Logistic regression training over encrypted data has been an attractive idea to security concerns for years. In this paper, we propose a faster gradient variant called $\texttt{quadratic gradient}$ for privacy-preserving logistic regression training. The core of $\texttt{quadratic gradient}$ can be seen as an extension of the simplified fixed Hessian. We enhance Nesterov's accelerated gradient (NAG) and Adaptive Gradient Algorithm (Adagrad) respectively with $\texttt{quadratic gradient}$ and evaluate the enhanced algorithms on several datasets. %gradient $ascent$ methods with this gradient variant on the gene dataset provided by the 2017 iDASH competition and other datasets. Experiments show that the enhanced methods have a state-of-the-art performance in convergence speed compared to the raw first-order gradient methods. We then adopt the enhanced NAG method to implement homomorphic logistic regression training, obtaining a comparable result by only $3$ iterations. There is a promising chance that $\texttt{quadratic gradient}$ could be used to enhance other first-order gradient methods for general numerical optimization problems.

The pre-insertion resistors (PIR) within high-voltage circuit breakers are critical components and warm up by generating Joule heat when an electric current flows through them. Elevated temperature can lead to temporary closure failure and, in severe cases, the rupture of PIR. To accurately predict the temperature of PIR, this study combines finite element simulation techniques with Support Vector Regression (SVR) optimized by an Improved Whale Optimization Algorithm (IWOA) approach. The IWOA includes Tent mapping, a convergence factor based on the sigmoid function, and the Ornstein-Uhlenbeck variation strategy. The IWOA-SVR model is compared with the SSA-SVR and WOA-SVR. The results reveal that the prediction accuracies of the IWOA-SVR model were 90.2% and 81.5% (above 100$^\circ$C) in the 3$^\circ$C temperature deviation range and 96.3% and 93.4% (above 100$^\circ$C) in the 4$^\circ$C temperature deviation range, surpassing the performance of the comparative models. This research demonstrates the method proposed can realize the online monitoring of the temperature of the PIR, which can effectively prevent thermal faults PIR and provide a basis for the opening and closing of the circuit breaker within a short period.

Missing data is a widespread problem in many domains, creating challenges in data analysis and decision making. Traditional techniques for dealing with missing data, such as excluding incomplete records or imputing simple estimates (e.g., mean), are computationally efficient but may introduce bias and disrupt variable relationships, leading to inaccurate analyses. Model-based imputation techniques offer a more robust solution that preserves the variability and relationships in the data, but they demand significantly more computation time, limiting their applicability to small datasets. This work enables efficient, high-quality, and scalable data imputation within a database system using the widely used MICE method. We adapt this method to exploit computation sharing and a ring abstraction for faster model training. To impute both continuous and categorical values, we develop techniques for in-database learning of stochastic linear regression and Gaussian discriminant analysis models. Our MICE implementations in PostgreSQL and DuckDB outperform alternative MICE implementations and model-based imputation techniques by up to two orders of magnitude in terms of computation time, while maintaining high imputation quality.

We propose a new method to improve the convergence speed of the Robbins-Monro algorithm by introducing prior information about the target point into the Robbins-Monro iteration. We achieve the incorporation of prior information without the need of a -- potentially wrong -- regression model, which would also entail additional constraints. We show that this prior-information Robbins-Monro sequence is convergent for a wide range of prior distributions, even wrong ones, such as Gaussian, weighted sum of Gaussians, e.g., in a kernel density estimate, as well as bounded arbitrary distribution functions greater than zero. We furthermore analyse the sequence numerically to understand its performance and the influence of parameters. The results demonstrate that the prior-information Robbins-Monro sequence converges faster than the standard one, especially during the first steps, which are particularly important for applications where the number of function measurements is limited, and when the noise of observing the underlying function is large. We finally propose a rule to select the parameters of the sequence.

We propose a deep neural network (DNN) based least distance (LD) estimator (DNN-LD) for a multivariate regression problem, addressing the limitations of the conventional methods. Due to the flexibility of a DNN structure, both linear and nonlinear conditional mean functions can be easily modeled, and a multivariate regression model can be realized by simply adding extra nodes at the output layer. The proposed method is more efficient in capturing the dependency structure among responses than the least squares loss, and robust to outliers. In addition, we consider $L_1$-type penalization for variable selection, crucial in analyzing high-dimensional data. Namely, we propose what we call (A)GDNN-LD estimator that enjoys variable selection and model estimation simultaneously, by applying the (adaptive) group Lasso penalty to weight parameters in the DNN structure. For the computation, we propose a quadratic smoothing approximation method to facilitate optimizing the non-smooth objective function based on the least distance loss. The simulation studies and a real data analysis demonstrate the promising performance of the proposed method.

