Showing papers by "Paris Dauphine University published in 2018"
University of Southern California1, Duke University2, Stockholm School of Economics3, University of Virginia4, Center for Open Science5, University of Amsterdam6, University of Pennsylvania7, University of North Carolina at Chapel Hill8, University of Regensburg9, California Institute of Technology10, New York University11, Research Institute of Industrial Economics12, Cardiff University13, Mathematica Policy Research14, Northwestern University15, Ohio State University16, University of Sussex17, Texas A&M University18, Royal Holloway, University of London19, University of Zurich20, University of Melbourne21, University of Wisconsin-Madison22, University of Michigan23, Stanford University24, Rutgers University25, Columbia University26, University of Washington27, University of Edinburgh28, National University of Singapore29, Utrecht University30, Arizona State University31, Princeton University32, University of California, Los Angeles33, Imperial College London34, University of Innsbruck35, Harvard University36, University of Chicago37, University of Pittsburgh38, University of Notre Dame39, University of California, Berkeley40, Johns Hopkins University41, University of Bristol42, University of New South Wales43, Dartmouth College44, Whitman College45, University of Puerto Rico46, University of Milan47, University of California, Irvine48, Paris Dauphine University49, University of British Columbia50, Ludwig Maximilian University of Munich51, Purdue University52, Washington University in St. Louis53, University of California, Davis54, Microsoft55
TL;DR: The default P-value threshold for statistical significance is proposed to be changed from 0.05 to 0.005 for claims of new discoveries in order to reduce uncertainty in the number of discoveries.
Abstract: We propose to change the default P-value threshold for statistical significance from 0.05 to 0.005 for claims of new discoveries.
1,586 citations
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TL;DR: In this article, the Sinkhorn divergences, a family of geometric divergence that interpolates between Maximum Mean Discrepancies (MMD) and Optimal Transport distances (OT), are studied.
Abstract: Comparing probability distributions is a fundamental problem in data sciences. Simple norms and divergences such as the total variation and the relative entropy only compare densities in a point-wise manner and fail to capture the geometric nature of the problem. In sharp contrast, Maximum Mean Discrepancies (MMD) and Optimal Transport distances (OT) are two classes of distances between measures that take into account the geometry of the underlying space and metrize the convergence in law.
This paper studies the Sinkhorn divergences, a family of geometric divergences that interpolates between MMD and OT. Relying on a new notion of geometric entropy, we provide theoretical guarantees for these divergences: positivity, convexity and metrization of the convergence in law. On the practical side, we detail a numerical scheme that enables the large scale application of these divergences for machine learning: on the GPU, gradients of the Sinkhorn loss can be computed for batches of a million samples.
251 citations
TL;DR: A new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport is presented, and of particular interest is the Wasserstein–Fisher–Rao metric, which belongs to this class of metrics and hence automatically benefits from a static Kantorovich formulation.
154 citations
TL;DR: A multiscale diagonalization scheme to study disordered one-dimensional chains, in particular, the transition between many-body localization and the ergodic phase, expected to be governed by resonant spots, shows that a few natural assumptions imply that the system is localized with probability one at criticality.
Abstract: We propose a multiscale diagonalization scheme to study disordered one-dimensional chains, in particular, the transition between many-body localization (MBL) and the ergodic phase, expected to be governed by resonant spots. Our scheme focuses on the dichotomy of MBL versus validity of the eigenstate thermalization hypothesis. We show that a few natural assumptions imply that the system is localized with probability one at criticality. On the ergodic side, delocalization is induced by a quantum avalanche seeded by large ergodic spots, whose size diverges at the transition. On the MBL side, the typical localization length tends to the inverse of the maximal entropy density at the transition, but there is a divergent length scale related to the response to an inclusion of large ergodic spots. A mean-field approximation analytically illustrates these results and predicts a power-law distribution for thermal inclusions at criticality.
152 citations
TL;DR: This review aims to provide an accessible introduction to the methodology of invariant Kalman filtering and to allow readers to gain insight into the relevance of the method as well as its important differences with the conventional EKF.
Abstract: The Kalman filter—or, more precisely, the extended Kalman filter (EKF)—is a fundamental engineering tool that is pervasively used in control and robotics and for various estimation tasks in autonomous systems. The recently developed field of invariant extended Kalman filtering uses the geometric structure of the state space and the dynamics to improve the EKF, notably in terms of mathematical guarantees. The methodology essentially applies in the fields of localization, navigation, and simultaneous localization and mapping (SLAM). Although it was created only recently, its remarkable robustness properties have already motivated a real industrial implementation in the aerospace field. This review aims to provide an accessible introduction to the methodology of invariant Kalman filtering and to allow readers to gain insight into the relevance of the method as well as its important differences with the conventional EKF. This should be of interest to readers intrigued by the practical application of mathemati...
