Majority subspace clustering (SC) algorithms depend on one or more hyperparameters that need to be carefully tuned for the SC algorithms to achieve high clustering performance. Hyperparameter optimization (HPO) is often performed using grid-search, assuming that some labeled data is available. In some domains, such as medicine, this assumption does not hold true in many cases. One avenue of research focuses on developing SC algorithms that are inherently free of hyperparameters. For hyperparameters-dependent SC algorithms, one approach to label-independent HPO tuning is based on internal clustering quality metrics (if available), whose performance should ideally match that of external (label-dependent) clustering quality metrics. In this paper, we propose a novel approach to label-independent HPO that uses clustering quality metrics, such as accuracy (ACC) or normalized mutual information (NMI), that are computed based on pseudo-labels obtained from the SC algorithm across a predefined grid of hyperparameters. Assuming that ACC (or NMI) is a smooth function of hyperparameter values it is possible to select subintervals of hyperparameters. These subintervals are then iteratively further split into halves or thirds until a relative error criterion is satisfied. In principle, the hyperparameters of any SC algorithm can be tuned using the proposed method. We demonstrate this approach on several single- and multi-view SC algorithms, comparing the achieved performance with their oracle versions across six datasets representing digits, faces and objects. The proposed method typically achieves clustering performance that is 5% to 7% lower than that of the oracle versions. We also make our proposed method interpretable by visualizing subspace bases, which are estimated from the computed clustering partitions. This aids in the initial selection of the hyperparameter search space.

Neural collapse, a newly identified characteristic, describes a property of solutions during model training. In this paper, we explore neural collapse in the context of imbalanced data. We consider the $L$-extended unconstrained feature model with a bias term and provide a theoretical analysis of global minimizer. Our findings include: (1) Features within the same class converge to their class mean, similar to both the balanced case and the imbalanced case without bias. (2) The geometric structure is mainly on the left orthonormal transformation of the product of $L$ linear classifiers and the right transformation of the class-mean matrix. (3) Some rows of the left orthonormal transformation of the product of $L$ linear classifiers collapse to zeros and others are orthogonal, which relies on the singular values of $\hat Y=(I_K-1/N\mathbf{n}1^\top_K)D$, where $K$ is class size, $\mathbf{n}$ is the vector of sample size for each class, $D$ is the diagonal matrix whose diagonal entries are given by $\sqrt{\mathbf{n}}$. Similar results are for the columns of the right orthonormal transformation of the product of class-mean matrix and $D$. (4) The $i$-th row of the left orthonormal transformation of the product of $L$ linear classifiers aligns with the $i$-th column of the right orthonormal transformation of the product of class-mean matrix and $D$. (5) We provide the estimation of singular values about $\hat Y$. Our numerical experiments support these theoretical findings.

Realised volatility has become increasingly prominent in volatility forecasting due to its ability to capture intraday price fluctuations. With a growing variety of realised volatility estimators, each with unique advantages and limitations, selecting an optimal estimator may introduce challenges. In this thesis, aiming to synthesise the impact of various realised volatility measures on volatility forecasting, we propose an extension of the Realised GARCH model that incorporates an autoencoder-generated synthetic realised measure, combining the information from multiple realised measures in a nonlinear manner. Our proposed model extends existing linear methods, such as Principal Component Analysis and Independent Component Analysis, to reduce the dimensionality of realised measures. The empirical evaluation, conducted across four major stock markets from January 2000 to June 2022 and including the period of COVID-19, demonstrates both the feasibility of applying an autoencoder to synthesise volatility measures and the superior effectiveness of the proposed model in one-step-ahead rolling volatility forecasting. The model exhibits enhanced flexibility in parameter estimations across each rolling window, outperforming traditional linear approaches. These findings indicate that nonlinear dimension reduction offers further adaptability and flexibility in improving the synthetic realised measure, with promising implications for future volatility forecasting applications.

