Autoregressive Asymmetric Linear Gaussian Hidden Markov Models

In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil this dynamical requirement and provide a framework where the trend of the process can be expressed as a latent variable. In this paper, we modify these recent asymmetric hidden Markov models to have an asymmetric autoregressive component, allowing the model to choose the order of autoregression that maximizes its penalized likelihood for a given training set. Additionally, we show how inference, hidden states decoding and parameter learning must be adapted to fit the proposed model. Finally, we run experiments with synthetic and real data to show the capabilities of this new model.Comment: 34 pages, 16 figures, intended to be published in IEEE Transactions on Pattern Analysis and Machine Intelligenc

Comparison Between Supervised and Unsupervised Classifications of Neuronal Cell Types: A Case Study

In the study of neural circuits, it becomes essential to discern the different neuronal cell types that build the circuit. Traditionally, neuronal cell types have been classified using qualitative descriptors. More recently, several attempts have been made to classify neurons quantitatively, using unsupervised clustering methods. While useful, these algorithms do not take advantage of previous information known to the investigator, which could improve the classification task. For neocortical GABAergic interneurons, the problem to discern among different cell types is particularly difficult and better methods are needed to perform objective classifications. Here we explore the use of supervised classification algorithms to classify neurons based on their morphological features, using a database of 128 pyramidal cells and 199 interneurons from mouse neocortex. To evaluate the performance of different algorithms we used, as a “benchmark,” the test to automatically distinguish between pyramidal cells and interneurons, defining “ground truth” by the presence or absence of an apical dendrite. We compared hierarchical clustering with a battery of different supervised classification algorithms, finding that supervised classifications outperformed hierarchical clustering. In addition, the selection of subsets of distinguishing features enhanced the classification accuracy for both sets of algorithms. The analysis of selected variables indicates that dendritic features were most useful to distinguish pyramidal cells from interneurons when compared with somatic and axonal morphological variables. We conclude that supervised classification algorithms are better matched to the general problem of distinguishing neuronal cell types when some information on these cell groups, in our case being pyramidal or interneuron, is known a priori. As a spin-off of this methodological study, we provide several methods to automatically distinguish neocortical pyramidal cells from interneurons, based on their morphologies

Conductance interaction identification by means of Boltzmann distribution and mutual information analysis in conductance-based neuron models

Conductance interaction identification by means of Boltzmann distribution and mutual information analysis in conductance-based neuron models

Learning an L1-regularized Gaussian Bayesian Network in the Equivalence Class Space

Learning the structure of a graphical model from data is a common task in a wide range of practical applications. In this paper, we focus on Gaussian Bayesian networks, i.e., on continuous data and directed acyclic graphs with a joint probability density of all variables given by a Gaussian. We propose to work in an equivalence class search space, specifically using the k-greedy equivalence search algorithm. This, combined with regularization techniques to guide the structure search, can learn sparse networks close to the one that generated the data. We provide results on some synthetic networks and on modeling the gene network of the two biological pathways regulating the biosynthesis of isoprenoids for the Arabidopsis thaliana plan

Forward Stagewise Naive Bayes

The naïve Bayes approach is a simple but often satisfactory method for supervised classification. In this paper, we focus on the naïve Bayes model and propose the application of regularization techniques to learn a naïve Bayes classifier. The main contribution of the paper is a stagewise version of the selective naïve Bayes, which can be considered a regularized version of the naïve Bayes model. We call it forward stagewise naïve Bayes. For comparison’s sake, we also introduce an explicitly regularized formulation of the naïve Bayes model, where conditional independence (absence of arcs) is promoted via an L 1/L 2-group penalty on the parameters that define the conditional probability distributions. Although already published in the literature, this idea has only been applied for continuous predictors. We extend this formulation to discrete predictors and propose a modification that yields an adaptive penalization. We show that, whereas the L 1/L 2 group penalty formulation only discards irrelevant predictors, the forward stagewise naïve Bayes can discard both irrelevant and redundant predictors, which are known to be harmful for the naïve Bayes classifier. Both approaches, however, usually improve the classical naïve Bayes model’s accuracy