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Generative Learning of Counterfactual for Synthetic Control Applications in Econometrics

arXiv.org Machine Learning

A common statistical problem in econometrics is to estimate the impact of a treatment on a treated unit given a control sample with untreated outcomes. Here we develop a generative learning approach to this problem, learning the probability distribution of the data, which can be used for downstream tasks such as post-treatment counterfactual prediction and hypothesis testing. We use control samples to transform the data to a Gaussian and homoschedastic form and then perform Gaussian process analysis in Fourier space, evaluating the optimal Gaussian kernel via non-parametric power spectrum estimation. We combine this Gaussian prior with the data likelihood given by the pre-treatment data of the single unit, to obtain the synthetic prediction of the unit post-treatment, which minimizes the error variance of synthetic prediction. Given the generative model the minimum variance counterfactual is unique, and comes with an associated error covariance matrix. We extend this basic formalism to include correlations of primary variable with other covariates of interest. Given the probabilistic description of generative model we can compare synthetic data prediction with real data to address the question of whether the treatment had a statistically significant impact. For this purpose we develop a hypothesis testing approach and evaluate the Bayes factor. We apply the method to the well studied example of California (CA) tobacco sales tax of 1988. We also perform a placebo analysis using control states to validate our methodology. Our hypothesis testing method suggests 5.8:1 odds in favor of CA tobacco sales tax having an impact on the tobacco sales, a value that is at least three times higher than any of the 38 control states.


A Self-supervised Approach to Hierarchical Forecasting with Applications to Groupwise Synthetic Controls

arXiv.org Machine Learning

When forecasting time series with a hierarchical structure, the existing state of the art is to forecast each time series independently, and, in a post-treatment step, to reconcile the time series in a way that respects the hierarchy (Hyndman et al., 2011; Wickramasuriya et al., 2018). We propose a new loss function that can be incorporated into any maximum likelihood objective with hierarchical data, resulting in reconciled estimates with confidence intervals that correctly account for additional uncertainty due to imperfect reconciliation. We evaluate our method using a non-linear model and synthetic data on a counterfactual forecasting problem, where we have access to the ground truth and contemporaneous covariates, and show that we largely improve over the existing state-of-the-art method.


Company Planning Synthetic Fuel Plant Gets $29M in Bonds

U.S. News

The Charleston Gazette-Mail reports a reimbursement resolution and a cap allocation application were approved to PPD of WV One on Thursday. The newly formed company aims to start plant construction next year in Greenbrier County.


Macedonian Police Seize Synthetic Drugs Worth $3 Million

U.S. News

Spasovski said Friday that the haul was the biggest of its kind in the Balkans, and the drugs seized, which weighed a total 125 kilograms (275 pounds), have an estimated market value of 2.5 million euros ($3 million). They would have been sent to Turkey.


Improved memory devices for synthetic cells

Science

Synthetic biologists have long sought to make cells more like computers. This is not because they think cells will be more efficient than silicon--current microelectronics make excellent computers and are less messy than cell cultures--but instead because synthetic cells can interface with biology to perform biochemical tasks. Synthetic cells might one day be capable of attacking tumors or releasing site-specific drugs inside the human body. But to carry out these tasks, synthetic biologists must be able to program cells much in the same way we program computers--by providing them with decision-making capabilities based on inputs. Indeed, prototypes of many of the genetic parts necessary for turning cells into biocomputers have been constructed, including transcriptional logic gates (1), timers (2, 3), counters (4), memory devices (5, 6), tunable sensors (7, 8), and even in vitro DNA systems that can perform complex calculations (9).