This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the stochastic subgradient method, preserve the $\mathcal{O} ( 1 / \sqrt{K})$ convergence rate with constant failure rate. Our analyses rest on rather weak assumptions: the Lipschitz parameter can be either bounded by a general growth function of $\|x\|$ or locally estimated through independent random samples.

The quantification of storm updrafts remains unavailable for operational forecasting despite their inherent importance to convection and its associated severe weather hazards. Updraft proxies, like overshooting top area from satellite images, have been linked to severe weather hazards but only relate to a limited portion of the total storm updraft. This study investigates if a machine learning model, namely U-Nets, can skillfully retrieve maximum vertical velocity and its areal extent from 3-dimensional gridded radar reflectivity alone. The machine learning model is trained using simulated radar reflectivity and vertical velocity from the National Severe Storm Laboratory's convection permitting Warn on Forecast System (WoFS). A parametric regression technique using the sinh-arcsinh-normal distribution is adapted to run with U-Nets, allowing for both deterministic and probabilistic predictions of maximum vertical velocity. The best models after hyperparameter search provided less than 50% root mean squared error, a coefficient of determination greater than 0.65 and an intersection over union (IoU) of more than 0.45 on the independent test set composed of WoFS data. Beyond the WoFS analysis, a case study was conducted using real radar data and corresponding dual-Doppler analyses of vertical velocity within a supercell. The U-Net consistently underestimates the dual-Doppler updraft speed estimates by 50$\%$. Meanwhile, the area of the 5 and 10 m s^-1 updraft cores show an IoU of 0.25. While the above statistics are not exceptional, the machine learning model enables quick distillation of 3D radar data that is related to the maximum vertical velocity which could be useful in assessing a storm's severe potential.

In continual learning, catastrophic forgetting is affected by multiple aspects of the tasks. Previous works have analyzed separately how forgetting is affected by either task similarity or overparameterization. In contrast, our paper examines how task similarity and overparameterization jointly affect forgetting in an analyzable model. Specifically, we focus on two-task continual linear regression, where the second task is a random orthogonal transformation of an arbitrary first task (an abstraction of random permutation tasks). We derive an exact analytical expression for the expected forgetting - and uncover a nuanced pattern. In highly overparameterized models, intermediate task similarity causes the most forgetting. However, near the interpolation threshold, forgetting decreases monotonically with the expected task similarity. We validate our findings with linear regression on synthetic data, and with neural networks on established permutation task benchmarks.

Hybrid variational quantum algorithms (VQAs) are promising for solving practical problems such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers. However, with typical random ansatz or quantum alternating operator ansatz, derived variational quantum algorithms become a black box for model interpretation. In this paper we construct a quantum regression algorithm wherein the quantum state directly encodes the classical data table and the variational parameters correspond directly to the regression coefficients which are real numbers by construction, providing a high degree of model interpretability and minimal cost to optimize with the right expressiveness. Instead of assuming the state preparation is given by granted, we discuss the state preparation with different encoders and their time complexity and overall resource cost. We can take advantage of the encoded data structure to cut down the algorithm time complexity. To the best of our knowledge, we show for the first time explicitly how the linkage of the classical data structure can be taken advantage of directly through quantum subroutines by construction. For nonlinear regression, our algorithm can be extended by building nonlinear features into the training data as demonstrated by numerical results. In addition, we demonstrate that the model trainability is achievable only when the number of features $M$ is much less than the number of records $L$ for the encoded data structure to justify $L\gg M$ in our resource estimation.

Recent works have demonstrated the effectiveness of machine learning (ML) techniques in detecting anxiety and stress using physiological signals, but it is unclear whether ML models are learning physiological features specific to stress. To address this ambiguity, we evaluated the generalizability of physiological features that have been shown to be correlated with anxiety and stress to high-arousal emotions. Specifically, we examine features extracted from electrocardiogram (ECG) and electrodermal (EDA) signals from the following three datasets: Anxiety Phases Dataset (APD), Wearable Stress and Affect Detection (WESAD), and the Continuously Annotated Signals of Emotion (CASE) dataset. We aim to understand whether these features are specific to anxiety or general to other high-arousal emotions through a statistical regression analysis, in addition to a within-corpus, cross-corpus, and leave-one-corpus-out cross-validation across instances of stress and arousal. We used the following classifiers: Support Vector Machines, LightGBM, Random Forest, XGBoost, and an ensemble of the aforementioned models. We found that models trained on an arousal dataset perform relatively well on a previously unseen stress dataset, and vice versa. Our experimental results suggest that the evaluated models may be identifying emotional arousal instead of stress. This work is the first cross-corpus evaluation across stress and arousal from ECG and EDA signals, contributing new findings about the generalizability of stress detection.

