Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the \emph{covariate shift}, where the input distributions of data change from training to testing stages while the input-conditional output distribution remains unchanged. In this paper, we initiate the study of a more challenging scenario -- \emph{continuous} covariate shift -- in which the test data appear sequentially, and their distributions can shift continuously. Our goal is to adaptively train the predictor such that its prediction risk accumulated over time can be minimized. Starting with the importance-weighted learning, we show the method works effectively if the time-varying density ratios of test and train inputs can be accurately estimated. However, existing density ratio estimation methods would fail due to data scarcity at each time step. To this end, we propose an online method that can appropriately reuse historical information. Our density ratio estimation method is proven to perform well by enjoying a dynamic regret bound, which finally leads to an excess risk guarantee for the predictor. Empirical results also validate the effectiveness.

We propose a paradigm for interpretable Manifold Learning for scientific data analysis, whereby we parametrize a manifold with $d$ smooth functions from a scientist-provided dictionary of meaningful, domain-related functions. When such a parametrization exists, we provide an algorithm for finding it based on sparse non-linear regression in the manifold tangent bundle, bypassing more standard manifold learning algorithms. We also discuss conditions for the existence of such parameterizations in function space and for successful recovery from finite samples. We demonstrate our method with experimental results from a real scientific domain.

Hello and welcome to this tutorial. We have learnt how to create Single and Multiple linear regression models. Now, let’s learn how to create Polynomial regression Models in R and where we would apply it to solve real life problems. According to Wikipedia, Polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modeled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the correspondent conditional mean of y. In this tutorial we are going to be […]

We study the relationship between two desiderata of algorithms in statistical inference and machine learning: differential privacy and robustness to adversarial data corruptions. Their conceptual similarity was first observed by Dwork and Lei (STOC 2009), who observed that private algorithms satisfy robustness, and gave a general method for converting robust algorithms to private ones. However, all general methods for transforming robust algorithms into private ones lead to suboptimal error rates. Our work gives the first black-box transformation that converts any adversarially robust algorithm into one that satisfies pure differential privacy. Moreover, we show that for any low-dimensional estimation task, applying our transformation to an optimal robust estimator results in an optimal private estimator. Thus, we conclude that for any low-dimensional task, the optimal error rate for $\varepsilon$-differentially private estimators is essentially the same as the optimal error rate for estimators that are robust to adversarially corrupting $1/\varepsilon$ training samples. We apply our transformation to obtain new optimal private estimators for several high-dimensional tasks, including Gaussian (sparse) linear regression and PCA. Finally, we present an extension of our transformation that leads to approximate differentially private algorithms whose error does not depend on the range of the output space, which is impossible under pure differential privacy.

To identify patients who are hospitalized because of COVID-19 as opposed to those who were admitted for other indications, we compared the performance of different computable phenotype definitions for COVID-19 hospitalizations that use different types of data from the electronic health records (EHR), including structured EHR data elements, provider notes, or a combination of both data types. And conduct a retrospective data analysis utilizing chart review-based validation. Participants are 586 hospitalized individuals who tested positive for SARS-CoV-2 during January 2022. We used natural language processing to incorporate data from provider notes and LASSO regression and Random Forests to fit classification algorithms that incorporated structured EHR data elements, provider notes, or a combination of structured data and provider notes. Results: Based on a chart review, 38% of 586 patients were determined to be hospitalized for reasons other than COVID-19 despite having tested positive for SARS-CoV-2. A classification algorithm that used provider notes had significantly better discrimination than one that used structured EHR data elements (AUROC: 0.894 vs 0.841, p < 0.001), and performed similarly to a model that combined provider notes with structured data elements (AUROC: 0.894 vs 0.893). Assessments of hospital outcome metrics significantly differed based on whether the population included all hospitalized patients who tested positive for SARS-CoV-2 versus those who were determined to have been hospitalized due to COVID-19. This work demonstrates the utility of natural language processing approaches to derive information related to patient hospitalizations in cases where there may be multiple conditions that could serve as the primary indication for hospitalization.