These authors contributed equally to this work. Noisy labels pose a substantial challenge in machine learning, often resulting in overfitting and poor generalization. Sharpness-Aware Minimization (SAM), as demonstrated by Foret et al. (2021), improves generalization over traditional Stochastic Gradient Descent (SGD) in classification tasks with noisy labels by implicitly slowing noisy learning. While SAM's ability to generalize in noisy environments has been studied in several simplified settings, its full potential in more realistic training settings remains underexplored. In this work, we analyze SAM's behavior at each iteration, identifying specific components of the gradient vector that contribute significantly to its robustness against noisy labels. Based on these insights, we propose SANER (Sharpness-Aware Noise-Explicit Reweighting), an effective variant that enhances SAM's ability to manage noisy fitting rate. Our experiments on CIFAR-10, CIFAR-100, and Mini-WebVision demonstrate that SANER consistently outperforms SAM, achieving up to an 8% increase on CIFAR-100 with 50% label noise. The issue of noisy labels due to human error annotation has been commonly observed in many largescale datasets such as CIFAR-10N, CIFAR-100N (Wei et al., 2022), Clothing1M (Xiao et al., 2015), and WebVision (Li et al., 2017). Over-parameterized deep neural networks, which have enough capacity to memorize entire large datasets, can easily overfit such noisy label data, leading to poor generalization performance (Zhang et al., 2021). Moreover, the lottery ticket hypothesis (Frankle & Carbin, 2019) indicates that only a subset of the network's parameters is crucial for generalization. This highlights the importance of noise-robust learning, where the goal is to train a robust classifier despite the presence of inaccurate or noisy labels in the training dataset. Sharpness-Aware Minimization (SAM), introduced by Foret et al. (2021), is an optimizer designed to find better generalization by searching for flat minima. It has shown superior performance over SGD in various tasks, especially in classification tasks involving noisy labels Baek et al. (2024). Understanding the mechanisms behind the success of SAM is crucial for further improvements in handling label noise.

While crowdsourcing has emerged as a practical solution for labeling large datasets, it presents a significant challenge in learning accurate models due to noisy labels from annotators with varying levels of expertise. Existing methods typically estimate the true label posterior, conditioned on the instance and noisy annotations, to infer true labels or adjust loss functions. These estimates, however, often overlook potential misspecification in the true label posterior, which can degrade model performances, especially in high-noise scenarios. To address this issue, we investigate learning from noisy annotations with an estimated true label posterior through the framework of conditional distributionally robust optimization (CDRO). We propose formulating the problem as minimizing the worst-case risk within a distance-based ambiguity set centered around a reference distribution. By examining the strong duality of the formulation, we derive upper bounds for the worst-case risk and develop an analytical solution for the dual robust risk for each data point. This leads to a novel robust pseudo-labeling algorithm that leverages the likelihood ratio test to construct a pseudo-empirical distribution, providing a robust reference probability distribution in CDRO. Moreover, to devise an efficient algorithm for CDRO, we derive a closed-form expression for the empirical robust risk and the optimal Lagrange multiplier of the dual problem, facilitating a principled balance between robustness and model fitting. Our experimental results on both synthetic and real-world datasets demonstrate the superiority of our method.

Robust medical Machine Learning (ML) models have the potential to revolutionize healthcare by accelerating clinical research, improving workflows and outcomes, and producing novel insights or capabilities. Developing such ML models from scratch is cost prohibitive and requires substantial compute, data, and time (e.g., expert labeling). To address these challenges, we introduce Health AI Developer Foundations (HAI-DEF), a suite of pre-trained, domain-specific foundation models, tools, and recipes to accelerate building ML for health applications. The models cover various modalities and domains, including radiology (X-rays and computed tomography), histopathology, dermatological imaging, and audio. These models provide domain specific embeddings that facilitate AI development with less labeled data, shorter training times, and reduced computational costs compared to traditional approaches. In addition, we utilize a common interface and style across these models, and prioritize usability to enable developers to integrate HAI-DEF efficiently. We present model evaluations across various tasks and conclude with a discussion of their application and evaluation, covering the importance of ensuring efficacy, fairness, and equity. Finally, while HAI-DEF and specifically the foundation models lower the barrier to entry for ML in healthcare, we emphasize the importance of validation with problem- and population-specific data for each desired usage setting. This technical report will be updated over time as more modalities and features are added.

In this position paper, we propose an approach for sustainable data collection in the field of optimal mix design for marble sludge reuse. Marble sludge, a calcium-rich residual from stone-cutting processes, can be repurposed by mixing it with various ingredients. However, determining the optimal mix design is challenging due to the variability in sludge composition and the costly, time-consuming nature of experimental data collection. Also, we investigate the possibility of using machine learning models using meta-learning as an optimization tool to estimate the correct quantity of stone-cutting sludge to be used in aggregates to obtain a mix design with specific mechanical properties that can be used successfully in the building industry. Our approach offers two key advantages: (i) through simulations, a large dataset can be generated, saving time and money during the data collection phase, and (ii) Utilizing machine learning models, with performance enhancement through hyper-parameter optimization via meta-learning, to estimate optimal mix designs reducing the need for extensive manual experimentation, lowering costs, minimizing environmental impact, and accelerating the processing of quarry sludge. Our idea promises to streamline the marble sludge reuse process by leveraging collective data and advanced machine learning, promoting sustainability and efficiency in the stonecutting sector.

