Title: Bayesian learning methods for neural coding.
Abstract: A primary goal in systems neuroscience is to understand how neural spike responses encode information about the external world. A popular approach to this problem is to build an explicit probabilistic model that characterizes the encoding relationship in terms of a cascade of stages: (1) linear dimensionality reduction of a high-dimensional stimulus space using a bank of filters or receptive fields (RFs); (2) a nonlinear function from filter outputs to spike rate; and (3) a stochastic spiking process with recurrent feedback. These models have described single- and multi-neuron spike responses in a wide variety of brain areas.
In this talk, I will present my Ph.D. work that focuses on developing Bayesian methods to efficiently estimate the linear and non-linear stages of the cascade encoding model. First, I will describe a novel Bayesian receptive field estimator based on a hierarchical prior that flexibly incorporates knowledge about the shapes of neural receptive fields. This estimator achieves error rates several times lower than existing methods, and can be applied to a variety of other neural inference problems such as extracting structure in fMRI data. Furthermore, I will present a novel low-rank description of the high dimensional receptive field, combined with a hierarchical prior for more efficient receptive field estimation. Second, I will describe new models for neural nonlinearities using Gaussian processes (GPs) and Bayesian active learning algorithms in ``closed-loop" neurophysiology experiments to rapidly estimate neural nonlinearities. These approaches significantly improve the efficiency of neurophysiology experiments, where data are often limited by the difficulty of maintaining stable recordings from a neuron or neural population.
Sunday, October 27, 2013
Saturday, October 19, 2013
Prof. Tian Zheng: Oct 16th
Title: Latent Space Model for Aggregated Relational Data
Abstract: Aggregated Relational Data (ARD) are indirect network data collected using survey questions of the form "how many X's do you know?" It is most often used to estimate the size of populations that are difficult to count directly and allows researchers to choose specific subpopulations of interest without sampling or surveying members of these subpopulations directly. What has been under-utilized is the indirect information on social structure captured by ARD. In this talk, I present a latent space model and Bayesian computation framework for inference and estimation of social structures using ARD from non-network samples in social networks, the variation of social structures in subnetworks, and the relations between (hard-to-reach) subpopulations.
Abstract: Aggregated Relational Data (ARD) are indirect network data collected using survey questions of the form "how many X's do you know?" It is most often used to estimate the size of populations that are difficult to count directly and allows researchers to choose specific subpopulations of interest without sampling or surveying members of these subpopulations directly. What has been under-utilized is the indirect information on social structure captured by ARD. In this talk, I present a latent space model and Bayesian computation framework for inference and estimation of social structures using ARD from non-network samples in social networks, the variation of social structures in subnetworks, and the relations between (hard-to-reach) subpopulations.
Sunday, October 6, 2013
Prof. Rahul Mazumder: Oct 9th
Title: Low-rank Matrix Regularization: Statistical Models and Large Scale Algorithms
Abstract: Low-rank matrix regularization is an important area of research in statistics and machine learning with a wide range of applications --- the task is to estimate X, under a low rank constraint and possibly additional affine (or more general convex) constraints on X. In practice, the matrix dimensions frequently range from hundreds of thousands to even a million --- leading to severe computational challenges. In this talk, I will describe computationally tractable models and scalable (convex) optimization based algorithms for a class of low-rank regularized problems. Exploiting problem-specific statistical insights, problem structure and using novel tools for large scale SVD computations play important roles in this task. I will describe how we can develop a unified, tractable convex optimization framework for general exponential family models, incorporating meta-features on the rows/columns.
Abstract: Low-rank matrix regularization is an important area of research in statistics and machine learning with a wide range of applications --- the task is to estimate X, under a low rank constraint and possibly additional affine (or more general convex) constraints on X. In practice, the matrix dimensions frequently range from hundreds of thousands to even a million --- leading to severe computational challenges. In this talk, I will describe computationally tractable models and scalable (convex) optimization based algorithms for a class of low-rank regularized problems. Exploiting problem-specific statistical insights, problem structure and using novel tools for large scale SVD computations play important roles in this task. I will describe how we can develop a unified, tractable convex optimization framework for general exponential family models, incorporating meta-features on the rows/columns.
Friday, September 27, 2013
Dean Eckles (Facebook): October 2nd
Title: Design and analysis of experiments in networks
Abstract: Random assignment of individuals to treatments is often used to predict what will happen if the treatment is applied to everyone, but resulting estimates can suffer substantial bias in the presence of peer effects (i.e., interference, spillovers, social interactions). We describe experimental designs that reduce this bias by producing treatment assignments that are correlated in the network. For example, we can use graph partitioning methods to construct clusters of individuals who are then assigned to treatment or control together. This clustered assignment alone can substantially reduce bias, as can incorporating information about peers' treatment assignments or behaviors into the analysis. Simulation results show how this bias reduction varies with network structure and the size of direct and peer effects. We illustrate this method with real experiments, including a large experiment on Thanksgiving Day 2012.
Abstract: Random assignment of individuals to treatments is often used to predict what will happen if the treatment is applied to everyone, but resulting estimates can suffer substantial bias in the presence of peer effects (i.e., interference, spillovers, social interactions). We describe experimental designs that reduce this bias by producing treatment assignments that are correlated in the network. For example, we can use graph partitioning methods to construct clusters of individuals who are then assigned to treatment or control together. This clustered assignment alone can substantially reduce bias, as can incorporating information about peers' treatment assignments or behaviors into the analysis. Simulation results show how this bias reduction varies with network structure and the size of direct and peer effects. We illustrate this method with real experiments, including a large experiment on Thanksgiving Day 2012.
