To understand the transmissibility and spread of infectious diseases, epidemiologists turn to estimates of the instantaneous reproduction number. While many estimation approaches exist, their utility may be limited. Challenges of surveillance data collection, model assumptions that are unverifiable with data alone, and computationally inefficient frameworks are critical limitations for many existing approaches. We propose a discrete spline-based approach that solves a convex optimization problem-Poisson trend filtering-using the proximal Newton method. It produces a locally adaptive estimator for instantaneous reproduction number estimation with heterogeneous smoothness. Our methodology remains accurate even under some process misspecifications and is computationally efficient, even for large-scale data. The implementation is easily accessible in a lightweight R package rtestim.

Trends in terrestrial temperature variability are perhaps more relevant for species viability than trends in mean temperature. In this paper, we develop methodology for estimating such trends using multi-resolution climate data from polar orbiting weather satellites. We derive two novel algorithms for computation that are tailored for dense, gridded observations over both space and time. We evaluate our methods with a simulation that mimics these data’s features and on a large, publicly available, global temperature dataset with the eventual goal of tracking trends in cloud reflectance temperature variability.

MOTIVATION: The discovery of relationships between gene expression measurements and phenotypic responses is hampered by both computational and statistical impediments. Conventional statistical methods are less than ideal because they either fail to select relevant genes, predict poorly, ignore the unknown interaction structure between genes, or are computationally intractable. Thus, the creation of new methods which can handle many expression measurements on relatively small numbers of patients while also uncovering gene-gene relationships and predicting well is desirable. RESULTS: We develop a new technique for using the marginal relationship between gene expression measurements and patient survival outcomes to identify a small subset of genes which appear highly relevant for predicting survival, produce a low-dimensional embedding based on this small subset, and amplify this embedding with information from the remaining genes. We motivate our methodology by using gene expression measurements to predict survival time for patients with diffuse large B-cell lymphoma, illustrate the behavior of our methodology on carefully constructed synthetic examples, and test it on a number of other gene expression datasets. Our technique is computationally tractable, generally outperforms other methods, is extensible to other phenotypes, and also identifies different genes (relative to existing methods) for possible future study. AVAILABILITY AND IMPLEMENTATION: All of the code and data are available at http://mypage.iu.edu/∼dajmcdon/research/ . CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary material is available at Bioinformatics online.

We derive generalization error bounds for traditional time- series forecasting models. Our results hold for many standard forecasting tools including autoregressive models, moving average models, and, more generally, linear state-space models. These non-asymptotic bounds need only weak assumptions on the data-generating process, yet allow forecasters to select among competing models and to guarantee, with high probability, that their chosen model will perform well. We motivate our techniques with and apply them to standard economic and financial forecasting tools---a GARCH model for predicting equity volatility and a dynamic stochastic general equilibrium model (DSGE), the standard tool in macroeconomic forecasting. We demonstrate in particular how our techniques can aid forecasters and policy makers in choosing models which behave well under uncertainty and mis-specification.

During the last fifteen years, the lasso procedure has been the target of a substantial amount of theoretical and applied research. Correspondingly, many results are known about its behavior for a fixed or optimally chosen smoothing parameter (given up to unknown constants). Much less, however, is known about the lasso’s behavior when the smoothing parameter is chosen in a data dependent way. To this end, we give the first result about the risk consistency of lasso when the smoothing parameter is chosen via cross-validation. We consider the high-dimensional setting wherein the number of predictors p=n^α, α>0 grows with the number of observations.