Continuous Blood Glucose (CGM) monitors have revolutionized the ability of diabetics to manage their blood glucose, and paved the way for artificial pancreas systems. In this paper we augment CGM data with sensor input collected by a smart phone and use it to provide analytical tools for patients and clinicians. We collected GPS data, activity classifications, and blood glucose data with a custom iOS application over a 9 month period from a single free-living type-1 diabetic patient. This data set is novel in terms of it's size, the inclusion of GPS data, and the fact that it was collected non-intrusively from a free-living patient. We describe a method to measure the occurrence of lifestyle \textit{events} based on GPS and activity data, and show that they can capture instances of food consumption and are therefore correlated to changes in blood glucose. Finally, we incorporate these event representations into our system to create useful visualizations and notifications to aid patients in managing their diabetes.

The unsupervised nature of the models makes them suitable for exploring topics in a corpus without prior knowledge. However, researchers find that these models often fail to measure specific concepts of substantive interest by inadvertently creating multiple topics with similar content and combining distinct themes into a single topic. In this paper, we empirically demonstrate that providing a small number of keywords can substantially enhance the measurement performance of topic models. An important advantage of the proposed keyword assisted topic model (keyATM) is that the specification of keywords requires researchers to label topics prior to fitting a model to the data. This contrasts with a widespread practice of post-hoc topic interpretation and adjustments that compromises the objectivity of empirical findings. In our application, we find that keyATM provides more interpretable results, has better document classification performance, and is less sensitive to the number of topics than the standard topic models. Finally, we show that keyATM can also incorporate covariates and model time trends. An open-source software package is available for implementing the proposed methodology. Verification Materials: The data and materials required to verify the computational reproducibility of the results, procedures and analyses in this article are available on the American Journal of Political Science Dataverse within the Harvard Dataverse Network, at: https://doi.org/10.7910/DVN/RKNNVL

Deep artificial neural networks show high predictive performance in many fields, but they do not afford statistical inferences and their black-box operations are too complicated for humans to comprehend. Because positing that a relationship exists is often more important than prediction in scientific experiments and research models, machine learning is far less frequently used than inferential statistics. Additionally, statistics calls for improving the test of theory by showing the magnitude of the phenomena being studied. This article extends current XAI methods and develops a model agnostic hypothesis testing framework for machine learning. First, Fisher's variable permutation algorithm is tweaked to compute an effect size measure equivalent to Cohen's f2 for OLS regression models. Second, the Mann-Kendall test of monotonicity and the Theil-Sen estimator is applied to Apley's accumulated local effect plots to specify a variable's direction of influence and statistical significance. The usefulness of this approach is demonstrated on an artificial data set and a social survey with a Python sandbox implementation.

Linearity: This assumption states that there is a linear relationship between the independent and dependent variables. The relationship should be expressed as a straight line on a scatter plot, and the residuals (the difference between the actual and predicted values) should be randomly dispersed around zero. If this assumption is violated, the regression results may be misleading and the model will not generalize well to new data. Independence: The observations in the data should be independent of each other, meaning that the value of one observation should not affect the value of another observation. If the observations are dependent, the standard errors of the regression coefficients will be biased and the results will not be valid.

The semiconductor industry is one of the most technology-evolving and capital-intensive market sectors. Effective inspection and metrology are necessary to improve product yield, increase product quality and reduce costs. In recent years, many semiconductor manufacturing equipments are equipped with sensors to facilitate real-time monitoring of the production process. These production-state and equipment-state sensor data provide an opportunity to practice machine-learning technologies in various domains, such as anomaly/fault detection, maintenance scheduling, quality prediction, etc. In this work, we focus on the task of soft sensing regression, which uses sensor data to predict impending inspection measurements that used to be measured in wafer inspection and metrology systems. We proposed an LSTM-based regressor and designed two loss functions for model training. Although engineers may look at our prediction errors in a subjective manner, a new piece-wise evaluation metric was proposed for assessing model accuracy in a mathematical way. The experimental results demonstrated that the proposed model can achieve accurate and early prediction of various types of inspections in complicated manufacturing processes.