A fundamental problem in visual data exploration concerns whether observed patterns are true or merely random noise. This problem is especially pertinent in visual analytics, where the user is presented with a barrage of patterns, without any guarantees of their statistical validity. Recently this problem has been formulated in terms of statistical testing and the multiple comparisons problem. In this paper, we identify two levels of multiple comparisons problems in visualization: the within-view and the between-view problem. We develop a statistical testing procedure for interactive data exploration that controls the family-wise error rate on both levels. The procedure enables the user to determine the compatibility of their assumptions about the data with visually observed patterns. We present use-cases where we visualize and evaluate patterns in real-world data.

Abstract Real-world datasets are often characterised by outliers; data items that do not follow the same structure as the rest of the data. These outliers might negatively influence modelling of the data. In data analysis it is, therefore, important to consider methods that are robust to outliers. In this paper we develop a robust regression method that finds the largest subset of data items that can be approximated using a sparse linear model to a given precision. We show that this can yield the best possible robustness to outliers. However, this problem is NP-hard and to solve it we present an efficient approximation algorithm, termed SLISE. Our method extends existing state-of-the-art robust regression methods, especially in terms of speed on high-dimensional datasets. We demonstrate our method by applying it to both synthetic and real-world regression problems.

Abstract Regression analysis is a standard supervised machine learning method used to model an outcome variable in terms of a set of predictor variables. In most real-world applications the true value of the outcome variable we want to predict is unknown outside the training data, i.e., the ground truth is unknown. Phenomena such as overfitting and concept drift make it difficult to directly observe when the estimate from a model potentially is wrong. In this paper we present an efficient framework for estimating the generalization error of regression functions, applicable to any family of regression functions when the ground truth is unknown. We present a theoretical derivation of the framework and empirically evaluate its strengths and limitations. We find that it performs robustly and is useful for detecting concept drift in datasets in several real-world domains.

Efficient explorative data analysis systems must take into account both what a user knows and wants to know. This paper proposes a principled framework for interactive visual exploration of relations in data, through views most informative given the user's current knowledge and objectives. The user can input pre-existing knowledge of relations in the data and also formulate specific exploration interests, which are then taken into account in the exploration. The idea is to steer the exploration process towards the interests of the user, instead of showing uninteresting or already known relations. The user's knowledge is modelled by a distribution over data sets parametrised by subsets of rows and columns of data, called tile constraints. We provide a computationally efficient implementation of this concept based on constrained randomisation. Furthermore, we describe a novel dimensionality reduction method for finding the views most informative to the user, which at the limit of no background knowledge and with generic objectives reduces to PCA. We show that the method is suitable for interactive use and is robust to noise, outperforms standard projection pursuit visualisation methods, and gives understandable and useful results in analysis of real-world data. We provide an open-source implementation of the framework.

Abstract Real-world datasets are often characterised by outliers, points far from the majority of the points, which might negatively influence modelling of the data. In data analysis it is hence important to use methods that are robust to outliers. In this paper we develop a robust regression method for finding the largest subset in the data that can be approximated using a sparse linear model to a given precision. We show that the problem is NP-hard and hard to approximate. We present an efficient algorithm, termedslise, to find solutions to the problem. Our method extends current state-of-the-art robust regression methods, especially in terms of scalability on large datasets. Furthermore, we show that our method can be used to yield interpretable explanations for individual decisions by opaque, black box, classifiers. Our approach solves shortcomings in other recent explanation methods by not requiring sampling of new data points and by being usable without modifications across various data domains. We demonstrate our method using both synthetic and real-world regression and classification problems.

In this paper we consider the following important problem: when we explore data visually and observe patterns, how can we determine their statistical significance? Patterns observed in exploratory analysis are traditionally met with scepticism, since the hypotheses are formulated while viewing the data, rather than before doing so. In contrast to this belief, we show that it is, in fact, possible to evaluate the significance of patterns also during exploratory analysis, and that the knowledge of the analyst can be leveraged to improve statistical power by reducing the amount of simultaneous comparisons. We develop a principled framework for determining the statistical significance of visually observed patterns. Furthermore, we show how the significance of visual patterns observed during iterative data exploration can be determined. We perform an empirical investigation on real and synthetic tabular data and time series, using different test statistics and methods for generating surrogate data. We conclude that the proposed framework allows determining the significance of visual patterns during exploratory analysis.

Today’s ever-increasing amount of data places new demands on cognitive ergonomics and requires new design ideas to ensure successful human–data interaction. Our aim was to identify the cognitive factors that must be considered when designing systems to improve decision-making based on large amounts of data. We constructed a task that simulates the typical cognitive demands people encounter in data analysis situations. We demonstrate some essential cognitive limitations using a behavioural experiment with 20 participants. The studied task presented the participants with critical and noncritical attributes that contained information on two groups of people. They had to select the response option (group) with the higher level of critical attributes. The results showed that accuracy of judgement decreased as the amount of information increased, and that judgement was affected by irrelevant information. Our results thus demonstrate critical cognitive limitations when people utilise data and suggest a cognitive bias in data-based decision-making. Therefore, when designing for cognition, we should consider the human cognitive limitations that are manifested in a data analysis context. Furthermore, we need general cognitive ergonomic guidelines for design that support the utilisation of data and improve data-based decision-making.