categorical counterfactuals via deep twin networks

First-order conditions for the optimal control of learning-informed nonsmooth PDEs

Estimating Categorical Counterfactuals via Deep Twin Networks

Contact Info

Product

Resources

About