Filling out the missing gaps: Time Series Imputation with Semi-Supervised Learning

Missing data in time series is a challenging issue affecting time series analysis. Missing data occurs due to problems like data drops or sensor malfunctioning. Imputation methods are used to fill in these values, with quality of imputation having a significant impact on downstream tasks like classification. In this work, we propose a semi-supervised imputation method, ST-Impute, that uses both unlabeled data along with downstream task's labeled data. ST-Impute is based on sparse self-attention and trains on tasks that mimic the imputation process. Our results indicate that the proposed method outperforms the existing supervised and unsupervised time series imputation methods measured on the imputation quality as well as on the downstream tasks ingesting imputed time series

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

COMMUNITY DETECTION IN GRAPHS

Thesis (Ph.D.) - Indiana University, Luddy School of Informatics, Computing, and Engineering/University Graduate School, 2020Community detection has always been one of the fundamental research topics in graph mining. As a type of unsupervised or semi-supervised approach, community detection aims to explore node high-order closeness by leveraging graph topological structure. By grouping similar nodes or edges into the same community while separating dissimilar ones apart into different communities, graph structure can be revealed in a coarser resolution. It can be beneficial for numerous applications such as user shopping recommendation and advertisement in e-commerce, protein-protein interaction prediction in the bioinformatics, and literature recommendation or scholar collaboration in citation analysis. However, identifying communities is an ill-defined problem. Due to the No Free Lunch theorem [1], there is neither gold standard to represent perfect community partition nor universal methods that are able to detect satisfied communities for all tasks under various types of graphs. To have a global view of this research topic, I summarize state-of-art community detection methods by categorizing them based on graph types, research tasks and methodology frameworks. As academic exploration on community detection grows rapidly in recent years, I hereby particularly focus on the state-of-art works published in the latest decade, which may leave out some classic models published decades ago. Meanwhile, three subtle community detection tasks are proposed and assessed in this dissertation as well. First, apart from general models which consider only graph structures, personalized community detection considers user need as auxiliary information to guide community detection. In the end, there will be fine-grained communities for nodes better matching user needs while coarser-resolution communities for the rest of less relevant nodes. Second, graphs always suffer from the sparse connectivity issue. Leveraging conventional models directly on such graphs may hugely distort the quality of generate communities. To tackle such a problem, cross-graph techniques are involved to propagate external graph information as a support for target graph community detection. Third, graph community structure supports a natural language processing (NLP) task to depict node intrinsic characteristics by generating node summarizations via a text generative model. The contribution of this dissertation is threefold. First, a decent amount of researches are reviewed and summarized under a well-defined taxonomy. Existing works about methods, evaluation and applications are all addressed in the literature review. Second, three novel community detection tasks are demonstrated and associated models are proposed and evaluated by comparing with state-of-art baselines under various datasets. Third, the limitations of current works are pointed out and future research tracks with potentials are discussed as well

Dynamic Machine Learning with Least Square Objectives

As of the writing of this thesis, machine learning has become one of the most active research fields. The interest comes from a variety of disciplines which include computer science, statistics, engineering, and medicine. The main idea behind learning from data is that, when an analytical model explaining the observations is hard to find ---often in contrast to the models in physics such as Newton's laws--- a statistical approach can be taken where one or more candidate models are tuned using data. Since the early 2000's this challenge has grown in two ways: (i) The amount of collected data has seen a massive growth due to the proliferation of digital media, and (ii) the data has become more complex. One example for the latter is the high dimensional datasets, which can for example correspond to dyadic interactions between two large groups (such as customer and product information a retailer collects), or to high resolution image/video recordings. Another important issue is the study of dynamic data, which exhibits dependence on time. Virtually all datasets fall into this category as all data collection is performed over time, however I use the term dynamic to hint at a system with an explicit temporal dependence. A traditional example is target tracking from signal processing literature. Here the position of a target is modeled using Newton's laws of motion, which relates it to time via the target's velocity and acceleration. Dynamic data, as I defined above, poses two important challenges. Firstly, the learning setup is different from the standard theoretical learning setup, also known as Probably Approximately Correct (PAC) learning. To derive PAC learning bounds one assumes a collection of data points sampled independently and identically from a distribution which generates the data. On the other hand, dynamic systems produce correlated outputs. The learning systems we use should accordingly take this difference into consideration. Secondly, as the system is dynamic, it might be necessary to perform the learning online. In this case the learning has to be done in a single pass. Typical applications include target tracking and electricity usage forecasting. In this thesis I investigate several important dynamic and online learning problems, where I develop novel tools to address the shortcomings of the previous solutions in the literature. The work is divided into three parts for convenience. The first part is about matrix factorization for time series analysis which is further divided into two chapters. In the first chapter, matrix factorization is used within a Bayesian framework to model time-varying dyadic interactions, with examples in predicting user-movie ratings and stock prices. In the next chapter, a matrix factorization which uses autoregressive models to forecast future values of multivariate time series is proposed, with applications in predicting electricity usage and traffic conditions. Inspired by the machinery we use in the first part, the second part is about nonlinear Kalman filtering, where a hidden state is estimated over time given observations. The nonlinearity of the system generating the observations is the main challenge here, where a divergence minimization approach is used to unify the seemingly unrelated methods in the literature, and propose new ones. This has applications in target tracking and options pricing. The third and last part is about cost sensitive learning, where a novel method for maximizing area under receiver operating characteristics curve is proposed. Our method has theoretical guarantees and favorable sample complexity. The method is tested on a variety of benchmark datasets, and also has applications in online advertising