RANK: Large-Scale Inference with Graphical Nonlinear Knockoffs

Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness for the model-free knockoffs procedure introduced recently in Cand\`{e}s, Fan, Janson and Lv (2016) in high-dimensional setting when the covariate distribution is characterized by Gaussian graphical model. We establish that under mild regularity conditions, the power of the oracle knockoffs procedure with known covariate distribution in high-dimensional linear models is asymptotically one as sample size goes to infinity. When moving away from the ideal case, we suggest the modified model-free knockoffs method called graphical nonlinear knockoffs (RANK) to accommodate the unknown covariate distribution. We provide theoretical justifications on the robustness of our modified procedure by showing that the false discovery rate (FDR) is asymptotically controlled at the target level and the power is asymptotically one with the estimated covariate distribution. To the best of our knowledge, this is the first formal theoretical result on the power for the knockoffs procedure. Simulation results demonstrate that compared to existing approaches, our method performs competitively in both FDR control and power. A real data set is analyzed to further assess the performance of the suggested knockoffs procedure.Comment: 37 pages, 6 tables, 9 pages supplementary materia

Tarihi Rami Kışlası yok ediliyor

Taha Toros Arşivi, Dosya No: 12-Fatih-Edirnekapıİstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

Tüm itirazlara karşın 5 yıldızlı otel yapılmasına karar verilen tarihi bina artık turistleri ağırlayacak:Elveda Sultanahmet Cezaevi

Taha Toros Arşivi, Dosya No: 6-Sultanahmetİstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

Eminönü'nde yolsuzluk köprüsü

Taha Toros Arşivi, Dosya No: 3-Eminönü-Sirkeciİstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

What is Opposition Good For?

Democratically elected governments may sometimes give in to pressures from extreme constituents thereby failing to adopt policies congruent with the median voter\u27s preferences. This situation is exacerbated by the inability or the reluctance of voters to acquire information about the consequences of policy alternatives. Opposition parties, in principle, could help remedy this problem using the prerogatives at their disposal such as participating in legislative debates and proposing bills, amendments or no confidence motions. In practice, however, they may have incentives to mislead the voters for policy or election purposes. Given the critical role of opposition parties to remedy problems of incongruence, it is essential to gain theoretical clarity and empirical knowledge as to when and how opposition parties use the tools available to them in legislatures. My dissertation contributes to the recently growing literature that studies the behavior of opposition parties in different institutional contexts, and the implications of that behavior for democratic representation. In particular, I examine the conditions under which opposition parties provide the voters with accurate information, thereby inducing the government to act in accordance with voters\u27 demands and interests. My analysis reconsiders the conventional wisdom that the influence of opposition parties on policy making is commensurate with their electoral strength or seat share in the legislature.In the first paper, I develop a formal model that examines the interaction between a government with control over a policy proposal and an opposition party faced with the decision whether to attract voters\u27 attention to the proposal by objecting to its adoption. The model assumes that the government has incentives to pursue policies divergent from voter preferences and that voters face non-trivial costs in monitoring the government\u27s legislative proposals. Voters can use the objection of the opposition party as a signal to identify adverse government proposals. However, for the mechanism to work, the opposition party should be responsible, i.e. not alarm the voters too frequently. I show that confrontation between the government and the opposition party is more likely when the chances of election for the opposition party are sufficiently low and the opposition activists are sufficiently distant in terms of their ideological positions from the government (as well as the voter and the opposition party itself). In addition to providing useful signals, the presence of a responsible opposition party may increase voters\u27 welfare by inducing the government to preemptively adjust its policies.In the second paper, I propose a formal model that explores whether the voters can receive accurate information from the opposition party under further constraints. More specifically, the model assumes that the voters do not have the means to verify the accuracy of information they receive about the policy and furthermore they have limited information about the preferences of the government and the opposition party. I show that the opposition party can discipline the government to choose policies congruent with voters\u27 preferences if the reputation of the opposition is high and the benefit of policy to the government is small relative to the benefit of winning elections. Under the same conditions, however, misleading messages of the opposition party may cause a good government to implement policies that bring about bad outcomes for the voters.In the the third paper, I examine when legislators withdraw their support from the bills that they cosponsored using an original dataset of cosponsorship in the US House of Representatives. I argue that the legislators take into account the preferences of their constituency in their cosponsorship decisions. Since acquiring information about the bills is costly, legislators use the cosponsorship decisions of their counterparts as signals for the acceptability of the bill for their constituency. My analysis shows that there is a relationship between the partisan composition of cosponsors and the likelihood that he/she decides to remove his/her name from the bill later. More specifically, a legislator is less likely to remove his/her name from a bill that he/she cosponsored as the difference between the number of his/her partisans that cosponsored the bill and the number of his/her opponents that cosponsored the bill increases

Long time behavior and stability of special solutions of nonlinear partial differential equations.

In this dissertation, in the first part, I study the long-time behavior of the solutions of the Kuramoto-Sivashinsky equation and the Burgers-Sivashinsky equation. First, I work on a two-dimensional modified KS equation and prove the existence of a global attractor on a bounded domain. Next, I study the long-time behavior of the solutions of the one-dimensional BS equation for general initial data as opposed to the usually considered odd initial data. Third, I study the long-time behavior of radially symmetric solutions of the KS equation in a shell domain in three-dimensions. In the second part, we deal with the conditional stability of radial steady state solutions for the one-dimensional Klein-Gordon equation. I consider the one-dimensional case and construct the infinite-dimensional invariant manifolds explicitly. The result is a precise center-stable manifold theorem, which includes the co-dimension of the manifolds and the decay rates

Phi-four solitary waves in a parabolic potentia: existence, stability, and collisional dynamics

We explore a φ4 model with an added external parabolic potential term. This term dramatically alters the spectral properties of the system. We identify single and multiple kink solutions and examine their stability features; importantly, all of the stationary structures turn out to be unstable. We complement these with a dynamical study of the evolution of a single kink in the trap, as well as of the scattering of kink and anti-kink solutions of the model. We observe that some of the key characteristics of kink-antikink collisions, such as the critical velocity and the multi-bounce windows, are sensitively dependent on the trap strength parameter, as well as the initial displacement of the kink and antikink.Accepted manuscrip