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Ensemble-based modifications of the well-known SHapley Additive exPlanations (SHAP) method for the local explanation of a black-box model are proposed. The modifications aim to simplify SHAP which is computationally expensive when there is a large number of features. The main idea behind the proposed modifications is to approximate SHAP by an ensemble of SHAPs with a smaller number of features. According to the first modification, called ER-SHAP, several features are randomly selected many times from the feature set, and Shapley values for the features are computed by means of "small" SHAPs. The explanation results are averaged to get the final Shapley values. According to the second modification, called ERW-SHAP, several points are generated around the explained instance for diversity purposes, and results of their explanation are combined with weights depending on distances between points and the explained instance. The third modification, called ER-SHAP-RF, uses the random forest for preliminary explanation of instances and determining a feature probability distribution which is applied to selection of features in the ensemble-based procedure of ER-SHAP. Many numerical experiments illustrating the proposed modifications demonstrate their efficiency and properties for local explanation.

We measure electronic transport through point contacts in the high-mobility electron gas in a Ga[Al]As heterostructure at different temperatures and bulk electron densities. The conductance through all point contacts increases with increasing temperature in a temperature window around $T \sim 10 K$ for all investigated electron densities and point contact widths. For high electron densities this conductance exceeds the fundamental ballistic limit (Sharvin limit). These observations are in agreement with a viscous electron transport model and previous experiments in graphene., Comment: 5 pages, 2 figures

A method for the local and global interpretation of a black-box model on the basis of the well-known generalized additive models is proposed. It can be viewed as an extension or a modification of the algorithm using the neural additive model. The method is based on using an ensemble of gradient boosting machines (GBMs) such that each GBM is learned on a single feature and produces a shape function of the feature. The ensemble is composed as a weighted sum of separate GBMs resulting a weighted sum of shape functions which form the generalized additive model. GBMs are built in parallel using randomized decision trees of depth 1, which provide a very simple architecture. Weights of GBMs as well as features are computed in each iteration of boosting by using the Lasso method and then updated by means of a specific smoothing procedure. In contrast to the neural additive model, the method provides weights of features in the explicit form, and it is simply trained. A lot of numerical experiments with an algorithm implementing the proposed method on synthetic and real datasets demonstrate its efficiency and properties for local and global interpretation.

The gradient boosting machine is one of the powerful tools for solving regression problems. In order to cope with its shortcomings, an approach for constructing ensembles of gradient boosting models is proposed. The main idea behind the approach is to use the stacking algorithm in order to learn a second-level meta-model which can be regarded as a model for implementing various ensembles of gradient boosting models. First, the linear regression of the gradient boosting models is considered as a simplest realization of the meta-model under condition that the linear model is differentiable with respect to its coefficients (weights). Then it is shown that the proposed approach can be simply extended on arbitrary differentiable combination models, for example, on neural networks which are differentiable and can implement arbitrary functions of gradient boosting models. Various numerical examples illustrate the proposed approach.

A method for counterfactual explanation of machine learning survival models is proposed. One of the difficulties of solving the counterfactual explanation problem is that the classes of examples are implicitly defined through outcomes of a machine learning survival model in the form of survival functions. A condition that establishes the difference between survival functions of the original example and the counterfactual is introduced. This condition is based on using a distance between mean times to event. It is shown that the counterfactual explanation problem can be reduced to a standard convex optimization problem with linear constraints when the explained black-box model is the Cox model. For other black-box models, it is proposed to apply the well-known Particle Swarm Optimization algorithm. A lot of numerical experiments with real and synthetic data demonstrate the proposed method., Comment: arXiv admin note: text overlap with arXiv:2005.02249

The gradient boosting machine is a powerful ensemble-based machine learning method for solving regression problems. However, one of the difficulties of its using is a possible discontinuity of the regression function, which arises when regions of training data are not densely covered by training points. In order to overcome this difficulty and to reduce the computational complexity of the gradient boosting machine, we propose to apply the partially randomized trees which can be regarded as a special case of the extremely randomized trees applied to the gradient boosting. The gradient boosting machine with the partially randomized trees is illustrated by means of many numerical examples using synthetic and real data.

A new modification of the explanation method SurvLIME called SurvLIME-Inf for explaining machine learning survival models is proposed. The basic idea behind SurvLIME as well as SurvLIME-Inf is to apply the Cox proportional hazards model to approximate the black-box survival model at the local area around a test example. The Cox model is used due to the linear relationship of covariates. In contrast to SurvLIME, the proposed modification uses $L_{\infty }$-norm for defining distances between approximating and approximated cumulative hazard functions. This leads to a simple linear programming problem for determining important features and for explaining the black-box model prediction. Moreover, SurvLIME-Inf outperforms SurvLIME when the training set is very small. Numerical experiments with synthetic and real datasets demonstrate the SurvLIME-Inf efficiency., Comment: arXiv admin note: substantial text overlap with arXiv:2003.08371, arXiv:2005.02249

A new robust algorithm based of the explanation method SurvLIME called SurvLIME-KS is proposed for explaining machine learning survival models. The algorithm is developed to ensure robustness to cases of a small amount of training data or outliers of survival data. The first idea behind SurvLIME-KS is to apply the Cox proportional hazards model to approximate the black-box survival model at the local area around a test example due to the linear relationship of covariates in the model. The second idea is to incorporate the well-known Kolmogorov-Smirnov bounds for constructing sets of predicted cumulative hazard functions. As a result, the robust maximin strategy is used, which aims to minimize the average distance between cumulative hazard functions of the explained black-box model and of the approximating Cox model, and to maximize the distance over all cumulative hazard functions in the interval produced by the Kolmogorov-Smirnov bounds. The maximin optimization problem is reduced to the quadratic program. Various numerical experiments with synthetic and real datasets demonstrate the SurvLIME-KS efficiency.

