Mismatches between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple-target tracking or multi-person contactless vital sign monitoring may be severely affected by mismatched sample-channel assignments. To systematically address this fundamental problem, we pose it as a signal reconstruction problem where we have lost correspondences between the samples and their respective channels. Assuming that we have a sensing matrix for the underlying signals, we show that the problem is equivalent to a structured unlabeled sensing problem, and establish sufficient conditions for unique recovery. To the best of our knowledge, a sampling result for the reconstruction of shuffled multi-channel signals has not been considered in the literature and existing methods for unlabeled sensing cannot be directly applied. We extend our results to the case where the signals admit a sparse representation in an overcomplete dictionary (i.e., the sensing matrix is not precisely known), and derive sufficient conditions for the reconstruction of shuffled sparse signals. We propose a robust reconstruction method that combines sparse signal recovery with robust linear regression for the two-channel case. The performance and robustness of the proposed approach is illustrated in an application related to whole-brain calcium imaging. The proposed methodology can be generalized to sparse signal representations other than the ones considered in this work to be applied in a variety of real-world problems with imprecise measurement or channel assignment.

Debiased machine learning estimators for nonparametric inference of smooth functionals of the data-generating distribution can suffer from excessive variability and instability. For this reason, practitioners may resort to simpler models based on parametric or semiparametric assumptions. However, such simplifying assumptions may fail to hold, and estimates may then be biased due to model misspecification. To address this problem, we propose Adaptive Debiased Machine Learning (ADML), a nonparametric framework that combines data-driven model selection and debiased machine learning techniques to construct asymptotically linear, adaptive, and superefficient estimators for pathwise differentiable functionals. By learning model structure directly from data, ADML avoids the bias introduced by model misspecification and remains free from the restrictions of parametric and semiparametric models. While they may exhibit irregular behavior for the target parameter in a nonparametric statistical model, we demonstrate that ADML estimators provides regular and locally uniformly valid inference for a projection-based oracle parameter. Importantly, this oracle parameter agrees with the original target parameter for distributions within an unknown but correctly specified oracle statistical submodel that is learned from the data. This finding implies that there is no penalty, in a local asymptotic sense, for conducting data-driven model selection compared to having prior knowledge of the oracle submodel and oracle parameter. To demonstrate the practical applicability of our theory, we provide a broad class of ADML estimators for estimating the average treatment effect in adaptive partially linear regression models.

The availability of both structured and unstructured databases, such as electronic health data, social media data, patent data, and surveys that are often updated in real time, among others, has grown rapidly over the past decade. With this expansion, the statistical and methodological questions around data integration, or rather merging multiple data sources, has also grown. Specifically, the science of the "data cleaning pipeline" contains four stages that allow an analyst to perform downstream tasks, predictive analyses, or statistical analyses on "cleaned data." This article provides a review of this emerging field, introducing technical terminology and commonly used methods. Statement of Significance: The article reviews the data cleaning pipeline, introducing technical terminology and commonly used methods.

Counterfactual inference for continuous rather than binary treatment variables is more common in real-world causal inference tasks. While there are already some sample reweighting methods based on Marginal Structural Model for eliminating the confounding bias, they generally focus on removing the treatment's linear dependence on confounders and rely on the accuracy of the assumed parametric models, which are usually unverifiable. In this paper, we propose a de-confounding representation learning (DRL) framework for counterfactual outcome estimation of continuous treatment by generating the representations of covariates disentangled with the treatment variables. The DRL is a non-parametric model that eliminates both linear and nonlinear dependence between treatment and covariates. Specifically, we train the correlations between the de-confounded representations and the treatment variables against the correlations between the covariate representations and the treatment variables to eliminate confounding bias. Further, a counterfactual inference network is embedded into the framework to make the learned representations serve both de-confounding and trusted inference. Extensive experiments on synthetic datasets show that the DRL model performs superiorly in learning de-confounding representations and outperforms state-of-the-art counterfactual inference models for continuous treatment variables. In addition, we apply the DRL model to a real-world medical dataset MIMIC and demonstrate a detailed causal relationship between red cell width distribution and mortality.

An effective interdisciplinary study between machine learning and solar-thermal desalination requires a sufficiently large and well-analyzed experimental datasets. This study develops a modified dataset collection and analysis process for studying solar-thermal desalination by machine learning. Based on the optimized water condensation and collection process, the proposed experimental method collects over one thousand datasets, which is ten times more than the average number of datasets in previous works, by accelerating data collection and reducing the time by 83.3%. On the other hand, the effects of dataset features are investigated by using three different algorithms, including artificial neural networks, multiple linear regressions, and random forests. The investigation focuses on the effects of dataset size and range on prediction accuracy, factor importance ranking, and the model's generalization ability. The results demonstrate that a larger dataset can significantly improve prediction accuracy when using artificial neural networks and random forests. Additionally, the study highlights the significant impact of dataset size and range on ranking the importance of influence factors. Furthermore, the study reveals that the extrapolation data range significantly affects the extrapolation accuracy of artificial neural networks. Based on the results, massive dataset collection and analysis of dataset feature effects are important steps in an effective and consistent machine learning process flow for solar-thermal desalination, which can promote machine learning as a more general tool in the field of solar-thermal desalination.

