David B. Dunson

Multitask Compressive Sensing

Compressive sensing (CS) is a framework whereby one performs N nonadaptive measurements to constitute a vector v isin RN used to recover an approximation u isin RM desired signal u isin RM with N << M this is performed under the assumption that u is sparse in the basis represented by the matrix Psi RMtimesM. It has been demonstrated that with appropriate design of the compressive measurements used to define v, the decompressive mapping vrarru may be performed with error ||u-u||2 2 having asymptotic properties analogous to those of the best adaptive transform-coding algorithm applied in the basis Psi. The mapping vrarru constitutes an inverse problem, often solved using l1 regularization or related techniques. In most previous research, if L > 1 sets of compressive measurements {vi}i=1,L are performed, each of the associated {ui}i=1,Lare recovered one at a time, independently. In many applications the L ldquotasksrdquo defined by the mappings virarrui are not statistically independent, and it may be possible to improve the performance of the inversion if statistical interrelationships are exploited. In this paper, we address this problem within a multitask learning setting, wherein the mapping vrarru for each task corresponds to inferring the parameters (here, wavelet coefficients) associated with the desired signal vi, and a shared prior is placed across all of the L tasks. Under this hierarchical Bayesian modeling, data from all L tasks contribute toward inferring a posterior on the hyperparameters, and once the shared prior is thereby inferred, the data from each of the L individual tasks is then employed to estimate the task-dependent wavelet coefficients. An empirical Bayesian procedure for the estimation of hyperparameters is considered; two fast inference algorithms extending the relevance vector machine (RVM) are developed. Example results on several data sets demonstrate the effectiveness and robustness of the proposed algorithms.

Genetic heterogeneity of diffuse large B-cell lymphoma

Diffuse large B-cell lymphoma (DLBCL) is the most common form of lymphoma in adults. The disease exhibits a striking heterogeneity in gene expression profiles and clinical outcomes, but its genetic causes remain to be fully defined. Through whole genome and exome sequencing, we characterized the genetic diversity of DLBCL. In all, we sequenced 73 DLBCL primary tumors (34 with matched normal DNA). Separately, we sequenced the exomes of 21 DLBCL cell lines. We identified 322 DLBCL cancer genes that were recurrently mutated in primary DLBCLs. We identified recurrent mutations implicating a number of known and not previously identified genes and pathways in DLBCL including those related to chromatin modification (ARID1A and MEF2B), NF-κB (CARD11 and TNFAIP3), PI3 kinase (PIK3CD, PIK3R1, and MTOR), B-cell lineage (IRF8, POU2F2, and GNA13), and WNT signaling (WIF1). We also experimentally validated a mutation in PIK3CD, a gene not previously implicated in lymphomas. The patterns of mutation demonstrated a classic long tail distribution with substantial variation of mutated genes from patient to patient and also between published studies. Thus, our study reveals the tremendous genetic heterogeneity that underlies lymphomas and highlights the need for personalized medicine approaches to treating these patients.

The genetic landscape of mutations in Burkitt lymphoma

Burkitt lymphoma is characterized by deregulation of MYC, but the contribution of other genetic mutations to the disease is largely unknown. Here, we describe the first completely sequenced genome from a Burkitt lymphoma tumor and germline DNA from the same affected individual. We further sequenced the exomes of 59 Burkitt lymphoma tumors and compared them to sequenced exomes from 94 diffuse large B-cell lymphoma (DLBCL) tumors. We identified 70 genes that were recurrently mutated in Burkitt lymphomas, including ID3, GNA13, RET, PIK3R1 and the SWI/SNF genes ARID1A and SMARCA4. Our data implicate a number of genes in cancer for the first time, including CCT6B, SALL3, FTCD and PC. ID3 mutations occurred in 34% of Burkitt lymphomas and not in DLBCLs. We show experimentally that ID3 mutations promote cell cycle progression and proliferation. Our work thus elucidates commonly occurring gene-coding mutations in Burkitt lymphoma and implicates ID3 as a new tumor suppressor gene.

The timing of the “fertile window” in the menstrual cycle: day specific estimates from a prospective study

Abstract Objectives: To provide specific estimates of the likely occurrence of the six fertile days (the “fertile window”) during the menstrual cycle. Design: Prospective cohort study. Participants: 221 healthy women who were planning a pregnancy. Main outcome measures: The timing of ovulation in 696 menstrual cycles, estimated using urinary metabolites of oestrogen and progesterone. Results: The fertile window occurred during a broad range of days in the menstrual cycle. On every day between days 6 and 21, women had at minimum a 10% probability of being in their fertile window. Women cannot predict a sporadic late ovulation; 4-6% of women whose cycles had not yet resumed were potentially fertile in the fifth week of their cycle. Conclusions: In only about 30% of women is the fertile window entirely within the days of the menstrual cycle identified by clinical guidelines—that is, between days 10 and 17. Most women reach their fertile window earlier and others much later. Women should be advised that the timing of their fertile window can be highly unpredictable, even if their cycles are usually regular.

