We present working notes for DS@GT team in the eRisk 2024 for Tasks 1 and 3. We propose a ranking system for Task 1 that predicts symptoms of depression based on the Beck Depression Inventory (BDI-II) questionnaire using binary classifiers trained on question relevancy as a proxy for ranking. We find that binary classifiers are not well calibrated for ranking, and perform poorly during evaluation. For Task 3, we use embeddings from BERT to predict the severity of eating disorder symptoms based on user post history. We find that classical machine learning models perform well on the task, and end up competitive with the baseline models. Representation of text data is crucial in both tasks, and we find that sentence transformers are a powerful tool for downstream modeling.

Amyotrophic Lateral Sclerosis (ALS) is characterized as a rapidly progressive neurodegenerative disease that presents individuals with limited treatment options in the realm of medical interventions and therapies. The disease showcases a diverse range of onset patterns and progression trajectories, emphasizing the critical importance of early detection of functional decline to enable tailored care strategies and timely therapeutic interventions. The present investigation, spearheaded by the iDPP@CLEF 2024 challenge, focuses on utilizing sensor-derived data obtained through an app. This data is used to construct various machine learning models specifically designed to forecast the advancement of the ALS Functional Rating Scale-Revised (ALSFRS-R) score, leveraging the dataset provided by the organizers. In our analysis, multiple predictive models were evaluated to determine their efficacy in handling ALS sensor data. The temporal aspect of the sensor data was compressed and amalgamated using statistical methods, thereby augmenting the interpretability and applicability of the gathered information for predictive modeling objectives. The models that demonstrated optimal performance were a naive baseline and ElasticNet regression. The naive model achieved a Mean Absolute Error (MAE) of 0.20 and a Root Mean Square Error (RMSE) of 0.49, slightly outperforming the ElasticNet model, which recorded an MAE of 0.22 and an RMSE of 0.50. Our comparative analysis suggests that while the naive approach yielded marginally better predictive accuracy, the ElasticNet model provides a robust framework for understanding feature contributions.

Learning rate schedulers have shown great success in speeding up the convergence of learning algorithms in practice. However, their convergence to a minimum has not been proven theoretically. This difficulty mainly arises from the fact that, while traditional convergence analysis prescribes to monotonically decreasing (or constant) learning rates, schedulers opt for rates that often increase and decrease through the training epochs. In this work, we aim to bridge the gap by proposing a probabilistic learning rate scheduler (PLRS), that does not conform to the monotonically decreasing condition, with provable convergence guarantees. In addition to providing detailed convergence proofs, we also show experimental results where the proposed PLRS performs competitively as other state-of-the-art learning rate schedulers across a variety of datasets and architectures.

Federated learning is one popular paradigm to train a joint model in a distributed, privacy-preserving environment. But partial annotations pose an obstacle meaning that categories of labels are heterogeneous over clients. We propose to learn a joint backbone in a federated manner, while each site receives its own multi-label segmentation head. By using Bayesian techniques we observe that the different segmentation heads although only trained on the individual client's labels also learn information about the other labels not present at the respective site. This information is encoded in their predictive uncertainty. To obtain a final prediction we leverage this uncertainty and perform a weighted averaging of the ensemble of distributed segmentation heads, which allows us to segment "locally unknown" structures. With our method, which we refer to as FUNAvg, we are even on-par with the models trained and tested on the same dataset on average.

Approximate nearest neighbor search (ANNS) in high-dimensional spaces is a pivotal challenge in the field of machine learning. In recent years, graph-based methods have emerged as the superior approach to ANNS, establishing a new state of the art. Although various optimizations for graph-based ANNS have been introduced, they predominantly rely on heuristic methods that lack formal theoretical backing. This paper aims to enhance routing within graph-based ANNS by introducing a method that offers a probabilistic guarantee when exploring a node's neighbors in the graph. We formulate the problem as probabilistic routing and develop two baseline strategies by incorporating locality-sensitive techniques. Subsequently, we introduce PEOs, a novel approach that efficiently identifies which neighbors in the graph should be considered for exact distance calculation, thus significantly improving efficiency in practice. Our experiments demonstrate that equipping PEOs can increase throughput on commonly utilized graph indexes (HNSW and NSSG) by a factor of 1.6 to 2.5, and its efficiency consistently outperforms the leading-edge routing technique by 1.1 to 1.4 times.

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.

This paper presents a comprehensive study on the convergence rates of the stochastic gradient descent (SGD) algorithm when applied to overparameterized two-layer neural networks. Our approach combines the Neural Tangent Kernel (NTK) approximation with convergence analysis in the Reproducing Kernel Hilbert Space (RKHS) generated by NTK, aiming to provide a deep understanding of the convergence behavior of SGD in overparameterized two-layer neural networks. Our research framework enables us to explore the intricate interplay between kernel methods and optimization processes, shedding light on the optimization dynamics and convergence properties of neural networks. In this study, we establish sharp convergence rates for the last iterate of the SGD algorithm in overparameterized two-layer neural networks. Additionally, we have made significant advancements in relaxing the constraints on the number of neurons, which have been reduced from exponential dependence to polynomial dependence on the sample size or number of iterations. This improvement allows for more flexibility in the design and scaling of neural networks, and will deepen our theoretical understanding of neural network models trained with SGD.

Hyperspherical Prototypical Learning (HPL) is a supervised approach to representation learning that designs class prototypes on the unit hypersphere. The prototypes bias the representations to class separation in a scale invariant and known geometry. Previous approaches to HPL have either of the following shortcomings: (i) they follow an unprincipled optimisation procedure; or (ii) they are theoretically sound, but are constrained to only one possible latent dimension. In this paper, we address both shortcomings. To address (i), we present a principled optimisation procedure whose solution we show is optimal. To address (ii), we construct well-separated prototypes in a wide range of dimensions using linear block codes. Additionally, we give a full characterisation of the optimal prototype placement in terms of achievable and converse bounds, showing that our proposed methods are near-optimal.

Kernels are a fundamental technical primitive in machine learning. In recent years, kernel-based methods such as Gaussian processes are becoming increasingly important in applications where quantifying uncertainty is of key interest. In settings that involve structured data defined on graphs, meshes, manifolds, or other related spaces, defining kernels with good uncertainty-quantification behavior, and computing their value numerically, is less straightforward than in the Euclidean setting. To address this difficulty, we present GeometricKernels, a software package which implements the geometric analogs of classical Euclidean squared exponential - also known as heat - and Mat\'ern kernels, which are widely-used in settings where uncertainty is of key interest. As a byproduct, we obtain the ability to compute Fourier-feature-type expansions, which are widely used in their own right, on a wide set of geometric spaces. Our implementation supports automatic differentiation in every major current framework simultaneously via a backend-agnostic design. In this companion paper to the package and its documentation, we outline the capabilities of the package and present an illustrated example of its interface. We also include a brief overview of the theory the package is built upon and provide some historic context in the appendix.

Low-discrepancy points (also called Quasi-Monte Carlo points) are deterministically and cleverly chosen point sets in the unit cube, which provide an approximation of the uniform distribution. We explore two methods based on such low-discrepancy points to reduce large data sets in order to train neural networks. The first one is the method of Dick and Feischl [4], which relies on digital nets and an averaging procedure. Motivated by our experimental findings, we construct a second method, which again uses digital nets, but Voronoi clustering instead of averaging. Both methods are compared to the supercompress approach of [14], which is a variant of the K-means clustering algorithm. The comparison is done in terms of the compression error for different objective functions and the accuracy of the training of a neural network.