printer friendly pageSTATS 315A: Modern Applied Statistics: Learning
Overview of supervised learning. Linear regression and related methods. Model selection, least angle regression and the lasso, stepwise methods. Classification. Linear discriminant analysis, logistic regression, and support vector machines (SVMs). Basis expansions, splines and regularization. Kernel methods. Generalized additive models. Kernel smoothing. Gaussian mixtures and the EM algorithm. Model assessment and selection: crossvalidation and the bootstrap. Pathwise coordinate descent. Sparse graphical models. Prerequisites:
STATS 305, 306A,B or consent of instructor.
Terms: Win
| Units: 2-3
Instructors:
Hastie, T. (PI)
STATS 315B: Modern Applied Statistics: Data Mining
Two-part sequence. New techniques for predictive and descriptive learning using ideas that bridge gaps among statistics, computer science, and artificial intelligence. Emphasis is on statistical aspects of their application and integration with more standard statistical methodology. Predictive learning refers to estimating models from data with the goal of predicting future outcomes, in particular, regression and classification models. Descriptive learning is used to discover general patterns and relationships in data without a predictive goal, viewed from a statistical perspective as computer automated exploratory analysis of large complex data sets.
Terms: Spr
| Units: 2-3
Instructors:
Friedman, J. (PI)
STATS 316: Stochastic Processes on Graphs
Local weak convergence, Gibbs measures on trees, cavity method, and replica symmetry breaking. Examples include random k-satisfiability, the assignment problem, spin glasses, and neural networks. Prerequisite: 310A or equivalent.
Terms: Aut
| Units: 1-3
Instructors:
Dembo, A. (PI)
;
Montanari, A. (PI)
STATS 317: Stochastic Processes
Semimartingales, stochastic integration, Ito's formula, Girsanov's theorem. Gaussian and related processes. Stationary/isotropic processes. Integral geometry and geometric probability. Maxima of random fields and applications to spatial statistics and imaging.
Terms: Spr
| Units: 3
Instructors:
Taylor, J. (PI)
STATS 319: Literature of Statistics
Literature study of topics in statistics and probability culminating in oral and written reports. May be repeated for credit.
Terms: Aut, Spr
| Units: 1-3
| Repeatable
for credit
Instructors:
Romano, J. (PI)
;
Wong, W. (PI)
STATS 324: Multivariate Analysis
Classic multivariate statistics: properties of the multivariate normal distribution, determinants, volumes, projections, matrix square roots, the singular value decomposition; Wishart distributions, Hotelling's T-square; principal components, canonical correlations, Fisher's discriminant, the Cauchy projection formula.
STATS 325: Multivariate Analysis and Random Matrices in Statistics
Topics on Multivariate Analysis and Random Matrices in Statistics (full description TBA)
Terms: Win
| Units: 2-3
STATS 330: An Introduction to Compressed Sensing (CME 362)
Compressed sensing is a new data acquisition theory asserting that one can design nonadaptive sampling techniques that condense the information in a compressible signal into a small amount of data. This revelation may change the way engineers think about signal acquisition. Course covers fundamental theoretical ideas, numerical methods in large-scale convex optimization, hardware implementations, connections with statistical estimation in high dimensions, and extensions such as recovery of data matrices from few entries (famous Netflix Prize).
Terms: Aut
| Units: 3
Instructors:
Donoho, D. (PI)
STATS 331: Survival Analysis
The course introduces basic concepts, theoretical basis and statistical methods associated with survival data. Topics include censoring, Kaplan-Meier estimation, logrank test, proportional hazards regression, accelerated failure time model, multivariate failure time analysis and competing risks. The traditional counting process/martingale methods as well as modern empirical process methods will be covered. Prerequisite: Understanding of basic probability theory and statistical inference methods.
Terms: Win
| Units: 2
Instructors:
Olshen, R. (PI)
;
Tian, L. (PI)
STATS 333: Modern Spectral Analysis
Traditional spectral analysis encompassed Fourier methods and their elaborations, under the assumption of a simple superposition of sinusoids, independent of time. This enables development of efficient and effective computational schemes, such as the FFT. Since many systems change in time, it becomes of interest to generalize classical spectral analysis to the time-varying setting. In addition, classical methods suffer from resolution limits which we hope to surpass. In this topics course, we follow two threads. On the one hand, we consider the ¿estimation of instantaneous frequencies and decomposition of source signals, which may be time-varying¿. The thread begins with the empirical mode decomposition (EMD) for non-stationary signal decomposition into intrinsic mode functions (IMF¿s), introduced by N. Huang et al [1], together with its machinery of the sifting process and computation of the Hilbert spectrum, resulting in the so-called adaptive harmonic model (AHM).nNext, this thread considers the wavelet synchrosqueezing transform (WSST) proposed by Daubechies et al [2], which attempts to estimate instantaneous frequencies (IF¿s), via the frequency re-assignment (FRA) rule, that facilitaes non-stationary signal decomposition. In reference [3], a real-time method is proposed for computing the FRA rule; and in reference [4], the exact number of AHM components is determined with more precise estimation of the IF¿s, for more accurate extraction of the signal components and polynomial-like trend. nIn another thread, recent developments in optimization have been applied to obtain time-varying spectra or very high-resolution spectra; in particular, references [5]-[8] give examples of recent results where convex estimation is applied to obtain new and more highly resolved spectral estimates, some with time-varying structure.
Terms: Spr
| Units: 3
Instructors:
Chui, C. (PI)
;
Donoho, D. (PI)
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