139 citations
TL;DR: In this article, the authors define a new transport metric over the space of nonnegative measures, which interpolates between the quadratic Wasserstein and the Fisher-Rao metrics and generalizes optimal transport to measures with different masses.
Abstract: This paper defines a new transport metric over the space of nonnegative measures. This metric interpolates between the quadratic Wasserstein and the Fisher–Rao metrics and generalizes optimal transport to measures with different masses. It is defined as a generalization of the dynamical formulation of optimal transport of Benamou and Brenier, by introducing a source term in the continuity equation. The influence of this source term is measured using the Fisher–Rao metric and is averaged with the transportation term. This gives rise to a convex variational problem defining the new metric. Our first contribution is a proof of the existence of geodesics (i.e., solutions to this variational problem). We then show that (generalized) optimal transport and Hellinger metrics are obtained as limiting cases of our metric. Our last theoretical contribution is a proof that geodesics between mixtures of sufficiently close Dirac measures are made of translating mixtures of Dirac masses. Lastly, we propose a numerical scheme making use of first-order proximal splitting methods and we show an application of this new distance to image interpolation.
128 citations
TL;DR: It is found that the public ignores these animals’ predicament and it is suggested it could be due to the observed biased perception of their abundance, based more on their profusion in the authors' culture than on their natural populations.
Abstract: A widespread opinion is that conservation efforts disproportionately benefit charismatic species. However, this doesn’t mean that they are not threatened, and which species are “charismatic” remains unclear. Here, we identify the 10 most charismatic animals and show that they are at high risk of imminent extinction in the wild. We also find that the public ignores these animals’ predicament and we suggest it could be due to the observed biased perception of their abundance, based more on their profusion in our culture than on their natural populations. We hypothesize that this biased perception impairs conservation efforts because people are unaware that the animals they cherish face imminent extinction and do not perceive their urgent need for conservation. By freely using the image of rare and threatened species in their product marketing, many companies may participate in creating this biased perception, with unintended detrimental effects on conservation efforts, which should be compensated by channeling part of the associated profits to conservation. According to our hypothesis, this biased perception would be likely to last as long as the massive cultural and commercial presence of charismatic species is not accompanied by adequate information campaigns about the imminent threats they face.
112 citations
TL;DR: In this article, the authors formulate the problem of optimal liquidation inside a mean field game (MFG) and provide a closed form formula of its solution, and address the case of heterogenous preferences when each participant has a different risk aversion.
Abstract: In this paper we formulate the now classical problem of optimal liquidation (or optimal trading) inside a mean field game (MFG). This is a noticeable change since usually mathematical frameworks focus on one large trader facing a “background noise” (or “mean field”). In standard frameworks, the interactions between the large trader and the price are a temporary and a permanent market impact terms, the latter influencing the public price. In this paper the trader faces the uncertainty of fair price changes too but not only. He also has to deal with price changes generated by other similar market participants, impacting the prices permanently too, and acting strategically. Our MFG formulation of this problem belongs to the class of “extended MFG”, we hence provide generic results to address these “MFG of controls”, before solving the one generated by the cost function of optimal trading. We provide a closed form formula of its solution, and address the case of “heterogenous preferences” (when each participant has a different risk aversion). Last but not least we give conditions under which participants do not need to instantaneously know the state of the whole system, but can “learn” it day after day, observing others’ behaviors.
93 citations
TL;DR: In this article, the authors present several techniques for accelerating the convergence of Markov Chain Monte Carlo (MCMC) algorithms at the exploration level and at the exploitation level (with Rao-Blackwellization and scalable methods).
Abstract: Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it also potentially induces a lengthy exploration of this target, with a requirement on the number of simulations that grows with the dimension of the problem and with the complexity of the data behind it. Several techniques are available toward accelerating the convergence of these Monte Carlo algorithms, either at the exploration level (as in tempering, Hamiltonian Monte Carlo and partly deterministic methods) or at the exploitation level (with Rao-Blackwellization and scalable methods). This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)Algorithms and Computational Methods > AlgorithmsStatistical and Graphical Methods of Data Analysis > Monte Carlo Methods.
85 citations
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TL;DR: Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions, which avoids heavy requests on understanding the nature of the target, but it also potentially induces a lengthy exploration of this target.