Symbolic Regression is a powerful data-driven technique that searches for mathematical expressions that explain the relationship between input variables and a target of interest. Due to its efficiency and flexibility, Genetic Programming can be seen as the standard search technique for Symbolic Regression. However, the conventional Genetic Programming algorithm requires storing all data in a central location, which is not always feasible due to growing concerns about data privacy and security. While privacy-preserving research has advanced recently and might offer a solution to this problem, their application to Symbolic Regression remains largely unexplored. Furthermore, the existing work only focuses on the horizontally partitioned setting, whereas the vertically partitioned setting, another popular scenario, has yet to be investigated. Herein, we propose an approach that employs a privacy-preserving technique called Secure Multiparty Computation to enable parties to jointly build Symbolic Regression models in the vertical scenario without revealing private data. Preliminary experimental results indicate that our proposed method delivers comparable performance to the centralized solution while safeguarding data privacy.

In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objective is to reveal the impact of the data manifold's extrinsic geometry on the regression. Specifically, we analyze the impact of the manifold's curvatures (or higher order nonlinearity in the parameterization when the curvatures are locally zero) on the uniqueness of the regression solution. Our findings suggest that the corresponding linear regression does not have a unique solution when the embedded submanifold is flat in some dimensions. Otherwise, the manifold's curvature (or higher order nonlinearity in the embedding) may contribute significantly, particularly in the solution associated with the normal directions of the manifold. Our findings thus reveal the role of data manifold geometry in ensuring the stability of regression models for out-of-distribution inferences.

To alleviate the shortage of computing power faced by clients in training deep neural networks (DNNs) using federated learning (FL), we leverage the edge computing and split learning to propose a model-splitting allowed FL (SFL) framework, with the aim to minimize the training latency without loss of test accuracy. Under the synchronized global update setting, the latency to complete a round of global training is determined by the maximum latency for the clients to complete a local training session. Therefore, the training latency minimization problem (TLMP) is modelled as a minimizing-maximum problem. To solve this mixed integer nonlinear programming problem, we first propose a regression method to fit the quantitative-relationship between the cut-layer and other parameters of an AI-model, and thus, transform the TLMP into a continuous problem. Considering that the two subproblems involved in the TLMP, namely, the cut-layer selection problem for the clients and the computing resource allocation problem for the parameter-server are relative independence, an alternate-optimization-based algorithm with polynomial time complexity is developed to obtain a high-quality solution to the TLMP. Extensive experiments are performed on a popular DNN-model EfficientNetV2 using dataset MNIST, and the results verify the validity and improved performance of the proposed SFL framework.

In the era of data-driven science, machine learning has emerged as a transformative tool, offering unprecedented solutions to complex problems across a wide range of scientific and technological domains. Specifically, machine learning has found applications in diverse fields such as biology, medicine, material science, engineering, energy, manufacturing, and agriculture. Notable examples include rapid detection of SARS-CoV-2 Ikponmwoba et al. [2022], advances in drug discovery and development Talevi et al. [2020], quality control and defect detection Wang et al. [2022], climate modeling and prediction Krasnopolsky and Fox-Rabinovitz [2006], as well as crop yield forecasting and optimization Di et al. [2022]. Some of these applications involve classification, which involves learning based on categorical data. In this regard, machine learning techniques, such as Support Vector Machines, Naive Bayes, K-nearest neighbor, and Neural Networks, have been used to extract texture features from images for subsequent classification Chola et al. [2022a,b]. Additionally, machine learning has facilitated the identification of high-order closure terms from fully kinetic simulations, a critical aspect of multi-scale modelingLaperre et al. [2022]. On the other hand, function approximation or regression involves estimating a continuous target quantity as a function of a set of input variables. Methods such as Sparse Identification of Nonlinear Dynamics (SINDy) Brunton et al. [2016], the Least Absolute Shrinkage and Selection Operator (LASSO) Tibshirani [1996], Dynamic Mode Decomposition (DMD) Schmid [2010], Mezić [2005], Koopman operator Mezić [2013] and the Eigensystem Realization Algorithm (ERA) Juang and Pappa [1985] have contributed significantly to understanding complex systems by offering effective strategies for model selection, variable regularization, decomposition of high-dimensional systems, and extraction of state-space models from input-output data.

In this paper, we find and analyze that we can easily drop the double descent by only adding one dropout layer before the fully-connected linear layer. The surprising double-descent phenomenon has drawn public attention in recent years, making the prediction error rise and drop as we increase either sample or model size. The current paper shows that it is possible to alleviate these phenomena by using optimal dropout in the linear regression model and the nonlinear random feature regression, both theoretically and empirically. % ${y}=X{\beta}^0+{\epsilon}$ with $X\in\mathbb{R}^{n\times p}$. We obtain the optimal dropout hyperparameter by estimating the ground truth ${\beta}^0$ with generalized ridge typed estimator $\hat{{\beta}}=(X^TX+\alpha\cdot\mathrm{diag}(X^TX))^{-1}X^T{y}$. Moreover, we empirically show that optimal dropout can achieve a monotonic test error curve in nonlinear neural networks using Fashion-MNIST and CIFAR-10. Our results suggest considering dropout for risk curve scaling when meeting the peak phenomenon. In addition, we figure out why previous deep learning models do not encounter double-descent scenarios -- because we already apply a usual regularization approach like the dropout in our models. To our best knowledge, this paper is the first to analyze the relationship between dropout and double descent.