The multivariate regression model basically offers the analysis of a single dataset with multiple responses. However, such a single-dataset analysis often leads to unsatisfactory results. Integrative analysis is an effective method to pool useful information from multiple independent datasets and provides better performance than single-dataset analysis. In this study, we propose a multivariate regression modeling in integrative analysis. The integration is achieved by sparse estimation that performs variable and group selection. Based on the idea of alternating direction method of multipliers, we develop its computational algorithm that enjoys the convergence property. The performance of the proposed method is demonstrated through Monte Carlo simulation and analyzing wastewater treatment data with microbe measurements.

Response curves exhibit the magnitude of the response of a sensitive system to a varying stimulus. However, response of such systems may be sensitive to multiple stimuli (i.e., input features) that are not necessarily independent. As a consequence, the shape of response curves generated for a selected input feature (referred to as "active feature") might depend on the values of the other input features (referred to as "passive features"). In this work, we consider the case of systems whose response is approximated using regression neural networks. We propose to use counterfactual explanations (CFEs) for the identification of the features with the highest relevance on the shape of response curves generated by neural network black boxes. CFEs are generated by a genetic algorithm-based approach that solves a multi-objective optimization problem. In particular, given a response curve generated for an active feature, a CFE finds the minimum combination of passive features that need to be modified to alter the shape of the response curve. We tested our method on a synthetic dataset with 1-D inputs and two crop yield prediction datasets with 2-D inputs. The relevance ranking of features and feature combinations obtained on the synthetic dataset coincided with the analysis of the equation that was used to generate the problem. Results obtained on the yield prediction datasets revealed that the impact on fertilizer responsivity of passive features depends on the terrain characteristics of each field.

Is overparameterization a privacy liability? In this work, we study the effect that the number of parameters has on a classifier's vulnerability to membership inference attacks. We first demonstrate how the number of parameters of a model can induce a privacy--utility trade-off: increasing the number of parameters generally improves generalization performance at the expense of lower privacy. However, remarkably, we then show that if coupled with proper regularization, increasing the number of parameters of a model can actually simultaneously increase both its privacy and performance, thereby eliminating the privacy--utility trade-off. Theoretically, we demonstrate this curious phenomenon for logistic regression with ridge regularization in a bi-level feature ensemble setting. Pursuant to our theoretical exploration, we develop a novel leave-one-out analysis tool to precisely characterize the vulnerability of a linear classifier to the optimal membership inference attack. We empirically exhibit this "blessing of dimensionality" for neural networks on a variety of tasks using early stopping as the regularizer.

When there are signals and noises, physicists try to identify signals by modeling them, whereas statisticians oppositely try to model noise to identify signals. In this study, we applied the statisticians' concept of signal detection of physics data with small-size samples and high dimensions without modeling the signals. Most of the data in nature, whether noises or signals, are assumed to be generated by dynamical systems; thus, there is essentially no distinction between these generating processes. We propose that the correlation length of a dynamical system and the number of samples are crucial for the practical definition of noise variables among the signal variables generated by such a system. Since variables with short-term correlations reach normal distributions faster as the number of samples decreases, they are regarded to be ``noise-like'' variables, whereas variables with opposite properties are ``signal-like'' variables. Normality tests are not effective for data of small-size samples with high dimensions. Therefore, we modeled noises on the basis of the property of a noise variable, that is, the uniformity of the histogram of the probability that a variable is a noise. We devised a method of detecting signal variables from the structural change of the histogram according to the decrease in the number of samples. We applied our method to the data generated by globally coupled map, which can produce time series data with different correlation lengths, and also applied to gene expression data, which are typical static data of small-size samples with high dimensions, and we successfully detected signal variables from them. Moreover, we verified the assumption that the gene expression data also potentially have a dynamical system as their generation model, and found that the assumption is compatible with the results of signal extraction.

We conduct the first comprehensive meta-analysis of deterministic solar forecasting based on skill score, screening 1,447 papers from Google Scholar and reviewing the full texts of 320 papers for data extraction. A database of 4,687 points was built and analyzed with multivariate adaptive regression spline modelling, partial dependence plots, and linear regression. The marginal impacts on skill score of ten factors were quantified. The analysis shows the non-linearity and complex interaction between variables in the database. Forecast horizon has a central impact and dominates other factors' impacts. Therefore, the analysis of solar forecasts should be done separately for each horizon. Climate zone variables have statistically significant correlation with skill score. Regarding inputs, historical data and spatial temporal information are highly helpful. For intra-day, sky and satellite images show the most importance. For day-ahead, numerical weather predictions and locally measured meteorological data are very efficient. All forecast models were compared. Ensemble-hybrid models achieve the most accurate forecasts for all horizons. Hybrid models show superiority for intra-hour while image-based methods are the most efficient for intra-day forecasts. More training data can enhance skill score. However, over-fitting is observed when there is too much training data (longer than 2000 days). There has been a substantial improvement in solar forecast accuracy, especially in recent years. More improvement is observed for intra-hour and intra-day than day-ahead forecasts. By controlling for the key differences between forecasts, including location variables, our findings can be applied globally.

