Recently, there has been a growing interest for mixed-categorical meta-models based on Gaussian process (GP) surrogates. In this setting, several existing approaches use different strategies either by using continuous kernels (e.g., continuous relaxation and Gower distance based GP) or by using a direct estimation of the correlation matrix. In this paper, we present a kernel-based approach that extends continuous exponential kernels to handle mixed-categorical variables. The proposed kernel leads to a new GP surrogate that generalizes both the continuous relaxation and the Gower distance based GP models. We demonstrate, on both analytical and engineering problems, that our proposed GP model gives a higher likelihood and a smaller residual error than the other kernel-based state-of-the-art models. Our method is available in the open-source software SMT.

In this paper we introduce MCCE: Monte Carlo sampling of realistic Counterfactual Explanations, a model-based method that generates counterfactual explanations by producing a set of feasible examples using conditional inference trees. Unlike algorithmic-based counterfactual methods that have to solve complex optimization problems or other model based methods that model the data distribution using heavy machine learning models, MCCE is made up of only two light-weight steps (generation and post-processing). MCCE is also straightforward for the end user to understand and implement, handles any type of predictive model and type of feature, takes into account actionability constraints when generating the counterfactual explanations, and generates as many counterfactual explanations as needed. In this paper we introduce MCCE and give a comprehensive list of performance metrics that can be used to compare counterfactual explanations. We also compare MCCE with a range of state-of-the-art methods and a new baseline method on benchmark data sets. MCCE outperforms all model-based methods and most algorithmic-based methods when also taking into account validity (i.e., a correctly changed prediction) and actionability constraints. Finally, we show that MCCE has the strength of performing almost as well when given just a small subset of the training data.

Clustering is an essential technique for discovering patterns in data. The steady increase in amount and complexity of data over the years led to improvements and development of new clustering algorithms. However, algorithms that can cluster data with mixed variable types (continuous and categorical) remain limited, despite the abundance of data with mixed types particularly in the medical field. Among existing methods for mixed data, some posit unverifiable distributional assumptions or that the contributions of different variable types are not well balanced. We propose a two-step hybrid density- and partition-based algorithm (HyDaP) that can detect clusters after variables selection. The first step involves both density-based and partition-based algorithms to identify the data structure formed by continuous variables and recognize the important variables for clustering; the second step involves partition-based algorithm together with a novel dissimilarity measure we designed for mixed data to obtain clustering results. Simulations across various scenarios and data structures were conducted to examine the performance of the HyDaP algorithm compared to commonly used methods. We also applied the HyDaP algorithm on electronic health records to identify sepsis phenotypes.

Distance is a numerical measurement of how far apart individuals are, i.e. a metrics used to measure proximity or similarity across individuals. Many distance metrics exist, and one is actually quite useful to crack our case, the Gower distance (1971). Gower distance is computed as the average of partial dissimilarities across individuals. Partial dissimilarities (d_ij f) computation depend on the type of variable being evaluated. This implies that a particular standardization will be applied to each feature, and the distance between two individuals is the average of all feature-specific distances.