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SHORT COURSE 2 Neuroscience 2016 Data Science and Data Skills for Neuroscientists Organizers: Konrad P SHORT COURSE 2 Neuroscience 2016 Data Science and Data Skills for Neuroscientists Organizers: Konrad P. Kording, PhD, and Alyson Fletcher, PhD Short Course 2 Data Science and Data Skills for Neuroscientists Organized by Konrad P. Kording, PhD, and Alyson Fletcher, PhD Please cite articles using the model: [AUTHOR’S LAST NAME, AUTHOR’S FIRST & MIDDLE INITIALS] (2016) [CHAPTER TITLE] In: Data Science and Data Skills for Neuroscientists. (Kording K, Fletcher A, eds) pp. [xx-xx]. San Diego, CA: Society for Neuroscience. All articles and their graphics are under the copyright of their respective authors. Cover graphics and design © 2016 Society for Neuroscience. SHORT COURSE 2 Data Science and Data Skills for Neuroscientists Organized by: Konrad P. Kording, PhD, and Alyson Fletcher, PhD Friday, November 11, 2016 Neuroscience 8 a.m.–6 p.m.. 2016 Location: San Diego Convention Center • Room: 6C • San Diego, CA TIME TALK TITLE SPEAKER 7:30–8 a.m. Check-in Konrad P. Kording, PhD • Northwestern University 8–8:10 a.m. Opening Remarks Alyson Fletcher, PhD • UCLA • Canonical data analysis cascade 8:10–9:10 a.m. • MATLAB for neuroscientists Pascal Wallisch, PhD • New York University • Peristimulus time histograms (PTSHs) • Fundamentals of statistics: densities, mean-squared error, and regression 9:10–10:10 a.m. • Bootstrapping and confidence intervals Robert Kass, PhD • Carnegie Mellon University • Time of maximal firing rates 10:10–10:30 a.m. Morning Break • Fitting tuning curves 10:30–11:10 a.m. Konrad P. Kording, PhD • Northwestern University • Error bars and model selection with bootstrap • Classification in neural systems 11:20 a.m.–12:10 p.m. • Poisson point process models for spiking Alyson Fletcher, PhD • UCLA • Model selection: cross-validation and overfitting 12:10–1:10 p.m. Lunch • Generalized linear models (GLMs) with spike history 1:10–2:10 p.m. • GLMs with neuron–neuron interactions Jonathan Pillow, PhD • Princeton University • Regularization, ridge regression, and smoothing 2:20–2:40 p.m. Sparsity in neural decoding Alyson Fletcher, PhD • UCLA 2:50–3:20 p.m. Multilayer models and deep learning Konrad P. Kording, PhD • Northwestern University 3:20–3:40 p.m. Afternoon Break • Neural population models principal component analysis (PCA) 3:40–4:40 p.m. • Time series models and Gaussian process factor analysis (GPFA) Maneesh Sahani, PhD • University College London • State space dynamical systems • Local network structure of neural data 4:50–5:50 p.m. • Clustering and modularity in networks Danielle Bassett, PhD • University of Pennsylvania • How networks change: the dynamics of graphs Konrad P. Kording, PhD • Northwestern University 5:50–6:00 p.m. Closing Remarks Alyson Fletcher, PhD • UCLA Table of Contents Introduction Konrad P. Kording, PhD, and Alyson Fletcher, PhD ......................................7 The Basics of Neural Coding Konrad P. Kording, PhD ....................................................9 Characterizing and Correlating Spike Trains Pascal Wallisch, PhD, and Erik Lee Nylen, PhD ...................................23 The Statistical Paradigm Robert E. Kass, PhD .....................................................49 Preface to Chapters by Jonathan Pillow, PhD ......................................59 Likelihood-Based Approaches to Modeling the Neural Code Jonathan W. Pillow, PhD ..................................................61 Spatiotemporal Correlations and Visual Signaling in a Complete Neuronal Population Jonathan W. Pillow, PhD, Jonathon Shlens, PhD, Liam Paninski, PhD, Alexander Sher, PhD, Alan M. Litke, PhD, E. J. Chichilnisky, PhD, and Eero P. Simoncelli, PhD .................75 Introduction Data skills and data science are moving away from being specialties that a small minority of computational scientists get excited about to becoming central tools used by the bulk of neuroscientists. The objectives for this short course are twofold. First, we will teach basic, useful data skills that should be in the toolkit of virtually all neuroscientists. Second, we will survey the field of more advanced data science methods to give participants an overview of which techniques to use under which circumstances. The course is structured around hands-on programming exercises. Lectures will go hand in hand with tutorials. During the day, the focus will be on participants solving many frequently encountered data analysis problems themselves, aided by lectures given by leading experts. The course will cover a broad range of topics. It will start with basic topics, including data cleanup, data visualization, and fundamental statistical ideas. It will then progress to everyday problems such as fitting functions to tuning curves, adding error bars, and