Bluebottles (\textit{Physalia} spp.) are marine stingers resembling jellyfish, whose presence on Australian beaches poses a significant public risk due to their venomous nature. Understanding the environmental factors driving bluebottles ashore is crucial for mitigating their impact, and machine learning tools are to date relatively unexplored. We use bluebottle marine stinger presence/absence data from beaches in Eastern Sydney, Australia, and compare machine learning models (Multilayer Perceptron, Random Forest, and XGBoost) to identify factors influencing their presence. We address challenges such as class imbalance, class overlap, and unreliable absence data by employing data augmentation techniques, including the Synthetic Minority Oversampling Technique (SMOTE), Random Undersampling, and Synthetic Negative Approach that excludes the negative class. Our results show that SMOTE failed to resolve class overlap, but the presence-focused approach effectively handled imbalance, class overlap, and ambiguous absence data. The data attributes such as the wind direction, which is a circular variable, emerged as a key factor influencing bluebottle presence, confirming previous inference studies. However, in the absence of population dynamics, biological behaviours, and life cycles, the best predictive model appears to be Random Forests combined with Synthetic Negative Approach. This research contributes to mitigating the risks posed by bluebottles to beachgoers and provides insights into handling class overlap and unreliable negative class in environmental modelling.

Class imbalance (CI) is a longstanding problem in machine learning, slowing down training and reducing performances. Although empirical remedies exist, it is often unclear which ones work best and when, due to the lack of an overarching theory. We address a common case of imbalance, that of anomaly (or outlier) detection. We provide a theoretical framework to analyze, interpret and address CI. It is based on an exact solution of the teacher-student perceptron model, through replica theory. Within this framework, one can distinguish several sources of CI: either intrinsic, train or test imbalance. Our analysis reveals that the optimal train imbalance is generally different from 50%, with a non trivial dependence on the intrinsic imbalance, the abundance of data and on the noise in the learning. Moreover, there is a crossover between a small noise training regime where results are independent of the noise level to a high noise regime where performances quickly degrade with noise. Our results challenge some of the conventional wisdom on CI and offer practical guidelines to address it.

Dataset poisoning attacks present a threat against machine learning models because they introduce subtle, ostensibly undetectable changes to the data on which the model will be trained. Moreover, attackers often craft attacks to deterministically change a model's behavior by invoking a latent trigger that they set in the resultant model. We will introduce the precise threat model in which we are interested in Section 2. Researchers often frame dataset poisoning and its analysis from the point of view of optimization theory [1]-[5]. E.g., in the computer vision setting, one might attempt to alter as few pixels as possible in as few images as possible while still producing targeted misclassifications. For text generation, one might aim to change as few tokens as possible to as few corpus sentences as possible while causing targeted semantic misalignment on the next phrase or sentence. In general, this vantage is convenient for conducting attacks. Even locally optimizing the criteria for an attack typically yields a dataset that effectively attacks models trained on it. From this perspective, it is natural to also frame detection of data poisoning as an optimization problem. For example, in [4], it is hypothesized that poisoning a dataset impacts the most dominant features in neural networks trained on it and it is shown that under this assumption poisoning can be provably detected by solving an optimization problem.

Dataset Distillation is the task of synthesizing small datasets from large ones while still retaining comparable predictive accuracy to the original uncompressed dataset. Despite significant empirical progress in recent years, there is little understanding of the theoretical limitations/guarantees of dataset distillation, specifically, what excess risk is achieved by distillation compared to the original dataset, and how large are distilled datasets? In this work, we take a theoretical view on kernel ridge regression (KRR) based methods of dataset distillation such as Kernel Inducing Points. By transforming ridge regression in random Fourier features (RFF) space, we provide the first proof of the existence of small (size) distilled datasets and their corresponding excess risk for shift-invariant kernels. We prove that a small set of instances exists in the original input space such that its solution in the RFF space coincides with the solution of the original data.

The widely observed'benign overfitting phenomenon' in the neural network literature raises the challenge to the bias-variance trade-off' doctrine in the statistical learning theory.Since the generalization ability of the'lazy trained' over-parametrized neural network can be well approximated by that of the neural tangent kernel regression,the curve of the excess risk (namely, the learning curve) of kernel ridge regression attracts increasing attention recently.However, most recent arguments on the learning curve are heuristic and are based on the'Gaussian design' assumption.In this paper, under mild and more realistic assumptions, we rigorously provide a full characterization of the learning curve in the asymptotic senseunder a power-law decay condition of the eigenvalues of the kernel and also the target function.The learning curve elaborates the effect and the interplay of the choice of the regularization parameter, the source condition and the noise.In particular, our results suggest that the'benign overfitting phenomenon' exists in over-parametrized neural networks only when the noise level is small.

