Danny Panknin

Stefan Haufe, Rick Wilming, Benedict Clark et al.

The field of "explainable artificial intelligence" (XAI) seemingly addresses the desire that decisions of machine learning systems should be human-understandable. However, in its current state, XAI itself needs scrutiny. Popular methods cannot reliably answer relevant questions about ML models, their training data, or test inputs, because they systematically attribute importance to input features that are independent of the prediction target. This limits the utility of XAI for diagnosing and correcting data and models, for scientific discovery, and for identifying intervention targets. The fundamental reason for this is that current XAI methods do not address well-defined problems and are not evaluated against targeted criteria of explanation correctness. Researchers should formally define the problems they intend to solve and design methods accordingly. This will lead to diverse use-case-dependent notions of explanation correctness and objective metrics of explanation performance that can be used to validate XAI algorithms.

Benedict Clark, Rick Wilming, Artur Dox et al.

The evolving landscape of explainable artificial intelligence (XAI) aims to improve the interpretability of intricate machine learning (ML) models, yet faces challenges in formalisation and empirical validation, being an inherently unsupervised process. In this paper, we bring together various benchmark datasets and novel performance metrics in an initial benchmarking platform, the Explainable AI Comparison Toolkit (EXACT), providing a standardised foundation for evaluating XAI methods. Our datasets incorporate ground truth explanations for class-conditional features, and leveraging novel quantitative metrics, this platform assesses the performance of post-hoc XAI methods in the quality of the explanations they produce. Our recent findings have highlighted the limitations of popular XAI methods, as they often struggle to surpass random baselines, attributing significance to irrelevant features. Moreover, we show the variability in explanations derived from different equally performing model architectures. This initial benchmarking platform therefore aims to allow XAI researchers to test and assure the high quality of their newly developed methods.

Danny Panknin, Klaus Robert Müller, Shinichi Nakajima

We propose a novel active learning strategy for regression, which is model-agnostic, robust against model mismatch, and interpretable. Assuming that a small number of initial samples are available, we derive the optimal training density that minimizes the generalization error of local polynomial smoothing (LPS) with its kernel bandwidth tuned locally: We adopt the mean integrated squared error (MISE) as a generalization criterion, and use the asymptotic behavior of the MISE as well as the locally optimal bandwidths (LOB) - the bandwidth function that minimizes MISE in the asymptotic limit. The asymptotic expression of our objective then reveals the dependence of the MISE on the training density, enabling analytic minimization. As a result,we obtain the optimal training density in a closed-form. The almost model-free nature of our approach thus helps to encode the essential properties of the target problem, providing a robust and model-agnostic active learning strategy. Furthermore, the obtained training density factorizes the influence of local function complexity, noise level and test density in a transparent and interpretable way. We validate our theory in numerical simulations, and show that the proposed active learning method outperforms the existing state-of-the-art model-agnostic approaches.

Danny Panknin, Stefan Chmiela, Klaus-Robert Müller et al.

Inhomogeneities in real-world data, e.g., due to changes in the observation noise level or variations in the structural complexity of the source function, pose a unique set of challenges for statistical inference. Accounting for them can greatly improve predictive power when physical resources or computation time is limited. In this paper, we draw on recent theoretical results on the estimation of local function complexity (LFC), derived from the domain of local polynomial smoothing (LPS), to establish a notion of local structural complexity, which is used to develop a model-agnostic active learning (AL) framework. Due to its reliance on pointwise estimates, the LPS model class is not robust and scalable concerning large input space dimensions that typically come along with real-world problems. Here, we derive and estimate the Gaussian process regression (GPR)-based analog of the LPS-based LFC and use it as a substitute in the above framework to make it robust and scalable. We assess the effectiveness of our LFC estimate in an AL application on a prototypical low-dimensional synthetic dataset, before taking on the challenging real-world task of reconstructing a quantum chemical force field for a small organic molecule and demonstrating state-of-the-art performance with a significantly reduced training demand.

Wikor Pronobis, Danny Panknin, Johannes Kirschnick et al.

Locality sensitive hashing (LSH) is a powerful tool for sublinear-time approximate nearest neighbor search, and a variety of hashing schemes have been proposed for different dissimilarity measures. However, hash codes significantly depend on the dissimilarity, which prohibits users from adjusting the dissimilarity at query time. In this paper, we propose {multiple purpose LSH (mp-LSH) which shares the hash codes for different dissimilarities. mp-LSH supports L2, cosine, and inner product dissimilarities, and their corresponding weighted sums, where the weights can be adjusted at query time. It also allows us to modify the importance of pre-defined groups of features. Thus, mp-LSH enables us, for example, to retrieve similar items to a query with the user preference taken into account, to find a similar material to a query with some properties (stability, utility, etc.) optimized, and to turn on or off a part of multi-modal information (brightness, color, audio, text, etc.) in image/video retrieval. We theoretically and empirically analyze the performance of three variants of mp-LSH, and demonstrate their usefulness on real-world data sets.

Irene Winkler, Danny Panknin, Daniel Bartz et al.

Inferring causal interactions from observed data is a challenging problem, especially in the presence of measurement noise. To alleviate the problem of spurious causality, Haufe et al. (2013) proposed to contrast measures of information flow obtained on the original data against the same measures obtained on time-reversed data. They show that this procedure, time-reversed Granger causality (TRGC), robustly rejects causal interpretations on mixtures of independent signals. While promising results have been achieved in simulations, it was so far unknown whether time reversal leads to valid measures of information flow in the presence of true interaction. Here we prove that, for linear finite-order autoregressive processes with unidirectional information flow, the application of time reversal for testing Granger causality indeed leads to correct estimates of information flow and its directionality. Using simulations, we further show that TRGC is able to infer correct directionality with similar statistical power as the net Granger causality between two variables, while being much more robust to the presence of measurement noise.

Tammo Krueger, Danny Panknin, Mikio Braun

With the increasing size of today's data sets, finding the right parameter configuration in model selection via cross-validation can be an extremely time-consuming task. In this paper we propose an improved cross-validation procedure which uses nonparametric testing coupled with sequential analysis to determine the best parameter set on linearly increasing subsets of the data. By eliminating underperforming candidates quickly and keeping promising candidates as long as possible, the method speeds up the computation while preserving the capability of the full cross-validation. Theoretical considerations underline the statistical power of our procedure. The experimental evaluation shows that our method reduces the computation time by a factor of up to 120 compared to a full cross-validation with a negligible impact on the accuracy.