Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors follow some geometric structure in the latent space. In this paper, we consider random dot product graphs, in which an edge is formed between two nodes with probability given by the inner product of their respective latent positions. We assume that the latent position vectors lie on an unknown one-dimensional curve and are coupled with a response covariate via a regression model. Using the geometry of the underlying latent position vectors, we propose a manifold learning and graph embedding technique to predict the response variable on out-of-sample nodes, and we establish convergence guarantees for these responses. Our theoretical results are supported by simulations and an application to Drosophila brain data.

In robotic laser surgery, shape prediction of an one-shot ablation cavity is an important problem for minimizing errant overcutting of healthy tissue during the course of pathological tissue resection and precise tumor removal. Since it is difficult to physically model the laser-tissue interaction due to the variety of optical tissue properties, complicated process of heat transfer, and uncertainty about the chemical reaction, we propose a 3D cavity prediction model based on an entirely data-driven method without any assumptions of laser settings and tissue properties. Based on the cavity prediction model, we formulate a novel robotic laser planning problem to determine the optimal laser incident configuration, which aims to create a cavity that aligns with the surface target (e.g. tumor, pathological tissue). To solve the one-shot ablation cavity prediction problem, we model the 3D geometric relation between the tissue surface and the laser energy profile as a non-linear regression problem that can be represented by a single-layer perceptron (SLP) network. The SLP network is encoded in a novel kinematic model to predict the shape of the post-ablation cavity with an arbitrary laser input. To estimate the SLP network parameters, we formulate a dataset of one-shot laser-phantom cavities reconstructed by the optical coherence tomography (OCT) B-scan images for the data-driven modelling. To verify the method. The learned cavity prediction model is applied to solve a simplified robotic laser planning problem modelled as a surface alignment error minimization problem. The initial results report (91.1 +- 3.0)% 3D-cavity-Intersection-over-Union (3D-cavity-IoU) for the 3D cavity prediction and an average of 97.9% success rate for the simulated surface alignment experiments.

Although many fairness criteria have been proposed to ensure that machine learning algorithms do not exhibit or amplify our existing social biases, these algorithms are trained on datasets that can themselves be statistically biased. In this paper, we investigate the robustness of a number of existing (demographic) fairness criteria when the algorithm is trained on biased data. We consider two forms of dataset bias: errors by prior decision makers in the labeling process, and errors in measurement of the features of disadvantaged individuals. We analytically show that some constraints (such as Demographic Parity) can remain robust when facing certain statistical biases, while others (such as Equalized Odds) are significantly violated if trained on biased data. We also analyze the sensitivity of these criteria and the decision maker's utility to biases. We provide numerical experiments based on three real-world datasets (the FICO, Adult, and German credit score datasets) supporting our analytical findings. Our findings present an additional guideline for choosing among existing fairness criteria, or for proposing new criteria, when available datasets may be biased.

Functions of the ratio of the densities $p/q$ are widely used in machine learning to quantify the discrepancy between the two distributions $p$ and $q$. For high-dimensional distributions, binary classification-based density ratio estimators have shown great promise. However, when densities are well separated, estimating the density ratio with a binary classifier is challenging. In this work, we show that the state-of-the-art density ratio estimators perform poorly on well-separated cases and demonstrate that this is due to distribution shifts between training and evaluation time. We present an alternative method that leverages multi-class classification for density ratio estimation and does not suffer from distribution shift issues. The method uses a set of auxiliary densities $\{m_k\}_{k=1}^K$ and trains a multi-class logistic regression to classify the samples from $p, q$, and $\{m_k\}_{k=1}^K$ into $K+2$ classes. We show that if these auxiliary densities are constructed such that they overlap with $p$ and $q$, then a multi-class logistic regression allows for estimating $\log p/q$ on the domain of any of the $K+2$ distributions and resolves the distribution shift problems of the current state-of-the-art methods. We compare our method to state-of-the-art density ratio estimators on both synthetic and real datasets and demonstrate its superior performance on the tasks of density ratio estimation, mutual information estimation, and representation learning. Code: https://www.blackswhan.com/mdre/

Transfer learning is an essential tool for improving the performance of primary tasks by leveraging information from auxiliary data resources. In this work, we propose Adaptive Robust Transfer Learning (ART), a flexible pipeline of performing transfer learning with generic machine learning algorithms. We establish the non-asymptotic learning theory of ART, providing a provable theoretical guarantee for achieving adaptive transfer while preventing negative transfer. Additionally, we introduce an ART-integrated-aggregating machine that produces a single final model when multiple candidate algorithms are considered. We demonstrate the promising performance of ART through extensive empirical studies on regression, classification, and sparse learning. We further present a real-data analysis for a mortality study.