Abstract: Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it also potentially induces a lengthy exploration of this target, with a requirement on the number of simulations that grows with the dimension of the problem and with the complexity of the data behind it. Several techniques are available towards accelerating the convergence of these Monte Carlo algorithms, either at the exploration level (as in tempering, Hamiltonian Monte Carlo and partly deterministic methods) or at the exploitation level (with Rao-Blackwellisation and scalable methods).
84 citations
TL;DR: This work considers a general formulation of the principal–agent problem with a lump-sum payment on a finite horizon, providing a systematic method for solving such problems, and relies on the backward stochastic differential equations approach to non-Markovian Stochastic control.
Abstract: We consider a general formulation of the principal–agent problem with a lump-sum payment on a finite horizon, providing a systematic method for solving such problems. Our approach is the following. We first find the contract that is optimal among those for which the agent’s value process allows a dynamic programming representation, in which case the agent’s optimal effort is straightforward to find. We then show that the optimization over this restricted family of contracts represents no loss of generality. As a consequence, we have reduced a non-zero-sum stochastic differential game to a stochastic control problem which may be addressed by standard tools of control theory. Our proofs rely on the backward stochastic differential equations approach to non-Markovian stochastic control, and more specifically on the recent extensions to the second order case.
TL;DR: It is found that longevity in individuals with DS will necessitate complex adult and geriatric care and more evidenced-based and standardized follow-up could support better long-term comorbidity management and dementia care among aging adults with DS.
Abstract: Importance As the life expectancy of people with Down syndrome (DS) has markedly increased over the past decades, older adults with DS may be experiencing a higher incidence of aging conditions. In addition to longevity, the amyloid precursor protein gene located on chromosome 21 places individuals with DS at a high risk for developing Alzheimer disease. Yet, few studies have determined prevalence of dementia and comorbidities among older people with DS. Objective To determine the prevalence of dementia and aging-related comorbidities in older adult individuals with DS. Design, Setting, and Participants Cross-sectional analysis of 2015 California Medicare claims data. We examined 1 year of cross-sectional Medicare claims data that included 100% of Californian Medicare beneficiaries enrolled in both Medicare Part A and B in 2015. Of these 3 001 977 Californian Medicare beneficiaries 45 years or older, 878 individuals were identified as having a diagnosis of DS. Data were analyzed between April 2017 and February 2018. Main Outcomes and Measures The frequency of DS dementia was assessed across different age categories. The number and frequency of 27 comorbidities were compared among individuals with DS with and without dementia and by age and sex groups. Results A total of 353 DS individuals (40%) were identified as having dementia diagnoses (mean, 58.7 years; 173 women [49%]) and 525 without dementia diagnoses (mean, 55.9 years; 250 women [48%]). The frequency of DS dementia among those 65 years or older rose to 49%. The mean number of comorbidities per individual increased with age in general. Comorbid conditions were more numerous among those with dementia compared with those with DS without dementia (mean, 3.4 vs 2.5, respectively), especially among those younger than 65 years. In particular, 4 treatable conditions, hypothyroidism, epilepsy, anemia, and weight loss, were much more frequent in DS dementia. Conclusions and Relevance Older Medicare beneficiaries in California with DS, especially those with dementia, have a high level of multimorbidity including several treatable conditions. While DS follow-up has long been confined to the pediatric sphere, we found that longevity in individuals with DS will necessitate complex adult and geriatric care. More evidenced-based and standardized follow-up could support better long-term comorbidity management and dementia care among aging adults with DS.
TL;DR: In this article, the authors carry out the construction of ill-posed multiplicative stochastic heat equations on unbounded domains by adapting the theory of regularity structures to the setting of weighted Besov spaces.
Abstract: We carry out the construction of some ill-posed multiplicative stochastic heat equations on unbounded domains. The two main equations our result covers are, on the one hand the parabolic Anderson model on $\mathbf{R}^3$, and on the other hand the KPZ equation on $\mathbf{R}$ via the Cole-Hopf transform. To perform these constructions, we adapt the theory of regularity structures to the setting of weighted Besov spaces. One particular feature of our construction is that it allows one to start both equations from a Dirac mass at the initial time.
TL;DR: In this paper, the authors show that with a suitable initialization procedure, the classical alternating projections (Gerchberg-Saxton) succeeds with high probability when $m\geq Cn$, for some $C>0$.
