Hyperparameter optimization (HPO) is an important step in machine learning (ML) model development, but common practices are archaic -- primarily relying on manual or grid searches. This is partly because adopting advanced HPO algorithms introduces added complexity to the workflow, leading to longer computation times. This poses a notable challenge to ML applications, as suboptimal hyperparameter selections curtail the potential of ML model performance, ultimately obstructing the full exploitation of ML techniques. In this article, we present a two-step HPO method as a strategic solution to curbing computational demands and wait times, gleaned from practical experiences in applied ML parameterization work. The initial phase involves a preliminary evaluation of hyperparameters on a small subset of the training dataset, followed by a re-evaluation of the top-performing candidate models post-retraining with the entire training dataset. This two-step HPO method is universally applicable across HPO search algorithms, and we argue it has attractive efficiency gains. As a case study, we present our recent application of the two-step HPO method to the development of neural network emulators for aerosol activation. Although our primary use case is a data-rich limit with many millions of samples, we also find that using up to 0.0025% of the data (a few thousand samples) in the initial step is sufficient to find optimal hyperparameter configurations from much more extensive sampling, achieving up to 135-times speedup. The benefits of this method materialize through an assessment of hyperparameters and model performance, revealing the minimal model complexity required to achieve the best performance. The assortment of top-performing models harvested from the HPO process allows us to choose a high-performing model with a low inference cost for efficient use in global climate models (GCMs).
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Supervised deep learning was recently introduced in high-contrast imaging (HCI) through the SODINN algorithm, a convolutional neural network designed for exoplanet detection in angular differential imaging (ADI) datasets. The benchmarking of HCI algorithms within the Exoplanet Imaging Data Challenge (EIDC) showed that (i) SODINN can produce a high number of false positives in the final detection maps, and (ii) algorithms processing images in a more local manner perform better. This work aims to improve the SODINN detection performance by introducing new local processing approaches and adapting its learning process accordingly. We propose NA-SODINN, a new deep learning binary classifier based on a convolutional neural network (CNN) that better captures image noise correlations in ADI-processed frames by identifying noise regimes. Our new approach was tested against its predecessor, as well as two SODINN-based hybrid models and a more standard annular-PCA approach, through local receiving operating characteristics (ROC) analysis of ADI sequences from the VLT/SPHERE and Keck/NIRC-2 instruments. Results show that NA-SODINN enhances SODINN in both sensitivity and specificity, especially in the speckle-dominated noise regime. NA-SODINN is also benchmarked against the complete set of submitted detection algorithms in EIDC, in which we show that its final detection score matches or outperforms the most powerful detection algorithms.Throughout the supervised machine learning case, this study illustrates and reinforces the importance of adapting the task of detection to the local content of processed images.
Detecting out of policy speech (OOPS) content is important but difficult. While machine learning is a powerful tool to tackle this challenging task, it is hard to break the performance ceiling due to factors like quantity and quality limitations on training data and inconsistencies in OOPS definition and data labeling. To realize the full potential of available limited resources, we propose a meta learning technique (MLT) that combines individual models built with different text representations. We analytically show that the resulting technique is numerically stable and produces reasonable combining weights. We combine the MLT with a threshold-moving (TM) technique to further improve the performance of the combined predictor on highly-imbalanced in-distribution and out-of-distribution datasets. We also provide computational results to show the statistically significant advantages of the proposed MLT approach. All authors contributed equally to this work.
Diffusion model has become a main paradigm for synthetic data generation in many subfields of modern machine learning, including computer vision, language model, or speech synthesis. In this paper, we leverage the power of diffusion model for generating synthetic tabular data. The heterogeneous features in tabular data have been main obstacles in tabular data synthesis, and we tackle this problem by employing the auto-encoder architecture. When compared with the state-of-the-art tabular synthesizers, the resulting synthetic tables from our model show nice statistical fidelities to the real data, and perform well in downstream tasks for machine learning utilities. We conducted the experiments over 15 publicly available datasets. Notably, our model adeptly captures the correlations among features, which has been a long-standing challenge in tabular data synthesis. Our code is available upon request and will be publicly released if paper is accepted.
Estimating the generalization error (GE) of machine learning models is fundamental, with resampling methods being the most common approach. However, in non-standard settings, particularly those where observations are not independently and identically distributed, resampling using simple random data divisions may lead to biased GE estimates. This paper strives to present well-grounded guidelines for GE estimation in various such non-standard settings: clustered data, spatial data, unequal sampling probabilities, concept drift, and hierarchically structured outcomes. Our overview combines well-established methodologies with other existing methods that, to our knowledge, have not been frequently considered in these particular settings. A unifying principle among these techniques is that the test data used in each iteration of the resampling procedure should reflect the new observations to which the model will be applied, while the training data should be representative of the entire data set used to obtain the final model. Beyond providing an overview, we address literature gaps by conducting simulation studies. These studies assess the necessity of using GE-estimation methods tailored to the respective setting. Our findings corroborate the concern that standard resampling methods often yield biased GE estimates in non-standard settings, underscoring the importance of tailored GE estimation.
