Model Based Automatic and Robust Spike Sorting for Large Volumes of Multi-channel Extracellular Data

abstract: Spike sorting is a critical step for single-unit-based analysis of neural activities extracellularly and simultaneously recorded using multi-channel electrodes. When dealing with recordings from very large numbers of neurons, existing methods, which are mostly semiautomatic in nature, become inadequate. This dissertation aims at automating the spike sorting process. A high performance, automatic and computationally efficient spike detection and clustering system, namely, the M-Sorter2 is presented. The M-Sorter2 employs the modified multiscale correlation of wavelet coefficients (MCWC) for neural spike detection. At the center of the proposed M-Sorter2 are two automatic spike clustering methods. They share a common hierarchical agglomerative modeling (HAM) model search procedure to strategically form a sequence of mixture models, and a new model selection criterion called difference of model evidence (DoME) to automatically determine the number of clusters. The M-Sorter2 employs two methods differing by how they perform clustering to infer model parameters: one uses robust variational Bayes (RVB) and the other uses robust Expectation-Maximization (REM) for Student’s -mixture modeling. The M-Sorter2 is thus a significantly improved approach to sorting as an automatic procedure. M-Sorter2 was evaluated and benchmarked with popular algorithms using simulated, artificial and real data with truth that are openly available to researchers. Simulated datasets with known statistical distributions were first used to illustrate how the clustering algorithms, namely REMHAM and RVBHAM, provide robust clustering results under commonly experienced performance degrading conditions, such as random initialization of parameters, high dimensionality of data, low signal-to-noise ratio (SNR), ambiguous clusters, and asymmetry in cluster sizes. For the artificial dataset from single-channel recordings, the proposed sorter outperformed Wave_Clus, Plexon’s Offline Sorter and Klusta in most of the comparison cases. For the real dataset from multi-channel electrodes, tetrodes and polytrodes, the proposed sorter outperformed all comparison algorithms in terms of false positive and false negative rates. The software package presented in this dissertation is available for open access.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Model-based clustering via linear cluster-weighted models

A novel family of twelve mixture models with random covariates, nested in the linear $t$ cluster-weighted model (CWM), is introduced for model-based clustering. The linear $t$ CWM was recently presented as a robust alternative to the better known linear Gaussian CWM. The proposed family of models provides a unified framework that also includes the linear Gaussian CWM as a special case. Maximum likelihood parameter estimation is carried out within the EM framework, and both the BIC and the ICL are used for model selection. A simple and effective hierarchical random initialization is also proposed for the EM algorithm. The novel model-based clustering technique is illustrated in some applications to real data. Finally, a simulation study for evaluating the performance of the BIC and the ICL is presented

Robustness and Outliers

Producción CientíficaUnexpected deviations from assumed models as well as the presence of certain amounts of outlying data are common in most practical statistical applications. This fact could lead to undesirable solutions when applying non-robust statistical techniques. This is often the case in cluster analysis, too. The search for homogeneous groups with large heterogeneity between them can be spoiled due to the lack of robustness of standard clustering methods. For instance, the presence of (even few) outlying observations may result in heterogeneous clusters artificially joined together or in the detection of spurious clusters merely made up of outlying observations. In this chapter we will analyze the effects of different kinds of outlying data in cluster analysis and explore several alternative methodologies designed to avoid or minimize their undesirable effects.Ministerio de Economía, Industria y Competitividad (MTM2014-56235-C2-1-P)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA212U13

Missing data imputation through generative topographic mapping as a mixture of t-distributions: Theoretical developments

The Generative Topographic Mapping (GTM) was originally conceived as a probabilistic alternative to the well-known, neural network-inspired, Self-Organizing Map (SOM). The GTM can also be interpreted as a constrained mixture of distributions model. In recent years, much attention has been directed towards Student t-distributions as an alternative to Gaussians in mixture models due to their robustness towards outliers. In this report, the GTM is redefined as a constrained mixture of t-distributions: the t-GTM, and the Expectation-Maximization algorithm that is used to fit the model to the data is modified to provide missing data imputation.Postprint (published version

Bayesian Two-Stage Robust Causal Modeling with Instrumental Variables using Student\u27s t Distributions

In causal inference research, the issue of the treatment endogeneity is commonly addressed using the two-stage least squares (2SLS) modeling with instrumental variables (IVs), where the local average treatment effect (LATE) is the causal effect of interest. Because practical data are usually heavy tailed or contain outliers, using traditional 2SLS modeling based on normality assumptions may result in inefficient or even biased LATE estimate. This study proposes four types of Bayesian two-stage robust causal models with IVs to model normal and nonnormal data, and evaluates the performance of the four types of models with IVs. The Monte Carlo simulation results show that the Bayesian two-stage robust causal modeling produces reliable parameter estimates and model fits. Particularly, in different types of the two-stage robust models with IVs, the models that take outliers into consideration and use Student’s t distributions in the second stage to model heavy-tailed data or data containing outliers provide more accurate and efficient LATE estimates and better model fits than other distribution models when data are contaminated. The preferred models are recommended to be adopted in general in the two-stage causal modeling with IVs

Robust nonlinear system identification: Bayesian mixture of experts using the t-distribution

A novel variational Bayesian mixture of experts model for robust regression of bifurcating and piece-wise continuous processes is introduced. The mixture of experts model is a powerful model which probabilistically splits the input space allowing different models to operate in the separate regions. However, current methods have no fail-safe against outliers. In this paper, a robust mixture of experts model is proposed which consists of Student-t mixture models at the gates and Student-t distributed experts, trained via Bayesian inference. The Student-t distribution has heavier tails than the Gaussian distribution, and so it is more robust to outliers, noise and nonnormality in the data. Using both simulated data and real data obtained from the Z24 bridge this robust mixture of experts performs better than its Gaussian counterpart when outliers are present. In particular, it provides robustness to outliers in two forms: unbiased parameter regression models, and robustness to overfitting/complex models