In open-set semi-supervised learning (OSSL), we consider unlabeled datasets that may contain unknown classes. Existing OSSL methods often use the softmax confidence for classifying data as in-distribution (ID) or out-of-distribution (OOD). Additionally, many works for OSSL rely on ad-hoc thresholds for ID/OOD classification, without considering the statistics of the problem. We propose a new score for ID/OOD classification based on angles in feature space between data and an ID subspace. Moreover, we propose an approach to estimate the conditional distributions of scores given ID or OOD data, enabling probabilistic predictions of data being ID or OOD. These components are put together in a framework for OSSL, termed \emph{ProSub}, that is experimentally shown to reach SOTA performance on several benchmark problems. Our code is available at https://github.com/walline/prosub.

In this paper, we revisit \textsf{ROOT-SGD}, an innovative method for stochastic optimization to bridge the gap between stochastic optimization and statistical efficiency. The proposed method enhances the performance and reliability of \textsf{ROOT-SGD} by integrating a carefully designed \emph{diminishing stepsize strategy}. This approach addresses key challenges in optimization, providing robust theoretical guarantees and practical benefits. Our analysis demonstrates that \textsf{ROOT-SGD} with diminishing achieves optimal convergence rates while maintaining computational efficiency. By dynamically adjusting the learning rate, \textsf{ROOT-SGD} ensures improved stability and precision throughout the optimization process. The findings of this study offer valuable insights for developing advanced optimization algorithms that are both efficient and statistically robust.

We propose a deep generative approach using latent temporal processes for modeling and holistically analyzing complex disease trajectories, with a particular focus on Systemic Sclerosis (SSc). We aim to learn temporal latent representations of the underlying generative process that explain the observed patient disease trajectories in an interpretable and comprehensive way. To enhance the interpretability of these latent temporal processes, we develop a semi-supervised approach for disentangling the latent space using established medical knowledge. By combining the generative approach with medical definitions of different characteristics of SSc, we facilitate the discovery of new aspects of the disease. We show that the learned temporal latent processes can be utilized for further data analysis and clinical hypothesis testing, including finding similar patients and clustering SSc patient trajectories into novel sub-types. Moreover, our method enables personalized online monitoring and prediction of multivariate time series with uncertainty quantification.

In this paper, we present a new ensemble-based filter method by reconstructing the analysis step of the particle filter through a transport map, which directly transports prior particles to posterior particles. The transport map is constructed through an optimization problem described by the Maximum Mean Discrepancy loss function, which matches the expectation information of the approximated posterior and reference posterior. The proposed method inherits the accurate estimation of the posterior distribution from particle filtering. To improve the robustness of Maximum Mean Discrepancy, a variance penalty term is used to guide the optimization. It prioritizes minimizing the discrepancy between the expectations of highly informative statistics for the approximated and reference posteriors. The penalty term significantly enhances the robustness of the proposed method and leads to a better approximation of the posterior. A few numerical examples are presented to illustrate the advantage of the proposed method over the ensemble Kalman filter.

We present a unified theory for Mahalanobis-type anomaly detection on Banach spaces, using ideas from Cameron-Martin theory applied to non-Gaussian measures. This approach leads to a basis-free, data-driven notion of anomaly distance through the so-called variance norm of a probability measure, which can be consistently estimated using empirical measures. Our framework generalizes the classical $\mathbb{R}^d$, functional $(L^2[0,1])^d$, and kernelized settings, including the general case of non-injective covariance operator. We prove that the variance norm depends solely on the inner product in a given Hilbert space, and hence that the kernelized Mahalanobis distance can naturally be recovered by working on reproducing kernel Hilbert spaces. Using the variance norm, we introduce the notion of a kernelized nearest-neighbour Mahalanobis distance for semi-supervised anomaly detection. In an empirical study on 12 real-world datasets, we demonstrate that the kernelized nearest-neighbour Mahalanobis distance outperforms the traditional kernelized Mahalanobis distance for multivariate time series anomaly detection, using state-of-the-art time series kernels such as the signature, global alignment, and Volterra reservoir kernels. Moreover, we provide an initial theoretical justification of nearest-neighbour Mahalanobis distances by developing concentration inequalities in the finite-dimensional Gaussian case.

Natural gas demand is a crucial factor for predicting natural gas prices and thus has a direct influence on the power system. However, existing methods face challenges in assessing the impact of shocks, such as the outbreak of the Russian-Ukrainian war. In this context, we apply deep neural network-based Granger causality to identify important drivers of natural gas demand. Furthermore, the resulting dependencies are used to construct a counterfactual case without the outbreak of the war, providing a quantifiable estimate of the overall effect of the shock on various German energy sectors. The code and dataset are available at https://github.com/bonaldli/CausalEnergy.

