We tackle the problem of bias mitigation of algorithmic decisions in a setting where both the output of the algorithm and the sensitive variable are continuous. Most of prior work deals with discrete sensitive variables, meaning that the biases are measured for subgroups of persons defined by a label, leaving out important algorithmic bias cases, where the sensitive variable is continuous. Typical examples are unfair decisions made with respect to the age or the financial status. In our work, we then propose a bias mitigation strategy for continuous sensitive variables, based on the notion of endogeneity which comes from the field of econometrics. In addition to solve this new problem, our bias mitigation strategy is a weakly supervised learning method which requires that a small portion of the data can be measured in a fair manner. It is model agnostic, in the sense that it does not make any hypothesis on the prediction model. It also makes use of a reasonably large amount of input observations and their corresponding predictions. Only a small fraction of the true output predictions should be known. This therefore limits the need for expert interventions. Results obtained on synthetic data show the effectiveness of our approach for examples as close as possible to real-life applications in econometrics.

This paper introduces a new structural causal model tailored for representing threshold-based IT systems and presents a new algorithm designed to rapidly detect root causes of anomalies in such systems. When root causes are not causally related, the method is proven to be correct; while an extension is proposed based on the intervention of an agent to relax this assumption. Our algorithm and its agent-based extension leverage causal discovery from offline data and engage in subgraph traversal when encountering new anomalies in online data. Our extensive experiments demonstrate the superior performance of our methods, even when applied to data generated from alternative structural causal models or real IT monitoring data.

The widely adopted spatial modeling method -- standard Gaussian process (GP) regression -- becomes inadequate in processing the growing sensing data of a large size. To overcome the computational challenge, this paper presents an environmental modeling framework using a sparse variant of GP called streaming sparse GP (SSGP). The SSGP is able to handle streaming data in an online and incremental manner, and is therefore suitable for long-term autonomous environmental monitoring. The SSGP summarizes the collected data using a small set of pseudo data points that best represent the whole dataset, and updates the hyperparameters and pseudo point locations in a streaming fashion, leading to high-quality approximation of the underlying environmental model with significantly reduced computational cost and memory demand.

If the aphorism "All models are wrong"- George Box, continues to be true in data analysis, particularly when analyzing real-world data, then we should annotate this wisdom with visible and explainable data-driven patterns. Such annotations can critically shed invaluable light on validity as well as limitations of statistical modeling as a data analysis approach. In an effort to avoid holding our real data to potentially unattainable or even unrealistic theoretical structures, we propose to utilize the data analysis paradigm called Categorical Exploratory Data Analysis (CEDA). We illustrate the merits of this proposal with two real-world data sets from the perspective of goodness-of-fit. In both data sets, the Normal distribution's bell shape seemingly fits rather well by first glance. We apply CEDA to bring out where and how each data fits or deviates from the model shape via several important distributional aspects. We also demonstrate that CEDA affords a version of tree-based p-value, and compare it with p-values based on traditional statistical approaches. Along our data analysis, we invest computational efforts in making graphic display to illuminate the advantages of using CEDA as one primary way of data analysis in Data Science education.

Mixture of Experts (MoE) is a popular framework for modeling heterogeneity in data for regression, classification and clustering. For continuous data which we consider here in the context of regression and cluster analysis, MoE usually use normal experts, that is, expert components following the Gaussian distribution. However, for a set of data containing a group or groups of observations with asymmetric behavior, heavy tails or atypical observations, the use of normal experts may be unsuitable and can unduly affect the fit of the MoE model. In this paper, we introduce new non-normal mixture of experts (NNMoE) which can deal with these issues regarding possibly skewed, heavy-tailed data and with outliers. The proposed models are the skew-normal MoE and the robust $t$ MoE and skew $t$ MoE, respectively named SNMoE, TMoE and STMoE. We develop dedicated expectation-maximization (EM) and expectation conditional maximization (ECM) algorithms to estimate the parameters of the proposed models by monotonically maximizing the observed data log-likelihood. We describe how the presented models can be used in prediction and in model-based clustering of regression data. Numerical experiments carried out on simulated data show the effectiveness and the robustness of the proposed models in terms modeling non-linear regression functions as well as in model-based clustering. Then, to show their usefulness for practical applications, the proposed models are applied to the real-world data of tone perception for musical data analysis, and the one of temperature anomalies for the analysis of climate change data.