Feature selection is an extensively studied technique in the machine learning literature where the main objective is to identify the subset of features that provides the highest predictive power. However, in causal inference, our goal is to identify the set of variables that are associated with both the treatment variable and outcome (i.e., the confounders). While controlling for the confounding variables helps us to achieve an unbiased estimate of causal effect, recent research shows that controlling for purely outcome predictors along with the confounders can reduce the variance of the estimate. In this paper, we propose an Outcome Adaptive Elastic-Net (OAENet) method specifically designed for causal inference to select the confounders and outcome predictors for inclusion in the propensity score model or in the matching mechanism. OAENet provides two major advantages over existing methods: it performs superiorly on correlated data, and it can be applied to any matching method and any estimates. In addition, OAENet is computationally efficient compared to state-of-the-art methods.

The Black Friday Udemy sale begins. Shop to save on thousands of online courses. Welcome to the Course Introduction to Deep Learning with TensorFlow 2.0: In this course, you will learn advanced linear regression technique process and with this, you can be able to build any regression problem. Using this you can solve real-world problems like customer lifetime value, predictive analytics, etc. All the above-mentioned techniques are explained in TensorFlow.

MARS is a popular method for nonparametric regression introduced by Friedman in 1991. MARS fits simple nonlinear and non-additive functions to regression data. We propose and study a natural LASSO variant of the MARS method. Our method is based on least squares estimation over a convex class of functions obtained by considering infinite-dimensional linear combinations of functions in the MARS basis and imposing a variation based complexity constraint. We show that our estimator can be computed via finite-dimensional convex optimization and that it is naturally connected to nonparametric function estimation techniques based on smoothness constraints. Under a simple design assumption, we prove that our estimator achieves a rate of convergence that depends only logarithmically on dimension and thus avoids the usual curse of dimensionality to some extent. We implement our method with a cross-validation scheme for the selection of the involved tuning parameter and show that it has favorable performance compared to the usual MARS method in simulation and real data settings.

Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between input variables and a response. Such relationships can be better described through  flexible approaches such as neural networks, but this results in less interpretable models and potential overfitting. Alternatively, specific parametric nonlinear functions can be used, but the specification of such functions is in general complicated. In this paper, we introduce a  flexible approach for the construction and selection of highly  flexible nonlinear parametric regression models. Nonlinear features are generated hierarchically, similarly to deep learning, but have additional  flexibility on the possible types of features to be considered. This  flexibility, combined with variable selection, allows us to find a small set of important features and thereby more interpretable models. Within the space of possible functions, a Bayesian approach, introducing priors for functions based on their complexity, is considered. A genetically modified mode jumping Markov chain Monte Carlo algorithm is adopted to perform Bayesian inference and estimate posterior probabilities for model averaging. In various applications, we illustrate how our approach is used to obtain meaningful nonlinear models. Additionally, we compare its predictive performance with several machine learning algorithms.  

Because of the widespread use of black box prediction methods such as random forests and neural nets, there is renewed interest in developing methods for quantifying variable importance as part of the broader goal of interpretable prediction. A popular approach is to define a variable importance parameter - known as LOCO (Leave Out COvariates) - based on dropping covariates from a regression model. This is essentially a nonparametric version of R-squared. This parameter is very general and can be estimated nonparametrically, but it can be hard to interpret because it is affected by correlation between covariates. We propose a method for mitigating the effect of correlation by defining a modified version of LOCO. This new parameter is difficult to estimate nonparametrically, but we show how to estimate it using semiparametric models.

In this work, we consider the algorithm to the (nonlinear) regression problems with $\ell_0$ penalty. The existing algorithms for $\ell_0$ based optimization problem are often carried out with a fixed step size, and the selection of an appropriate step size depends on the restricted strong convexity and smoothness for the loss function, hence it is difficult to compute in practical calculation. In sprite of the ideas of support detection and root finding \cite{HJK2020}, we proposes a novel and efficient data-driven line search rule to adaptively determine the appropriate step size. We prove the $\ell_2$ error bound to the proposed algorithm without much restrictions for the cost functional. A large number of numerical comparisons with state-of-the-art algorithms in linear and logistic regression problems show the stability, effectiveness and superiority of the proposed algorithms.

In modeling multivariate time series for either forecast or policy analysis, it would be beneficial to have figured out the cause-effect relations within the data. Regression analysis, however, is generally for correlation relation, and very few researches have focused on variance analysis for causality discovery. We first set up an equilibrium for the cause-effect relations using a fictitious vector autoregressive model. In the equilibrium, long-run relations are identified from noise, and spurious ones are negligibly close to zero. The solution, called causality distribution, measures the relative strength causing the movement of all series or specific affected ones. If a group of exogenous data affects the others but not vice versa, then, in theory, the causality distribution for other variables is necessarily zero. The hypothesis test of zero causality is the rule to decide a variable is endogenous or not. Our new approach has high accuracy in identifying the true cause-effect relations among the data in the simulation studies. We also apply the approach to estimating the causal factors' contribution to climate change.

The recent abundance of data on electricity consumption at different scales opens new challenges and highlights the need for new techniques to leverage information present at finer scales in order to improve forecasts at wider scales. In this work, we take advantage of the similarity between this hierarchical prediction problem and multi-scale transfer learning. We develop two methods for hierarchical transfer learning, based respectively on the stacking of generalized additive models and random forests, and on the use of aggregation of experts. We apply these methods to two problems of electricity load forecasting at national scale, using smart meter data in the first case, and regional data in the second case. For these two usecases, we compare the performances of our methods to that of benchmark algorithms, and we investigate their behaviour using variable importance analysis. Our results demonstrate the interest of both methods, which lead to a significant improvement of the predictions.

Bob has started his own mobile company. He wants to give a tough fight to big companies like Apple, Samsung etc. He does not know how to estimate the price of mobiles his company creates. In this competitive mobile phone market, you cannot simply assume things. To solve this problem he collects sales data of mobile phones of various companies.

In December 2019, a novel virus called COVID-19 had caused an enormous number of causalities to date. The battle with the novel Coronavirus is baffling and horrifying after the Spanish Flu 2019. While the front-line doctors and medical researchers have made significant progress in controlling the spread of the highly contiguous virus, technology has also proved its significance in the battle. Moreover, Artificial Intelligence has been adopted in many medical applications to diagnose many diseases, even baffling experienced doctors. Therefore, this survey paper explores the methodologies proposed that can aid doctors and researchers in early and inexpensive methods of diagnosis of the disease. Most developing countries have difficulties carrying out tests using the conventional manner, but a significant way can be adopted with Machine and Deep Learning. On the other hand, the access to different types of medical images has motivated the researchers. As a result, a mammoth number of techniques are proposed. This paper first details the background knowledge of the conventional methods in the Artificial Intelligence domain. Following that, we gather the commonly used datasets and their use cases to date. In addition, we also show the percentage of researchers adopting Machine Learning over Deep Learning. Thus we provide a thorough analysis of this scenario. Lastly, in the research challenges, we elaborate on the problems faced in COVID-19 research, and we address the issues with our understanding to build a bright and healthy environment.