Computational Statistics
Computational Statistics (Stat GR6104), Spring 2022
This is a Ph.D.level course in computational statistics. A link to the most recent previous iteration of this course is here.
Note: instructor permission is required to take this class for students outside of the Statistics Ph.D. program.
Time: Tu 2:103:40pm
Place: Zoom for a while, then JLG L7119
Professor: Liam Paninski; Email: liam at stat dot columbia dot edu. Hours by appointment.
Course goals: (partially adapted from the preface of Givens' and Hoeting's book): Computation plays a central role in modern statistics and machine learning. This course aims to cover topics needed to develop a broad working knowledge of modern computational statistics. We seek to develop a practical understanding of how and why existing methods work, enabling effective use of modern statistical methods. Achieving these goals requires familiarity with diverse topics in statistical computing, computational statistics, computer science, and numerical analysis. Our choice of topics reflects our view of what is central to this evolving field, and what will be interesting and useful. A key theme is scalability to problems of high dimensionality, which are of most interest to many recent applications.
Some important topics will be omitted because highquality solutions are already available in most software. For example, the generation of pseudorandom numbers is a classic topic, but existing methods built in to standard software packages will suffice for our needs. On the other hand, we will spend a bit of time on some classical numerical linear algebra ideas, because choosing the right method for solving a linear equation (for example) can have a huge impact on the time it takes to solve a problem in practice, particularly if there is some special structure that we can exploit.
Audience: The course will be aimed at first and secondyear students in the Statistics Ph.D. program. Students from other departments or programs are welcome, space permitting; instructor permission required.
Background: The level of mathematics expected does not extend much beyond standard calculus and linear algebra. Breadth of mathematical training is more helpful than depth; we prefer to focus on the big picture of how algorithms work and to sweep under the rug some of the nittygritty numerical details. The expected level of statistics is equivalent to that obtained by a graduate student in his or her first year of study of the theory of statistics and probability. An understanding of maximum likelihood methods, Bayesian methods, elementary asymptotic theory, Markov chains, and linear models is most important.
Programming: With respect to computer programming, good students can learn as they go. We'll forgo much languagespecific examples, algorithms, or coding; I won't be teaching much programming per se, but rather will focus on the overarching ideas and techniques. For the exercises and projects, I recommend you choose a highlevel, interactive package that permits the flexible design of graphical displays and includes supporting statistics and probability functions, e.g., R, Python, or MATLAB.
Evaluation: Final grades will be based on class participation and a student project.
Topics:
Deterministic optimization
 NewtonRaphson, conjugate gradients, preconditioning, quasiNewton methods, Fisher scoring, EM and its various derivatives
 Numerical recipes for linear algebra: matrix inverse, LU, Cholesky decompositions, lowrank updates, SVD, banded matrices, Toeplitz matrices and the FFT, Kronecker products (separable matrices), sparse matrix solvers
 Convex analysis: convex functions, duality, KKT conditions, interior point methods, projected gradients, augmented Lagrangian methods, convex relaxations
 Applications: support vector machines, splines, Gaussian processes, isotonic regression, LASSO and LARS regression
Graphical models: dynamic programming, hidden Markov models, forwardbackward algorithm, Kalman filter, Markov random fields
Stochastic optimization: RobbinsMonro and KieferWolfowitz algorithms, simulated annealing, stochastic gradient methods
Deterministic integration: Gaussian quadrature, quasiMonte Carlo. Application: expectation propagation
Monte Carlo methods
 Rejection sampling, importance sampling, variance reduction methods (RaoBlackwellization, stratified sampling)
 MCMC methods: Gibbs sampling, MetropolisHastings, Langevin methods, Hamiltonian Monte Carlo, slice sampling. Implementation issues: burnin, monitoring convergence
 Sequential Monte Carlo (particle filtering)
 Variational and stochastic variational inference
References:
Givens and Hoeting (2005) Computational statistics
Robert and Casella (2004) Monte Carlo Statistical Methods
Boyd and Vandenberghe (2004), Convex Optimization.
Press et al, Numerical Recipes
Sun and Yuan (2006), Optimization theory and methods
Fletcher (2000) Practical methods of optimization
Searle (2006) Matrix Algebra Useful for Statistics
Spall (2003), Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control
Shewchuk (1994), An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
Boyd et al (2011), Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
Mathematical Tools
Mathematical Tools for Theoretical Neuroscience (NBHV GU4359)
Spring 2022
Class Assistants: Dan Tyulmankov ([email protected]), Zhenrui Liao ([email protected]), Ching Fang ([email protected]), Jack Lindsey ([email protected]), Amol Pasarkar ([email protected])
Faculty contact: Prof. Ken Miller ([email protected])
Time: Tuesdays, Thursdays 10:10  11:25am
Place: L8084
Webpage: CourseWorks (announcements, assignments, readings)
Credits: 3
Description: An introduction to mathematical concepts used in theoretical neuroscience aimed to give a minimal requisite background for NBHV G4360, Introduction to Theoretical Neuroscience. The target audience is students with limited mathematical background who are interested in rapidly acquiring the vocabulary and basic mathematical skills for studying theoretical neuroscience, or who wish to gain a deeper exposure to mathematical concepts than offered by NBHV G4360. Topics include single and multivariable calculus, linear algebra, differential equations, signals and systems, and probability. Examples and applications are drawn primarily from theoretical and computational neuroscience.
Prerequisites: Basic prior exposure to trigonometry, calculus, and vector/matrix operations at the high school level.
Registration:
 Undergraduate and graduate students: Must register** on SSOL.
 All others: Please fill out this form.
(**If you’re only interested in attending a subset of lectures, register Pass/Fail and contact Dan)
Mathematical Tools for Theoretical Neuroscience (Spring 2021)
Mathematical Tools for Theoretical Neuroscience (Spring 2020)
Advanced Theory
Spring 2022
Meetings: Tuesdays, 10.00 am
Location: Jerome L Greene Science Center, Room L7119
For the zoom link contact [email protected]
Schedule:
Methods for decoding and interpreting neural data