``Benign overfitting'', the ability of certain algorithms to interpolate noisy training data and yet perform well out-of-sample, has been a topic of considerable recent interest. We show, using a fixed design setup, that an important class of predictors, kernel machines with translation-invariant kernels, does not exhibit benign overfitting in fixed dimensions. In particular, the estimated predictor does not converge to the ground truth with increasing sample size, for any non-zero regression function and any (even adaptive) bandwidth selection. To prove these results, we give exact expressions for the generalization error, and its decomposition in terms of an approximation error and an estimation error that elicits a trade-off based on the selection of the kernel bandwidth. Our results apply to commonly used translation-invariant kernels such as Gaussian, Laplace, and Cauchy.

We propose a novel generative model for time series based on Schr{\"o}dinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respecting the temporal dynamics of the time series distribution. We can estimate the drift function from data samples either by kernel regression methods or with LSTM neural networks, and the simulation of the SB diffusion yields new synthetic data samples of the time series. The performance of our generative model is evaluated through a series of numerical experiments. First, we test with a toy autoregressive model, a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal and temporal dependencies metrics. Next, we use our SB generated synthetic samples for the application to deep hedging on real-data sets. Finally, we illustrate the SB approach for generating sequence of images.

This article presents a novel hybrid approach using statistics and machine learning to forecast the national demand of electricity. As investment and operation of future energy systems require long-term electricity demand forecasts with hourly resolution, our mathematical model fills a gap in energy forecasting. The proposed methodology was constructed using hourly data from Ukraine's electricity consumption ranging from 2013 to 2020. To this end, we analysed the underlying structure of the hourly, daily and yearly time series of electricity consumption. The long-term yearly trend is evaluated using macroeconomic regression analysis. The mid-term model integrates temperature and calendar regressors to describe the underlying structure, and combines ARIMA and LSTM ``black-box'' pattern-based approaches to describe the error term. The short-term model captures the hourly seasonality through calendar regressors and multiple ARMA models for the residual. Results show that the best forecasting model is composed by combining multiple regression models and a LSTM hybrid model for residual prediction. Our hybrid model is very effective at forecasting long-term electricity consumption on an hourly resolution. In two years of out-of-sample forecasts with 17520 timesteps, it is shown to be within 96.83 \% accuracy.

This study aims to determine a predictive model to learn students probability to pass their courses taken at the earliest stage of the semester. To successfully discover a good predictive model with high acceptability, accurate, and precision rate which delivers a useful outcome for decision making in education systems, in improving the processes of conveying knowledge and uplifting students academic performance, the proponent applies and strictly followed the CRISP-DM (Cross-Industry Standard Process for Data Mining) methodology. This study employs classification for data mining techniques, and decision tree for algorithm. With the utilization of the newly discovered predictive model, the prediction of students probabilities to pass the current courses they take gives 0.7619 accuracy, 0.8333 precision, 0.8823 recall, and 0.8571 f1 score, which shows that the model used in the prediction is reliable, accurate, and recommendable. Considering the indicators and the results, it can be noted that the prediction model used in this study is highly acceptable. The data mining techniques provides effective and efficient innovative tools in analyzing and predicting student performances. The model used in this study will greatly affect the way educators understand and identify the weakness of their students in the class, the way they improved the effectiveness of their learning processes gearing to their students, bring down academic failure rates, and help institution administrators modify their learning system outcomes. Further study for the inclusion of some students demographic information, vast amount of data within the dataset, automated and manual process of predictive criteria indicators where the students can regulate to which criteria, they must improve more for them to pass their courses taken at the end of the semester as early as midterm period are highly needed.

Deep Learning (DL) can predict biomarkers from cancer histopathology. Several clinically approved applications use this technology. Most approaches, however, predict categorical labels, whereas biomarkers are often continuous measurements. We hypothesized that regression-based DL outperforms classification-based DL. Therefore, we developed and evaluated a new self-supervised attention-based weakly supervised regression method that predicts continuous biomarkers directly from images in 11,671 patients across nine cancer types. We tested our method for multiple clinically and biologically relevant biomarkers: homologous repair deficiency (HRD) score, a clinically used pan-cancer biomarker, as well as markers of key biological processes in the tumor microenvironment. Using regression significantly enhances the accuracy of biomarker prediction, while also improving the interpretability of the results over classification. In a large cohort of colorectal cancer patients, regression-based prediction scores provide a higher prognostic value than classification-based scores. Our open-source regression approach offers a promising alternative for continuous biomarker analysis in computational pathology.