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In survival analysis, complex machine learning algorithms have been increasingly used for predictive modeling. Given a collection of features available for inclusion in a predictive model, it may be of interest to quantify the relative importance of a subset of features for the prediction task at hand. In particular, in HIV vaccine trials, participant baseline characteristics are used to predict the probability of infection over the intended follow-up period, and investigators may wish to understand how much certain types of predictors, such as behavioral factors, contribute toward overall predictiveness. Time-to-event outcomes such as time to infection are often subject to right censoring, and existing methods for assessing variable importance are typically not intended to be used in this setting. We describe a broad class of algorithm-agnostic variable importance measures for prediction in the context of survival data. We propose a nonparametric efficient estimation procedure that incorporates flexible learning of nuisance parameters, yields asymptotically valid inference, and enjoys double-robustness. We assess the performance of our proposed procedure via numerical simulations and analyze data from the HVTN 702 study to inform enrollment strategies for future HIV vaccine trials.

In many applications, it is of interest to identify a parsimonious set of features, or panel, from multiple candidates that achieves a desired level of performance in predicting a response. This task is often complicated in practice by missing data arising from the sampling design or other random mechanisms. Most recent work on variable selection in missing data contexts relies in some part on a finite-dimensional statistical model, e.g., a generalized or penalized linear model. In cases where this model is misspecified, the selected variables may not all be truly scientifically relevant and can result in panels with suboptimal classification performance. To address this limitation, we propose a nonparametric variable selection algorithm combined with multiple imputation to develop flexible panels in the presence of missing-at-random data. We outline strategies based on the proposed algorithm that achieve control of commonly used error rates. Through simulations, we show that our proposal has good operating characteristics and results in panels with higher classification and variable selection performance compared to several existing penalized regression approaches in cases where a generalized linear model is misspecified. Finally, we use the proposed method to develop biomarker panels for separating pancreatic cysts with differing malignancy potential in a setting where complicated missingness in the biomarkers arose due to limited specimen volumes.

Quantized tensor trains (QTTs) have recently emerged as a framework for the numerical discretization of continuous functions, with the potential for widespread applications in numerical analysis. However, the theory of QTT approximation is not fully understood. In this work, we advance this theory from the point of view of multiscale polynomial interpolation. This perspective clarifies why QTT ranks decay with increasing depth, quantitatively controls QTT rank in terms of smoothness of the target function, and explains why certain functions with sharp features and poor quantitative smoothness can still be well approximated by QTTs. The perspective also motivates new practical and efficient algorithms for the construction of QTTs from function evaluations on multiresolution grids.

With advances in scientific computing and mathematical modeling, complex scientific phenomena such as galaxy formations and rocket propulsion can now be reliably simulated. Such simulations can however be very time-intensive, requiring millions of CPU hours to perform. One solution is multi-fidelity emulation, which uses data of different fidelities to train an efficient predictive model which emulates the expensive simulator. For complex scientific problems and with careful elicitation from scientists, such multi-fidelity data may often be linked by a directed acyclic graph (DAG) representing its scientific model dependencies. We thus propose a new Graphical Multi-fidelity Gaussian Process (GMGP) model, which embeds this DAG structure (capturing scientific dependencies) within a Gaussian process framework. We show that the GMGP has desirable modeling traits via two Markov properties, and admits a scalable algorithm for recursive computation of the posterior mean and variance along at each depth level of the DAG. We also present a novel experimental design methodology over the DAG given an experimental budget, and propose a nonlinear extension of the GMGP via deep Gaussian processes. The advantages of the GMGP are then demonstrated via a suite of numerical experiments and an application to emulation of heavy-ion collisions, which can be used to study the conditions of matter in the Universe shortly after the Big Bang. The proposed model has broader uses in data fusion applications with graphical structure, which we further discuss.

Partial differential equations with highly oscillatory input terms are hardly ever solvable analytically and their numerical treatment is difficult. Modulated Fourier expansion used as an {\it ansatz} is a well known and extensively investigated tool in asymptotic numerical approach for this kind of problems. Although the efficiency of this approach has been recognised, its error analysis has not been investigated rigorously for general forms of linear PDEs. In this paper, we start such kind of investigations for a general form of linear PDEs with an input term characterised by a single high frequency. More precisely we derive an analytical form of such an expansion and provide a formula for the error of its truncation. Theoretical investigations are illustrated by computational simulations.

The nonparametric estimators built by minimizing the mean squared relative error are gaining in popularity for their robustness in the presence of outliers in comparison to the Nadaraya Watson estimators. In this paper we build a relative error regression function estimator in the case of a functional explanatory variable and a left truncated and right censored scalar variable. The pointwise and uniform convergence of the estimator is proved and its performance is assessed by a numerical study in particularly the robustness which is highlighted using the influence function as a measure of robustness.

We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization of extrapolation methods and multi-product expansions. A general analysis is provided and new methods up to order 8 are built and tested. The new approach is shown to reduce the latency problem when implemented in a parallel environment and leads to schemes that are significantly more efficient than standard extrapolation when the linear combination is delayed by a number of steps.

We propose a simple multivariate normality test based on Kac-Bernstein's characterization, which can be conducted by utilising existing statistical independence tests for sums and differences of data samples. We also perform its empirical investigation, which reveals that for high-dimensional data, the proposed approach may be more efficient than the alternative ones. The accompanying code repository is provided at \url{//shorturl.at/rtuy5}.

Pairwise sequence comparison is one of the most fundamental problems in string processing. The most common metric to quantify the similarity between sequences S and T is edit distance, d(S,T), which corresponds to the number of characters that need to be substituted, deleted from, or inserted into S to generate T. However, fewer edit operations may be sufficient for some string pairs to transform one string to the other if larger rearrangements are permitted. Block edit distance refers to such changes in substring level (i.e., blocks) that "penalizes" entire block removals, insertions, copies, and reversals with the same cost as single-character edits (Lopresti & Tomkins, 1997). Most studies to calculate block edit distance to date aimed only to characterize the distance itself for applications in sequence nearest neighbor search without reporting the full alignment details. Although a few tools try to solve block edit distance for genomic sequences, such as GR-Aligner, they have limited functionality and are no longer maintained. Here, we present SABER, an algorithm to solve block edit distance that supports block deletions, block moves, and block reversals in addition to the classical single-character edit operations. Our algorithm runs in O(m^2.n.l_range) time for |S|=m, |T|=n and the permitted block size range of l_range; and can report all breakpoints for the block operations. We also provide an implementation of SABER currently optimized for genomic sequences (i.e., generated by the DNA alphabet), although the algorithm can theoretically be used for any alphabet. SABER is available at //github.com/BilkentCompGen/saber

The influence of natural image transformations on receptive field responses is crucial for modelling visual operations in computer vision and biological vision. In this regard, covariance properties with respect to geometric image transformations in the earliest layers of the visual hierarchy are essential for expressing robust image operations and for formulating invariant visual operations at higher levels. This paper defines and proves a joint covariance property under compositions of spatial scaling transformations, spatial affine transformations, Galilean transformations and temporal scaling transformations, which makes it possible to characterize how different types of image transformations interact with each other. Specifically, the derived relations show the receptive field parameters need to be transformed, in order to match the output from spatio-temporal receptive fields with the underlying spatio-temporal image transformations.