Structural Intervention Distance (SID) for Evaluating Causal Graphs

Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-) distance between DAGs, the structural intervention distance (SID). The SID is based on a graphical criterion only and quantifies the closeness between two DAGs in terms of their corresponding causal inference statements. It is therefore well-suited for evaluating graphs that are used for computing interventions. Instead of DAGs it is also possible to compare CPDAGs, completed partially directed acyclic graphs that represent Markov equivalence classes. Since it differs significantly from the popular Structural Hamming Distance (SHD), the SID constitutes a valuable additional measure. We discuss properties of this distance and provide an efficient implementation with software code available on the first author's homepage (an R package is under construction)

Invariant Causal Prediction for Sequential Data

We investigate the problem of inferring the causal predictors of a response $Y$ from a set of $d$ explanatory variables $(X^1,\dots,X^d)$. Classical ordinary least squares regression includes all predictors that reduce the variance of $Y$. Using only the causal predictors instead leads to models that have the advantage of remaining invariant under interventions, loosely speaking they lead to invariance across different "environments" or "heterogeneity patterns". More precisely, the conditional distribution of $Y$ given its causal predictors remains invariant for all observations. Recent work exploits such a stability to infer causal relations from data with different but known environments. We show that even without having knowledge of the environments or heterogeneity pattern, inferring causal relations is possible for time-ordered (or any other type of sequentially ordered) data. In particular, this allows detecting instantaneous causal relations in multivariate linear time series which is usually not the case for Granger causality. Besides novel methodology, we provide statistical confidence bounds and asymptotic detection results for inferring causal predictors, and present an application to monetary policy in macroeconomics.Comment: 55 page

The disruption and electrification of liquid jets

Imperial Users onl

Scalable wavelet-based coding of irregular meshes with interactive region-of-interest support

This paper proposes a novel functionality in wavelet-based irregular mesh coding, which is interactive region-of-interest (ROI) support. The proposed approach enables the user to define the arbitrary ROIs at the decoder side and to prioritize and decode these regions at arbitrarily high-granularity levels. In this context, a novel adaptive wavelet transform for irregular meshes is proposed, which enables: 1) varying the resolution across the surface at arbitrarily fine-granularity levels and 2) dynamic tiling, which adapts the tile sizes to the local sampling densities at each resolution level. The proposed tiling approach enables a rate-distortion-optimal distribution of rate across spatial regions. When limiting the highest resolution ROI to the visible regions, the fine granularity of the proposed adaptive wavelet transform reduces the required amount of graphics memory by up to 50%. Furthermore, the required graphics memory for an arbitrary small ROI becomes negligible compared to rendering without ROI support, independent of any tiling decisions. Random access is provided by a novel dynamic tiling approach, which proves to be particularly beneficial for large models of over 10(6) similar to 10(7) vertices. The experiments show that the dynamic tiling introduces a limited lossless rate penalty compared to an equivalent codec without ROI support. Additionally, rate savings up to 85% are observed while decoding ROIs of tens of thousands of vertices

Growth Effects of Government Expenditure and Taxation in Rich Countries: A Comment

In a recent article Stefan Fölster and Magnus Henrekson [2001] argue that “…the more the econometric problems that are addressed, the more robust the relationship between government size and economic growth appears”. But in failing to control for simultaneity in a valid manner the regressions reported by Fölster/Henrekson are flawed. Moreover, using theoretically valid instruments we find that the estimated partial correlation between size of the public sector and economic growth is statistically insignificant and highly unstable across specifications. A policy-maker who wants to promote growth is well-advised to look for other evidence than cross-country growth regressions.Economic growth; public sector; cross-country regressions; panel regressions

Regulated Expansion of Electricity Transmission Networks: The Effects of Fluctuating Demand and Wind Generation

We study the performance of different regulatory approaches for the expansion of electricity transmission networks in the light of realistic demand patterns and fluctuating wind power. In particular, we are interested in the relative performance of a combined merchant-regulatory mechanism compared to a cost-based and a merchant-like approach. In contrast to earlier research, we explicitly include both an hourly time resolution and fluctuating wind power, which allows representing demand in a very realistic way. This substantially increases the real-world applicability of results compared to previous analyses, which were based on simplifying assumptions. We show that a combined merchant-regulatory regulation, which draws on a cap over the two-part tariff of the Transco, leads to welfare outcomes far superior to the modeled alternatives. This result proves to be robust over a range of different cases and sensitivity analyses. We also find that the intertemporal rebalancing of the two-part tariff carried out by the Transco so as to expand the network is such that the fixed tariff part turns out to be relatively large compared to extension costs.Electricity, Regulation, Transmission Expansion, Wind Power