Lexin Li

Model-Free Feature Screening for Ultrahigh Dimensional Data

With the recent explosion of scientific data of unprecedented size and complexity, feature ranking and screening are playing an increasingly important role in many scientific studies. In this article, we propose a novel feature screening procedure under a unified model framework, which covers a wide variety of commonly used parametric and semiparametric models. The new method does not require imposing a specific model structure on regression functions, and thus is particularly appealing to ultrahigh-dimensional regressions, where there are a huge number of candidate predictors but little information about the actual model forms. We demonstrate that, with the number of predictors growing at an exponential rate of the sample size, the proposed procedure possesses consistency in ranking, which is both useful in its own right and can lead to consistency in selection. The new procedure is computationally efficient and simple, and exhibits a competent empirical performance in our intensive simulations and real data analysis.

Tensor Regression with Applications in Neuroimaging Data Analysis

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays (tensors). Traditional statistical and computational methods are proving insufficient for analysis of these high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we propose a new family of tensor regression models that efficiently exploit the special structure of tensor covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data. Supplementary materials for this article are available online.

FMR1 CGG repeat length predicts motor dysfunction in premutation carriers

Background: Fragile X–associated tremor/ataxia syndrome (FXTAS) is a recently described, underrecognized neurodegenerative disorder of aging fragile X mental retardation 1 (FMR1) premutation carriers, particularly men. Core motor features are action tremor, gait ataxia, and parkinsonism. Carriers have expanded CGG repeats (55 to 200); larger expansions cause fragile X syndrome, the most common heritable cause of mental retardation and autism. This study determines whether CGG repeat length correlates with severity and type of motor dysfunction in premutation carriers. Methods: Persons aged ≥50 years with a family history of fragile X syndrome underwent structured videotaping. Movement disorder neurologists, blinded to carrier status, scored the tapes using modified standardized rating scales. CGG repeat length analyses for women incorporated the activation ratio, which measures the percentage of normal active chromosome X alleles. Results: Male carriers (n = 54) had significantly worse total motor scores, especially in tremor and ataxia, than age-matched male noncarriers (n = 51). There was a trend toward a difference between women carriers (n = 82) and noncarriers (n = 39). In men, increasing CGG repeat correlated with greater impairment in all motor signs. In women, when activation ratio was considered, increasing CGG correlated with greater ataxia. Conclusions: CGG repeat size is significantly associated with overall motor impairment in premutation carriers. Whereas this association is most pronounced for men and covers overall motor impairment—tremor, ataxia, and parkinsonism—the association exists for ataxia among women carriers. This is the first report of a significant correlation between the premutation status and a motor feature of fragile X–associated tremor/ataxia syndrome in women. GLOSSARY: AR = activation ratio; FXTAS = fragile X-associated tremor/ataxia syndrome; MCP = middle cerebellar peduncle; mRNA = messenger RNA.

CGG repeat length correlates with age of onset of motor signs of the fragile X-associated tremor/ataxia syndrome (FXTAS).

Fragile X‐associated tremor/ataxia syndrome (FXTAS) is a late‐onset neurological disorder among carriers of premutation CGG‐repeat expansions within the FMR1 gene. Principal features of FXTAS include progressive action tremor and gait ataxia, with associated features of parkinsonism, peripheral neuropathy, dysautonomia, and cognitive decline. Although both clinical and neuropathologic features of FXTAS are known to be highly associated with CGG repeat length, the relationship between repeat length and age‐of‐onset is not known. To address this issue, the ages of onset of action tremor and gait ataxia were documented by history for 93 male carriers. For this cohort, the mean ages of onset were 62.6 ± 8.1 years (range, 39–78 years) for tremor, and 63.6 ± 7.3 years (range, 47–78 years) for ataxia; the mean CGG repeat number was 88.5 ± 14 (range, 60–133). Analysis of the relationship between clinical onset and molecular measures revealed significant correlations between CGG repeat number and onset of both tremor (P = 0.001) and ataxia (P = 0.002), as well as overall onset (P < 0.0001). Our findings indicate that the CGG repeat number is a potential predictor of the age of onset of core motor features of FXTAS.

Lifespan changes in working memory in fragile X premutation males

Fragile X syndrome is the worlds most common hereditary cause of developmental delay in males and is now well characterized at the biological, brain and cognitive levels. The disorder is caused by the silencing of a single gene on the X chromosome, the FMR1 gene. The premutation (carrier) status, however, is less well documented but has an emerging literature that highlights a more subtle profile of executive cognitive deficiencies that mirror those reported in fully affected males. Rarely, however, has the issue of age-related declines in cognitive performance in premutation males been addressed. In the present study, we focus specifically on the cognitive domain of working memory and its subcomponents (verbal, spatial and central executive memory) and explore performance across a broad sample of premutation males aged 18-69 years matched on age and IQ to unaffected comparison males. We further tease apart the premutation status into those males with symptoms of the newly identified neurodegenerative disorder, the fragile X-associated tremor/ataxia syndrome (FXTAS) and those males currently symptom-free. Our findings indicate a specific vulnerability in premutation males on tasks that require simultaneous manipulation and storage of new information, so-called executive control of memory. Furthermore, this vulnerability appears to exist regardless of the presence of FXTAS symptoms. Males with FXTAS symptoms demonstrated a more general impairment encompassing phonological working memory in addition to central executive working memory. Among asymptomatic premutation males, we observed the novel finding of a relationship between increased CGG repeat size and impairment to central executive working memory.

