Thursday, January 22nd

One of the key developments in biological sequence analysis during the past decade has been the emergence of graphical models as a unifying formalism for developing algorithms. Examples of graphical models that have been used include hidden Markov models for annotation and pair hidden Markov models for alignments, as well as tree models for phylogenetics. A single algorithm, the sum-product algorithm, solves many of the inference problems associated with different models. We will present a geometric version of the sum-product algorithm, called the polytope propagation algorithm, that can be used to analyze the parametric behavior of maximum a posteriori inference calculations. For example, in the case of hidden Markov models, the polytope propagation algorithm identifies all the parameters that result in the same Viterbi path for a fixed observed sequence. We also describe efficient algorithms for parametric sequence alignment with multiple parameters.

This is joint work with Bernd Sturmfels.

Thursday, January 29th

Current statistical inference problems in genomic data analyses involve parameter estimation for high-dimensional multivariate distributions such that statistical models for the data generating distribution correspond to large and complex parameter spaces. A general estimation framework has been developed to address such problems which includes as three main steps: (1.) definition of the parameter of interest in terms of a loss function, (2.) construction of candidate estimators based on a loss function, and (3.) cross-validation for estimator selection and performance assessment. After having defined the parameter of interest as the risk minimizer for a particular loss function, one must generate a sequence of candidate estimators by minimizing the empirical risk over subspaces of increasing dimension approximating the complete parameter space. In this talk, I'll propose an aggressive and flexible algorithm for minimizing risk over index sets according to three types of moves for the elements in a given index set: deletions, substitutions, and additions. I refer to this general algorithm as the Deletion/Substitution/Addition algorithm. The main features of this algorithm will be summarized for tensor product basis functions (e.g tensor products of univariate polynomial basis functions in polynomial regression).

Thursday, February 5th

Clinicians and researchers collect a tremendous amount of data on cancer patients in the hopes of finding significant prognostic factors. Medical studies commonly involve thousands of clinical, epidemiological, and genomic measurements collected on each patient, along with a time to the clinical event of interest, such as disease recurrence or death. Over the past several decades there have been numerous attempts to use nonparametric methods with this type of data to find an estimator of outcome. A common approach is to modify classification and regression trees (CART) (Breiman, et al., 1984) specifically for right censored data. This presentation includes a generalization of CART based on a unified strategy for estimator construction, selection, and performance assessment in the presence of censoring. In this approach, the parameter of interest is defined as the risk minimizer for a suitable loss function and candidate estimators are generated with CART using this loss function. Cross-validation is applied to select an optimal estimator among the candidates and to assess the overall performance of the resulting estimator.

As this strategy is not limited to CART, a new more aggressive algorithm for generating possible predictors will be introduced. This algorithm finds the best partition of the the feature space by optimizing a cross-validated risk estimate over possible moves including deletion, addition and substitution. To illustrate this approach, both CART and the new algorithm have been applied to simulation studies as well as example data from Comparative Genomic Hybridization array analysis. The proposed approach is applicable to numerous settings, including univariate and multivariate prediction and density estimation. Thus, this method provides a powerful predictive tool for linking complex data sets with censored (or non-censored) outcomes.

Thursday, February 12th

Plasmodium falciparum is the parasite responsible for the most acute form of malaria in humans. Recently, the serine repeat antigen (SERA) in P. falciparum has attracted attention as a potential vaccine target. In this talk, we will examine attempts to infer the evolutionary history of a family of SERA genes in 7 different species of Plasmodium, and two particular problems that the gene family presents for inference: significant variation in GC content between species, and the need to reconcile any inferred gene tree with one of two conflicting Plasmodium species trees that have appeared in the literature. We will see, first, that GC content CAN lead to incorrect inference in a naive analysis, and discuss several approaches for overcoming this problem. Next, we will examine a simple method for using a known or hypothesized species tree to distinguishing between speciation and duplication events in an inferred gene tree. This information is of interest in its own right, and can also be used to infer root location for unrooted gene trees, to select a species tree among a set of candidate trees, and to assess and improve on gene tree phylogenies obtained from standard distance methods, Maximum Likelihood, or Maximum Parsimony. In the present case, reconciliation suggested two minor improvements to a poorly resolved region of the inferred gene tree, and produced an inferred set of 8 missing or deleted SERA family genes. A review of new Plasmodium genome data made available after the original analysis was complete turned up sequences consistent with 7 of these 8 missing genes.

