Predicting the outcome of AI-models is inherently difficult, and understanding and trusting the models and decisions based on them are challenging. To help us, various explainable artificial intelligence (XAI) methods have been developed. Sometimes, explanations are requested in hindsight, for example after an accident has occurred due to unexpected or erroneous model outcomes. In such situations, our focus is on answering why the model failed to produce an accurate prediction. But since XAI-methods are typically made without knowledge of the true outcome values, the explanations concern the prediction and not the prediction error. In this paper, we change perspective and assume that the true values are known and propose an explanation method that quantifies how different subsets/clusters of the training data impact how the predicted values deviate from the true values, the so-called residuals. In this way, the proposed method lets us explain the accuracy of individual predictions, in hindsight. By focusing on explanations in hindsight, rather than the predictions per se, the proposed method offers a novel perspective to the field of XAI. The method is demonstrated and evaluated using both synthetic and real-world data. To objectively evaluate the method we propose, we utilize the explanations we generate to tailor a training data acquisition strategy and show how this leads to improved prediction performance. The proposed method is fully generic, and applicable to any industry. In the presentation offered here, most examples are related to the maritime industry. • Proposes a novel, model-agnostic approach for explainable artificial intelligence. • Focuses on explanations in hindsight. • Explanations based on comparing predicted values and their true counterparts. • Demonstrated and evaluated using both synthetic and real-world data. • Presented using practical examples, particularly from the maritime industry.

Abstract This paper proposes a novel approach to explain the predictions made by data-driven methods. Since such predictions rely heavily on the data used for training, explanations that convey information about how the training data affects the predictions are useful. The paper proposes a novel approach to quantify how different data-clusters of the training data affect a prediction. The quantification is based on Shapley values, a concept which originates from coalitional game theory, developed to fairly distribute the payout among a set of cooperating players. A player’s Shapley value is a measure of that player’s contribution. Shapley values are often used to quantify feature importance, ie. how features affect a prediction. This paper extends this to cluster importance, letting clusters of the training data act as players in a game where the predictions are the payouts. The novel methodology proposed in this paper lets us explore and investigate how different clusters of the training data affect the predictions made by any black-box model, allowing new aspects of the reasoning and inner workings of a prediction model to be conveyed to the users. The methodology is fundamentally different from existing explanation methods, providing insight which would not be available otherwise, and should complement existing explanation methods, including explanations based on feature importance.

Abstract Shapley values originated in cooperative game theory but are extensively used today as a model-agnostic explanation framework to explain predictions made by complex machine learning models in the industry and academia. There are several algorithmic approaches for computing different versions of Shapley value explanations. Here, we consider Shapley values incorporating feature dependencies, referred to as conditional Shapley values, for predictive models fitted to tabular data. Estimating precise conditional Shapley values is difficult as they require the estimation of non-trivial conditional expectations. In this article, we develop new methods, extend earlier proposed approaches, and systematize the new refined and existing methods into different method classes for comparison and evaluation. The method classes use either Monte Carlo integration or regression to model the conditional expectations. We conduct extensive simulation studies to evaluate how precisely the different method classes estimate the conditional expectations, and thereby the conditional Shapley values, for different setups. We also apply the methods to several real-world data experiments and provide recommendations for when to use the different method classes and approaches. Roughly speaking, we recommend using parametric methods when we can specify the data distribution almost correctly, as they generally produce the most accurate Shapley value explanations. When the distribution is unknown, both generative methods and regression models with a similar form as the underlying predictive model are good and stable options. Regression-based methods are often slow to train but quickly produce the Shapley value explanations once trained. The vice versa is true for Monte Carlo-based methods, making the different methods appropriate in different practical situations.

Shapley values are today extensively used as a model-agnostic explanation framework to explain complex predictive machine learning models. Shapley values have desirable theoretical properties and a sound mathematical foundation in the field of cooperative game theory. Precise Shapley value estimates for dependent data rely on accurate modeling of the dependencies between all feature combinations. In this paper, we use a variational autoencoder with arbitrary conditioning (VAEAC) to model all feature dependencies simultaneously. We demonstrate through comprehensive simulation studies that our VAEAC approach to Shapley value estimation outperforms the state-of-the-art methods for a wide range of settings for both continuous and mixed dependent features. For high-dimensional settings, our VAEAC approach with a non-uniform masking scheme significantly outperforms competing methods. Finally, we apply our VAEAC approach to estimate Shapley value explanations for the Abalone data set from the UCI Machine Learning Repository.