Many problems in machine learning, optimization, uncertainty quantification and sensitivity analysis suffer from the curse of dimensionality, where the performance and the complexity of the model worsens dramatically with the number of input variables. To alleviate this problem, one is interested in dimensionality reduction techniques. For instance, in machine learning, variable/feature selection methods Guyon and Elisseeff (2003) aim to find a subset of variables so as to improve the predictive performance of a learning algorithm, and in some algorithms, such as decision trees, the variable selection is an inherent part of the learning process. The field of sensitivity analysis mostly deals with identifying the subset of inputs parameters whose uncertainty contributes significantly to that of the model output Saltelli et al. (2008); Da Veiga et al. (2021). They are focused on the effects of the initial variables and their interactions. However, it might be the case that the model or function of interest varies the most along directions not aligned with the coordinate axes. The widely used dimensionality reduction method of principal component analysis (PCA) (also Karhunen-Loeve method) can be used to find a linear subspace of the input/output space containing the most of its variance, but, by default, it does not take into account the input-output relationship. In ecological sciences, the redundancy analysis applies PCA to the fitted values from a linear regression model to identify a subset of input parameters contributing significantly to the variation in the response matrix Legendre et al. (2011).

Quantitative technology forecasting uses quantitative methods to understand and project technological changes. It is a broad field encompassing many different techniques and has been applied to a vast range of technologies. A widely used approach in this field is trend extrapolation. Based on the publications available to us, there has been little or no attempt made to systematically review the empirical evidence on quantitative trend extrapolation techniques. This study attempts to close this gap by conducting a systematic review of technology forecasting literature addressing the application of quantitative trend extrapolation techniques. We identified 25 studies relevant to the objective of this research and classified the techniques used in the studies into different categories, among which growth curves and time series methods were shown to remain popular over the past decade, while newer methods, such as machine learning-based hybrid models, have emerged in recent years. As more effort and evidence are needed to determine if hybrid models are superior to traditional methods, we expect to see a growing trend in the development and application of hybrid models to technology forecasting.

Ultrasound imaging has recently been introduced as a sensing interface for joint motion estimation. The use of ultrasound images as an estimation method is expected to improve the control performance of assistive devices and human--machine interfaces. This study aimed to estimate continuous wrist joint angles using ultrasound images. Specifically, in an experiment, joint angle information was obtained during extension--flexion movements, and ultrasound images of the associated muscles were acquired. Using the features obtained from ultrasound images, a multivariate linear regression model was used to estimate the joint angles. The coordinates of the feature points obtained using optical flow from the ultrasound images were used as explanatory variables of the multivariate linear regression model. The model was trained and tested for each trial by each participant to verify the estimation accuracy. The results show that the mean and standard deviation of the estimation accuracy for all trials were root mean square error (RMSE)=1.82 $\pm$ 0.54 deg and coefficient of determination (R2)=0.985 $\pm$ 0.009. Our method achieves a highly accurate estimation of joint angles compared with previous studies using other signals, such as surface electromyography, while the multivariate linear regression model is simple and both computational and model training costs are low.

Fake news detection models are critical to countering disinformation but can be manipulated through adversarial attacks. In this position paper, we analyze how an attacker can compromise the performance of an online learning detector on specific news content without being able to manipulate the original target news. In some contexts, such as social networks, where the attacker cannot exert complete control over all the information, this scenario can indeed be quite plausible. Therefore, we show how an attacker could potentially introduce poisoning data into the training data to manipulate the behavior of an online learning method. Our initial findings reveal varying susceptibility of logistic regression models based on complexity and attack type.

Predicting the solubility of given molecules remains crucial in the pharmaceutical industry. In this study, we revisited this extensively studied topic, leveraging the capabilities of contemporary computing resources. We employed two machine learning models: a linear regression model and a graph convolutional neural network (GCNN) model, using various experimental datasets. Both methods yielded reasonable predictions, with the GCNN model exhibiting the highest level of performance. However, the present GCNN model has limited interpretability while the linear regression model allows scientists for a greater in-depth analysis of the underlying factors through feature importance analysis, although more human inputs and evaluations on the overall dataset is required. From the perspective of chemistry, using the linear regression model, we elucidated the impact of individual atom species and functional groups on overall solubility, highlighting the significance of comprehending how chemical structure influences chemical properties in the drug development process. It is learned that introducing oxygen atoms can increase the solubility of organic molecules, while almost all other hetero atoms except oxygen and nitrogen tend to decrease solubility.