Abstract: We consider a phase retrieval problem, where we want to reconstruct a $n$ -dimensional vector from its phaseless scalar products with $m$ sensing vectors, independently sampled from complex normal distributions. We show that, with a suitable initialization procedure, the classical algorithm of alternating projections (Gerchberg–Saxton) succeeds with high probability when $m\geq Cn$ , for some $C>0$ . We conjecture that this result is still true when no special initialization procedure is used, and present numerical experiments that support this conjecture.
TL;DR: An alternative perspective on the problem is developed, using a System Dynamics Model (SDM), exploring how different actions can influence the decision-making processes of various stakeholders involved in the IS, highlighting its criticalities.
TL;DR: In this article, the authors explore which employee work practices are more conducive to firm-level innovation in corporate sustainability and find that intrinsic and extrinsic rewards can work in tandem to facilitate sustainable innovation.
Abstract: Corporate sustainable innovation is a major driver of institutional change, and its success can be largely attributed to employees. While some scholars have described the importance of intrinsic motivations and flexibility to facilitate innovation, others have argued that constraints and extrinsic motivations stimulate innovation. In the context of sustainable innovation, we explore which employee work practices are more conducive to firm-level innovation in corporate sustainability. Our results, based on a sample of 4640 French employees from 1764 firms, confirm the positive impact of intrinsic motivations (through employee social interactions), and the negative impact of job strain (through high imposed work pace), on corporate sustainable innovation. We also find that extrinsic rewards, through pay satisfaction, counteract the negative effect of job strain to promote sustainable innovation. This indicates that intrinsic and extrinsic rewards can work in tandem to facilitate sustainable innovation.
TL;DR: The strengths and weaknesses of the Choquet integral are discussed as appearing in the case study, proposing as well insights related to the interaction of the experts within a focus group.
TL;DR: In this article, the authors used a two-regime Markov switching model to disentangle the impact of wind and solar generation, depending on the price being high or low.
TL;DR: In this article, a meta-regression analysis on parametric and nonparametric estimations of Mean Technical Efficiency (MTE) in micro-finance, using a data set of 262 observations from 38 studies, is presented.
TL;DR: In this paper, a theory a la Conley is proposed for cone fields using a notion of relaxed orbits based on cone enlargements, in the spirit of space time geometry, which generalizes the equivalence between stable causality and the existence of temporal functions.
Abstract: We propose a theory “a la Conley” for cone fields using a notion of relaxed orbits based on cone enlargements, in the spirit of space time geometry. We work in the setting of closed (or equivalently semi-continuous) cone fields with singularities. This setting contains (for questions which are parametrization independent such as the existence of Lyapounov functions) the case of continuous vector-fields on manifolds, of differential inclusions, of Lorentzian metrics, and of continuous cone fields. We generalize to this setting the equivalence between stable causality and the existence of temporal functions. We also generalize the equivalence between global hyperbolicity and the existence of a steep temporal function.
TL;DR: In this article, a stochastic control problem for a class of nonlinear kernels is considered and a dynamic programming principle for this control problem in an abstract setting is presented, which is then used to provide a semimartingale characterization of the value function.
Abstract: We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimization, over a set of possibly nondominated probability measures, of solutions of backward stochastic differential equations (BSDEs). Since BSDEs are nonlinear generalizations of the traditional (linear) expectations, this problem can be understood as stochastic control of a family of nonlinear expectations, or equivalently of nonlinear kernels. Our first main contribution is to prove a dynamic programming principle for this control problem in an abstract setting, which we then use to provide a semimartingale characterization of the value function. We next explore several applications of our results. We first obtain a wellposedness result for second order BSDEs (as introduced in Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149–190]) which does not require any regularity assumption on the terminal condition and the generator. Then we prove a nonlinear optional decomposition in a robust setting, extending recent results of Nutz [Stochastic Process. Appl. 125 (2015) 4543–4555], which we then use to obtain a super-hedging duality in uncertain, incomplete and nonlinear financial markets. Finally, we relate, under additional regularity assumptions, the value function to a viscosity solution of an appropriate path–dependent partial differential equation (PPDE).
TL;DR: In this paper, the authors investigated the benefit of combining stationary wavelet transforms to produce one day-ahead forecasts of half-hourly electric load in France by decomposing the aggregate load into several sub-series with a wavelet transform each component is predicted separately and aggregated to get the final forecast.
TL;DR: In this paper, the authors consider the asymptotic behavior of the posterior obtained from approximate Bayesian computation (ABC) and the ensuing posterior mean, and give general results on: (i) the rate of concentration of the ABC posterior on sets containing the true parameter (vector); (ii) the limiting shape of posterior; and (iii) the asyptotic distribution of ABC posterior mean.