BACKGROUND: Identifying gene interactions is a topic of great importance in genomics, and approaches based on network models provide a powerful tool for studying these. Assuming a Gaussian graphical model, a gene association network may be estimated from multiomic data based on the non-zero entries of the inverse covariance matrix. Inferring such biological networks is challenging because of the high dimensionality of the problem, making traditional estimators unsuitable. The graphical lasso is constructed for the estimation of sparse inverse covariance matrices in such situations, using [Formula: see text]-penalization on the matrix entries. The weighted graphical lasso is an extension in which prior biological information from other sources is integrated into the model. There are however issues with this approach, as it naïvely forces the prior information into the network estimation, even if it is misleading or does not agree with the data at hand. Further, if an associated network based on other data is used as the prior, the method often fails to utilize the information effectively. RESULTS: We propose a novel graphical lasso approach, the tailored graphical lasso, that aims to handle prior information of unknown accuracy more effectively. We provide an R package implementing the method, tailoredGlasso. Applying the method to both simulated and real multiomic data sets, we find that it outperforms the unweighted and weighted graphical lasso in terms of all performance measures we consider. In fact, the graphical lasso and weighted graphical lasso can be considered special cases of the tailored graphical lasso, and a parameter determined by the data measures the usefulness of the prior information. We also find that among a larger set of methods, the tailored graphical is the most suitable for network inference from high-dimensional data with prior information of unknown accuracy. With our method, mRNA data are demonstrated to provide highly useful prior information for protein-protein interaction networks. CONCLUSIONS: The method we introduce utilizes useful prior information more effectively without involving any risk of loss of accuracy should the prior information be misleading.

Autonomous ships are promoted as the future of the maritime transport industry aiming to overcome conventional vessels in terms of performance, safety and environmental impact. Yet their tangled cyber-physical-social interactions and new emerging properties induce questions regarding their liability and trustworthiness. Digital simulations and sea trials are launched to assure the safety requirements and social expectations are met a priori. This paper presents the design of realistic testbed scenarios from huge historical data through a high-performance computational method to recommend a complete set of navigation scenarios for autonomy tests. The developed approach integrates traffic big data from Automatic Identification System (AIS) with high-resolution digital maps, vessel information registry, and digital nautical charts. All historical vessel-to-ground and vessel-to-vessel interactions are efficiently analyzed through a hierarchical method for collision and grounding conflicts assessment with a 15-minutes prediction horizon. Relative risk is evaluated accurately over full periods of predicted close-quarters situations subject to physical limits and sea-room availability for evasive maneuverers under COLREG rules and traffic separation schemes. Spatial dependencies among multiple conflicts define risky momentary traffic situations modelled through directed graph representation of nested interactions. Their temporal dependencies describe navigation scenarios through dynamic co-behaviors between multiple participating vessels over a period of time. Finally, we analyze negative/positive actions that increase/decrease the complexity. The presented algorithms are computationally very efficient, they scale to several (country*year)s where millions of scenarios are extracted, classified, and scored by their relative risk, complexity, and likelihood for firm post-test conclusions.

The generation and systematic collection of genome-wide data is ever-increasing. This vast amount of data has enabled researchers to study relations between a variety of genomic and epigenomic features, including genetic variation, gene regulation and phenotypic traits. Such relations are typically investigated by comparatively assessing genomic co-occurrence. Technically, this corresponds to assessing the similarity of pairs of genome-wide binary vectors. A variety of similarity measures have been proposed for this problem in other fields like ecology. However, while several of these measures have been employed for assessing genomic co-occurrence, their appropriateness for the genomic setting has never been investigated. We show that the choice of similarity measure may strongly influence results and propose two alternative modelling assumptions that can be used to guide this choice. On both simulated and real genomic data, the Jaccard index is strongly altered by dataset size and should be used with caution. The Forbes coefficient (fold change) and tetrachoric correlation are less influenced by dataset size, but one should be aware of increased variance for small datasets. All results on simulated and real data can be inspected and reproduced at https://hyperbrowser.uio.no/sim-measure.

We propose novel modifications to an anomaly detection methodology based on multivariate signal reconstruction followed by residuals analysis. The reconstructions are made using Auto Associative Kernel Regression (AAKR), where the query observations are compared to historical observations called memory vectors, representing normal operation. When the data set with historical observations grows large, the naive approach where all observations are used as memory vectors will lead to unacceptable large computational loads, hence a reduced set of memory vectors should be intelligently selected. The residuals between the observed and the reconstructed signals are analysed using standard Sequential Probability Ratio Tests (SPRT), where appropriate alarms are raised based on the sequential behaviour of the residuals. The modifications we introduce include: a novel cluster based method to select memory vectors to be considered by the AAKR, which gives an extensive reduction in computation time; a generalization of the distance measure, which makes it possible to distinguish between explanatory and response variables; and a regional credibility estimation used in the residuals analysis, to let the time used to identify if a sequence of query vectors represents an anomalous state or not, depend on the amount of data situated close to or surrounding the query vector. We demonstrate how the anomaly detection method and the proposed modifications can be successfully applied for anomaly detection on a set of imbalanced benchmark data sets, as well as on recent data from a marine diesel engine in operation.

