This article was published as a part of the Data Science Blogathon. For this article, we will be using sklearn's make_classification dataset with four features This is the vectorised form of the gradient descent expression, which we will be using in our code. Now that we are done with every part, we will put everything together in a single class. You can fiddle around with hyper-parameters and see the behaviour of cost function. Now, let's see how our logistic regression fares in comparison to sklearn's logistic regression.

Time series forecasting is fundamental for various use cases in different domains such as energy systems and economics. Creating a forecasting model for a specific use case requires an iterative and complex design process. The typical design process includes the five sections (1) data pre-processing, (2) feature engineering, (3) hyperparameter optimization, (4) forecasting method selection, and (5) forecast ensembling, which are commonly organized in a pipeline structure. One promising approach to handle the ever-growing demand for time series forecasts is automating this design process. The present paper, thus, analyzes the existing literature on automated time series forecasting pipelines to investigate how to automate the design process of forecasting models. Thereby, we consider both Automated Machine Learning (AutoML) and automated statistical forecasting methods in a single forecasting pipeline. For this purpose, we firstly present and compare the proposed automation methods for each pipeline section. Secondly, we analyze the automation methods regarding their interaction, combination, and coverage of the five pipeline sections. For both, we discuss the literature, identify problems, give recommendations, and suggest future research. This review reveals that the majority of papers only cover two or three of the five pipeline sections. We conclude that future research has to holistically consider the automation of the forecasting pipeline to enable the large-scale application of time series forecasting.

When estimating the causal function between a vector of covariates X and a response Y in the presence of unobserved confounding, standard regression procedures such as ordinary least squares (OLS) are even asymptotically biased. Instrumental variable approaches (Wright, 1928; Imbens and Angrist, 1994; Newey, 2013) exploit the existence of exogenous heterogeneity in the form of an instrumental variable (IV) Z and estimate, under suitable conditions, the causal function consistently. Importantly, the errors in Y and the hidden confounders U should be uncorrelated with the instruments Z. Usually, this has to be argued for with background knowledge. When the data generating process is modeled by a structural causal model (SCM) (Pearl, 2009; Bongers et al., 2021) (so that the distribution is Markov with respect to the induced graph), then the above condition is satisfied if Y and U are d-separated from Z in the graph obtained by removing the edge from X to Y. Furthermore, in this case the errors in Y and U are even independent from Z. Using that the errors and instruments are not only uncorrelated but also independent comes with several benefits. For example, even in settings, where the causal function can be identified by classical approaches based on uncorrelatedness, the independence can be exploited to construct estimators that achieve the semiparametric efficiency bound, at least when the error distribution comes from a known, parametric family (Hansen et al., 2010). Furthermore, the independence constraint is stronger than uncorrelatedness and therefore yields stronger identifiability results, which has been reported in the field of econometrics (e.g., Imbens and Newey, 2009; Chesher, 2003).

Missing values are more and more present as the size of datasets increases. These missing values can occur for a variety of reasons, such as sensor failures, refusals to answer poll questions, or aggregations of data coming from different sources (with different methods of data collection). There may be different processes of missing value generation on the same dataset, which makes the task of data cleaning difficult or impossible without creating large biases. In his leading work, Rubin [1976] distinguishes three missing values scenarios: Missing Completely At Random (MCAR), Missing At Random (MAR), and Missing Not At Random (MNAR), depending on the links between the observed variables, the missing ones, and the missing pattern. In the linear regression framework, most of the literature focuses on parameter estimation [Little, 1992, Jones, 1996], using sometimes a sparse prior leading to the Lasso estimator [Loh and Wainwright, 2012] or the Dantzig selector [Rosenbaum and Tsybakov, 2010]. Note that the robust estimation literature [Dalalyan and Thompson, 2019, Chen and Caramanis, 2013] could be also used to handle missing values, as the latter can be reinterpreted as a multiplicative noise in linear models.

