Structure Learning with Continuous Optimization: A Sober Look and Beyond

This paper investigates in which cases continuous optimization for directed acyclic graph (DAG) structure learning can and cannot perform well and why this happens, and suggests possible directions to make the search procedure more reliable. Reisach et al. (2021) suggested that the remarkable performance of several continuous structure learning approaches is primarily driven by a high agreement between the order of increasing marginal variances and the topological order, and demonstrated that these approaches do not perform well after data standardization. We analyze this phenomenon for continuous approaches assuming equal and non-equal noise variances, and show that the statement may not hold in either case by providing counterexamples, justifications, and possible alternative explanations. We further demonstrate that nonconvexity may be a main concern especially for the non-equal noise variances formulation, while recent advances in continuous structure learning fail to achieve improvement in this case. Our findings suggest that future works should take into account the non-equal noise variances formulation to handle more general settings and for a more comprehensive empirical evaluation. Lastly, we provide insights into other aspects of the search procedure, including thresholding and sparsity, and show that they play an important role in the final solutions

Generator Identification for Linear SDEs with Additive and Multiplicative Noise

In this paper, we present conditions for identifying the generator of a linear stochastic differential equation (SDE) from the distribution of its solution process with a given fixed initial state. These identifiability conditions are crucial in causal inference using linear SDEs as they enable the identification of the post-intervention distributions from its observational distribution. Specifically, we derive a sufficient and necessary condition for identifying the generator of linear SDEs with additive noise, as well as a sufficient condition for identifying the generator of linear SDEs with multiplicative noise. We show that the conditions derived for both types of SDEs are generic. Moreover, we offer geometric interpretations of the derived identifiability conditions to enhance their understanding. To validate our theoretical results, we perform a series of simulations, which support and substantiate the established findings

Estimation of the flux at 1450MHz of OB stars for FAST and SKA

Radio observation is crucial to understanding the wind mechanism of OB stars but very scarce. This work estimates the flux at 1450MHz ($S_{\rm 1.4GHz}$) of about 5,000 OB stars identified by the LAMOST spectroscopic survey and confirmed by the Gaia astrometric as well as astrophysical measurements. The calculation is performed under the free-free emission mechanism for wind with the mass loss rate derived from stellar parameters. The estimated $S_{\rm 1.4GHz}$ distributes from $10^{-11}$Jy to $10^{-3}$Jy with the peak at about $10^{-8}$Jy. This implies that the complete SKA-II can detect more than half of them, and some tens of objects are detectable by FAST without considering source confusion. An array of FAST would increase the detectable sample by two orders of magnitude.Comment: 15 pages. 8 figure

Advancing Counterfactual Inference through Quantile Regression

The capacity to address counterfactual "what if" inquiries is crucial for understanding and making use of causal influences. Traditional counterfactual inference usually assumes a structural causal model is available. However, in practice, such a causal model is often unknown and may not be identifiable. This paper aims to perform reliable counterfactual inference based on the (learned) qualitative causal structure and observational data, without a given causal model or even directly estimating conditional distributions. We re-cast counterfactual reasoning as an extended quantile regression problem using neural networks. The approach is statistically more efficient than existing ones, and further makes it possible to develop the generalization ability of the estimated counterfactual outcome to unseen data and provide an upper bound on the generalization error. Experiment results on multiple datasets strongly support our theoretical claims