SUMMARY: As machine learning has become increasingly popular over the last few decades, so too has the number of machine-learning interfaces for implementing these models. Whilst many R libraries exist for machine learning, very few offer extended support for survival analysis. This is problematic considering its importance in fields like medicine, bioinformatics, economics, engineering and more. mlr3proba provides a comprehensive machine-learning interface for survival analysis and connects with mlr3's general model tuning and benchmarking facilities to provide a systematic infrastructure for survival modelling and evaluation. AVAILABILITY AND IMPLEMENTATION: mlr3proba is available under an LGPL-3 licence on CRAN and at https://github.com/mlr-org/mlr3proba, with further documentation at https://mlr3book.mlr-org.com/survival.html.

We present a novel framework for learning with sequential data of any kind, such as multivariate time series, strings, or sequences of graphs. The main result is a ”sequentialization” that transforms any kernel on a given domain into a kernel for sequences in that domain. This procedure preserves properties such as positive definiteness, the associated kernel feature map is an ordered variant of sample (cross-)moments, and this sequentialized kernel is consistent in the sense that it converges to a kernel for paths if sequences converge to paths (by discretization). Further, classical kernels for sequences arise as special cases of this method. We use dynamic programming and low-rank techniques for tensors to provide efficient algorithms to compute this sequentialized kernel.

We compare various extensions of the Bradley–Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley–Terry extensions are estimated by maximizing the log-likelihood, or an appropriately penalized version of it, while the posterior densities of the parameters of the hierarchical Poisson log-linear model are approximated using integrated nested Laplace approximations. The prediction performance of the various modeling approaches is assessed using a novel, context-specific framework for temporal validation that is found to deliver accurate estimates of the test error. The direct modeling of outcomes via the various Bradley–Terry extensions and the modeling of match scores using the hierarchical Poisson log-linear model demonstrate similar behavior in terms of predictive performance.

We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that a certain number of generic rank-one or generic linear measurements are sufficient to enable signal reconstruction for generic signals, and slightly more generic measurements yield reconstructability for all signals. Our results solve few open problems stated in the recent literature. Furthermore, we show how the algebraic estimation problem can be solved by a closed-form algebraic estimation technique, termed ideal regression, providing non-asymptotic success guarantees.

We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperforming alternative to the gold standard PARAFAC over which it has the advantages that it can intrinsically detect the true rank, avoids spurious components, and is stable with respect to outliers and non-Gaussian noise.

We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless case our algorithm is exact. For rank-one matrices, the new algorithm is fast, admits a highly-parallel implementation, and produces an error minimizing estimate that is qualitatively close to our theoretical and the state-of-the-art Nuclear Norm and OptSpace methods.