In this work, we study the numerical solution of inverse eigenvalue problems from a machine learning perspective. Two different problems are considered: the inverse Strum-Liouville eigenvalue problem for symmetric potentials and the inverse transmission eigenvalue problem for spherically symmetric refractive indices. Firstly, we solve the corresponding direct problems to produce the required eigenvalues datasets in order to train the machine learning algorithms. Next, we consider several examples of inverse problems and compare the performance of each model to predict the unknown potentials and refractive indices respectively, from a given small set of the lowest eigenvalues. The supervised regression models we use are k-Nearest Neighbours, Random Forests and Multi-Layer Perceptron. Our experiments show that these machine learning methods, under appropriate tuning on their parameters, can numerically solve the examined inverse eigenvalue problems.

The primary aim of this research was to find a model that best predicts which fallen angel bonds would either potentially rise up back to investment grade bonds and which ones would fall into bankruptcy. To implement the solution, we thought that the ideal method would be to create an optimal machine learning model that could predict bankruptcies. Among the many machine learning models out there we decided to pick four classification methods: logistic regression, KNN, SVM, and NN. We also utilized an automated methods of Google Cloud's machine learning. The results of our model comparisons showed that the models did not predict bankruptcies very well on the original data set with the exception of Google Cloud's machine learning having a high precision score. However, our over-sampled and feature selection data set did perform very well. This could likely be due to the model being over-fitted to match the narrative of the over-sampled data (as in, it does not accurately predict data outside of this data set quite well). Therefore, we were not able to create a model that we are confident that would predict bankruptcies. However, we were able to find value out of this project in two key ways. The first is that Google Cloud's machine learning model in every metric and in every data set either outperformed or performed on par with the other models. The second is that we found that utilizing feature selection did not reduce predictive power that much. This means that we can reduce the amount of data to collect for future experimentation regarding predicting bankruptcies.

Sometimes as engineers and scientists, we think of data only as bytes on RAM, matrices in GPUs, and numeric features that go into our predictive black-box. We forget they represent changes in some real-world patterns. For example, when real world events and trends arise, we tend to defer to Google first to acquire related information (i.e where to go for a hike, what does term X mean) -- which makes Google Search Trends a very good source of data for interpreting and understanding what is going on live around us. This is why we decided to study a complex interplay between Google Search trends using it to predict other temporal data, and see if perhaps it could be used as features for a temporal machine learning model, and any insights we can draw from it. In this project, we looked at how Google Trends data could be used as features for times series models or regression models.

Six machine-learning prediction models (logistic regression with and without splines, lasso regression, random forest, gradient-boosting machines [ …

This work studies the problem of transfer learning under the functional linear regression model framework, which aims to improve the estimation and prediction of the target model by leveraging the information from related source models. We measure the relatedness between target and source models using Reproducing Kernel Hilbert Spaces (RKHS) norm, allowing the type of information being transferred to be interpreted by the structural properties of the spaces. Two transfer learning algorithms are proposed: one transfers information from source tasks when we know which sources to use, while the other one aggregates multiple transfer learning results from the first algorithm to achieve robust transfer learning without prior information about the sources. Furthermore, we establish the optimal convergence rates for the prediction risk in the target model, making the statistical gain via transfer learning mathematically provable. The theoretical analysis of the prediction risk also provides insights regarding what factors are affecting the transfer learning effect, i.e. what makes source tasks useful to the target task. We demonstrate the effectiveness of the proposed transfer learning algorithms on extensive synthetic data as well as real financial data application.