When domain knowledge is limited and experimentation is restricted by ethical, financial, or time constraints, practitioners turn to observational causal discovery methods to recover the causal structure, exploiting the statistical properties of their data. Because causal discovery without further assumptions is an ill-posed problem, each algorithm comes with its own set of usually untestable assumptions, some of which are hard to meet in real datasets. Motivated by these considerations, this paper extensively benchmarks the empirical performance of recent causal discovery methods on observational iid data generated under different background conditions, allowing for violations of the critical assumptions required by each selected approach. Our experimental findings show that score matching-based methods demonstrate surprising performance in the false positive and false negative rate of the inferred graph in these challenging scenarios, and we provide theoretical insights into their performance. This work is also the first effort to benchmark the stability of causal discovery algorithms with respect to the values of their hyperparameters.

We consider an important problem in scientific discovery, namely identifying sparse governing equations for nonlinear dynamical systems. This involves solving sparse ridge regression problems to provable optimality in order to determine which terms drive the underlying dynamics. We propose a fast algorithm, OKRidge, for sparse ridge regression, using a novel lower bound calculation involving, first, a saddle point formulation, and from there, either solving (i) a linear system or (ii) using an ADMM-based approach, where the proximal operators can be efficiently evaluated by solving another linear system and an isotonic regression problem. We also propose a method to warm-start our solver, which leverages a beam search. Experimentally, our methods attain provable optimality with run times that are orders of magnitude faster than those of the existing MIP formulations solved by the commercial solver Gurobi.

Detecting out-of-distribution (OOD) data is crucial for ensuring the safe deployment of machine learning models in real-world applications. However, existing OOD detection approaches primarily rely on the feature maps or the full gradient space information to derive OOD scores neglecting the role of \textbf{most important parameters} of the pre-trained network over In-Distribution data. In this study, we propose a novel approach called GradOrth to facilitate OOD detection based on one intriguing observation that the important features to identify OOD data lie in the lower-rank subspace of in-distribution (ID) data.In particular, we identify OOD data by computing the norm of gradient projection on \textit{the subspaces considered \textbf{important} for the in-distribution data}. A large orthogonal projection value (i.e. a small projection value) indicates the sample as OOD as it captures a weak correlation of the in-distribution (ID) data. This simple yet effective method exhibits outstanding performance, showcasing a notable reduction in the average false positive rate at a 95\% true positive rate (FPR95) of up to 8\% when compared to the current state-of-the-art methods.

The Partial Area Under the ROC Curve (PAUC), typically including One-way Partial AUC (OPAUC) and Two-way Partial AUC (TPAUC), measures the average performance of a binary classifier within a specific false positive rate and/or true positive rate interval, which is a widely adopted measure when decision constraints must be considered. Consequently, PAUC optimization has naturally attracted increasing attention in the machine learning community within the last few years. Nonetheless, most of the existing methods could only optimize PAUC approximately, leading to inevitable biases that are not controllable. Fortunately, a recent work presents an unbiased formulation of the PAUC optimization problem via distributional robust optimization. However, it is based on the pair-wise formulation of AUC, which suffers from the limited scalability w.r.t.

Deep neural networks (DNNs) are notorious for making more mistakes for the classes that have substantially fewer samples than the others during training. Such class imbalance is ubiquitous in clinical applications and very crucial to handle because the classes with fewer samples most often correspond to critical cases (e.g., cancer) where misclassifications can have severe consequences.Not to miss such cases, binary classifiers need to be operated at high True Positive Rates (TPRs) by setting a higher threshold, but this comes at the cost of very high False Positive Rates (FPRs) for problems with class imbalance. Existing methods for learning under class imbalance most often do not take this into account. We argue that prediction accuracy should be improved by emphasizing the reduction of FPRs at high TPRs for problems where misclassification of the positive, i.e. critical, class samples are associated with higher cost.To this end, we pose the training of a DNN for binary classification as a constrained optimization problem and introduce a novel constraint that can be used with existing loss functions to enforce maximal area under the ROC curve (AUC) through prioritizing FPR reduction at high TPR. We solve the resulting constrained optimization problem using an Augmented Lagrangian method (ALM).Going beyond binary, we also propose two possible extensions of the proposed constraint for multi-class classification problems.We present experimental results for image-based binary and multi-class classification applications using an in-house medical imaging dataset, CIFAR10, and CIFAR100.