Thursday, February 19th

We propose general single-step and step-down multiple testing procedures for controlling Type I error rates defined as arbitrary parameters of the distribution of the number of Type I errors (e.g., generalized family-wise error rate). The approach is based on a null distribution for the test statistics, rather than a data generating null distribution, and provides asymptotic control of the Type I error rate without the need for conditions such as subset pivotality. For general null hypotheses, corresponding to submodels for the data generating distribution, the proposed null distribution is the asymptotic distribution of the vector of null-value shifted and scaled test statistics. Resampling procedures (e.g., based on the non-parametric or model-based bootstrap) are provided to conveniently obtain consistent estimators of the null distribution. In the special case of family-wise error rate (FWER) control, this general approach reduces to the minP and maxT procedures based on minima of p-values and maxima of test statistics, respectively. We propose simple augmentations of FWER-controlling multiple testing procedures to control the proportion of false positives among the rejected hypotheses and the generalized family-wise error rate. Finally, we establish the equivalence between single-step multiple testing and error rate specific confidence regions.

The following applications to multiple testing problems in genomics will be discussed: identification of differentially expressed genes in microarray experiments, genetic mapping of complex traits using single nucleotide polymorphisms (SNPs), and testing for associations between microarray measures of gene expression and Gene Ontology (GO) annotations.

Joint work with Mark van der Laan, Katie Pollard, Merrill Birkner, and Melanie Courtine.

Thursday, February 26th

The talk considers statistical principles such as unbiasedness, minimaxity, monotonicity, Bayes, and likelihood ratio. I discuss a number of examples in which these principles lead to strongly conflicting solutions, and examine the difficult choices which then have to be faced.
Please note the change in location for this talk: Room 4 Haviland.

Thursday, March 11th

In this talk, we will give an introduction to MDL and its basic forms for model selection. Then we will concentrate on a particular form gMDL for regression models that bridges between AIC and BIC. Finally, we will apply gMDL to simultaneously cluster and select subsets of genes based on microarray data.

(This is based on joint work with Mark Hansen and Rebecka Jornsten.)

Thursday, March 18th

Thursday, April 1st

Thursday, April 15th

Ancestral graph models, introduced by Richardson and Spirtes (2002), are a new class of graphical models that generalize the Bayesian networks, which have, for example, been used to recover gene interactions from microarray data (Friedman, Linial, Nachman and Pe'er, 2000). A key feature of ancestral graphs is that they can encode all conditional independence structures which may arise from a Bayesian network with selection and unobserved variables. Thus, ancestral graph models provide a potentially very useful framework for exploratory model selection when the existence of unobserved variables cannot be excluded.

In this talk, we consider Gaussian ancestral graph models and present a new algorithm for maximum likelihood estimation. We call this algorithm iterative conditional fitting (ICF) since in each step of the procedure, a conditional distribution is estimated, subject to constraints, while a marginal distribution is held fixed. We show that in the considered Gaussian case, ICF may be implemented by regressions on "pseudo-variables". The ICF algorithm is in duality to the well-known iterative proportional fitting algorithm, in which a marginal distribution is fitted for a fixed conditional distribution.

Joint work with Thomas Richardson, Department of Statistics, University of Washington.

Thursday, April 22nd

Neural networks are a popular method for predicting the secondary structure of a protein from its amino acid sequence (Rost and Sander, 1993, Jones, 1999). However, overfitting poses a serious obstacle to effective use of neural networks for this and other problems. Due to the huge number of parameters in a typical neural network, one may obtain a network fit which perfectly predicts the training data yet fails to generalize to other data sets. Overfitting may be avoided by altering the network topology so that some connections are removed, thus reducing the total number of parameters. In the area of secondary structure prediction, work has focused on optimizing the network architecture by hand based on subject-matter knowledge (Riis and Krogh, 1996). We propose instead a method for selecting an optimal network architecture in a data-adaptive fashion using the Deletion/Substitution/Addition algorithm introduced in Sinisi and van der Laan (2003) and Molinaro and van der Laan (2003), and demonstrate the application of this approach to protein secondary-structure prediction.

Jones, D. (1999) Protein secondary structure prediction based on position-specific scoring matrices. J. Mol. Biol, 292, 195--202.

Molinaro, A. and van der Laan, M. (2003) A Deletion/Substitution/Addition algorithm for paritioning the covariate space in prediction. Technical report, Division of Biostatistics, UC Berkeley. (In preparation).

Riis, S.K. and Krogh, A. (1996) Improving prediction of protein secondary structure using structured neural networks and multiple sequences alignments. J. Comp. Biol., 3, 163--183.

Rost, B. and Sander, C. (1993) Prediction of protein secondary structure at better than 70% accuracy. J. Mol. Biol., 232, 584--599.

Sinisi, S. and van der Laan, M. (2003) A general Deletion/Substitution/Addition algorithm in prediction. Technical report, Division of Biostatistics, UC Berkeley. (In preparation).

Thursday, April 29th

Thursday, May 6th

Thursday, May 13th

Thursday, May 27th