Kernel functions based on triplet comparisons

Given only information in the form of similarity triplets "Object A is more similar to object B than to object C" about a data set, we propose two ways of defining a kernel function on the data set. While previous approaches construct a low-dimensional Euclidean embedding of the data set that reflects the given similarity triplets, we aim at defining kernel functions that correspond to high-dimensional embeddings. These kernel functions can subsequently be used to apply any kernel method to the data set

Beyond Classical Statistics: Optimality In Transfer Learning And Distributed Learning

During modern statistical learning practice, statisticians are dealing with increasingly huge, complicated and structured data sets. New opportunities can be found during the learning process with better structured data sets as well as powerful data analytic resources. Also, there are more and more challenges we need to address when dealing with large data sets, due to limitation of computation, communication resources or privacy concerns. Under decision-theoretical framework, statistical optimality should be reconsidered with new type of data or new constraints. Under the framework of minimax theory, this thesis aims to address the following four problems:1. The first part of this thesis aims to develop an optimality theory for transfer learning for nonparametric classification. An near optimal adaptive classifier is also established. 2. In the second part, we study distributed Gaussian mean estimation with known vari- ance under communication constraints. The exact distributed minimax rate of con- vergence is derived under three different communication protocols. 3. In the third part, we study distributed Gaussian mean estimation with unknown vari- ance under communication constraints. The results show that the amount of additional communication cost depends on the type of underlying communication protocol. 4. In the fourth part, we investigate the minimax optimality and communication cost of adaptation for distributed nonparametric function estimation under communication constraints

Efficient Data Analytics on Augmented Similarity Triplets

Many machine learning methods (classification, clustering, etc.) start with a known kernel that provides similarity or distance measure between two objects. Recent work has extended this to situations where the information about objects is limited to comparisons of distances between three objects (triplets). Humans find the comparison task much easier than the estimation of absolute similarities, so this kind of data can be easily obtained using crowd-sourcing. In this work, we give an efficient method of augmenting the triplets data, by utilizing additional implicit information inferred from the existing data. Triplets augmentation improves the quality of kernel-based and kernel-free data analytics tasks. Secondly, we also propose a novel set of algorithms for common supervised and unsupervised machine learning tasks based on triplets. These methods work directly with triplets, avoiding kernel evaluations. Experimental evaluation on real and synthetic datasets shows that our methods are more accurate than the current best-known techniques

This city is not a bin: crowdmapping the distribution of urban litter

Industrial Ecolog