GT-PCA: Effective and Interpretable Dimensionality Reduction with General Transform-Invariant Principal Component Analysis

Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used dimension reduction technique, it lacks robustness with respect to these transformations. Modern alternatives, such as autoencoders, can be invariant with respect to specific transformations but are generally not interpretable. We introduce General Transform-Invariant Principal Component Analysis (GT-PCA) as an effective and interpretable alternative to PCA and autoencoders. We propose a neural network that efficiently estimates the components and show that GT-PCA significantly outperforms alternative methods in experiments based on synthetic and real data.

Monitoring Machine Learning Models: Online Detection of Relevant Deviations

Machine learning models are essential tools in various domains, but their performance can degrade over time due to changes in data distribution or other factors. On one hand, detecting and addressing such degradations is crucial for maintaining the models' reliability. On the other hand, given enough data, any arbitrary small change of quality can be detected. As interventions, such as model re-training or replacement, can be expensive, we argue that they should only be carried out when changes exceed a given threshold. We propose a sequential monitoring scheme to detect these relevant changes. The proposed method reduces unnecessary alerts and overcomes the multiple testing problem by accounting for temporal dependence of the measured model quality. Conditions for consistency and specified asymptotic levels are provided. Empirical validation using simulated and real data demonstrates the superiority of our approach in detecting relevant changes in model quality compared to benchmark methods. Our research contributes a practical solution for distinguishing between minor fluctuations and meaningful degradations in machine learning model performance, ensuring their reliability in dynamic environments.

Functional Neural Networks: Shift invariant models for functional data with applications to EEG classification

It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of neural networks that are shift invariant and preserve smoothness of the data: functional neural networks (FNNs). For this, we use methods from functional data analysis (FDA) to extend multi-layer perceptrons and convolutional neural networks to functional data. We propose different model architectures, show that the models outperform a benchmark model from FDA in terms of accuracy and successfully use FNNs to classify electroencephalography (EEG) data.