A new method called SurvLIME for explaining machine learning survival models is proposed. It can be viewed as an extension or modification of the well-known method LIME. The main idea behind the proposed method is to apply the Cox proportional hazards model to approximate the survival model at the local area around a test example. The Cox model is used because it considers a linear combination of the example covariates such that coefficients of the covariates can be regarded as quantitative impacts on the prediction. Another idea is to approximate cumulative hazard functions of the explained model and the Cox model by using a set of perturbed points in a local area around the point of interest. The method is reduced to solving an unconstrained convex optimization problem. A lot of numerical experiments demonstrate the SurvLIME efficiency.

A new method for explaining the Siamese neural network is proposed. It uses the following main ideas. First, the explained feature vector is compared with the prototype of the corresponding class computed at the embedding level (the Siamese neural network output). The important features at this level are determined as features which are close to the same features of the prototype. Second, an autoencoder is trained in a special way in order to take into account the embedding level of the Si-amese network, and its decoder part is used for reconstructing input data with the corresponding changes. Numerical experiments with the well-known dataset MNIST illustrate the propose method., Comment: International Scientific Conference Telecommunications, Computing and Control (TELECCON-2019)

A new meta-algorithm for estimating the conditional average treatment effects is proposed in the paper. The main idea underlying the algorithm is to consider a new dataset consisting of feature vectors produced by means of concatenation of examples from control and treatment groups, which are close to each other. Outcomes of new data are defined as the difference between outcomes of the corresponding examples comprising new feature vectors. The second idea is based on the assumption that the number of controls is rather large and the control outcome function is precisely determined. This assumption allows us to augment treatments by generating feature vectors which are closed to available treatments. The outcome regression function constructed on the augmented set of concatenated feature vectors can be viewed as an estimator of the conditional average treatment effects. A simple modification of the Co-learner based on the random subspace method or the feature bagging is also proposed. Various numerical simulation experiments illustrate the proposed algorithm and show its outperformance in comparison with the well-known T-learner and X-learner for several types of the control and treatment outcome functions.

The GERmanium Detector Array (GERDA) experiment at the Gran Sasso underground laboratory (LNGS) of INFN is searching for neutrinoless double-beta ($0\nu\beta\beta$) decay of $^{76}$Ge. The technological challenge of GERDA is to operate in a "background-free" regime in the region of interest (ROI) after analysis cuts for the full 100$\,$kg$\cdot$yr target exposure of the experiment. A careful modeling and decomposition of the full-range energy spectrum is essential to predict the shape and composition of events in the ROI around $Q_{\beta\beta}$ for the $0\nu\beta\beta$ search, to extract a precise measurement of the half-life of the double-beta decay mode with neutrinos ($2\nu\beta\beta$) and in order to identify the location of residual impurities. The latter will permit future experiments to build strategies in order to further lower the background and achieve even better sensitivities. In this article the background decomposition prior to analysis cuts is presented for GERDA Phase II. The background model fit yields a flat spectrum in the ROI with a background index (BI) of $16.04^{+0.78}_{-0.85} \cdot 10^{-3}\,$cts/(kg$\cdot$keV$\cdot$yr) for the enriched BEGe data set and $14.68^{+0.47}_{-0.52} \cdot 10^{-3}\,$cts/(kg$\cdot$keV$\cdot$yr) for the enriched coaxial data set. These values are similar to the one of Gerda Phase I despite a much larger number of detectors and hence radioactive hardware components.

A modification of the confidence screening mechanism based on adaptive weighing of every training instance at each cascade level of the Deep Forest is proposed. The idea underlying the modification is very simple and stems from the confidence screening mechanism idea proposed by Pang et al. to simplify the Deep Forest classifier by means of updating the training set at each level in accordance with the classification accuracy of every training instance. However, if the confidence screening mechanism just removes instances from training and testing processes, then the proposed modification is more flexible and assigns weights by taking into account the classification accuracy. The modification is similar to the AdaBoost to some extent. Numerical experiments illustrate good performance of the proposed modification in comparison with the original Deep Forest proposed by Zhou and Feng.

A weighted random survival forest is presented in the paper. It can be regarded as a modification of the random forest improving its performance. The main idea underlying the proposed model is to replace the standard procedure of averaging used for estimation of the random survival forest hazard function by weighted avaraging where the weights are assigned to every tree and can be veiwed as training paremeters which are computed in an optimal way by solving a standard quadratic optimization problem maximizing Harrell's C-index. Numerical examples with real data illustrate the outperformance of the proposed model in comparison with the original random survival forest.

In superfluid $^3$He-B confined in a slab geometry, domain walls between regions of different order parameter orientation are predicted to be energetically stable. Formation of the spatially-modulated superfluid stripe phase has been proposed. We confined $^3$He in a 1.1 $\mu$m high microfluidic cavity and cooled it into the B phase at low pressure, where the stripe phase is predicted. We measured the surface-induced order parameter distortion with NMR, sensitive to the formation of domains. The results rule out the stripe phase, but are consistent with 2D modulated superfluid order., Comment: 9 pages, 9 figures

A computationally simple genome-wide association study (GWAS) algorithm for estimating the main and epistatic effects of markers or single nucleotide polymorphisms (SNPs) is proposed. It is based on the intuitive assumption that changes of alleles corresponding to important SNPs in a pair of individuals lead to large difference of phenotype values of these individuals. The algorithm is based on considering pairs of individuals instead of SNPs or pairs of SNPs. The main advantage of the algorithm is that it weakly depends on the number of SNPs in a genotype matrix. It mainly depends on the number of individuals, which is typically very small in comparison with the number of SNPs. Numerical experiments with real data sets illustrate the proposed algorithm.