On Consistency of Graph-based Semi-supervised Learning

Graph-based semi-supervised learning is one of the most popular methods in machine learning. Some of its theoretical properties such as bounds for the generalization error and the convergence of the graph Laplacian regularizer have been studied in computer science and statistics literatures. However, a fundamental statistical property, the consistency of the estimator from this method has not been proved. In this article, we study the consistency problem under a non-parametric framework. We prove the consistency of graph-based learning in the case that the estimated scores are enforced to be equal to the observed responses for the labeled data. The sample sizes of both labeled and unlabeled data are allowed to grow in this result. When the estimated scores are not required to be equal to the observed responses, a tuning parameter is used to balance the loss function and the graph Laplacian regularizer. We give a counterexample demonstrating that the estimator for this case can be inconsistent. The theoretical findings are supported by numerical studies.Comment: This paper is accepted by 2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS

Training Group Orthogonal Neural Networks with Privileged Information

Learning rich and diverse representations is critical for the performance of deep convolutional neural networks (CNNs). In this paper, we consider how to use privileged information to promote inherent diversity of a single CNN model such that the model can learn better representations and offer stronger generalization ability. To this end, we propose a novel group orthogonal convolutional neural network (GoCNN) that learns untangled representations within each layer by exploiting provided privileged information and enhances representation diversity effectively. We take image classification as an example where image segmentation annotations are used as privileged information during the training process. Experiments on two benchmark datasets -- ImageNet and PASCAL VOC -- clearly demonstrate the strong generalization ability of our proposed GoCNN model. On the ImageNet dataset, GoCNN improves the performance of state-of-the-art ResNet-152 model by absolute value of 1.2% while only uses privileged information of 10% of the training images, confirming effectiveness of GoCNN on utilizing available privileged knowledge to train better CNNs.Comment: Proceedings of the IJCAI-1

Synthesis and evaluation of polymer mosaics as highly tunable biomaterials for biomedical applications

Biomaterials are composed of a wide array of macromolecules and have impacted multiple biomedical technologies. Structurally, each of these materials typically only include a small set of monomers that limits their structural complexity, tunability, and functionality. There is a critical need to develop novel biomaterials with greater complexity and tailored functionalities to meet the demands of emerging new technologies in drug delivery, tissue engineering, and regenerative medicine. Inspired by proteins, where complexity and functionality are driven by the organization of thousands of functional domains, we hypothesized that tethering different biomaterial backbones into a domain-structured single-chain polymer (a polymer mosaic) will impart structural complexity with emergent physicochemical properties, novel functionalities, and defined secondary structures. In this thesis, we designed and characterized a series of polymer mosaics designed to test this hypothesis. We first designed and synthesized an alginate-b-polyethylene glycol (PEG)-b-polylactide (PLA) triblock copolymers utilizing a modular click-chemistry strategy. This triblock copolymer was investigated as an amphiphilic material for controlled drug release. The incorporation of a hydrophobic PLA domain and a hydrophilic alginate domain in a single polymer made it an attractive platform for both the encapsulation and release of both hydrophilic and hydrophobic small molecules. Nanoparticles (NPs) formulated from this triblock displayed morphologically discrete compartmentalization of the alginate domains, superior loading efficiencies of both hydrophilic and hydrophobic small molecules, and potential as a drug-combination delivery platform. Next, we evaluated the potential of alginate-b-PLA diblock copolymers to function as degradable hydrogels by combining the hydrogel-forming feature of alginate with the degradation properties of a PLA domain. The fabricated hydrogels had tunable degradation properties from days to weeks by modulating their formulation, and are being evaluated as potential sacrificial scaffolds for tissue engineering. Finally, poly (L-lactide)- poly (amido saccharide) (PLLA-PAS) were synthesized as polymer mosaics amphiphiles with defined secondary structures that formulate into chiral nanoparticles. These chiral particles assembled a unique protein corona of 22 proteins when incubated with mouse serum and analyzed by SDS-PAGE and LC/MS-based proteomics. This result will build a foundation to further our understanding of surface chirality on the protein corona and its potential delivery applications. In summary, we successfully synthesized and developed polymer mosaics with complementary properties, tailored functionalities, and defined secondary structures. These new materials can pave the way for advances in new technologies for drug delivery and tissue engineering