Controlled ovarian stimulation is tailored to the patient based on clinical parameters but estimating the number of retrieved metaphase II (MII) oocytes is a challenge. Here, we have developed a model that takes advantage of the patient's genetic and clinical characteristics simultaneously for predicting the stimulation outcome. Sequence variants in reproduction-related genes identified by next-generation sequencing were matched to groups of various MII oocyte counts using ranking, correspondence analysis, and self-organizing map methods. The gradient boosting machine technique was used to train models on a clinical dataset of 8,574 or a clinical-genetic dataset of 516 ovarian stimulations. The clinical-genetic model predicted the number of MII oocytes better than that based on clinical data. Anti-Müllerian hormone level and antral follicle count were the two most important predictors while a genetic feature consisting of sequence variants in the GDF9, LHCGR, FSHB, ESR1, and ESR2 genes was the third. The combined contribution of genetic features important for the prediction was over one-third of that revealed for anti-Müllerian hormone. Predictions of our clinical-genetic model accurately matched individuals' actual outcomes preventing over- or underestimation. The genetic data upgrades the personalized prediction of ovarian stimulation outcomes, thus improving the in vitro fertilization procedure.

The Shapley value – a fundamental game-theoretic solution concept – has recently become one of the main tools used to explain predictions of tree ensemble models. Another well-known game-theoretic solution concept is the Banzhaf value. Although the Banzhaf value is closely related to the Shapley value, its properties w.r.t. feature attribution have not been understood equally well. This paper shows that, for tree ensemble models, the Banzhaf value offers some crucial advantages over the Shapley value while providing similar feature attributions. In particular, we first give an optimal O(TL + n) time algorithm for computing the Banzhaf value-based attribution of a tree ensemble model’s output. Here, T is the number of trees, L is the maximum number of leaves in a tree, and n is the number of features. In comparison, the state-of-the-art Shapley value-based algorithm runs in O(TLD^2 + n) time, where D denotes the maximum depth of a tree in the ensemble. Next, we experimentally compare the Banzhaf and Shapley values for tree ensemble models. Both methods deliver essentially the same average importance scores for the studied datasets using two different tree ensemble models (the sklearn implementation of Decision Trees or xgboost implementation of Gradient Boosting Decision Trees). However, our results indicate that, on top of being computable faster, the Banzhaf is more numerically robust than the Shapley value.

Publikacja bezkosztowa

In this paper, we report progress on answering the open problem presented by Pagh [11], who considered the near neighbor search without false negatives for the Hamming distance. We show new data structures for solving the c-approximate near neighbors problem without false negatives for Euclidean high dimensional space \mathcal{R}^d. These data structures work for any c = \omega(\sqrt{\log{\log{n}}}), where n is the number of points in the input set, with poly-logarithmic query time and polynomial pre-processing time. This improves over the known algorithms, which require c to be \Omega(\sqrt{d}). This improvement is obtained by applying a sequence of reductions, which are interesting on their own. First, we reduce the problem to d instances of dimension logarithmic in n. Next, these instances are reduced to a number of c-approximate near neighbor search without false negatives instances in \big(\Rspace^k\big)^L space equipped with metric m(x,y) = \max_{1 \le i \leL}(\dist{x_i - y_i}_2).

We introduce random directed acyclic graph and use it to model the information diffusion network. Subsequently, we analyze the cascade generation model (CGM) introduced by Leskovec et al. [19]. Until now only empirical studies of this model were done. In this paper, we present the first theoretical proof that the sizes of cascades generated by the CGM follow the power-law distribution, which is consistent with multiple empirical analysis of the large social networks. We compared the assumptions of our model with the Twitter social network and tested the goodness of approximation.