A Functional Extension of Semi-Structured Networks

Semi-structured networks (SSNs) merge the structures familiar from additive models with deep neural networks, allowing the modeling of interpretable partial feature effects while capturing higher-order non-linearities at the same time. A significant challenge in this integration is maintaining the interpretability of the additive model component. Inspired by large-scale biomechanics datasets, this paper explores extending SSNs to functional data. Existing methods in functional data analysis are promising but often not expressive enough to account for all interactions and non-linearities and do not scale well to large datasets. Although the SSN approach presents a compelling potential solution, its adaptation to functional data remains complex. In this work, we propose a functional SSN method that retains the advantageous properties of classical functional regression approaches while also improving scalability. Our numerical experiments demonstrate that this approach accurately recovers underlying signals, enhances predictive performance, and performs favorably compared to competing methods.

Achieving interpretable machine learning by functional decomposition of black-box models into explainable predictor effects

Machine learning (ML) has seen significant growth in both popularity and importance. The high prediction accuracy of ML models is often achieved through complex black-box architectures that are difficult to interpret. This interpretability problem has been hindering the use of ML in fields like medicine, ecology and insurance, where an understanding of the inner workings of the model is paramount to ensure user acceptance and fairness. The need for interpretable ML models has boosted research in the field of interpretable machine learning (IML). Here we propose a novel approach for the functional decomposition of black-box predictions, which is considered a core concept of IML. The idea of our method is to replace the prediction function by a surrogate model consisting of simpler subfunctions. Similar to additive regression models, these functions provide insights into the direction and strength of the main feature contributions and their interactions. Our method is based on a novel concept termed stacked orthogonality, which ensures that the main effects capture as much functional behavior as possible and do not contain information explained by higher-order interactions. Unlike earlier functional IML approaches, it is neither affected by extrapolation nor by hidden feature interactions. To compute the subfunctions, we propose an algorithm based on neural additive modeling and an efficient post-hoc orthogonalization procedure.

How Inverse Conditional Flows Can Serve as a Substitute for Distributional Regression

Neural network representations of simple models, such as linear regression, are being studied increasingly to better understand the underlying principles of deep learning algorithms. However, neural representations of distributional regression models, such as the Cox model, have received little attention so far. We close this gap by proposing a framework for distributional regression using inverse flow transformations (DRIFT), which includes neural representations of the aforementioned models. We empirically demonstrate that the neural representations of models in DRIFT can serve as a substitute for their classical statistical counterparts in several applications involving continuous, ordered, time-series, and survival outcomes. We confirm that models in DRIFT empirically match the performance of several statistical methods in terms of estimation of partial effects, prediction, and aleatoric uncertainty quantification. DRIFT covers both interpretable statistical models and flexible neural networks opening up new avenues in both statistical modeling and deep learning.

Generalizing Orthogonalization for Models with Non-linearities

The complexity of black-box algorithms can lead to various challenges, including the introduction of biases. These biases present immediate risks in the algorithms' application. It was, for instance, shown that neural networks can deduce racial information solely from a patient's X-ray scan, a task beyond the capability of medical experts. If this fact is not known to the medical expert, automatic decision-making based on this algorithm could lead to prescribing a treatment (purely) based on racial information. While current methodologies allow for the "orthogonalization" or "normalization" of neural networks with respect to such information, existing approaches are grounded in linear models. Our paper advances the discourse by introducing corrections for non-linearities such as ReLU activations. Our approach also encompasses scalar and tensor-valued predictions, facilitating its integration into neural network architectures. Through extensive experiments, we validate our method's effectiveness in safeguarding sensitive data in generalized linear models, normalizing convolutional neural networks for metadata, and rectifying pre-existing embeddings for undesired attributes.

Position Paper: Rethinking Empirical Research in Machine Learning: Addressing Epistemic and Methodological Challenges of Experimentation

We warn against a common but incomplete understanding of empirical research in machine learning (ML) that leads to non-replicable results, makes findings unreliable, and threatens to undermine progress in the field. To overcome this alarming situation, we call for more awareness of the plurality of ways of gaining knowledge experimentally but also of some epistemic limitations. In particular, we argue most current empirical ML research is fashioned as confirmatory research while it should rather be considered exploratory.