Reinforcement learning (RL) has helped improve decision-making in several applications. However, applying traditional RL is challenging in some applications, such as rehabilitation of people with a spinal cord injury (SCI). Among other factors, using RL in this domain is difficult because there are many possible treatments (i.e., large action space) and few patients (i.e., limited training data). Treatments for SCIs have natural groupings, so we propose two approaches to grouping treatments so that an RL agent can learn effectively from limited data. One relies on domain knowledge of SCI rehabilitation and the other learns similarities among treatments using an embedding technique. We then use Fitted Q Iteration to train an agent that learns optimal treatments. Through a simulation study designed to reflect the properties of SCI rehabilitation, we find that both methods can help improve the treatment decisions of physiotherapists, but the approach based on domain knowledge offers better performance. Our findings provide a "proof of concept" that RL can be used to help improve the treatment of those with an SCI and indicates that continued efforts to gather data and apply RL to this domain are worthwhile.
Obtaining the solutions of partial differential equations based on machine learning methods has drawn more and more attention in the fields of scientific computation and engineering applications. In this work, we first propose a coupled Extreme Learning Machine(called CELM) method incorporated with the physical laws to solve a class of fourth-order biharmonic equations by reformulating it into two well-posed Poisson problems. In addition, some activation functions including tangent, gaussian, sine, and trigonometric functions are introduced to assess our CELM method. Furthermore, we introduce several activation functions, such as tangent, Gaussian, sine, and trigonometric functions, to evaluate the performance of our CELM method. Notably, the sine and trigonometric functions demonstrate a remarkable ability to effectively minimize the approximation error of the CELM model. In the end, several numerical experiments are performed to study the initializing ways for both the weights and biases of the hidden units in our CELM model and explore the required number of hidden units. Numerical results show the proposed CELM algorithm is high-precision and efficient to address the biharmonic equations on both regular and irregular domains.
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such symmetry holding and ostensibly fail if symmetry is broken. This work considers under what conditions a sequence of probability measures asymptotically gains such symmetry or invariance to a collection of group actions. Considering the many symmetries of the Gaussian distribution, this work effectively proposes a non-parametric type of central limit theorem. That is, a Lipschitz function of a high dimensional random vector will be asymptotically invariant to the actions of certain compact topological groups. Applications of this include a partial law of the iterated logarithm for uniformly random points in an $\ell_p^n$-ball and an asymptotic equivalence between classical parametric statistical tests and their randomization counterparts even when invariance assumptions are violated.
A new mechanical model on noncircular shallow tunnelling considering initial stress field is proposed in this paper by constraining far-field ground surface to eliminate displacement singularity at infinity, and the originally unbalanced tunnel excavation problem in existing solutions is turned to an equilibrium one of mixed boundaries. By applying analytic continuation, the mixed boundaries are transformed to a homogenerous Riemann-Hilbert problem, which is subsequently solved via an efficient and accurate iterative method with boundary conditions of static equilibrium, displacement single-valuedness, and traction along tunnel periphery. The Lanczos filtering technique is used in the final stress and displacement solution to reduce the Gibbs phenomena caused by the constrained far-field ground surface for more accurte results. Several numerical cases are conducted to intensively verify the proposed solution by examining boundary conditions and comparing with existing solutions, and all the results are in good agreements. Then more numerical cases are conducted to investigate the stress and deformation distribution along ground surface and tunnel periphery, and several engineering advices are given. Further discussions on the defects of the proposed solution are also conducted for objectivity.
Robust generalization is a major challenge in deep learning, particularly when the number of trainable parameters is very large. In general, it is very difficult to know if the network has memorized a particular set of examples or understood the underlying rule (or both). Motivated by this challenge, we study an interpretable model where generalizing representations are understood analytically, and are easily distinguishable from the memorizing ones. Namely, we consider two-layer neural networks trained on modular arithmetic tasks where ($\xi \cdot 100\%$) of labels are corrupted (\emph{i.e.} some results of the modular operations in the training set are incorrect). We show that (i) it is possible for the network to memorize the corrupted labels \emph{and} achieve $100\%$ generalization at the same time; (ii) the memorizing neurons can be identified and pruned, lowering the accuracy on corrupted data and improving the accuracy on uncorrupted data; (iii) regularization methods such as weight decay, dropout and BatchNorm force the network to ignore the corrupted data during optimization, and achieve $100\%$ accuracy on the uncorrupted dataset; and (iv) the effect of these regularization methods is (``mechanistically'') interpretable: weight decay and dropout force all the neurons to learn generalizing representations, while BatchNorm de-amplifies the output of memorizing neurons and amplifies the output of the generalizing ones. Finally, we show that in the presence of regularization, the training dynamics involves two consecutive stages: first, the network undergoes the \emph{grokking} dynamics reaching high train \emph{and} test accuracy; second, it unlearns the memorizing representations, where train accuracy suddenly jumps from $100\%$ to $100 (1-\xi)\%$.
Most state-of-the-art machine learning techniques revolve around the optimisation of loss functions. Defining appropriate loss functions is therefore critical to successfully solving problems in this field. We present a survey of the most commonly used loss functions for a wide range of different applications, divided into classification, regression, ranking, sample generation and energy based modelling. Overall, we introduce 33 different loss functions and we organise them into an intuitive taxonomy. Each loss function is given a theoretical backing and we describe where it is best used. This survey aims to provide a reference of the most essential loss functions for both beginner and advanced machine learning practitioners.
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