Norm inequalities in weighted amalgam

Kumar, Suraj

doi:10.14712/1213-7243.2015.257

Cited by 1 publication

(1 citation statement)

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“…Instead, we choose to define the adjacency matrix as the L 2 norm of the derivative ∂ i f j with respect to the probability distribution of X, which we denote P X . While the theory of Sobolev spaces plays no further role in our work, to adapt the language of [7], models are defined over the weighted Sobolev space H 1 (R d , P X ) [16]. This is simply to say that the models' function and first (weak) derivatives are squareintegrable with respect to P X .…”

Section: A Definition Of the Optimization Problemmentioning

confidence: 99%

Dagma-DCE: Interpretable, Non-Parametric Differentiable Causal Discovery

Waxman,

Butler,

Djurić

2024

IEEE Open J. Signal Process.

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We introduce DAGMA-DCE, an interpretable and model-agnostic scheme for differentiable causal discovery. Current non-or over-parameteric methods in differentiable causal discovery use opaque proxies of "independence" to justify the inclusion or exclusion of a causal relationship. We show theoretically and empirically that these proxies may be arbitrarily different than the actual causal strength. Juxtaposed to existing differentiable causal discovery algorithms, DAGMA-DCE uses an interpretable measure of causal strength to define weighted adjacency matrices. In a number of simulated datasets, we show our method achieves state-of-the-art level performance. We additionally show that DAGMA-DCE allows for principled thresholding and sparsity penalties by domain-experts. The code for our method is available open-source at https://github.com/DanWaxman/DAGMA-DCE, and can easily be adapted to arbitrary differentiable models.

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Section: A Definition Of the Optimization Problemmentioning

confidence: 99%