Herein the topics of (natural) gradient descent, data decorrelation, and approximate methods for backpropagation are brought into a dialogue. Natural gradient descent illuminates how gradient vectors, pointing at directions of steepest descent, can be improved by considering the local curvature of loss landscapes. We extend this perspective and show that to fully solve the problem illuminated by natural gradients in neural networks, one must recognise that correlations in the data at any linear transformation, including node responses at every layer of a neural network, cause a non-orthonormal relationship between the model's parameters. To solve this requires a solution to decorrelate inputs at each individual layer of a neural network. We describe a range of methods which have been proposed for decorrelation and whitening of node output, while providing a novel method specifically useful for distributed computing and computational neuroscience. Implementing decorrelation within multi-layer neural networks, we can show that not only is training via backpropagation sped up significantly but also existing approximations of backpropagation, which have failed catastrophically in the past, are made performant once more. This has the potential to provide a route forward for approximate gradient descent methods which have previously been discarded, training approaches for analogue and neuromorphic hardware, and potentially insights as to the efficacy and utility of decorrelation processes in the brain.

Many real-world graphs frequently present challenges for graph learning due to the presence of both heterophily and heterogeneity. However, existing benchmarks for graph learning often focus on heterogeneous graphs with homophily or homogeneous graphs with heterophily, leaving a gap in understanding how methods perform on graphs that are both heterogeneous and heterophilic. To bridge this gap, we introduce H2GB, a novel graph benchmark that brings together the complexities of both the heterophily and heterogeneity properties of graphs. Our benchmark encompasses 9 diverse real-world datasets across 5 domains, 28 baseline model implementations, and 26 benchmark results. In addition, we present a modular graph transformer framework UnifiedGT and a new model variant, H2G-former, that excels at this challenging benchmark. By integrating masked label embeddings, cross-type heterogeneous attention, and type-specific FFNs, H2G-former effectively tackles graph heterophily and heterogeneity. Extensive experiments across 26 baselines on H2GB reveal inadequacies of current models on heterogeneous heterophilic graph learning, and demonstrate the superiority of our H2G-former over existing solutions. Both the benchmark and the framework are available on GitHub (https://github.com/junhongmit/H2GB) and PyPI (https://pypi.org/project/H2GB), and documentation can be found at https://junhongmit.github.io/H2GB/.

The use of DMs has grown to become the method of choice for image generation. A central problem in machine learning (ML) is how to train a model to efficiently generate samples from a The standard formulation of DMs in terms of Brownian probability distribution of interest [1, 2]. Two typical motion and stochastic differential equations presents scenarios are where this target distribution is only known three main challenges. The first one is the estimation through sampled data, or where relative probabilities are of the denoising SDE via the score [9], which has to be known but the overall normalisation is not [3]. There learned as a function over the whole domain of the target are many ML strategies to address this problem, a subset probability from sparse and high dimensional training of which is based on the idea that a model can be data. The second one is how to resolve the "mismatch trained to transform a "noise" distribution (such as a in time" [12]: under Brownian dynamics the mapping Gaussian) into a non-trivial distribution of interest over from the target distribution to a noisy Gaussian happens the same domain, in such a way that (easily extractable) only asymptotically, while in practice the denoising noise samples from the first distribution can be transformed process is run over finite times, thus incurring in a reconstruction into (difficult to generate) samples of the target error. The third challenge is how to precisely one. This is the general approach of both "normalising estimate the likelihood of generated configurations from flows" [4-6], and of the so-called diffusion models [7-10] the learned score.

Binding affinity optimization is crucial in early-stage drug discovery. While numerous machine learning methods exist for predicting ligand potency, their comparative efficacy remains unclear. This study evaluates the performance of classical tree-based models and advanced neural networks in protein-ligand binding affinity prediction. Our comprehensive benchmarking encompasses 2D models utilizing ligand-only RDKit embeddings and Large Language Model (LLM) ligand representations, as well as 3D neural networks incorporating bound protein-ligand conformations. We assess these models across multiple standard datasets, examining various predictive scenarios including classification, ranking, regression, and active learning. Results indicate that simpler models can surpass more complex ones in specific tasks, while 3D models leveraging structural information become increasingly competitive with larger training datasets containing compounds with labelled affinity data against multiple targets. Pre-trained 3D models, by incorporating protein pocket environments, demonstrate significant advantages in data-scarce scenarios for specific binding pockets. Additionally, LLM pretraining on 2D ligand data enhances complex model performance, providing versatile embeddings that outperform traditional RDKit features in computational efficiency. Finally, we show that combining 2D and 3D model strengths improves active learning outcomes beyond current state-of-the-art approaches. These findings offer valuable insights for optimizing machine learning strategies in drug discovery pipelines.