Abstract: Approximate Bayesian computation (ABC) is becoming an accepted tool for statistical analysis in models with intractable likelihoods. With the initial focus being primarily on the practical import of ABC, exploration of its formal statistical properties has begun to attract more attention. In this paper we consider the asymptotic behavior of the posterior obtained from ABC and the ensuing posterior mean. We give general results on: (i) the rate of concentration of the ABC posterior on sets containing the true parameter (vector); (ii) the limiting shape of the posterior; and\ (iii) the asymptotic distribution of the ABC posterior mean. These results hold under given rates for the tolerance used within ABC, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Using simple illustrative examples that have featured in the literature, we demonstrate that the required identification condition is far from guaranteed. The implications of the theoretical results for practitioners of ABC are also highlighted.
TL;DR: In this article, the authors study the nonasymptotic behavior of Coulomb gases in dimension two and more and obtain concentration of measure inequalities for the empirical distribution of such gases around their equilibrium measure, with respect to bounded Lipschitz and Wasserstein distances.
TL;DR: In this paper, the Langevin Monte Carlo (LMC) algorithm was extended to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD).
Abstract: We extend the Langevin Monte Carlo (LMC) algorithm to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD). We show that (projected) LMC allows to sample in polynomial time from a log-concave distribution with smooth potential. This gives a new Markov chain to sample from a log-concave distribution. Our main result shows in particular that when the target distribution is uniform, LMC mixes in O(n 7) steps (where n is the dimension). We also provide preliminary experimental evidence that LMC performs at least as well as hit-and-run, for which a better mixing time of O(n 4) was proved by Lovasz and Vempala.
TL;DR: In this article, the authors proposed a regular and progressive policy when transitioning to PV self-consumption to allow enough time for stakeholders to adapt to the new market situation and showed that PV selfconsumption with batteries has a smaller impact on the power system than full grid injection.
TL;DR: In this article, the authors introduce the notion of stable solutions in mean field game theory, which are locally isolated solutions of the mean field games system and prove that such solutions exist in potential mean fields games and are local attractors for learning procedures.
Abstract: We introduce the notion of stable solution in mean field game theory: they are locally isolated solutions of the mean field game system. We prove that such solutions exist in potential mean field games and are local attractors for learning procedures.
TL;DR: In this paper, a tractable continuous-time risk-sharing model is developed, where heterogeneous mean-variance investors trade subject to a quadratic transaction cost, and the corresponding equilibrium is characterized as the unique solution of a system of coupled but linear forward-backward stochastic differential equations.
Abstract: We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean–variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique solution of a system of coupled but linear forward–backward stochastic differential equations. Explicit solutions are obtained in a number of concrete settings. The sluggishness of the frictional portfolios makes the corresponding equilibrium returns mean-reverting. Compared to the frictionless case, expected returns are higher if the more risk-averse agents are net sellers or if the asset supply expands over time.
TL;DR: In this article, a new class of mean-field game systems of equations is introduced and studied mathematically, allowing one major player (or agent) and a large group of small players.
TL;DR: In this paper, the authors established quantitative homogenization, large-scale regularity and Liouville results for the random conductance model on a supercritical (Bernoulli bond) percolation cluster.
Abstract: We establish quantitative homogenization, large-scale regularity and Liouville results for the random conductance model on a supercritical (Bernoulli bond) percolation cluster. The results are also new in the case that the conductivity is constant on the cluster. The argument passes through a series of renormalization steps: first, we use standard percolation results to find a large scale above which the geometry of the percolation cluster behaves (in a sense made precise) like that of Euclidean space. Then, following the work of Barlow, we find a succession of larger scales on which certain functional and elliptic estimates hold. This gives us the analytic tools to adapt the quantitative homogenization program of Armstrong and Smart to estimate the yet larger scale on which solutions on the cluster can be well-approximated by harmonic functions on $\mathbb{R}^d$. This is the first quantitative homogenization result in a porous medium and the harmonic approximation allows us to estimate the scale on which a higher-order regularity theory holds. The size of each of these random scales is shown to have at least a stretched exponential moment. As a consequence of this regularity theory, we obtain a Liouville-type result that states that, for each $k\in\mathbb{N}$, the vector space of solutions growing at most like $o(|x|^{k+1})$ as $|x|\to \infty$ has the same dimension as the set of harmonic polynomials of degree at most $k$, generalizing a result of Benjamini, Duminil-Copin, Kozma, and Yadin from $k\le1$ to $k\in\mathbb{N}$.