Objective: Traumatic brain injury can be caused by head impacts, but many brain injury risk estimation models are not equally accurate across the variety of impacts that patients may undergo and the characteristics of different types of impacts are not well studied. We investigated the spectral characteristics of different head impact types with kinematics classification. Methods: Data was analyzed from 3,262 head impacts from lab reconstruction, American football, mixed martial arts, and publicly available car crash data. A random forest classifier with spectral densities of linear acceleration and angular velocity was built to classify head impact types (e.g., football, car crash, mixed martial arts). To test the classifier robustness, another 271 lab-reconstructed impacts were obtained from 5 other instrumented mouthguards. Finally, with the classifier, type-specific, nearest-neighbor regression models were built for brain strain. Results: The classifier reached a median accuracy of 96% over 1,000 random partitions of training and test sets. The most important features in the classification included both low-frequency and high-frequency features, both linear acceleration features and angular velocity features. Different head impact types had different distributions of spectral densities in low-frequency and high-frequency ranges (e.g., the spectral densities of MMA impacts were higher in high-frequency range than in the low-frequency range). The type-specific regression showed a generally higher R^2-value than baseline models without classification. Conclusion: The machine-learning-based classifier enables a better understanding of the impact kinematics spectral density in different sports, and it can be applied to evaluate the quality of impact-simulation systems and on-field data augmentation.

As machine learning (ML) systems get adopted in more critical areas, it has become increasingly crucial to address the bias that could occur in these systems. Several fairness pre-processing algorithms are available to alleviate implicit biases during model training. These algorithms employ different concepts of fairness, often leading to conflicting strategies with consequential trade-offs between fairness and accuracy. In this work, we evaluate three popular fairness pre-processing algorithms and investigate the potential for combining all algorithms into a more robust pre-processing ensemble. We report on lessons learned that can help practitioners better select fairness algorithms for their models.

Efficient and accurate detection of subtle motion generated from small objects in noisy environments, as needed for vital sign monitoring, is challenging, but can be substantially improved with magnification. We developed a complex Gabor filter-based decomposition method to amplify phases at different spatial wavelength levels to magnify motion and extract 1D motion signals for fundamental frequency estimation. The phase-based complex Gabor filter outputs are processed and then used to train machine learning models that predict respiration and heart rate with greater accuracy. We show that our proposed technique performs better than the conventional temporal FFT-based method in clinical settings, such as sleep laboratories and emergency departments, as well for a variety of human postures.

This paper presents a successful attempt to overcome the uncertainties in seismicstratigraphic interpretation of the complex rock section with good accuracy for the early stage of field maturity. The deliverable included the model of restored regression relationship between the values of natural radioactivity of rocks and seismic wave field attributes with an acceptable prediction quality. Acceptable quality of the forecast is confirmed both by model validation with complete removal of some data from the learning process, and by the data obtained following the results of a new well drilled 150 meters away from the well from the learning sample. The regression relationship between the natural radioactivity of rocks and effective porosity of reservoirs was restored based on well tops data and log interpretation data - transition to reservoir properties of the target was carried out. The result was achieved with help of process stack consisting of machine learning methods, methods of enriching the source data with synthetic data, algorithms of creating new features using the function for regression model reconstruction as the target one, measurements of natural radioactivity of rocks, including for horizontal segments of wells. Two approaches were developed to enriching the source sample (geophysical data augmentations): spindle method and with help of Conditional Generative Adversarial Nets architecture (CGAN).

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper, consisting of probability measures. Although a Positive Definite kernel can be defined by using a suitable distance -- the Wasserstein distance -- the common procedure for learning the Gaussian Process model can fail due to numerical issues, arising earlier and more frequently than in the case of an Euclidean input space and, as demonstrated in this paper, that cannot be avoided by adding artificial noise (nugget effect) as usually done. This paper uncovers the main reason of these issues, that is a non-stationarity relationship between the Wasserstein-based squared exponential kernel and its Euclidean-based counterpart. As a relevant result, the Gaussian Process model is learned by assuming the input space as Euclidean and then an algebraic transformation, based on the uncovered relation, is used to transform it into a non-stationary and Wasserstein-based Gaussian Process model over probability measures. This algebraic transformation is simpler than log-exp maps used in the case of data belonging to Riemannian manifolds and recently extended to consider the pseudo-Riemannian structure of an input space equipped with the Wasserstein distance.