Learning Compositional Visual Concepts with Mutual Consistency

Compositionality of semantic concepts in image synthesis and analysis is appealing as it can help in decomposing known and generatively recomposing unknown data. For instance, we may learn concepts of changing illumination, geometry or albedo of a scene, and try to recombine them to generate physically meaningful, but unseen data for training and testing. In practice however we often do not have samples from the joint concept space available: We may have data on illumination change in one data set and on geometric change in another one without complete overlap. We pose the following question: How can we learn two or more concepts jointly from different data sets with mutual consistency where we do not have samples from the full joint space? We present a novel answer in this paper based on cyclic consistency over multiple concepts, represented individually by generative adversarial networks (GANs). Our method, ConceptGAN, can be understood as a drop in for data augmentation to improve resilience for real world applications. Qualitative and quantitative evaluations demonstrate its efficacy in generating semantically meaningful images, as well as one shot face verification as an example application.Comment: 10 pages, 8 figures, 4 tables, CVPR 201

Winners and Losers of Tax Competition in the European Union

This paper quantifies the macroeconomic effects of capital income tax competition in the European Union using a two-country neoclassical dynamic general equilibrium model. This model incorporates three key externalities of tax competition: the relative price externality, the wealth distribution externality and the fiscal solvency externality. We consider tax strategies limited to the class of time-invariant taxes and allow governments to issue debt to smooth the tax burden. The analysis starts from a pre-tax-competition equilibrium calibrated to represent the United Kingdom and Continental Europe (France, Germany and Italy) using data from the early 1980s, just before the European integration of financial markets. When labor taxes adjust to maintain fiscal solvency, competition does not trigger a race to the bottom' in capital taxes. The UK makes a large welfare gain and cuts its capital tax. Continental Europe increases both labor and capital taxes and suffers a large welfare loss. These results are consistent with evidence showing that over the last two decades the UK lowered its capital tax, while Continental Europe increased both capital and labor taxes. When consumption taxes adjust to maintain fiscal solvency, there is a race to the bottom' in capital taxes but both the UK and Continental Europe are better off than in the pre-tax-competition equilibrium. The gains from coordination in all of these experiments are trivial.

Distributed Approximation of Maximum Independent Set and Maximum Matching

We present a simple distributed $\Delta$-approximation algorithm for maximum weight independent set (MaxIS) in the $\mathsf{CONGEST}$ model which completes in $O(\texttt{MIS}(G)\cdot \log W)$ rounds, where $\Delta$ is the maximum degree, $\texttt{MIS}(G)$ is the number of rounds needed to compute a maximal independent set (MIS) on $G$, and $W$ is the maximum weight of a node. %Whether our algorithm is randomized or deterministic depends on the \texttt{MIS} algorithm used as a black-box. Plugging in the best known algorithm for MIS gives a randomized solution in $O(\log n \log W)$ rounds, where $n$ is the number of nodes. We also present a deterministic $O(\Delta +\log^* n)$-round algorithm based on coloring. We then show how to use our MaxIS approximation algorithms to compute a $2$-approximation for maximum weight matching without incurring any additional round penalty in the $\mathsf{CONGEST}$ model. We use a known reduction for simulating algorithms on the line graph while incurring congestion, but we show our algorithm is part of a broad family of \emph{local aggregation algorithms} for which we describe a mechanism that allows the simulation to run in the $\mathsf{CONGEST}$ model without an additional overhead. Next, we show that for maximum weight matching, relaxing the approximation factor to ($2+\varepsilon$) allows us to devise a distributed algorithm requiring $O(\frac{\log \Delta}{\log\log\Delta})$ rounds for any constant $\varepsilon>0$. For the unweighted case, we can even obtain a $(1+\varepsilon)$-approximation in this number of rounds. These algorithms are the first to achieve the provably optimal round complexity with respect to dependency on $\Delta$

Winners and Losers of Tax Competition in the European Union

This paper quantifies the macroeconomic effects of capital income tax competition in the European Union using a two-country neoclassical dynamic general equilibrium model. This model incorporates three key externalities of tax competition: the relative price externality, the wealth distribution externality and the fiscal solvency externality. We consider tax strategies limited to the class of time-invariant taxes and allow governments to issue debt to smooth the tax burden. The analysis starts from a pre-tax-competition equilibrium calibrated to represent the United Kingdom and Continental Europe (France, Germany and Italy) using data from the early 1980s, just before the European integration of financial markets. When labor taxes adjust to maintain fiscal solvency, competition does not trigger a “race to the bottom” in capital taxes. The UK makes a large welfare gain and cuts its capital tax. Continental Europe increases both labor and capital taxes and suffers a large welfare loss. These results are consistent with evidence showing that over the last two decades the UK lowered its capital tax, while Continental Europe increased both capital and labor taxes. When consumption taxes adjust to maintain fiscal solvency, there is a “race to the bottom” in capital taxes but both the UK and Continental Europe are better off than in the pre-tax-competition equilibrium. The gains from coordination in all of these experiments are trivial.