We develop a general approach to valid inference after model selection. At the core of our framework is a result that characterizes the distribution of a post-selection estimator conditioned on the selection event. We specialize the approach to model selection by the lasso to form valid confidence intervals for the selected coefficients and test whether all relevant variables have been included in the model.Comment: Published at http://dx.doi.org/10.1214/15-AOS1371 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type methods for minimizing smooth functions, even when search directions are computed inexactly. Many popular methods tailored to problems arising in bioinformatics, signal processing, and statistical learning are special cases of proximal Newton-type methods, and our analysis yields new convergence results for some of these methods.

We present a Communication-efficient Surrogate Likelihood (CSL) framework for solving distributed statistical inference problems. CSL provides a communication-efficient surrogate to the global likelihood that can be used for low-dimensional estimation, high-dimensional regularized estimation and Bayesian inference. For low-dimensional estimation, CSL provably improves upon naive averaging schemes and facilitates the construction of confidence intervals. For high-dimensional regularized estimation, CSL leads to a minimax-optimal estimator with controlled communication cost. For Bayesian inference, CSL can be used to form a communication-efficient quasi-posterior distribution that converges to the true posterior. This quasi-posterior procedure significantly improves the computational efficiency of MCMC algorithms even in a non-distributed setting. We present both theoretical analysis and experiments to explore the properties of the CSL approximation.

The TGF-beta signaling pathway has a complex role in regulating mammary carcinogenesis. Here we demonstrate that the type III TGF-beta receptor (TbetaRIII, or betaglycan), a ubiquitously expressed TGF-beta coreceptor, regulated breast cancer progression and metastasis. Most human breast cancers lost TbetaRIII expression, with loss of heterozygosity of the TGFBR3 gene locus correlating with decreased TbetaRIII expression. TbetaRIII expression decreased during breast cancer progression, and low TbetaRIII levels predicted decreased recurrence-free survival in breast cancer patients. Restoring TbetaRIII expression in breast cancer cells dramatically inhibited tumor invasiveness in vitro and tumor invasion, angiogenesis, and metastasis in vivo. TbetaRIII appeared to inhibit tumor invasion by undergoing ectodomain shedding and producing soluble TbetaRIII, which binds and sequesters TGF-beta to decrease TGF-beta signaling and reduce breast cancer cell invasion and tumor-induced angiogenesis. Our results indicate that loss of TbetaRIII through allelic imbalance is a frequent genetic event during human breast cancer development that increases metastatic potential.

The covalent attachment of ubiquitin to cellular proteins is a powerful mechanism for controlling protein activity and localization. Ubiquitination is a reversible modification promoted by ubiquitin ligases and antagonized by deubiquitinating proteases. Ubiquitin-dependent mechanisms regulate many important processes including cell-cycle progression, apoptosis and transcriptional regulation. Here we show that ubiquitin-dependent mechanisms regulate synaptic development at the Drosophila neuromuscular junction (NMJ). Neuronal overexpression of the deubiquitinating protease fat facets leads to a profound disruption of synaptic growth control; there is a large increase in the number of synaptic boutons, an elaboration of the synaptic branching pattern, and a disruption of synaptic function. Antagonizing the ubiquitination pathway in neurons by expression of the yeast deubiquitinating protease UBP2 (ref. 5) also produces synaptic overgrowth and dysfunction. Genetic interactions between fat facets and highwire, a negative regulator of synaptic growth that has structural homology to a family of ubiquitin ligases, suggest that synaptic development may be controlled by the balance between positive and negative regulators of ubiquitination.