Graph-based representations are considered to be the future for reference genomes, as they allow integrated representation of the steadily increasing data on individual variation. Currently available tools allow de novo assembly of graph-based reference genomes, alignment of new read sets to the graph representation as well as certain analyses like variant calling and haplotyping. We here present a first method for calling ChIP-Seq peaks on read data aligned to a graph-based reference genome. The method is a graph generalization of the peak caller MACS2, and is implemented in an open source tool, Graph Peak Caller. By using the existing tool vg to build a pan-genome of Arabidopsis thaliana, we validate our approach by showing that Graph Peak Caller with a pan-genome reference graph can trace variants within peaks that are not part of the linear reference genome, and find peaks that in general are more motif-enriched than those found by MACS2.

BACKGROUND: It has been proposed that future reference genomes should be graph structures in order to better represent the sequence diversity present in a species. However, there is currently no standard method to represent genomic intervals, such as the positions of genes or transcription factor binding sites, on graph-based reference genomes. RESULTS: We formalize offset-based coordinate systems on graph-based reference genomes and introduce methods for representing intervals on these reference structures. We show the advantage of our methods by representing genes on a graph-based representation of the newest assembly of the human genome (GRCh38) and its alternative loci for regions that are highly variable. CONCLUSION: More complex reference genomes, containing alternative loci, require methods to represent genomic data on these structures. Our proposed notation for genomic intervals makes it possible to fully utilize the alternative loci of the GRCh38 assembly and potential future graph-based reference genomes. We have made a Python package for representing such intervals on offset-based coordinate systems, available at https://github.com/uio-cels/offsetbasedgraph . An interactive web-tool using this Python package to visualize genes on a graph created from GRCh38 is available at https://github.com/uio-cels/genomicgraphcoords .

Integration of retroviral vectors in the human genome follows non random patterns that favor insertional deregulation of gene expression and may cause risks of insertional mutagenesis when used in clinical gene therapy. Understanding how viral vectors integrate into the human genome is a key issue in predicting these risks. We provide a new statistical method to compare retroviral integration patterns. We identified the positions where vectors derived from the Human Immunodeficiency Virus (HIV) and the Moloney Murine Leukemia Virus (MLV) show different integration behaviors in human hematopoietic progenitor cells. Non-parametric density estimation was used to identify candidate comparative hotspots, which were then tested and ranked. We found 100 significative comparative hotspots, distributed throughout the chromosomes. HIV hotspots were wider and contained more genes than MLV ones. A Gene Ontology analysis of HIV targets showed enrichment of genes involved in antigen processing and presentation, reflecting the high HIV integration frequency observed at the MHC locus on chromosome 6. Four histone modifications/variants had a different mean density in comparative hotspots (H2AZ, H3K4me1, H3K4me3, H3K9me1), while gene expression within the comparative hotspots did not differ from background. These findings suggest the existence of epigenetic or nuclear three-dimensional topology contexts guiding retroviral integration to specific chromosome areas.

Abstract Summary: CGH-Explorer is a program for visualization and statistical analysis of microarray-based comparative genomic hybridization (array-CGH) data. The program has preprocessing facilities, tools for graphical exploration of individual arrays or groups of arrays, and tools for statistical identification of regions of amplification and deletion. Availability: The program is available as Java class files that runs on any platform with the Java 2 runtime environment (J2SE JRE) installed, and as a Windows executable. Java source files are also available. See http://www.ifi.uio.no/bioinf/Papers/CGH/ Contact: [email protected]

MOTIVATION: Missing values are problematic for the analysis of microarray data. Imputation methods have been compared in terms of the similarity between imputed and true values in simulation experiments and not of their influence on the final analysis. The focus has been on missing at random, while entries are missing also not at random. RESULTS: We investigate the influence of imputation on the detection of differentially expressed genes from cDNA microarray data. We apply ANOVA for microarrays and SAM and look to the differentially expressed genes that are lost because of imputation. We show that this new measure provides useful information that the traditional root mean squared error cannot capture. We also show that the type of missingness matters: imputing 5% missing not at random has the same effect as imputing 10-30% missing at random. We propose a new method for imputation (LinImp), fitting a simple linear model for each channel separately, and compare it with the widely used KNNimpute method. For 10% missing at random, KNNimpute leads to twice as many lost differentially expressed genes as LinImp. AVAILABILITY: The R package for LinImp is available at http://folk.uio.no/idasch/imp.