Likelihood of conception with a single act of intercourse: providing benchmark rates for assessment of post-coital contraceptives

Emergency post-coital contraceptives effectively reduce the risk of pregnancy, but their degree of efficacy remains uncertain. Measurement of efficacy depends on the pregnancy rate without treatment, which cannot be measured directly. We provide indirect estimates of such pregnancy rates, using data from a prospective study of 221 women who were attempting to conceive. We previously estimated the probability of pregnancy with an act of intercourse relative to ovulation. In this article, we extend these data to estimate the probability of pregnancy relative to intercourse on a given cycle day (counting from onset of previous menses). In assessing the efficacy of post-coital contraceptives, other approaches have not incorporated accurate information on the variability of ovulation. We find that the possibility of late ovulation produces a persistent risk of pregnancy even into the sixth week of the cycle. Post-coital contraceptives may be indicated even when intercourse has occurred late in the cycle.

Increased infertility with age in men and women.

OBJECTIVE: To estimate the effects of aging on the percentage of outwardly healthy couples who are sterile (completely unable to conceive without assisted reproduction) or infertile (unable to conceive within a year of unprotected intercourse). METHODS: A prospective fecundability study was conducted in a sample of 782 couples recruited from 7 European centers for natural family planning. Women aged 18–40 years were eligible. Daily intercourse records were used to adjust for timing and frequency of intercourse when estimating the per-menstrual-cycle probability of conception. The number of menstrual cycles required to conceive a clinical pregnancy and the probability of sterility and infertility were derived from the estimated fecundability distributions for men and women of different ages. RESULTS: Sterility was estimated at about 1%; this percent did not change with age. The percentage infertility was estimated at 8% for women aged 19–26 years, 13–14% for women aged 27–34 years and 18% for women aged 35–39 years. Starting in the late 30s, male age was an important factor, with the percentage failing to conceive within 12 cycles increasing from an estimated 18–28% between ages 35 and 40 years. The estimated percentage of infertile couples that would be able to conceive after an additional 12 cycles of trying varied from 43–63% depending on age. CONCLUSION: Increased infertility in older couples is attributable primarily to declines in fertility rates rather than to absolute sterility. Many infertile couples will conceive if they try for an additional year. LEVEL OF EVIDENCE: II-2

Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images

Nonparametric Bayesian methods are considered for recovery of imagery based upon compressive, incomplete, and/or noisy measurements. A truncated beta-Bernoulli process is employed to infer an appropriate dictionary for the data under test and also for image recovery. In the context of compressive sensing, significant improvements in image recovery are manifested using learned dictionaries, relative to using standard orthonormal image expansions. The compressive-measurement projections are also optimized for the learned dictionary. Additionally, we consider simpler (incomplete) measurements, defined by measuring a subset of image pixels, uniformly selected at random. Spatial interrelationships within imagery are exploited through use of the Dirichlet and probit stick-breaking processes. Several example results are presented, with comparisons to other methods in the literature.

Bayesian latent variable models for clustered mixed outcomes

A general framework is proposed for modelling clustered mixed outcomes. A mixture of generalized linear models is used to describe the joint distribution of a set of underlying variables, and an arbitrary function relates the underlying variables to be observed outcomes. The model accommodates multilevel data structures, general covariate effects and distinct link functions and error distributions for each underlying variable. Within the framework proposed, novel models are developed for clustered multiple binary, unordered categorical and joint discrete and continuous outcomes. A Markov chain Monte Carlo sampling algorithm is described for estimating the posterior distributions of the parameters and latent variables. Because of the flexibility of the modelling framework and estimation procedure, extensions to ordered categorical outcomes and more complex data structures are straightforward. The methods are illustrated by using data from a reproductive toxicity study.

The Nested Dirichlet Process

In multicenter studies, subjects in different centers may have different outcome distributions. This article is motivated by the problem of nonparametric modeling of these distributions, borrowing information across centers while also allowing centers to be clustered. Starting with a stick-breaking representation of the Dirichlet process (DP), we replace the random atoms with random probability measures drawn from a DP. This results in a nested DP prior, which can be placed on the collection of distributions for the different centers, with centers drawn from the same DP component automatically clustered together. Theoretical properties are discussed, and an efficient Markov chain Monte Carlo algorithm is developed for computation. The methods are illustrated using a simulation study and an application to quality of care in U.S. hospitals.

Compressive Sensing on Manifolds Using a Nonparametric Mixture of Factor Analyzers: Algorithm and Performance Bounds

Nonparametric Bayesian methods are employed to constitute a mixture of low-rank Gaussians, for data x ∈ RN that are of high dimension N but are constrained to reside in a low-dimensional subregion of RN. The number of mixture components and their rank are inferred automatically from the data. The resulting algorithm can be used for learning manifolds and for reconstructing signals from manifolds, based on compressive sensing (CS) projection measurements. The statistical CS inversion is performed analytically. We derive the required number of CS random measurements needed for successful reconstruction, based on easily-computed quantities, drawing on block-sparsity properties. The proposed methodology is validated on several synthetic and real datasets.