To implement machine learning, it is essential to first determine an appropriate algorithm for the dataset. Different algorithms may produce a large number of different models with different hyperparameter configurations, and it usually takes a lot of time to run the model on a large dataset when the model is relatively complex. Therefore, how to predict the performance of a model on a dataset is an fundamental problem to be solved. This thesis designs a prediction system based on matrix factorization to predict the classification accuracy of a specific model on a particular dataset. In this thesis, we conduct a comprehensive empirical research on more than fifty datasets that we collected from the openml web site.

We propose EBLIME to explain black-box machine learning models and obtain the distribution of feature importance using Bayesian ridge regression models. We provide mathematical expressions of the Bayesian framework and theoretical outcomes including the significance of ridge parameter. Case studies were conducted on benchmark datasets and a real-world industrial application of locating internal defects in manufactured products. Compared to the state-of-the-art methods, EBLIME yields more intuitive and accurate results, with better uncertainty quantification in terms of deriving the posterior distribution, credible intervals, and rankings of the feature importance.

Medical studies frequently require to extract the relationship between each covariate and the outcome with statistical confidence measures. To do this, simple parametric models are frequently used (e.g. coefficients of linear regression) but usually fitted on the whole dataset. However, it is common that the covariates may not have a uniform effect over the whole population and thus a unified simple model can miss the heterogeneous signal. For example, a linear model may be able to explain a subset of the data but fail on the rest due to the nonlinearity and heterogeneity in the data. In this paper, we propose DDGroup (data-driven group discovery), a data-driven method to effectively identify subgroups in the data with a uniform linear relationship between the features and the label. DDGroup outputs an interpretable region in which the linear model is expected to hold. It is simple to implement and computationally tractable for use. We show theoretically that, given a large enough sample, DDGroup recovers a region where a single linear model with low variance is well-specified (if one exists), and experiments on real-world medical datasets confirm that it can discover regions where a local linear model has improved performance. Our experiments also show that DDGroup can uncover subgroups with qualitatively different relationships which are missed by simply applying parametric approaches to the whole dataset.

LASSO regularized logistic regression is particularly useful for its built-in feature selection, allowing coefficients to be removed from deployment and producing sparse solutions. Differentially private versions of LASSO logistic regression have been developed, but generally produce dense solutions, reducing the intrinsic utility of the LASSO penalty. In this paper, we present a differentially private method for sparse logistic regression that maintains hard zeros. Our key insight is to first train a non-private LASSO logistic regression model to determine an appropriate privatized number of non-zero coefficients to use in final model selection. To demonstrate our method's performance, we run experiments on synthetic and real-world datasets.

The COVID 19 pandemic and ongoing political and regional conflicts have a highly detrimental impact on the global supply chain, causing significant delays in logistics operations and international shipments. One of the most pressing concerns is the uncertainty surrounding the availability dates of products, which is critical information for companies to generate effective logistics and shipment plans. Therefore, accurately predicting availability dates plays a pivotal role in executing successful logistics operations, ultimately minimizing total transportation and inventory costs. We investigate the prediction of product availability dates for General Electric (GE) Gas Power's inbound shipments for gas and steam turbine service and manufacturing operations, utilizing both numerical and categorical features. We evaluate several regression models, including Simple Regression, Lasso Regression, Ridge Regression, Elastic Net, Random Forest (RF), Gradient Boosting Machine (GBM), and Neural Network models. Based on real world data, our experiments demonstrate that the tree based algorithms (i.e., RF and GBM) provide the best generalization error and outperforms all other regression models tested. We anticipate that our prediction models will assist companies in managing supply chain disruptions and reducing supply chain risks on a broader scale.