The paper is devoted to the study of the model fairness and process fairness of the Russian demographic dataset by making predictions of divorce of the 1st marriage, religiosity, 1st employment and completion of education. Our goal was to make classifiers more equitable by reducing their reliance on sensitive features while increasing or at least maintaining their accuracy. We took inspiration from "dropout" techniques in neural-based approaches and suggested a model that uses "feature drop-out" to address process fairness. To evaluate a classifier's fairness and decide the sensitive features to eliminate, we used "LIME Explanations". This results in a pool of classifiers due to feature dropout whose ensemble has been shown to be less reliant on sensitive features and to have improved or no effect on accuracy. Our empirical study was performed on four families of classifiers (Logistic Regression, Random Forest, Bagging, and Adaboost) and carried out on real-life dataset (Russian demographic data derived from Generations and Gender Survey), and it showed that all of the models became less dependent on sensitive features (such as gender, breakup of the 1st partnership, 1st partnership, etc.) and showed improvements or no impact on accuracy

A surprising phenomenon in modern machine learning is the ability of a highly overparameterized model to generalize well (small error on the test data) even when it is trained to memorize the training data (zero error on the training data). This has led to an arms race towards increasingly overparameterized models (c.f., deep learning). In this paper, we study an underexplored hidden cost of overparameterization: the fact that overparameterized models are more vulnerable to privacy attacks, in particular the membership inference attack that predicts the (potentially sensitive) examples used to train a model. We significantly extend the relatively few empirical results on this problem by theoretically proving for an overparameterized linear regression model with Gaussian data that the membership inference vulnerability increases with the number of parameters. Moreover, a range of empirical studies indicates that more complex, nonlinear models exhibit the same behavior. Finally, we study different methods for mitigating such attacks in the overparameterized regime, such as noise addition and regularization, and conclude that simply reducing the parameters of an overparameterized model is an effective strategy to protect it from membership inference without greatly decreasing its generalization error.

Sparse linear prediction methods suffer from decreased prediction accuracy when the predictor variables have cluster structure (e.g. there are highly correlated groups of variables). To improve prediction accuracy, various methods have been proposed to identify variable clusters from the data and integrate cluster information into a sparse modeling process. But none of these methods achieve satisfactory performance for prediction, variable selection and variable clustering simultaneously. This paper presents Variable Cluster Principal Component Regression (VC-PCR), a prediction method that supervises variable selection and variable clustering in order to solve this problem. Experiments with real and simulated data demonstrate that, compared to competitor methods, VC-PCR achieves better prediction, variable selection and clustering performance when cluster structure is present.

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We review sufficient dimension reduction (SDR) estimators with multivariate response in this paper. A wide range of SDR methods are characterized as inverse regression SDR estimators or forward regression SDR estimators. The inverse regression family include pooled marginal estimators, projective resampling estimators, and distance-based estimators. Ordinary least squares, partial least squares, and semiparametric SDR estimators, on the other hand, are discussed as estimators from the forward regression family.

Tree-based models such as decision trees and random forests (RF) are a cornerstone of modern machine-learning practice. To mitigate overfitting, trees are typically regularized by a variety of techniques that modify their structure (e.g. pruning). We introduce Hierarchical Shrinkage (HS), a post-hoc algorithm that does not modify the tree structure, and instead regularizes the tree by shrinking the prediction over each node towards the sample means of its ancestors. The amount of shrinkage is controlled by a single regularization parameter and the number of data points in each ancestor. Since HS is a post-hoc method, it is extremely fast, compatible with any tree growing algorithm, and can be used synergistically with other regularization techniques. Extensive experiments over a wide variety of real-world datasets show that HS substantially increases the predictive performance of decision trees, even when used in conjunction with other regularization techniques. Moreover, we find that applying HS to each tree in an RF often improves accuracy, as well as its interpretability by simplifying and stabilizing its decision boundaries and SHAP values. We further explain the success of HS in improving prediction performance by showing its equivalence to ridge regression on a (supervised) basis constructed of decision stumps associated with the internal nodes of a tree. All code and models are released in a full-fledged package available on Github (github.com/csinva/imodels)