Statistical Machine Learning Methods for High-dimensional Neural Population Data Analysis

Advances in techniques have been producing increasingly complex neural recordings, posing significant challenges for data analysis. This thesis discusses novel statistical methods for analyzing high-dimensional neural data. Part one discusses two extensions of state space models tailored to neural data analysis. First, we propose using a flexible count data distribution family in the observation model to faithfully capture over-dispersion and under-dispersion of the neural observations. Second, we incorporate nonlinear observation models into state space models to improve the flexibility of the model and get a more concise representation of the data. For both extensions, novel variational inference techniques are developed for model fitting, and simulated and real experiments show the advantages of our extensions. Part two discusses a fast region of interest (ROI) detection method for large-scale calcium imaging data based on structured matrix factorization. Part three discusses a method for sampling from a maximum entropy distribution with complicated constraints, which is useful for hypothesis testing for neural data analysis and many other applications related to maximum entropy formulation. We conclude the thesis with discussions and future works

Model Augmented Deep Neural Networks for Medical Image Reconstruction Problems

Solving an ill-posed inverse problem is difficult because it doesn\u27t have a unique solution. In practice, for some important inverse problems, the conventional methods, e.g. ordinary least squares and iterative methods, cannot provide a good estimate. For example, for single image super-resolution and CT reconstruction, the results of these conventional methods cannot satisfy the requirements of these applications. While having more computational resources and high-quality data, researchers try to use machine-learning-based methods, especially deep learning to solve these ill-posed problems. In this dissertation, a model augmented recursive neural network is proposed as a general inverse problem method to solve these difficult problems. In the dissertation, experiments show the satisfactory performance of the proposed method for single image super-resolution, CT reconstruction, and metal artifact reduction

Learning with Single View Co-training and Marginalized Dropout

The generalization properties of most existing machine learning techniques are predicated on the assumptions that 1) a sufficiently large quantity of training data is available; 2) the training and testing data come from some common distribution. Although these assumptions are often met in practice, there are also many scenarios in which training data from the relevant distribution is insufficient. We focus on making use of additional data, which is readily available or can be obtained easily but comes from a different distribution than the testing data, to aid learning. We present five learning scenarios, depending on how the distribution we used to sample the additional training data differs from the testing distribution: 1) learning with weak supervision; 2) domain adaptation; 3) learning from multiple domains; 4) learning from corrupted data; 5) learning with partial supervision. We introduce two strategies and manifest them in five ways to cope with the difference between the training and testing distribution. The first strategy, which gives rise to Pseudo Multi-view Co-training: PMC) and Co-training for Domain Adaptation: CODA), is inspired by the co-training algorithm for multi-view data. PMC generalizes co-training to the more common single view data and allows us to learn from weakly labeled data retrieved free from the web. CODA integrates PMC with an another feature selection component to address the feature incompatibility between domains for domain adaptation. PMC and CODA are evaluated on a variety of real datasets, and both yield record performance. The second strategy marginalized dropout leads to marginalized Stacked Denoising Autoencoders: mSDA), Marginalized Corrupted Features: MCF) and FastTag: FastTag). mSDA diminishes the difference between distributions associated with different domains by learning a new representation through marginalized corruption and reconstruciton. MCF learns from a known distribution which is created by corrupting a small set of training data, and improves robustness of learned classifiers by training on ``infinitely\u27\u27 many data sampled from the distribution. FastTag applies marginalized dropout to the output of partially labeled data to recover missing labels for multi-label tasks. These three algorithms not only achieve the state-of-art performance in various tasks, but also deliver orders of magnitude speed up at training and testing comparing to competing algorithms