Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience.

Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox-called seqNMF-with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral datas. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs

Scalable Learning Adaptive to Unknown Dynamics and Graphs

University of Minnesota Ph.D. dissertation.June 2019. Major: Electrical/Computer Engineering. Advisor: Georgios B. Giannakis. 1 computer file (PDF); xii, 174 pages.With the scale of information growing every day, the key challenges in machine learning include the high-dimensionality and sheer volume of feature vectors that may consist of real and categorical data, as well as the speed and the typically streaming format of data acquisition that may also entail outliers and misses. The latter may be present, either unintentionally or intentionally, in order to cope with scalability, privacy, and adversarial behavior. These challenges provide ample opportunities for algorithmic and analytical innovations in online and nonlinear subspace learning approaches. Among the available nonlinear learning tools, those based on kernels have merits that are well documented. However, most rely on a preselected kernel, whose prudent choice presumes task-specific prior information that is generally not available. It is also known that kernel-based methods do not scale well with the size or dimensionality of the data at hand. Besides data science, the urgent need for scalable tools is a core issue also in network science that has recently emerged as a means of collectively understanding the behavior of complex interconnected entities. The rich spectrum of application domains comprises communication, social, financial, gene-regulatory, brain, and power networks, to name a few. Prominent tasks in all network science applications are those of topology identification and inference of nodal processes evolving over graphs. Most contemporary graph-driven inference approaches rely on linear and static models that are simple and tractable, but also presume that the nodal processes are directly observable. To cope with these challenges, the present thesis first introduces a novel online categorical subspace learning approach to track the latent structure of categorical data `on the fly.' Leveraging the random feature approximation, it then develops an adaptive online multi-kernel learning approach (termed AdaRaker), which accounts not only for data-driven learning of the kernel combination, but also for the unknown dynamics. Performance analysis is provided in terms of both static and dynamic regrets to quantify the novel learning function approximation. In addition, the thesis introduces a kernel-based topology identification approach that can even account for nonlinear dependencies among nodes and across time. To cope with nodal processes that may not be directly observable in certain applications, tensor-based algorithms that leverage piecewise stationary statistics of nodal processes are developed, and pertinent identifiability conditions are established. To facilitate real-time operation and inference of time-varying networks, an adaptive tensor decomposition based scheme is put forth to track the topologies of time-varying networks. Last but not least, the present thesis offers a unifying framework to deal with various learning tasks over possibly dynamic networks. These tasks include dimensionality reduction, classification, and clustering. Tests on both synthetic and real datasets from the aforementioned application domains are carried out to showcase the effectiveness of the novel algorithms throughout

Cell Type-specific Analysis of Human Interactome and Transcriptome

Cells are the fundamental building block of complex tissues in higher-order organisms. These cells take different forms and shapes to perform a broad range of functions. What makes a cell uniquely eligible to perform a task, however, is not well-understood; neither is the defining characteristic that groups similar cells together to constitute a cell type. Even for known cell types, underlying pathways that mediate cell type-specific functionality are not readily available. These functions, in turn, contribute to cell type-specific susceptibility in various disorders