Neuropathic features in fragile X premutation carriers

Fragile X‐associated tremor/ataxia syndrome (FXTAS) is a progressive neurological condition occurring in fragile X premutation carriers, predominantly males, and resulting in CNS dysfunction including tremor, ataxia, Parkinsonism, and cognitive decline. Neuropathic signs have also been described. The objective of this study was to compare neuropathic signs in fragile X premutation carriers versus controls and determine the relationship of these signs to CGG repeat length and tremor/ataxia. A neuropathy scale was utilized to compare distal tendon reflexes and vibration sense in subjects from a large cohort of carriers and controls undergoing neurological exam and structured videotaping sessions for movement disorder rating. The male carrier group displayed more impairment on total neuropathy, vibration and reflex scores than the corresponding control group, while female carriers were not significantly different from controls. In males, after correction for age effects, there was a correlation between CGG repeat length and both total neuropathy and reflex impairments. Age‐adjusted partial correlation analyses showed an association between neuropathy scores and severity of ataxia but not tremor in carrier males and females. These data suggest that neuropathic signs are associated with the fragile X premutation, presumably occurring through the same mechanism proposed for CNS disease, namely, toxicity from expanded‐CGG‐repeat FMR1 mRNA.

Dimension reduction methods for microarrays with application to censored survival data

MOTIVATION Recent research has shown that gene expression profiles can potentially be used for predicting various clinical phenotypes, such as tumor class, drug response and survival time. While there has been extensive studies on tumor classification, there has been less emphasis on other phenotypic features, in particular, patient survival time or time to cancer recurrence, which are subject to right censoring. We consider in this paper an analysis of censored survival time based on microarray gene expression profiles. RESULTS We propose a dimension reduction strategy, which combines principal components analysis and sliced inverse regression, to identify linear combinations of genes, that both account for the variability in the gene expression levels and preserve the phenotypic information. The extracted gene combinations are then employed as covariates in a predictive survival model formulation. We apply the proposed method to a large diffuse large-B-cell lymphoma dataset, which consists of 240 patients and 7399 genes, and build a Cox proportional hazards model based on the derived gene expression components. The proposed method is shown to provide a good predictive performance for patient survival, as demonstrated by both the significant survival difference between the predicted risk groups and the receiver operator characteristics analysis. AVAILABILITY R programs are available upon request from the authors. SUPPLEMENTARY INFORMATION http://dna.ucdavis.edu/~hli/bioinfo-surv-supp.pdf.

Data-driven multi-touch attribution models

In digital advertising, attribution is the problem of assigning credit to one or more advertisements for driving the user to the desirable actions such as making a purchase. Rather than giving all the credit to the last ad a user sees, multi-touch attribution allows more than one ads to get the credit based on their corresponding contributions. Multi-touch attribution is one of the most important problems in digital advertising, especially when multiple media channels, such as search, display, social, mobile and video are involved. Due to the lack of statistical framework and a viable modeling approach, true data-driven methodology does not exist today in the industry. While predictive modeling has been thoroughly researched in recent years in the digital advertising domain, the attribution problem focuses more on accurate and stable interpretation of the influence of each user interaction to the final user decision rather than just user classification. Traditional classification models fail to achieve those goals. In this paper, we first propose a bivariate metric, one measures the variability of the estimate, and the other measures the accuracy of classifying the positive and negative users. We then develop a bagged logistic regression model, which we show achieves a comparable classification accuracy as a usual logistic regression, but a much more stable estimate of individual advertising channel contributions. We also propose an intuitive and simple probabilistic model to directly quantify the attribution of different advertising channels. We then apply both the bagged logistic model and the probabilistic model to a real-world data set from a multi-channel advertising campaign for a well-known consumer software and services brand. The two models produce consistent general conclusions and thus offer useful cross-validation. The results of our attribution models also shed several important insights that have been validated by the advertising team. We have implemented the probabilistic model in the production advertising platform of the first authors company, and plan to implement the bagged logistic regression in the next product release. We believe availability of such data-driven multi-touch attribution metric and models is a break-through in the digital advertising industry.

Sparse sliced inverse regression

Sliced inverse regression (SIR) is an innovative and effective method for dimension reduction and data visualization of high-dimensional problems. It replaces the original variables with low-dimensional linear combinations of predictors without any loss of regression information and without the need to prespecify a model or an error distribution. However, it suffers from the fact that each SIR component is a linear combination of all the original predictors; thus, it is often difficult to interpret the extracted components. By representing SIR as a regression-type optimization problem, we propose in this article a new method, called sparse SIR, that combines the shrinkage idea of the lasso with SIR to produce both accurate and sparse solutions. The efficacy of the proposed method is verified by simulation, and a real data example is given.

Regularized matrix regression

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry and electroencephalography, matrix-type covariates frequently arise when measurements are obtained for each combination of two underlying variables. To address scientific questions arising from those data, new regression methods that take matrices as covariates are needed, and sparsity or other forms of regularization are crucial owing to the ultrahigh dimensionality and complex structure of the matrix data. The popular lasso and related regularization methods hinge on the sparsity of the true signal in terms of the number of its non-zero coefficients. However, for the matrix data, the true signal is often of, or can be well approximated by, a low rank structure. As such, the sparsity is frequently in the form of low rank of the matrix parameters, which may seriously violate the assumption of the classical lasso. We propose a class of regularized matrix regression methods based on spectral regularization. A highly efficient and scalable estimation algorithm is developed, and a degrees-of-freedom formula is derived to facilitate model selection along the regularization path. Superior performance of the method proposed is demonstrated on both synthetic and real examples.