Most current domain adaptation methods address either covariate shift or label shift, but are not applicable where they occur simultaneously and are confounded with each other. Domain adaptation approaches which do account for such confounding are designed to adapt covariates to optimally predict a particular label whose shift is confounded with covariate shift. In this paper, we instead seek to achieve general-purpose data backwards compatibility. This would allow the adapted covariates to be used for a variety of downstream problems, including on pre-existing prediction models and on data analytics tasks. To do this we consider a special case of generalized label shift (GLS), which we call confounded shift. We present a novel framework for this problem, based on minimizing the expected divergence between the source and target conditional distributions, conditioning on possible confounders. Within this framework, we propose using the reverse Kullback-Leibler divergence, demonstrating the use of parametric and nonparametric Gaussian estimators of the conditional distribution. We also propose using the Maximum Mean Discrepancy (MMD), introducing a dynamic strategy for choosing the kernel bandwidth, which is applicable even outside the confounded shift setting. Finally, we demonstrate our approach on synthetic and real datasets.

Nonconvex penalties are utilized for regularization in high-dimensional statistical learning algorithms primarily because they yield unbiased or nearly unbiased estimators for the parameters in the model. Nonconvex penalties existing in the literature such as SCAD, MCP, Laplace and arctan have a singularity at origin which makes them useful also for variable selection. However, in several high-dimensional frameworks such as deep learning, variable selection is less of a concern. In this paper, we present a nonconvex penalty which is smooth at origin. The paper includes asymptotic results for ordinary least squares estimators regularized with the new penalty function, showing asymptotic bias that vanishes exponentially fast. We also conducted an empirical study employing deep neural network architecture on three datasets and convolutional neural network on four datasets. The empirical study showed better performance for the new regularization approach in five out of the seven datasets.

In this paper, we present a study of a kernel-based consensual aggregation on randomly projected high-dimensional features of predictions for regression. The aggregation scheme is composed of two steps: the high-dimensional features of predictions, given by a large number of regression estimators, are randomly projected into a smaller subspace using Johnson-Lindenstrauss Lemma in the first step, and a kernel-based consensual aggregation is implemented on the projected features in the second step. We theoretically show that the performance of the aggregation scheme is close to the performance of the aggregation implemented on the original high-dimensional features, with high probability. Moreover, we numerically illustrate that the aggregation scheme upholds its performance on very large and highly correlated features of predictions given by different types of machines. The aggregation scheme allows us to flexibly merge a large number of redundant machines, plainly constructed without model selection or cross-validation. The efficiency of the proposed method is illustrated through several experiments evaluated on different types of synthetic and real datasets.

DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of two vectors), where each low-rank tensor is generated by a deep network (DN) that is trained in a self-supervised manner to minimize the mean-squared approximation error. Our key observation is that the implicit regularization inherent in DNs enables them to capture nonlinear signal structures (e.g., manifolds) that are out of the reach of classical linear methods like the singular value decomposition (SVD) and principal component analysis (PCA). Furthermore, in contrast to the SVD and PCA, whose performance deteriorates when the tensor's entries deviate from additive white Gaussian noise, we demonstrate that the performance of DeepTensor is robust to a wide range of distributions. We validate that DeepTensor is a robust and computationally efficient drop-in replacement for the SVD, PCA, nonnegative matrix factorization (NMF), and similar decompositions by exploring a range of real-world applications, including hyperspectral image denoising, 3D MRI tomography, and image classification. In particular, DeepTensor offers a 6dB signal-to-noise ratio improvement over standard denoising methods for signals corrupted by Poisson noise and learns to decompose 3D tensors 60 times faster than a single DN equipped with 3D convolutions.

In urban areas, global navigation satellite system (GNSS) signals are often reflected or blocked by buildings, thus resulting in large positioning errors. In this study, we proposed a machine learning approach for global positioning system (GPS) multipath detection that uses dual antennas. A machine learning model that could classify GPS signal reception conditions was trained with several GPS measurements selected as suggested features. We applied five features for machine learning, including a feature obtained from the dual antennas, and evaluated the classification performance of the model, after applying four machine learning algorithms: gradient boosting decision tree (GBDT), random forest, decision tree, and K-nearest neighbor (KNN). It was found that a classification accuracy of 82%-96% was achieved when the test data set was collected at the same locations as those of the training data set. However, when the test data set was collected at locations different from those of the training data, a classification accuracy of 44%-77% was obtained.

This formula-free summary provides a short overview about how PCA (principal component analysis) works for dimension reduction, that is, to select k features (also called variables) among a larger set of n features, with k much smaller than n. This smaller set of k features built with PCA is the best subset of k features, in the sense that it minimizes the variance of the residual noise when fitting data to a linear model. Note that PCA transforms the initial features into new ones, that are linear combinations of the original features. The proportion of the variance that each eigenvector represents can be calculated by dividing the eigenvalue corresponding to that eigenvector by the sum of all eigenvalues. If the original features are highly correlated, the solution will be very unstable.

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The gait patterns of patients with multiple sclerosis (MS) were found to be discriminable from those of healthy controls using machine learning methods, according to an article published in BioMedical Engineering OnLine. The study utilized a standard set of gait features with a support vector machine learning model to differentiate the gaits of patients with MS from those of healthy controls with an accuracy of 81%, precision of 95%, recall of 81%, and F1-score of 87%. When an additional set of novel gait features (toe direction, hull area, base of support area, foot length, foot width, and foot area) were added to the support vector machine, the accuracy increased to 88%, recall to 90%, and F1-score to 93%. The precision level was unchanged. "These results demonstrate that machine learning models trained on new features from raw walkway data can more effectively separate patient and control targets and could potentially be served as an alternative method for identifying gait abnormalities in MS," the authors said.

An optimizer is a function or an algorithm that customizes the attributes of the neural network, such as weights and discovering rate. Hence, it assists in decreasing the overall loss and also enhance the accuracy. The problem of picking the ideal weights for the version is an overwhelming job, as a deep learning version usually includes numerous parameters. It increases the requirement to pick an appropriate optimization algorithm for your application. You can utilize different optimizers to make changes in your weights as well as learning price.

Experimental observations and convincing conceptual arguments indicate that the present understanding of fundamental physics is not complete. Our theoretical formulation of the fundamental laws of Nature, the Standard Model, has been predicting with extremely high precision an impressive amount of data collected at past and ongoing experiments. On the other hand, the Standard Model does not provide answer to a multitude of questions including the origin of the electroweak scale, the mass of neutrinos, the flavour structure in the quark, lepton and neutrino sectors, and is unable to account for observed phenomena like the origin and the composition of the dark matter of the baryon asymmetry in the Universe. Further, it does not provide a microscopic description of gravity. These considerations guarantee the existence of more fundamental laws of Nature waiting to be unveiled. In order to access these laws, we must search the experimental data for phenomena that depart from the Standard Model predictions. Currently, the most common searching strategy is to test the data for the presence of specific new physics models, one at the time. Each search is then optimized to be sensitive to the features specific of the considered new physics scenario. This approach is in general insensitive to sources of discrepancy that differ from those considered.