Sunday, September 22, 2013
Donald Pianto: September 25th
Title: Dealing with monotone likelihood in a model for speckled data
Abstract: In this paper we study maximum likelihood estimation (MLE) of the roughness parameter of the G_{A}^{0} distribution for speckled imagery (Frery et al., 1997). We discover that when a certain criterion is satisfied by the sample moments, the likelihood function is monotone and MLE estimates are infinite, implying an extremely homogeneous region. We implement three corrected estimators in an attempt to obtain finite parameter estimates. Two of the estimators are taken from the literature on monotone likelihood (Firth, 1993; Jeffreys, 1946) and one, based on resampling, is proposed by the authors. We perform Monte Carlo experiments to compare the three estimators. We find the estimator based on the Jeffreys prior to be the worst. The choice between Firth’s estimator and the Bootstrap
estimator depends on the value of the number of looks (which is given before estimation) and the specific needs of the user. We also apply the estimators to real data obtained from synthetic aperture radar (SAR). These results corroborate the Monte Carlo findings.
Abstract: In this paper we study maximum likelihood estimation (MLE) of the roughness parameter of the G_{A}^{0} distribution for speckled imagery (Frery et al., 1997). We discover that when a certain criterion is satisfied by the sample moments, the likelihood function is monotone and MLE estimates are infinite, implying an extremely homogeneous region. We implement three corrected estimators in an attempt to obtain finite parameter estimates. Two of the estimators are taken from the literature on monotone likelihood (Firth, 1993; Jeffreys, 1946) and one, based on resampling, is proposed by the authors. We perform Monte Carlo experiments to compare the three estimators. We find the estimator based on the Jeffreys prior to be the worst. The choice between Firth’s estimator and the Bootstrap
estimator depends on the value of the number of looks (which is given before estimation) and the specific needs of the user. We also apply the estimators to real data obtained from synthetic aperture radar (SAR). These results corroborate the Monte Carlo findings.
Sunday, September 15, 2013
Prof. John Paisley: September 18th
Title: Variational Inference and Big Data
Abstract: I will discuss a scalable algorithm for approximating posterior distributions called stochastic variational inference. Stochastic variational inference lets one apply complex Bayesian models to massive data sets. This technique applies to a large class of probabilistic models and outperforms traditional batch variational inference, which can only handle small data sets. Stochastic inference is a simple modification to the batch approach, so a significant part of the discussion will focus on reviewing this traditional batch inference method.
Abstract: I will discuss a scalable algorithm for approximating posterior distributions called stochastic variational inference. Stochastic variational inference lets one apply complex Bayesian models to massive data sets. This technique applies to a large class of probabilistic models and outperforms traditional batch variational inference, which can only handle small data sets. Stochastic inference is a simple modification to the batch approach, so a significant part of the discussion will focus on reviewing this traditional batch inference method.
Friday, September 6, 2013
David Carlson: September 11th
Title: Real-Time Inference for a Gamma Process Model of Neural Spiking
Abstract: With simultaneous measurements from ever increasing populations of neurons, there is a growing need for sophisticated tools to recover signals from individual neurons. In electrophysiology experiments, this classically proceeds in a two-step process: (i) threshold the waveforms to detect putative spikes and (ii) cluster the waveforms into single units (neurons). We extend previous Bayesian nonparametric models of neural spiking to jointly detect and cluster neurons using a Gamma process model. We develop an online approximate inference scheme enabling real-time analysis, with performance exceeding the previous state-of-the-art. Via exploratory data analysis we find several features of our model collectively contribute to our improved performance including: (i) accounting for colored noise, (ii) detecting overlapping spikes, (iii) tracking waveform dynamics, and (iv) using multiple channels.
In my talk, I will give a brief overview of the Bayesian nonparametric structures that have been used in the spike-sorting problem. From there, I will give details on how we've taken the spike sorting model and integrated it with a Poisson process to improve the noisy detection problem, and give details on learning the model using real-time online methods. Additionally, I will discuss extensions to evolving waveform dynamics and multiple channels, and present results from a tetrode as well as from novel 3-channel and 8-channel multi-electrode arrays where action potentials may appear on some but not all of the channels.
Abstract: With simultaneous measurements from ever increasing populations of neurons, there is a growing need for sophisticated tools to recover signals from individual neurons. In electrophysiology experiments, this classically proceeds in a two-step process: (i) threshold the waveforms to detect putative spikes and (ii) cluster the waveforms into single units (neurons). We extend previous Bayesian nonparametric models of neural spiking to jointly detect and cluster neurons using a Gamma process model. We develop an online approximate inference scheme enabling real-time analysis, with performance exceeding the previous state-of-the-art. Via exploratory data analysis we find several features of our model collectively contribute to our improved performance including: (i) accounting for colored noise, (ii) detecting overlapping spikes, (iii) tracking waveform dynamics, and (iv) using multiple channels.
In my talk, I will give a brief overview of the Bayesian nonparametric structures that have been used in the spike-sorting problem. From there, I will give details on how we've taken the spike sorting model and integrated it with a Poisson process to improve the noisy detection problem, and give details on learning the model using real-time online methods. Additionally, I will discuss extensions to evolving waveform dynamics and multiple channels, and present results from a tetrode as well as from novel 3-channel and 8-channel multi-electrode arrays where action potentials may appear on some but not all of the channels.
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