Recently, the selection of machine learning model based on only the data distribution without concerning the noise of the data. This study aims to distinguish, which models perform well under noisy data, and establish whether stacking machine learning models actually provide robustness to otherwise weak-to-noise models. The electrochemical data were tested with 12 standalone models and stacking model. This includes XGB, LGBM, RF, GB, ADA, NN, ELAS, LASS, RIDGE, SVM, KNN, DT, and the stacking model. It is found that linear models handle noise well with the average error of (slope) to 1.75 F g-1 up to error per 100% percent noise added; but it suffers from prediction accuracy due to having an average of 60.19 F g-1 estimated at minimal error at 0% noise added. Tree-based models fail in terms of noise handling (average slope is 55.24 F g-1 at 100% percent noise), but it can provide higher prediction accuracy (lowest error of 23.9 F g-1) than that of linear. To address the controversial between prediction accuracy and error handling, the stacking model was constructed, which is not only show high accuracy (intercept of 25.03 F g-1), but it also exhibits good noise handling (slope of 43.58 F g-1), making stacking models a relatively low risk and viable choice for beginner and experienced machine learning research in electrochemistry. Even though neural networks (NN) are gaining popularity in the electrochemistry field. However, this study presents that NN is not suitable for electrochemical data, and improper tuning resulting in a model that is susceptible to noise. Thus, STACK models should provide better benefits in that even with untuned base models, they can achieve an accurate and noise-tolerant model. Overall, this work provides insight into machine learning model selection for electrochemical data, which should aid the understanding of data science in chemistry context.

Semi-structured regression models enable the joint modeling of interpretable structured and complex unstructured feature effects. The structured model part is inspired by statistical models and can be used to infer the input-output relationship for features of particular importance. The complex unstructured part defines an arbitrary deep neural network and thereby provides enough flexibility to achieve competitive prediction performance. While these models can also account for aleatoric uncertainty, there is still a lack of work on accounting for epistemic uncertainty. In this paper, we address this problem by presenting a Bayesian approximation for semi-structured regression models using subspace inference. To this end, we extend subspace inference for joint posterior sampling from a full parameter space for structured effects and a subspace for unstructured effects. Apart from this hybrid sampling scheme, our method allows for tunable complexity of the subspace and can capture multiple minima in the loss landscape. Numerical experiments validate our approach's efficacy in recovering structured effect parameter posteriors in semi-structured models and approaching the full-space posterior distribution of MCMC for increasing subspace dimension. Further, our approach exhibits competitive predictive performance across simulated and real-world datasets.

When selecting data for training large-scale models, standard practice is to filter for examples that match human notions of data quality. Such filtering yields qualitatively clean datapoints that intuitively should improve model behavior. However, in practice the opposite can often happen: we find that selecting according to similarity with "high quality" data sources may not increase (and can even hurt) performance compared to randomly selecting data. To develop better methods for selecting data, we start by framing dataset selection as an optimization problem that we can directly solve for: given target tasks, a learning algorithm, and candidate data, select the subset that maximizes model performance. This framework thus avoids handpicked notions of data quality, and instead models explicitly how the learning process uses train datapoints to predict on the target tasks. Our resulting method greatly improves language model (LM) performance on both pre-specified tasks and previously unseen tasks. Specifically, choosing target tasks representative of standard LM problems and evaluating on diverse held-out benchmarks, our selected datasets provide a 2x compute multiplier over baseline methods.

Consider the nonparametric logistic regression problem. In the logistic regression, we usually consider the maximum likelihood estimator, and the excess risk is the expectation of the Kullback-Leibler (KL) divergence between the true and estimated conditional class probabilities. However, in the nonparametric logistic regression, the KL divergence could diverge easily, and thus, the convergence of the excess risk is difficult to prove or does not hold. Several existing studies show the convergence of the KL divergence under strong assumptions. In most cases, our goal is to estimate the true conditional class probabilities. Thus, instead of analyzing the excess risk itself, it suffices to show the consistency of the maximum likelihood estimator in some suitable metric. In this paper, using a simple unified approach for analyzing the nonparametric maximum likelihood estimator (NPMLE), we directly derive the convergence rates of the NPMLE in the Hellinger distance under mild assumptions. Although our results are similar to the results in some existing studies, we provide simple and more direct proofs for these results. As an important application, we derive the convergence rates of the NPMLE with deep neural networks and show that the derived rate nearly achieves the minimax optimal rate.

This paper proposes a novel contact and wearable sensing system for estimating the upper body posture and joint angles (ankle, knee, and hip) of the human body using foot pressure distribution information obtained from a sensor attached to the plantar region. In the proposed estimation method, sensors are installed only on the plantar region, which is the end of the human body and the point of contact with the environment. The posture and joint angles of other parts of the body are estimated using only this information. As a contact and wearable sensor, the proposed system differs from previous measurement systems in the sense that the sensor does not need to be placed near the target joint or body. The estimation was carried out using a multivariate linear regression model with the foot pressure distribution as the input and the joint angle or posture as the output. The results reveal that it is possible to estimate the posture and joint angles of the human body from foot pressure distribution information (R2$\fallingdotseq$0.9). The proposed estimation method was validated by morphological computation to confirm that it is enabled by foot morphology. The validation approach compared the estimation accuracy achieved when an object was interposed between the foot pressure distribution sensor and the plantar region and the morphological relationship of the plantar region to the environment varied. The results reveal that there is a significant difference in the estimation accuracy between cases with and without an intervening object, suggesting that the morphology of the plantar region contributes to the estimation. Furthermore, the proposed estimation method is considered as physical reservoir computing, wherein the human foot is used as a computational resource.