decoding. More advanced topics will include generalized linear models, dimensionality reduction, time-series data, and networks. In this way, the course should impart a solid understanding of the basic techniques used for neural data analysis. The Basics of Neural Coding Konrad P. Kording, PhD Rehabilitation Institute of Chicago Northwestern University Chicago, Illinois © 2016 Kording The Basics of Neural Coding 11 The Basics of Neural Coding distribution and therefore can carry implicit NOTES How do neurons represent the knowledge of uncertainty. As an introduction to neural modeling and population coding, the present world? chapter is limited in scope. Our main goal here is to At first glance, there seems to be a world of difference provide the necessary background information for an between fundamental physiological features of understanding of the representation of probability at neurons, such as firing rates and tuning curves, and the neural level. the quantitative measurements of perception and behavior. Yet we know that somehow, neuronal processes must underlie all of perception and A focus on generative models behavior. The goal in this chapter is to indicate how of neurons this gap can be bridged. We will start by summarizing When we define the generative model with respect how neurons encode variables in the world. to world states and sensory observations, we conveniently represent the sensory observation as Historically, we have treated the brain as a “black box” a measurement that lives in the same space as the that performs probabilistic inference. This suffices if stimulus. For instance, we conceive a sound stimulus one is interested primarily in modeling behavior. at a particular location as producing an observation However, in systems neuroscience, elucidating the drawn from a Gaussian distribution centered at that link between biological and psychological states is location. At the neurobiological level, however, a central objective. In this chapter, we explore the the sensory observation is not such a measurement, connection between behavior and neural activity but rather neuronal activity evoked by the sensory from the perspective of our normative framework. stimulus: neurons encode the physical stimulus as Because we have seen that abundant evidence exists a pattern of spiking activity, and the brain must for Bayesian optimality at the behavioral level, at least somehow decode this activity in order to infer the in simple tasks, we will ask the following questions: world state. Here we take a first look at the neuronal level, and we consider the mapping from sensory • How do neurons represent states of the world? stimuli to the spiking activity produced in sensory neurons. Once we fully specify how sensory stimuli • How do neurons represent likelihood functions? give rise, in a probabilistic way, to neural activities, we will be in a position to formulate how neurons • How do neurons use these representations to may encode uncertain stimuli and how the brain can calculate posterior distributions? infer the state of the world from neuronal activity. The Bayesian normative framework offers a means The brain does not have direct access to the sensory of addressing these questions that runs counter input, I. Rather, the sensory input activates receptor to the bulk of neural modeling work. Modelers cells such as auditory hair cells or photoreceptors, often construct neural networks out of simulated, which in turn activate nerve fibers (axons), causing more or less biophysically plausible elements, and electrical impulses (action potentials or spikes) to examine their emergent dynamics. In many cases, travel into the CNS. These impulses are the data upon this “bottom-up” approach has the disadvantage that which the brain makes inferences about the world. The the link of these networks to behavior is tenuous or activity of neurons in a relevant brain area in response only qualitative. In contrast, it is possible to take a to a stimulus, denoted r, constitutes the internal top-down approach to neural computation, in which representation or observation of that stimulus. Neural the construction of a neural model is guided by a activity is variable: when the same sensory input I is normative behavioral model. In this approach, the presented repeatedly, r will be different every time. search for a neural implementation of a perceptual This is to the result of stochastic processes that inject phenomenon is guided simultaneously by behavioral variability: photon noise, stochastic neurotransmitter and physiological constraints. release, stochastic opening and closing of ion channels, etc. Thus, a probability distribution p(r | I) is needed In this chapter, we will first computationally describe to describe the neural activity. neurons, formalizing them as a generative
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