With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fr\'echet regression model (Peterson & M\"uller 2019) provides a promising framework for regression analysis with metric space-valued responses. In this paper, we introduce a flexible sufficient dimension reduction (SDR) method for Fr\'echet regression to achieve two purposes: to mitigate the curse of dimensionality caused by high-dimensional predictors, and to provide a tool for data visualization for Fr\'echet regression. Our approach is flexible enough to turn any existing SDR method for Euclidean (X,Y) into one for Euclidean X and metric space-valued Y. The basic idea is to first map the metric-space valued random object $Y$ to a real-valued random variable $f(Y)$ using a class of functions, and then perform classical SDR to the transformed data. If the class of functions is sufficiently rich, then we are guaranteed to uncover the Fr\'echet SDR space. We showed that such a class, which we call an ensemble, can be generated by a universal kernel. We established the consistency and asymptotic convergence rate of the proposed methods. The finite-sample performance of the proposed methods is illustrated through simulation studies for several commonly encountered metric spaces that include Wasserstein space, the space of symmetric positive definite matrices, and the sphere. We illustrated the data visualization aspect of our method by exploring the human mortality distribution data across countries and by studying the distribution of hematoma density.

In the supervised machine learning world, there are two types of algorithmic tasks often performed. One is called regression (predicting continuous values) and the other is called classification (predicting discrete values). In this blog, I have presented an example of a binary classification algorithm called "Binary Logistic Regression" which comes under the Binomial family with a…

Logistic regression is a statistical model that in its basic form uses a logistic function to model a binary dependent variable, although many more complex extension exists. Integration analysis, logistic regression is estimating the parameters of logistic model which is the form of binary regression. In order to introduce this logistic regression to the students, this course of logistic regression for text classification is generated for all the graduates and postgraduates students who wish to begin with data science and machine learning for natural language processing. This course content contains video lectures which will give you the basic understanding of theoretical concepts of logistic regression along with the overview of the Practical implementation. This course have used the application domain of movie reviews for sentiment analysis from textual data.

If you want to learn how to perform the most useful statistical analyses in the R program, you have come to the right place. Now you don't have to scour the web endlessly in order to find how to do a Pearson or Spearman correlation, an independent t test or a factorial ANOVA, how to perform a sequential regression analysis or how to compute the Cronbach's alpha. Everything is here, in this course, explained visually, step by step. So, what will you learn in this course? First of all, you will learn how to perform association tests in R, both parametric and non-parametric: the Pearson correlation, the Spearman and Kendall correlation, the partial correlation and the chi-square test for independence.

We present the submission of team DICoE for FinSim-3, the 3rd Shared Task on Learning Semantic Similarities for the Financial Domain. The task provides a set of terms in the financial domain and requires to classify them into the most relevant hypernym from a financial ontology. After augmenting the terms with their Investopedia definitions, our system employs a Logistic Regression classifier over financial word embeddings and a mix of hand-crafted and distance-based features. Also, for the first time in this task, we employ different replacement methods for out-of-vocabulary terms, leading to improved performance. Finally, we have also experimented with word representations generated from various financial corpora. Our best-performing submission ranked 4th on the task's leaderboard.

Many machine learning tasks that involve predicting an output response can be solved by training a weighted regression model. Unfortunately, the predictive power of this type of models may severely deteriorate under low sample sizes or under covariate perturbations. Reweighting the training samples has aroused as an effective mitigation strategy to these problems. In this paper, we propose a novel and coherent scheme for kernel-reweighted regression by reparametrizing the sample weights using a doubly non-negative matrix. When the weighting matrix is confined in an uncertainty set using either the log-determinant divergence or the Bures-Wasserstein distance, we show that the adversarially reweighted estimate can be solved efficiently using first-order methods. Numerical experiments show that our reweighting strategy delivers promising results on numerous datasets.

It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust high-dimensional regression with coefficient thresholding, in which an efficient nonconvex estimation procedure is proposed through a thresholding function and the robust Huber loss. The proposed regularization method accounts for complex dependence structures in predictors and is robust against outliers in outcomes. Theoretically, we analyze rigorously the landscape of the population and empirical risk functions for the proposed method. The fine landscape enables us to establish both {statistical consistency and computational convergence} under the high-dimensional setting. The finite-sample properties of the proposed method are examined by extensive simulation studies. An illustration of real-world application concerns a scalar-on-image regression analysis for an association of psychiatric disorder measured by the general factor of psychopathology with features extracted from the task functional magnetic resonance imaging data in the Adolescent Brain Cognitive Development study.

Linear regression is one of the most popular techniques in data science. It can help you predict many different scenarios. Although it is a widespread technique, it is not a one-size-fits-all model because not all relationships in life are linear. "All models are wrong, but some are useful." You are interested in predicting physical and downloaded album sales from money spent on advertising. Your boss comes into the office and asks how many albums you would sell if you spend $100,000 advertising.

Children's health studies support an association between maternal environmental exposures and children's birth and health outcomes. A common goal in such studies is to identify critical windows of susceptibility -- periods during gestation with increased association between maternal exposures and a future outcome. The associations and timings of critical windows are likely heterogeneous across different levels of individual, family, and neighborhood characteristics. However, the few studies that have considered effect modification were limited to a few pre-specified subgroups. We propose a statistical learning method to estimate critical windows at the individual level and identify important characteristics that induce heterogeneity. The proposed approach uses distributed lag models (DLMs) modified by Bayesian additive regression trees to account for effect heterogeneity based on a potentially high-dimensional set of modifying factors. We show in a simulation study that our model can identify both critical windows and modifiers responsible for DLM heterogeneity. We estimate the relationship between weekly exposures to fine particulate matter during gestation and birth weight in an administrative Colorado birth cohort. We identify maternal body mass index (BMI), age, Hispanic designation, and education as modifiers of the distributed lag effects and find non-Hispanics with increased BMI to be a susceptible population.

Traditionally, fault detection and isolation community has used system dynamic equations to generate diagnosers and to analyze detectability and isolability of the dynamic systems. Model-based fault detection and isolation methods use system model to generate a set of residuals as the bases for fault detection and isolation. However, in many complex systems it is not feasible to develop highly accurate models for the systems and to keep the models updated during the system lifetime. Recently, data-driven solutions have received an immense attention in the industries systems for several practical reasons. First, these methods do not require the initial investment and expertise for developing accurate models. Moreover, it is possible to automatically update and retrain the diagnosers as the system or the environment change over time. Finally, unlike the model-based methods it is straight forward to combine time series measurements such as pressure and voltage with other sources of information such as system operating hours to achieve a higher accuracy. In this paper, we extend the traditional model-based fault detection and isolation concepts such as residuals, and detectable and isolable faults to the data-driven domain. We then propose an algorithm to automatically generate residuals from the normal operating data. We present the performance of our proposed approach through a comparative case study.