Vasilis Gkolemis

Vasilis Gkolemis, Theodore Dalamagas, Christos Diou

Accumulated Local Effect (ALE) is a method for accurately estimating feature effects, overcoming fundamental failure modes of previously-existed methods, such as Partial Dependence Plots. However, ALE's approximation, i.e. the method for estimating ALE from the limited samples of the training set, faces two weaknesses. First, it does not scale well in cases where the input has high dimensionality, and, second, it is vulnerable to out-of-distribution (OOD) sampling when the training set is relatively small. In this paper, we propose a novel ALE approximation, called Differential Accumulated Local Effects (DALE), which can be used in cases where the ML model is differentiable and an auto-differentiable framework is accessible. Our proposal has significant computational advantages, making feature effect estimation applicable to high-dimensional Machine Learning scenarios with near-zero computational overhead. Furthermore, DALE does not create artificial points for calculating the feature effect, resolving misleading estimations due to OOD sampling. Finally, we formally prove that, under some hypotheses, DALE is an unbiased estimator of ALE and we present a method for quantifying the standard error of the explanation. Experiments using both synthetic and real datasets demonstrate the value of the proposed approach.

Vasilis Gkolemis, Theodore Dalamagas, Eirini Ntoutsi et al.

Accumulated Local Effects (ALE) is a widely-used explainability method for isolating the average effect of a feature on the output, because it handles cases with correlated features well. However, it has two limitations. First, it does not quantify the deviation of instance-level (local) effects from the average (global) effect, known as heterogeneity. Second, for estimating the average effect, it partitions the feature domain into user-defined, fixed-sized bins, where different bin sizes may lead to inconsistent ALE estimations. To address these limitations, we propose Robust and Heterogeneity-aware ALE (RHALE). RHALE quantifies the heterogeneity by considering the standard deviation of the local effects and automatically determines an optimal variable-size bin-splitting. In this paper, we prove that to achieve an unbiased approximation of the standard deviation of local effects within each bin, bin splitting must follow a set of sufficient conditions. Based on these conditions, we propose an algorithm that automatically determines the optimal partitioning, balancing the estimation bias and variance. Through evaluations on synthetic and real datasets, we demonstrate the superiority of RHALE compared to other methods, including the advantages of automatic bin splitting, especially in cases with correlated features.

Vasilis Gkolemis, Anargiros Tzerefos, Theodore Dalamagas et al.

Generalized Additive Models (GAMs) are widely used explainable-by-design models in various applications. GAMs assume that the output can be represented as a sum of univariate functions, referred to as components. However, this assumption fails in ML problems where the output depends on multiple features simultaneously. In these cases, GAMs fail to capture the interaction terms of the underlying function, leading to subpar accuracy. To (partially) address this issue, we propose Regionally Additive Models (RAMs), a novel class of explainable-by-design models. RAMs identify subregions within the feature space where interactions are minimized. Within these regions, it is more accurate to express the output as a sum of univariate functions (components). Consequently, RAMs fit one component per subregion of each feature instead of one component per feature. This approach yields a more expressive model compared to GAMs while retaining interpretability. The RAM framework consists of three steps. Firstly, we train a black-box model. Secondly, using Regional Effect Plots, we identify subregions where the black-box model exhibits near-local additivity. Lastly, we fit a GAM component for each identified subregion. We validate the effectiveness of RAMs through experiments on both synthetic and real-world datasets. The results confirm that RAMs offer improved expressiveness compared to GAMs while maintaining interpretability.

Vasilis Gkolemis, Michael Gutmann, Henri Pesonen

Performing inference in statistical models with an intractable likelihood is challenging, therefore, most likelihood-free inference (LFI) methods encounter accuracy and efficiency limitations. In this paper, we present the implementation of the LFI method Robust Optimisation Monte Carlo (ROMC) in the Python package ELFI. ROMC is a novel and efficient (highly-parallelizable) LFI framework that provides accurate weighted samples from the posterior. Our implementation can be used in two ways. First, a scientist may use it as an out-of-the-box LFI algorithm; we provide an easy-to-use API harmonized with the principles of ELFI, enabling effortless comparisons with the rest of the methods included in the package. Additionally, we have carefully split ROMC into isolated components for supporting extensibility. A researcher may experiment with novel method(s) for solving part(s) of ROMC without reimplementing everything from scratch. In both scenarios, the ROMC parts can run in a fully-parallelized manner, exploiting all CPU cores. We also provide helpful functionalities for (i) inspecting the inference process and (ii) evaluating the obtained samples. Finally, we test the robustness of our implementation on some typical LFI examples.

Vasilis Gkolemis, Christos Diou, Dimitris Kyriakopoulos et al.

Effector is a Python package for interpreting machine learning (ML) models that are trained on tabular data through global and regional feature effects. Global effects, like Partial Dependence Plot (PDP) and Accumulated Local Effects (ALE), are widely used for explaining tabular ML models due to their simplicity -- each feature's average influence on the prediction is summarized by a single 1D plot. However, when features are interacting, global effects can be misleading. Regional effects address this by partitioning the input space into disjoint subregions with minimal interactions within each and computing a separate regional effect per subspace. Regional effects are then visualized by a set of 1D plots per feature. Effector provides efficient implementations of state-of-the-art global and regional feature effects methods under a unified API. The package integrates seamlessly with major ML libraries like scikit-learn and PyTorch. It is designed to be modular and extensible, and comes with comprehensive documentation and tutorials. Effector is an open-source project publicly available on Github at https://github.com/givasile/effector.

Vasilis Gkolemis, Loukas Kavouras, Dimitrios Kyriakopoulos et al.

Generalized additive models (GAMs) offer interpretability through independent univariate feature effects but underfit when interactions are present in data. GA$^2$Ms add selected pairwise interactions which improves accuracy, but sacrifices interpretability and limits model auditing. We propose \emph{Conditionally Additive Local Models} (CALMs), a new model class, that balances the interpretability of GAMs with the accuracy of GA$^2$Ms. CALMs allow multiple univariate shape functions per feature, each active in different regions of the input space. These regions are defined independently for each feature as simple logical conditions (thresholds) on the features it interacts with. As a result, effects remain locally additive while varying across subregions to capture interactions. We further propose a principled distillation-based training pipeline that identifies homogeneous regions with limited interactions and fits interpretable shape functions via region-aware backfitting. Experiments on diverse classification and regression tasks show that CALMs consistently outperform GAMs and achieve accuracy comparable with GA$^2$Ms. Overall, CALMs offer a compelling trade-off between predictive accuracy and interpretability.

Vasilis Gkolemis, Christos Diou, Michael Gutmann

Bayesian parameter inference for complex stochastic simulators is challenging due to intractable likelihood functions. Existing simulation-based inference methods often require large number of simulations and become costly to use in high-dimensional parameter spaces or in problems with partially uninformative outputs. We propose a new method for differentiable simulators that delivers accurate posterior inference with substantially reduced runtimes. Building on the Optimization Monte Carlo framework, our approach reformulates stochastic simulation as deterministic optimization problems. Gradient-based methods are then applied to efficiently navigate toward high-density posterior regions and avoid wasteful simulations in low-probability areas. A JAX-based implementation further enhances the performance through vectorization of key method components. Extensive experiments, including high-dimensional parameter spaces, uninformative outputs, multiple observations and multimodal posteriors show that our method consistently matches, and often exceeds, the accuracy of state-of-the-art approaches, while reducing the runtime by a substantial margin.