Post-Training Network Compression for 3D Medical Image Segmentation: Reducing Computational Efforts via Tucker Decomposition

We address the computational barrier of deploying advanced deep learning segmentation models in clinical settings by studying the efficacy of network compression through tensor decomposition. We propose a post-training Tucker factorization that enables the decomposition of pre-existing models to reduce computational requirements without impeding segmentation accuracy. We applied Tucker decomposition to the convolutional kernels of the TotalSegmentator (TS) model, an nnU-Net model trained on a comprehensive dataset for automatic segmentation of 117 anatomical structures. Our approach reduced the floating-point operations (FLOPs) and memory required during inference, offering an adjustable trade-off between computational efficiency and segmentation quality. This study utilized the publicly available TS dataset, employing various downsampling factors to explore the relationship between model size, inference speed, and segmentation performance. The application of Tucker decomposition to the TS model substantially reduced the model parameters and FLOPs across various compression rates, with limited loss in segmentation accuracy. We removed up to 88% of the model's parameters with no significant performance changes in the majority of classes after fine-tuning. Practical benefits varied across different graphics processing unit (GPU) architectures, with more distinct speed-ups on less powerful hardware. Post-hoc network compression via Tucker decomposition presents a viable strategy for reducing the computational demand of medical image segmentation models without substantially sacrificing accuracy. This approach enables the broader adoption of advanced deep learning technologies in clinical practice, offering a way to navigate the constraints of hardware capabilities.

Training Survival Models using Scoring Rules

Survival Analysis provides critical insights for partially incomplete time-to-event data in various domains. It is also an important example of probabilistic machine learning. The probabilistic nature of the predictions can be exploited by using (proper) scoring rules in the model fitting process instead of likelihood-based optimization. Our proposal does so in a generic manner and can be used for a variety of model classes. We establish different parametric and non-parametric sub-frameworks that allow different degrees of flexibility. Incorporated into neural networks, it leads to a computationally efficient and scalable optimization routine, yielding state-of-the-art predictive performance. Finally, we show that using our framework, we can recover various parametric models and demonstrate that optimization works equally well when compared to likelihood-based methods.

Interpretable Machine Learning for TabPFN

The recently developed Prior-Data Fitted Networks (PFNs) have shown very promising results for applications in low-data regimes. The TabPFN model, a special case of PFNs for tabular data, is able to achieve state-of-the-art performance on a variety of classification tasks while producing posterior predictive distributions in mere seconds by in-context learning without the need for learning parameters or hyperparameter tuning. This makes TabPFN a very attractive option for a wide range of domain applications. However, a major drawback of the method is its lack of interpretability. Therefore, we propose several adaptations of popular interpretability methods that we specifically design for TabPFN. By taking advantage of the unique properties of the model, our adaptations allow for more efficient computations than existing implementations. In particular, we show how in-context learning facilitates the estimation of Shapley values by avoiding approximate retraining and enables the use of Leave-One-Covariate-Out (LOCO) even when working with large-scale Transformers. In addition, we demonstrate how data valuation methods can be used to address scalability challenges of TabPFN. Our proposed methods are implemented in a package tabpfn_iml and made available at https://github.com/david-rundel/tabpfn_iml.

Position Paper: Bayesian Deep Learning in the Age of Large-Scale AI

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

Scalable Higher-Order Tensor Product Spline Models

In the current era of vast data and transparent machine learning, it is essential for techniques to operate at a large scale while providing a clear mathematical comprehension of the internal workings of the method. Although there already exist interpretable semi-parametric regression methods for large-scale applications that take into account non-linearity in the data, the complexity of the models is still often limited. One of the main challenges is the absence of interactions in these models, which are left out for the sake of better interpretability but also due to impractical computational costs. To overcome this limitation, we propose a new approach using a factorization method to derive a highly scalable higher-order tensor product spline model. Our method allows for the incorporation of all (higher-order) interactions of non-linear feature effects while having computational costs proportional to a model without interactions. We further develop a meaningful penalization scheme and examine the induced optimization problem. We conclude by evaluating the predictive and estimation performance of our method.