Federated Learning (FL) is a distributed machine learning paradigm that achieves a globally robust model through decentralized computation and periodic model synthesis, primarily focusing on the global model's accuracy over aggregated datasets of all participating clients. Personalized Federated Learning (PFL) instead tailors exclusive models for each client, aiming to enhance the accuracy of clients' individual models on specific local data distributions. Despite of their wide adoption, existing FL and PFL works have yet to comprehensively address the class-imbalance issue, one of the most critical challenges within the realm of data heterogeneity in PFL and FL research. In this paper, we propose FedReMa, an efficient PFL algorithm that can tackle class-imbalance by 1) utilizing an adaptive inter-client co-learning approach to identify and harness different clients' expertise on different data classes throughout various phases of the training process, and 2) employing distinct aggregation methods for clients' feature extractors and classifiers, with the choices informed by the different roles and implications of these model components. Specifically, driven by our experimental findings on inter-client similarity dynamics, we develop critical co-learning period (CCP), wherein we introduce a module named maximum difference segmentation (MDS) to assess and manage task relevance by analyzing the similarities between clients' logits of their classifiers. Outside the CCP, we employ an additional scheme for model aggregation that utilizes historical records of each client's most relevant peers to further enhance the personalization stability. We demonstrate the superiority of our FedReMa in extensive experiments.

Understanding the neurobiology of opioid use disorder (OUD) using resting-state functional magnetic resonance imaging (rs-fMRI) may help inform treatment strategies to improve patient outcomes. Recent literature suggests temporal characteristics of rs-fMRI blood oxygenation level-dependent (BOLD) signals may offer complementary information to functional connectivity analysis. However, existing studies of OUD analyze BOLD signals using measures computed across all time points. This study, for the first time in the literature, employs data-driven machine learning (ML) modeling of rs-fMRI BOLD features representing multiple time points to identify region(s) of interest that differentiate OUD subjects from healthy controls (HC). Following the triple network model, we obtain rs-fMRI BOLD features from the default mode network (DMN), salience network (SN), and executive control network (ECN) for 31 OUD and 45 HC subjects. Then, we use the Boruta ML algorithm to identify statistically significant BOLD features that differentiate OUD from HC, identifying the DMN as the most salient functional network for OUD. Furthermore, we conduct brain activity mapping, showing heightened neural activity within the DMN for OUD. We perform 5-fold cross-validation classification (OUD vs. HC) experiments to study the discriminative power of functional network features with and without fusing demographic features. The DMN shows the most discriminative power, achieving mean AUC and F1 scores of 80.91% and 73.97%, respectively, when fusing BOLD and demographic features. Follow-up Boruta analysis using BOLD features extracted from the medial prefrontal cortex, posterior cingulate cortex, and left and right temporoparietal junctions reveals significant features for all four functional hubs within the DMN.

Time Series Forecasting (TSF) is key functionality in numerous fields, including in finance, weather services, and energy management. While TSF methods are emerging these days, many of them require domain-specific data collection and model training and struggle with poor generalization performance on new domains. Foundation models aim to overcome this limitation. Pre-trained on large-scale language or time series data, they exhibit promising inferencing capabilities in new or unseen data. This has spurred a surge in new TSF foundation models. We propose a new benchmark, FoundTS, to enable thorough and fair evaluation and comparison of such models. FoundTS covers a variety of TSF foundation models, including those based on large language models and those pretrained on time series. Next, FoundTS supports different forecasting strategies, including zero-shot, few-shot, and full-shot, thereby facilitating more thorough evaluations. Finally, FoundTS offers a pipeline that standardizes evaluation processes such as dataset splitting, loading, normalization, and few-shot sampling, thereby facilitating fair evaluations. Building on this, we report on an extensive evaluation of TSF foundation models on a broad range of datasets from diverse domains and with different statistical characteristics. Specifically, we identify pros and cons and inherent limitations of existing foundation models, and we identify directions for future model design. We make our code and datasets available at https://anonymous.4open.science/r/FoundTS-C2B0.