The Gaussian Multiple Access Diamond Channel

In this paper, we study the capacity of the diamond channel. We focus on the special case where the channel between the source node and the two relay nodes are two separate links with finite capacities and the link from the two relay nodes to the destination node is a Gaussian multiple access channel. We call this model the Gaussian multiple access diamond channel. We first propose an upper bound on the capacity. This upper bound is a single-letterization of an $n$-letter upper bound proposed by Traskov and Kramer, and is tighter than the cut-set bound. As for the lower bound, we propose an achievability scheme based on sending correlated codes through the multiple access channel with superposition structure. We then specialize this achievable rate to the Gaussian multiple access diamond channel. Noting the similarity between the upper and lower bounds, we provide sufficient and necessary conditions that a Gaussian multiple access diamond channel has to satisfy such that the proposed upper and lower bounds meet. Thus, for a Gaussian multiple access diamond channel that satisfies these conditions, we have found its capacity.Comment: submitted to IEEE Transactions on Information Theor

Advanced topics in multi-label learning

University of Technology Sydney. Faculty of Engineering and Information Technology.Multi-label learning, in which each instance can belong to multiple labels simultaneously, has significantly attracted the attention of researchers as a result of its wide range of applications, which range from document classification and automatic image annotation to video annotation. Many multi-label learning models have been developed to capture label dependency. Amongst them, the classifier chain (CC) model is one of the most popular methods due to its simplicity and promising experimental results. However, CC suffers from three important problems: Does the label order affect the performance of CC? Is there any globally optimal classifier chain which can achieve the optimal prediction performance for CC? If yes, how can the globally optimal classifier chain be found? It is non-trivial to answer these problems. Another important branch of methods for capturing label dependency is encoding-decoding paradigm. Based on structural SVMs, maximum margin output coding (MMOC) has become one of the most representative encoding-decoding methods and shown promising results for multi-label classification. Unfortunately, MMOC suffers from two major limitations: 1) Inconsistent performance: D. McAllester has already proved that structural SVMs fail to converge on the optimal decoder even with infinite training data. 2) Prohibitive computational cost: the training of MMOC involves a complex quadratic programming (QP) problem over the combinatorial space, and its computational cost on the data sets with many labels is prohibitive. Therefore, it is non-trivial to break the bottlenecks of MMOC, and develop efficient and consistent algorithms for solving multi-label learning tasks. The prediction of most multi-label learning methods either scales linearly with the number of labels or involves an expensive decoding process, which usually requires solving a combinatorial optimization. Such approaches become unacceptable when tackling thousands of labels, and are impractical for real-world applications, such as document annotation. It is imperative to design an efficient, yet accurate multi-label learning algorithm with the minimum number of predictions. This thesis systematically studies how to efficiently solve aforementioned issues with provable guarantee

TURNING POINTS IN LATE ADOLESCENCE: A STUDY OF HIGH SCHOOL GRADUATION AND ADULT OFFENDING IN A LIFE COURSE FRAMEWORK

Guided by the general theoretical paradigm of life course criminology, this study investigates the relationship between high school graduation and adult offending. This dissertation builds upon the idea of turning points in reducing offending behavior and extends this idea from adulthood to late adolescence/early adulthood, and considers high school graduation as a turning point in reducing adult offending behavior. This dissertation identifies the research gap on the high school graduation/dropout-delinquency relationship, that is, most previous studies could not reject the alternative hypothesis, i.e. not graduating from high school and adult offending can both be explained by prior processes. This dissertation investigates the causal relationship between high school graduation, as a turning point that opens up future opportunities, and early adult offending. After establishing a causal relationship between graduation and adult offending, this study further explores the mechanisms of the graduation effect. In particular, this study investigates whether and to what extent turning points in adulthood, i.e. employment and intimate relationships, mediate such a causal relationship. The sample used in this dissertation consists of 460 males from the data collected by Johns Hopkins Prevention Intervention Research Center (JHU PIRC). The analytical methods used in this study include propensity score matching, sensitivity analysis (to address selection bias due to possible omitted covariates), and mediation analysis. In terms of the causal relationship between graduation and offending, it was found that high school graduates are 93% less likely to have an adult offending record than dropouts similar on early processes. Such a finding is robust to selection bias due to possible omitted covariates. It was concluded that for those who are at great risk for dropping out, staying in school and finishing their education provides a turning point in reducing adult offending. In terms of the mechanisms of the graduation effect, it was found that post graduation experiences, employment in particular, help explain the graduate-dropout differences in offending during early adulthood. For dropouts, employment may be another turning point. Implications for life course criminology and policy are discussed

Asymptotic Theory for GARCH-in-mean Models

The GARCH-in-mean process is an important extension of the standard GARCH (generalized autoregressive conditional heteroscedastic) process and it has wide applications in economics and finance. The parameter estimation of GARCH type models usually involves the quasi-maximum likelihood (QML) technique as it produces consistent and asymptotically Gaussian distributed estimators under certain regularity conditions. For a pure GARCH model, such conditions were already found with asymptotic properties of its QML estimator well understood. However, when it comes to GARCH-in-mean models those properties are still largely unknown. The focus of this work is to establish a set of conditions under which the QML estimator of GARCH-in-mean models will have the desired asymptotic properties. Some general Markov model tools are applied to derive the result. Keywords: GARCH, GARCH-in-mean, asymptotic theory, Markov mode

Existence and stability analysis of solutions for a new kind of boundary value problems of nonlinear fractional differential equations

This research work is dedicated to an investigation for a new kind of boundary value problem of nonlinear fractional differential equation supplemented with general boundary condition. A full analysis of existence and uniqueness of positive solutions is respectively proved by Leray–Schauder nonlinear alternative theorem and Boyd–Wong’s contraction principles. Furthermore, we prove the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) stability of solutions. An example illustrating the validity of the existence result is also discussed

Coverage-Guaranteed Prediction Sets for Out-of-Distribution Data

Out-of-distribution (OOD) generalization has attracted increasing research attention in recent years, due to its promising experimental results in real-world applications. In this paper,we study the confidence set prediction problem in the OOD generalization setting. Split conformal prediction (SCP) is an efficient framework for handling the confidence set prediction problem. However, the validity of SCP requires the examples to be exchangeable, which is violated in the OOD setting. Empirically, we show that trivially applying SCP results in a failure to maintain the marginal coverage when the unseen target domain is different from the source domain. To address this issue, we develop a method for forming confident prediction sets in the OOD setting and theoretically prove the validity of our method. Finally, we conduct experiments on simulated data to empirically verify the correctness of our theory and the validity of our proposed method