STATS 316: Stochastic Processes on Graphs
Local weak convergence, Gibbs measures on trees, cavity method, and replica symmetry breaking. Examples include random ksatisfiability, the assignment problem, spin glasses, and neural networks. Prerequisite: 310A or equivalent.
Terms: Aut

Units: 13

Grading: Letter or Credit/No Credit
Instructors:
Dembo, A. (PI)
;
Montanari, A. (PI)
STATS 318: Modern Markov Chains
Tools for understanding Markov chains as they arise in applications. Random walk on graphs, reversible Markov chains, Metropolis algorithm, Gibbs sampler, hybrid Monte Carlo, auxiliary variables, hit and run, SwedsonWong algorithms, geometric theory, PoincareNashChegerLogSobolov inequalities. Comparison techniques, coupling, stationary times, Harris recurrence, central limit theorems, and large deviations.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
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: 13

Repeatable for credit

Grading: Satisfactory/No Credit
Instructors:
Romano, J. (PI)
;
Wong, W. (PI)
STATS 320: Heterogeneous Data with Kernels
Mathematical and computational methods necessary to understanding analysis of heterogeneous data using generalized inner products and Kernels. For areas that need to integrate data from various sources, biology, environmental and chemical engineering, molecular biology, bioinformatics. Topics: Distances, inner products and duality. Multivariate projections. Complex heterogeneous data structures (networks, trees, categorical as well as multivariate continuous data). Canonical correlation analysis, canonical correspondence analysis. Kernel methods in Statistics. Representer theorem. Kernels on graphs. Kernel versions of standard statistical procedures. Data cubes and tensor methods.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
STATS 321: Modern Applied Statistics: Transposable Data
Topics: clustering, biclustering, and spectral clustering. Data analysis using the singular value decomposition, nonnegative decomposition, and generalizations. Plaid model, aspect model, and additive clustering. Correspondence analysis, Rasch model, and independent component analysis. Page rank, hubs, and authorities. Probabilistic latent semantic indexing. Recommender systems. Applications to genomics and information retrieval. Prerequisites: 315A,B, 305/306A,B, or consent of instructor.
Terms: not given this year

Units: 23

Grading: Letter or Credit/No Credit
STATS 322: Function Estimation in White Noise
Gaussian white noise model sequence space form. Hyperrectangles, quadratic convexity, and Pinsker's theorem. Minimax estimation on Lp balls and Besov spaces. Role of wavelets and unconditional bases. Linear and threshold estimators. Oracle inequalities. Optimal recovery and universal thresholding. Stein's unbiased risk estimator and threshold choice. Complexity penalized model selection. Connecting fast wavelet algorithms and theory. Beyond orthogonal bases.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
STATS 325: Multivariate Analysis and Random Matrices in Statistics
Topics on Multivariate Analysis and Random Matrices in Statistics (full description TBA)
Terms: not given this year

Units: 23

Grading: Letter or Credit/No Credit
STATS 329: LargeScale Simultaneous Inference
Estimation, testing, and prediction for microarraylike data. Modern scientific technologies, typified by microarrays and imaging devices, produce inference problems with thousands of parallel cases to consider simultaneously. Topics: empirical Bayes techniques, JamesStein estimation, largescale simultaneous testing, false discovery rates, local fdr, proper choice of null hypothesis (theoretical, permutation, empirical nulls), power, effects of correlation on tests and estimation accuracy, prediction methods, related sets of cases ("enrichment"), effect size estimation. Theory and methods illustrated on a variety of largescale data sets.
Terms: not given this year

Units: 13

Grading: Letter or Credit/No Credit
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 largescale 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

Grading: Letter or Credit/No Credit
Instructors:
Donoho, D. (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 timevarying 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 timevarying¿. The thread begins with the empirical mode decomposition (EMD) for nonstationary 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 socalled 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 reassignment (FRA) rule, that facilitaes nonstationary signal decomposition. In reference [3], a realtime 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 polynomiallike trend. nIn another thread, recent developments in optimization have been applied to obtain timevarying spectra or very highresolution 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 timevarying structure.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Chui, C. (PI)
;
Donoho, D. (PI)
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