CSCI-6971: Mathematics for mobile robotics Spring 2006 |
Wes Huang
(whuang@cs.rpi.edu) Kris Beevers (beevek@gmail.com) Flip Lamoureux (lamoup@cs.rpi.edu) RPI Algorithmic Robotics Laboratory |
Class | Topics | Preparer |
01/17 | Linear algebra basics, Gaussian elimination, Gauss-Jordan elimination, inverses, LU decomposition, Crout's algorithm, rank, singular matrices | Wes |
01/19 | Vector properties, fundamental spaces of a matrix, eigen values and eigenvectors | Wes |
01/24 | Inverse existence/uniqueness, projections, solving inconsistent systems, bases, Gram-Schmidt orthogonalization, QR decomposition, pseudoinverses, SVD, properties of determinants | Wes |
01/26 | Eigenvalues and eigenvectors and their properties, matrix diagonalization, matrix exponentials, positive definite matrices | Wes |
01/31 | Properties of probabilities and random variables, convolutions, least squares estimation, Normal random variables, central limit theorem, Markov inequality, Chebyshev inequality, weak law of large numbers, Jensen's inequality, Chernoff bounds | Kris |
02/02 | General stochastic processes, Bernoulli process, Poisson process, random incidence paradox, Markov chains | Kris |
02/07 | Markov chains, Hidden Markov Models, Baum-Welch algorithm, Viterbi algorithm, training problem | Flip |
02/09 | Continuous HMM, null transition HMM, variable duration HMM, HMMs with sparse data, dynamic structure HMM, hybrid HMM | Flip |
02/14 | Markov decision processes (MDP), partial observability (POMDP), mobile robotics POMDP example | Flip |
02/16 | Monte Carlo integration, random number generation, variance reduction, antithetic variates, common random variates, control variates | Kris |
02/21 | Rao-Blackwellization, stratified sampling, importance sampling | Kris |
03/07 | Importance sampling, sequential importance sampling, sequential Monte Carlo | Kris |
03/09 | Double session: Sequential Monte Carlo, bootstrap/particle filter, sampling distributions, resampling strategies | Kris |
04/06 | Markov-chain Monte Carlo, Metropolis-Hastings, MCMC convergence, Gibbs sampling | Kris |
04/26 | Graphical models, belief propagation, loopy BP, nonparametric BP | Kris |
03/14 | Spring break | |
03/16 | Spring break | |
03/23 | Nonlinear optimization basics, univariate minimization | Flip |
03/28 | Steepest descent, convergence of steepest descent, conjugate gradient descent | Flip |
04/04 | Unconstrained optimization, random walk, pattern search, Powell's method, steepest descent, conjugate gradient, quasi-Newton methods, second-order methods, Wolfe's rule, Goldstein-Price | Flip |
04/11 | Constrained linear programming, Simplex, constrained nonlinear programming, exterior penalty function method, augmented Lagrange multiplier method | Flip |
04/13 | Simplex example, convergence rate, Levenberg-Marquardt, nonlinear least squares | Flip |
04/18 | Direct constrained optimization, sequential linear programming, sequential quadratic programming, generalized reduced gradient, sequential gradient restoration | Flip |
04/13 | Lagrange multipliers | Wes |
04/20 | Lagrange multipliers, quadratic programming with equality constraints, quadratic programming with inequality constraints, Karush-Kuhn-Tucker (KKT) condition | Wes |