Current: Tutorial

VIVA toturial topics

Welcome! VIVA tutorial speech is holding evey Thursdays during Summer 2018.
List of broad interests:
  • Bagging and Boosting, adaBoost, GBM and XGBoost (This is NEW)
  • Regression, Multilinear regression, Ridge regression, Lasso regression, Logistic regression, Support vector regression, Group Lasso, Fused Lasso, Elastic net, graphLasso (This is NEW)
  • Baye's theorem, Bayesian network, Bayesian inference
  • Markov property, Markov chain, Reducible and irreducible Markov chain, homogeneous and inhomogeneous Markov chain
  • Regularization, L1, L2, L12, L0, L_inf, Tikhonov, TV minimization
  • PCA, Spike-triggered Covariance (only in Neuroscience), Factor Analysis, LDA, ICA, Canonical PCA, Sparse PCA, SVD, LLE, nonnegative Matrix factorization (NMF), Isomap, CUR (This is NEW), t-SNE (This is NEW)
  • Sampling, downsampling, upsampling, kNN sampling (This is new), particle sampling, Particle filter
  • Fourier, Polar Fourier, Bessel-Fourier
  • Kernel, kernel regularization, Kernel projection, Kernel properties, Different types of kernels and their usage, kernel generation
  • Gradient descent, Newtonian descent, stochastic gradient descent, conjugate dradient descent, BFGS, momentum, Nesterov, ADAM (widely used now a days)
  • Convex optimization, convex set, convex function, Primal-dual, KKT, Linear Program, Lagrangian, relaxation, convex relaxation, soft-max
  • Nonconvex optimization, pareto set, alternating direction minimization, variable splitting
  • Least squares, weighted least squares, partial least squares, least mean squares, recursive least squares, lattice recursive least squares
  • Tensor, tensor analysis, tensor factorization, covariant and contravariant derivative
  • Manifold and topology : differences and properties, construction, sampling on manifold, tangent space on manifold, principal curvatures, saddle points, finding geodesic on manifold, Log-exponential map, curvature-extrinsic and intrinsic, Gaussian curvature, Ricci curvature (optional)
  • Distance measure: (See Statistics section also) Euclidean, Hamming, graph edit, Dice, Levenshtein, Minkowski, Manhattan
  • Convergence, boundedness, and staibility, Lyapunov stability, BIBO stability, Asymptotic stability ,function--functional--functor, summability, Euler-Lagrange (very useful), Functional derivative, Green function
Statistics:
  • mean, variance, correlation, covariance, rank correlation (Spearman), skewness, kurtosis, bias-variance trade-off
  • random variable, probability space, distribution, sampling from distribution, conditional distribution, multivariate analysis, expectation-maximization, Maximum likelihood estimator, Bayesian statistics
  • Types of distributions, important but old and classic distributions (Bernoulli, Binomial, Poisson, Gaussian, Negative Binomial, Geometric, Laplace, Hypergeometric, exponential), distributions which our lab does not use but widely used in the literature (log-Normal, Cauchy, Langevin, Dirichlet, scale-free, Weibull, Hotelling T-squared, Inverse Gaussian, heavy-tailed, Wishart, matrix Normal, matrix t, multinomial, wrapped Cauchy, wrapped exponential, Frechet, Yule-Simon)
  • Estimation of distribution, measure (such as, Fisher information metric, Kolmogorov-Smirnov, KL divergence, Jensen Log divergence, Bregman's divergence, Mahalanobis, Chebychev, Hamming)