Optimal Tuning for Divide-and-conquer Kernel Ridge Regression with Massive Data

Divide-and-conquer is a powerful approach for large and massive data analysis. In the nonparameteric regression setting, although various theoretical frameworks have been established to achieve optimality in estimation or hypothesis testing, how to choose the tuning parameter in a practically effective way is still an open problem. In this paper, we propose a data-driven procedure based on divide-and-conquer for selecting the tuning parameters in kernel ridge regression by modifying the popular Generalized Cross-validation (GCV, Wahba, 1990). While the proposed criterion is computationally scalable for massive data sets, it is also shown under mild conditions to be asymptotically optimal in the sense that minimizing the proposed distributed-GCV (dGCV) criterion is equivalent to minimizing the true global conditional empirical loss of the averaged function estimator, extending the existing optimality results of GCV to the divide-and-conquer framework

A Graph Theoretical Approach to Network Encoding Complexity

Consider an acyclic directed network $G$ with sources $S_1, S_2,..., S_l$ and distinct sinks $R_1, R_2,..., R_l$. For $i=1, 2,..., l$, let $c_i$ denote the min-cut between $S_i$ and $R_i$. Then, by Menger's theorem, there exists a group of $c_i$ edge-disjoint paths from $S_i$ to $R_i$, which will be referred to as a group of Menger's paths from $S_i$ to $R_i$ in this paper. Although within the same group they are edge-disjoint, the Menger's paths from different groups may have to merge with each other. It is known that by choosing Menger's paths appropriately, the number of mergings among different groups of Menger's paths is always bounded by a constant, which is independent of the size and the topology of $G$. The tightest such constant for the all the above-mentioned networks is denoted by $\mathcal{M}(c_1, c_2,..., c_2)$ when all $S_i$'s are distinct, and by $\mathcal{M}^*(c_1, c_2,..., c_2)$ when all $S_i$'s are in fact identical. It turns out that $\mathcal{M}$ and $\mathcal{M}^*$ are closely related to the network encoding complexity for a variety of networks, such as multicast networks, two-way networks and networks with multiple sessions of unicast. Using this connection, we compute in this paper some exact values and bounds in network encoding complexity using a graph theoretical approach.Comment: 44 pages, 22 figure

Diffusion and entanglement of a kicked particle in an infinite square well under frequent measurements

We investigate the dynamics of a kicked particle in an infinite square well undergoing frequent measurements of energy. For a large class of periodic kicking force, constant diffusion is found in such a non-KAM system. The influence of phase shift of the kicking potential on the short-time dynamical behavior is discussed. The general asymptotical measurement-assisted diffusion rate is obtained. The entanglement between the particle and the measuring apparatus is investigated. There exist two distinct dynamical behaviors of entanglement. The bipartite entanglement grows with the kicking steps and it gains larger value for the more chaotic system. However, the pairwise entanglement between the system of interest and the partial spins of the measuring apparatus decreases with the kicking steps. The relation between the entanglement and quantum diffusion is also analyzed. PACS numbers: 05.45.Mt, 03.65.TaComment: 7 pages, 5 figures, RevTex4, Accepted by Phys. Rev.

A platform for otakus to gradually learn and adapt to social conventions

It is believed that good design should not only satisfy users’ needs, but also improve their overall quality of life. Nowadays, with the rapidly increasing amounts of time spent on the internet, more and more people, the majority of them youngsters, claim themselves as otakus since they cut themselves off from face-to-face communication. From my primary and secondary user studies, most otakus have difficulties interacting with strangers in real world contexts, but some do want to expand their social networks. This design hypothesis is to provide opportunities for otakus to meet people and build friendships in real life. The purpose of this thesis is to use design methodologies to accomplish this hypothesis. The objective is to adopt design approaches to enhance the connections among otakus in face-to-face scenarios by incorporating what is learned from research on and with the target group. Based on the analysis of the user group who regard themselves as otakus, my final design adopts a user-centered approach in order to accurately address the problems. Previous otaku studies are valuable and inform this interaction design. Yet with such general information as a guide, it is still essential to identify the otakus users’ needs and problems they face in their daily routines. Therefore, I conducted a survey to learn about otakus’ social-phobias techniques skills and needs. The interview data provided more detailed information to identify user requirements and needs. According to the survey data, 79% of otakus are willing to meet more friends in real life, which indicated that most otakus wanted to meet more people in real belief as long as they are able to choose where and when to meet, as if they were playing a game. They lack the face-to-face communication practice with live people in various scenarios. The mobile phone is the best medium to reach out to otakus; cell phones are the most highly-used electronic device of all screen technologies. Thus, this design thesis developed the mobile app “Say Hey,” a social app with a role-playing game format. “Say Hey” a social app with a role-playing game platform. Using this app, otakus will act as game characters and finish a set of tasks, which involves offline entertainments, including interacting with their physical surroundings. In this way, participating otakus will start to connect the virtual world (mobile application) and the real world (offline activities). By using this app, they will have to collaborate with other people to finish tasks, which will connect them with other players and people in real life, starting a trivia challenge. As a result, the objective is that Say Hey will improve their interpersonal communication skills. The ultimate design goal of this thesis project is to help otakus gradually get involved in real society and frequent interpersonal communications in daily life