High-dimensional prediction considers data with more variables than samples. Generic research goals are to find the best predictor or to select variables. Results may be improved by exploiting prior information in the form of co-data, providing complementary data not on the samples, but on the variables. We consider adaptive ridge penalised generalised linear and Cox models, in which the variable specific ridge penalties are adapted to the co-data to give a priori more weight to more important variables. The R-package ecpc originally accommodated various and possibly multiple co-data sources, including categorical co-data, i.e. groups of variables, and continuous co-data. Continuous co-data, however, was handled by adaptive discretisation, potentially inefficiently modelling and losing information. Here, we present an extension to the method and software for generic co-data models, particularly for continuous co-data. At the basis lies a classical linear regression model, regressing prior variance weights on the co-data. Co-data variables are then estimated with empirical Bayes moment estimation. After placing the estimation procedure in the classical regression framework, extension to generalised additive and shape constrained co-data models is straightforward. Besides, we show how ridge penalties may be transformed to elastic net penalties with the R-package squeezy. In simulation studies we first compare various co-data models for continuous co-data from the extension to the original method. Secondly, we compare variable selection performance to other variable selection methods. Moreover, we demonstrate use of the package in several examples throughout the paper.

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy matrix-valued predictors. To address these issues, this paper proposes a framework of matrix variate regression models based on a rank constraint, vector regularization (e.g., sparsity), and a general loss function with three special cases considered: ordinary matrix regression, robust matrix regression, and matrix logistic regression. We also propose an alternating projected gradient descent algorithm. Based on analyzing our objective functions on manifolds with bounded curvature, we show that the algorithm is guaranteed to converge, all accumulation points of the iterates have estimation errors in the order of $O(1/\sqrt{n})$ asymptotically and substantially attaining the minimax rate. Our theoretical analysis can be applied to general optimization problems on manifolds with bounded curvature and can be considered an important technical contribution to this work. We validate the proposed method through simulation studies and real image data examples.

In this project we will be working with a data set, indicating whether or not a particular internet user clicked on an Advertisement. We will try to create a model that will predict whether or not they will click on an ad based off the features of that user. Welcome to this project on predict Ads Click in Apache Spark Machine Learning using Databricks platform community edition server which allows you to execute your spark code, free of cost on their server just by registering through email id. In this project, we explore Apache Spark and Machine Learning on the Databricks platform. I am a firm believer that the best way to learn is by doing.

Hello Guys, This blog contains all you need to know about regularization. This blog is all about mathematical intuition behind regularization and its Implementation in python.This blog is intended specially for newbies who are finding regularization difficult to digest. For any machine learning enthusiast, understanding the mathematical intuition and background working is more important then just implementing the model. I am new to world of blogging so If anyone encounters any problem whether conceptual or language-related please comment below. Back in the days, when I came across regularization it became difficult for me to to get mathematical intuition behind it.

This article was written by Prashant Gupta. One of the major aspects of training your machine learning model is avoiding overfitting. The model will have a low accuracy if it is overfitting. This happens because your model is trying too hard to capture the noise in your training dataset. By noise we mean the data points that don't really represent the true properties of your data, but random chance.

In late December 2019, the novel coronavirus (Sars-Cov-2) and the resulting disease COVID-19 were first identified in Wuhan China. The disease slipped through containment measures, with the first known case in the United States being identified on January 20th, 2020. In this paper, we utilize survey data from the Inter-university Consortium for Political and Social Research and apply several statistical and machine learning models and techniques such as Decision Trees, Multinomial Logistic Regression, Naive Bayes, k-Nearest Neighbors, Support Vector Machines, Neural Networks, Random Forests, Gradient Tree Boosting, XGBoost, CatBoost, LightGBM, Synthetic Minority Oversampling, and Chi-Squared Test to analyze the impacts the COVID-19 pandemic has had on the mental health of frontline workers in the United States. Through the interpretation of the many models applied to the mental health survey data, we have concluded that the most important factor in predicting the mental health decline of a frontline worker is the healthcare role the individual is in (Nurse, Emergency Room Staff, Surgeon, etc.), followed by the amount of sleep the individual has had in the last week, the amount of COVID-19 related news an individual has consumed on average in a day, the age of the worker, and the usage of alcohol and cannabis.

Linear Regression is a linear approach to modeling the relationship between a target variable and one or more independent variables. This modeled relationship is then used for predictive analytics. Working on the linear regression algorithm is just half the work done. For linear regression to work on the given data, it is assumed that Errors (residuals) follow a normal distribution. Although this is not necessarily required when the sample size is very large.

Federated learning (FL) enables distributed participants to collaboratively learn a global model without revealing their private data to each other. Recently, vertical FL, where the participants hold the same set of samples but with different features, has received increased attention. This paper first presents one label inference attack method to investigate the potential privacy leakages of the vertical logistic regression model. Specifically, we discover that the attacker can utilize the residue variables, which are calculated by solving the system of linear equations constructed by local dataset and the received decrypted gradients, to infer the privately owned labels. To deal with this, we then propose three protection mechanisms, e.g., additive noise mechanism, multiplicative noise mechanism, and hybrid mechanism which leverages local differential privacy and homomorphic encryption techniques, to prevent the attack and improve the robustness of the vertical logistic regression. model. Experimental results show that both the additive noise mechanism and the multiplicative noise mechanism can achieve efficient label protection with only a slight drop in model testing accuracy, furthermore, the hybrid mechanism can achieve label protection without any testing accuracy degradation, which demonstrates the effectiveness and efficiency of our protection techniques

Accounting for the uncertainty in the predictions of modern neural networks is a challenging and important task in many domains. Existing algorithms for uncertainty estimation require modifying the model architecture and training procedure (e.g., Bayesian neural networks) or dramatically increase the computational cost of predictions such as approaches based on ensembling. This work proposes a new algorithm that can be applied to a given trained neural network and produces approximate prediction intervals. The method is based on the classical delta method in statistics but achieves computational efficiency by using matrix sketching to approximate the Jacobian matrix. The resulting algorithm is competitive with state-of-the-art approaches for constructing predictive intervals on various regression datasets from the UCI repository.

We study a fully decentralized federated learning algorithm, which is a novel gradient descent algorithm executed on a communication-based network. For convenience, we refer to it as a network gradient descent (NGD) method. In the NGD method, only statistics (e.g., parameter estimates) need to be communicated, minimizing the risk of privacy. Meanwhile, different clients communicate with each other directly according to a carefully designed network structure without a central master. This greatly enhances the reliability of the entire algorithm. Those nice properties inspire us to carefully study the NGD method both theoretically and numerically. Theoretically, we start with a classical linear regression model. We find that both the learning rate and the network structure play significant roles in determining the NGD estimator's statistical efficiency. The resulting NGD estimator can be statistically as efficient as the global estimator, if the learning rate is sufficiently small and the network structure is well balanced, even if the data are distributed heterogeneously. Those interesting findings are then extended to general models and loss functions. Extensive numerical studies are presented to corroborate our theoretical findings. Classical deep learning models are also presented for illustration purpose.