What is Extreme Gradient Boosting?

This course is a lead-in to deep learning and neural networks - it covers a popular and fundamental technique used in machine learning, data science and statistics: logistic regression. We cover the theory from the ground up: derivation of the solution, and applications to real-world problems. We show you how one might code their own logistic regression module in Python. This course does not require any external materials. Everything needed (Python, and some Python libraries) can be obtained for free.

We study meta-learning in Markov Decision Processes (MDP) with linear transition models in the undiscounted episodic setting. Under a task sharedness metric based on model proximity we study task families characterized by a distribution over models specified by a bias term and a variance component. We then propose BUC-MatrixRL, a version of the UC-Matrix RL algorithm, and show it can meaningfully leverage a set of sampled training tasks to quickly solve a test task sampled from the same task distribution by learning an estimator of the bias parameter of the task distribution. The analysis leverages and extends results in the learning to learn linear regression and linear bandit setting to the more general case of MDP's with linear transition models. We prove that compared to learning the tasks in isolation, BUC-Matrix RL provides significant improvements in the transfer regret for high bias low variance task distributions.

Beta coefficients for linear regression models represent the ideal form of an interpretable feature effect. However, for non-linear models and especially generalized linear models, the estimated coefficients cannot be interpreted as a direct feature effect on the predicted outcome. Hence, marginal effects are typically used as approximations for feature effects, either in the shape of derivatives of the prediction function or forward differences in prediction due to a change in a feature value. While marginal effects are commonly used in many scientific fields, they have not yet been adopted as a model-agnostic interpretation method for machine learning models. This may stem from their inflexibility as a univariate feature effect and their inability to deal with the non-linearities found in black box models. We introduce a new class of marginal effects termed forward marginal effects. We argue to abandon derivatives in favor of better-interpretable forward differences. Furthermore, we generalize marginal effects based on forward differences to multivariate changes in feature values. To account for the non-linearity of prediction functions, we introduce a non-linearity measure for marginal effects. We argue against summarizing feature effects of a non-linear prediction function in a single metric such as the average marginal effect. Instead, we propose to partition the feature space to compute conditional average marginal effects on feature subspaces, which serve as conditional feature effect estimates.

We consider the problem of finding tuned regularized parameter estimators for linear models. We start by showing that three known optimal linear estimators belong to a wider class of estimators that can be formulated as a solution to a weighted and constrained minimization problem. The optimal weights, however, are typically unknown in many applications. This begs the question, how should we choose the weights using only the data? We propose using the covariance fitting SPICE-methodology to obtain data-adaptive weights and show that the resulting class of estimators yields tuned versions of known regularized estimators - such as ridge regression, LASSO, and regularized least absolute deviation. These theoretical results unify several important estimators under a common umbrella. The resulting tuned estimators are also shown to be practically relevant by means of a number of numerical examples.

Data can be broadly divided into continuous data, those that can take an infinite number of points within a given range such as distance or time, and categorical/discrete data, which contain a finite number of points or categories within a given group of data such as payment methods or customer complaints. We have already seen examples of applying regression to continuous prediction problems in the form of linear regression where we predicted sales, but in order to predict categorical outputs we can use logistic regression. While we are still using regression to predict outcomes, the main aim of logistic regression is to be able to predict which category and observation belongs to rather than an exact value. Examples of questions which this method can be used for include: "How likely is a person to suffer from a disease (outcome) given their age, sex, smoking status, etc (variables/features)?" "How likely is this email to be spam?" "Will a student pass a test given some predictors of performance?".

Conjoint analysis is a popular experimental design used to measure multidimensional preferences. Researchers examine how varying a factor of interest, while controlling for other relevant factors, influences decision-making. Currently, there exist two methodological approaches to analyzing data from a conjoint experiment. The first focuses on estimating the average marginal effects of each factor while averaging over the other factors. Although this allows for straightforward design-based estimation, the results critically depend on the distribution of other factors and how interaction effects are aggregated. An alternative model-based approach can compute various quantities of interest, but requires researchers to correctly specify the model, a challenging task for conjoint analysis with many factors and possible interactions. In addition, a commonly used logistic regression has poor statistical properties even with a moderate number of factors when incorporating interactions. We propose a new hypothesis testing approach based on the conditional randomization test to answer the most fundamental question of conjoint analysis: Does a factor of interest matter in any way given the other factors? Our methodology is solely based on the randomization of factors, and hence is free from assumptions. Yet, it allows researchers to use any test statistic, including those based on complex machine learning algorithms. As a result, we are able to combine the strengths of the existing design-based and model-based approaches. We illustrate the proposed methodology through conjoint analysis of immigration preferences and political candidate evaluation. We also extend the proposed approach to test for regularity assumptions commonly used in conjoint analysis.

In this post, I'll take a look at how you can compare regression models. Comparing regression models is perhaps one of the trickiest tasks to complete in the "comparing models" arena; The reason is that there are literally dozens of statistics you can calculate to compare regression models, including: This list isn't exhaustive–there are many other tools, tests and plots at your disposal. Rather than discuss the statistics in detail, I chose to focus this post on comparing a few of the most popular regression model evaluation techniques and discuss when you might want to use them (or when you might not want to). The techniques listed below tend to be on the "easier to use and understand" end of the spectrum, so if you're new to model comparison it's a good place to start. The first question you should be asking is: How well do I know my data?

Machine learning and 5G can attract more people in the metaverse, blurring the lines between the virtual and real worlds. The concept of metaverse is closely related to advanced technologies such as artificial intelligence (AI), machine learning (ML), augmented reality (AR), virtual reality (VR), blockchain, 5G and the internet of things (IoT). Improved technology will allow avatars to use body language effectively and better convey human emotions producing a feeling of real communication in a virtual space. AR and VR won't be the only critical components of the metaverse, 5G and machine learning are also crucial. The metaverse is a future iteration of the internet, made up of 3D virtual spaces linked into a perceived virtual universe.

In the statistical learning course, the instructors introduced Lasso regression, which is a linear regression method which performs shrinkage on the parameters of the linear model. LASSO (Least Absolute Shrinkage and Selection Operator) can be used to combat collinearity issues, overfitting and variable selection (facilitates interpretability).