Feb 01 Methods on calculating receptive fields (Ji Xia) Material

Feb 08 Information theory (Jeff Johnston)

Feb 15 cancelled
Neural representations

Feb 22 Geometry of abstractions (theory session) (Valeria Fascianelli) slides

Mar 01 Geometry of abstractions (handson session) (Lorenzo Posani)
Network dynamics

Mar 08 Solving very nonlinear problems with Homotopy Analysis Method (Serena Di Santo) notes notebook

Mar 29 Forgetting in attractor networks (Samuel Muscinelli)

Apr 05 Meanfield models of network dynamics (Alessandro Sanzeni + Mario Dipoppa)
Dynamics of learning

Apr 12 Learning dynamics in feedforward neural networks (Manuel Beiran + Rainer Engelken)

Apr 19 Learning dynamics recurrent neural networks (Manuel Beiran + Rainer Engelken)
Causality

Apr 26 Introduction to some causality issues in neuroscience (Laureline Logiaco)

May 3 Causality and latent variable models (Josh Glaser)

May 10 student presentations

May 17 Bonus session: Many methods, one problem: modern inference techniques as applied to linear regression (Juri Minxha)
Advanced Theory Seminar (Summer/Fall 2020)
Advanced Theory Seminar (Spring 2020) website
Advanced Theory Seminar (Spring 2019) website
Intro to Theory
Computational Neuroscience, Fall 2021
Larry Abbott, Ken Miller, Ashok Litwin Kumar, Stefano Fusi, Sean Escola
TAs: Elom Amematsro, Ramin Khajeh, Minni Sun, Denis Turcu
Meetings: Tuesdays & Thursdays 2:003:30
Text  Theoretical Neuroscience by P. Dayan and L.F. Abbott (MIT Press)
Webpage  https://ctn.zuckermaninstitute.columbia.edu/courses
September
9 (Larry) Introduction to Course and to Computational Neuroscience
14 (Larry) Electrical Properties of Neurons, IntegrateandFire Model
16 (Stefano) Adaptation, Synapses, Synaptic Plasticity
21 (Larry) The HodgkinHuxley Model (Assignment 1)
23 (Larry) Types of Neuron Models and Networks
28 (Larry) Numerical Methods, Filtering (Assignment 2)
29 Assignment 1 Due
30 (Sean) Generalized Linear Models
October
5 (Ken) Linear Algebra (Assignment 3)
6 Assignment 2 Due
7 (Ken) PCA and Dimensionality Reduction
12 (Ken) Rate Networks/EI networks I (Assignment 4)
13 Assignment 3 Due
14 (Ken) Rate Networks/EI networks II
19 (Ken) Unsupervised/Hebbian Learning, Developmental Models (Assignment 5)
20 Assignment 4 Due
21 (Ashok) Introduction to Probability, Encoding, Decoding
26 (Ashok) Decoding, Fisher Information I
27 Assignment 5 Due
28 (Ashok) Decoding, Fisher Information II (Assignment 6)
November
2 Holiday
4 (Ashok) Information Theory
9 (Ashok) Optimization I (Assignment 7)
10 Assignment 6 Due
11 (Ashok) Optimization II
16 (Stefano) The Perceptron (Assignment 8)
17 Assignment 7 Due
18 (Stefano) Multilayer Perceptrons and Mixed Selectivity
23 Holiday
25 Holiday
30 (Stefano) Deep Learning (Assignment 8)
December
1 Assignment 8 Due
2 (Sean) Learning in Recurrent Networks
7 (Stefano) Continual Learning and Catastrophic Forgetting (Assignment 10)
8 Assignment 9 Due
9 (Stefano) Reinforcement Learning
15 Assignment 10 Due
Introduction to Theoretical Neuroscience (Spring 2021)
Introduction to Theoretical Neuroscience (Spring 2020)
Statistical analysis of neural data
Statistical analysis of neural data (GR8201), Fall 2021
This is a Ph.D.level topics course in statistical analysis of neural data. Students from statistics, neuroscience, and engineering are all welcome to attend. A link to the last iteration of this course is here.
Time: F 1011:30
Place: JLG L8084
Professor: Liam Paninski; Office: Zoom. Email: [email protected]. Hours by appointment.
View Schedule
Prerequisite: A good working knowledge of basic statistical concepts (likelihood, Bayes' rule, Poisson processes, Markov chains, Gaussian random vectors), including especially linearalgebraic concepts related to regression and principal components analysis, is necessary. No previous experience with neural data is required.
Evaluation: Final grades will be based on class participation and a student project. Additional informal exercises will be suggested, but not required. The project can involve either the implementation and justification of a novel analysis technique, or a standard analysis applied to a novel data set. Students can work in pairs or alone (if you work in pairs, of course, the project has to be twice as impressive). See this page for some links to available datasets; or talk to other students in the class, many of whom have collected their own datasets.
Course goals: We will introduce a number of advanced statistical techniques relevant in neuroscience. Each technique will be illustrated via application to problems in neuroscience. The focus will be on the analysis of single and multiple spike train and calcium imaging data, with a few applications to analyzing intracellular voltage and dendritic imaging data. Note that this class will not focus on MRI or EEG data. A brief list of statistical concepts and corresponding neuroscience applications is below.
Page Last Updated: 3/9/2022