We consider the problem of estimating piecewise regular functions in an online setting, i.e., the data arrive sequentially and at any round our task is to predict the value of the true function at the next revealed point using the available data from past predictions. We propose a suitably modified version of a recently developed online learning algorithm called the sleeping experts aggregation algorithm. We show that this estimator satisfies oracle risk bounds simultaneously for all local regions of the domain. As concrete instantiations of the expert aggregation algorithm proposed here, we study an online mean aggregation and an online linear regression aggregation algorithm where experts correspond to the set of dyadic subrectangles of the domain. The resulting algorithms are near linear time computable in the sample size. We specifically focus on the performance of these online algorithms in the context of estimating piecewise polynomial and bounded variation function classes in the fixed design setup. The simultaneous oracle risk bounds we obtain for these estimators in this context provide new and improved (in certain aspects) guarantees even in the batch setting and are not available for the state of the art batch learning estimators.

Additionally, ggplot2 is a powerful visualization library that allows us to easily render the scatterplot and the regression line for a quick inspection. If you're interested in producing similar results in Python, the best way is to use the OLS ( Ordinary Least Squares) model from statsmodels. It has the closest output to the base R lm package producing a similar summary table. We'll start by importing the packages we need to run the model. Next, let's prepare our data.

Originally published on Towards AI the World's Leading AI and Technology News and Media Company. If you are building an AI-related product or service, we invite you to consider becoming an AI sponsor. At Towards AI, we help scale AI and technology startups. Let us help you unleash your technology to the masses. Logistic Regression is known for modeling classification problems.

In this post, I will provide an overview of generalized additive models (GAMs) and their desirable features. Predictive accuracy has long been an important goal of machine learning. But model interpretability has received more attention in recent years. Stakeholders, such as executives, regulators, and domain experts, often want to understand how and why a model makes its predictions before they trust it enough to use it in practice. However, when you train a machine learning model, you typically face a tradeoff between accuracy and interpretability.

One particular problem arises at this stage. How do we know what model to choose as the meta-model? Unfortunately, there has't been any research into this area and the selection of a meta-model is more of an art than a science. In most of the papers discussing stacked models, the meta-model used is often just a simple model such as Linear Regression for regression tasks and Logistic Regression for classification tasks. One reason why more complex meta-models are often not chosen is because there is a much higher chance that the meta-model may overfit to the predictions from the base models.

Originally published on Towards AI the World's Leading AI and Technology News and Media Company. If you are building an AI-related product or service, we invite you to consider becoming an AI sponsor. At Towards AI, we help scale AI and technology startups. Let us help you unleash your technology to the masses. Logistic Regression is a Supervised Machine Learning algorithm that is used in classification problems where we have to distinguish the dependent variable between two or more categories or classes by using the independent variables.

Stragglers, Byzantine workers, and data privacy are the main bottlenecks in distributed cloud computing. Some prior works proposed coded computing strategies to jointly address all three challenges. They require either a large number of workers, a significant communication cost or a significant computational complexity to tolerate Byzantine workers. Much of the overhead in prior schemes comes from the fact that they tightly couple coding for all three problems into a single framework. In this paper, we propose Adaptive Verifiable Coded Computing (AVCC) framework that decouples the Byzantine node detection challenge from the straggler tolerance. AVCC leverages coded computing just for handling stragglers and privacy, and then uses an orthogonal approach that leverages verifiable computing to mitigate Byzantine workers. Furthermore, AVCC dynamically adapts its coding scheme to trade-off straggler tolerance with Byzantine protection. We evaluate AVCC on a compute-intensive distributed logistic regression application. Our experiments show that AVCC achieves up to $4.2\times$ speedup and up to $5.1\%$ accuracy improvement over the state-of-the-art Lagrange coded computing approach (LCC). AVCC also speeds up the conventional uncoded implementation of distributed logistic regression by up to $7.6\times$, and improves the test accuracy by up to $12.1\%$.

Linear regression finds the optimal linear relationship between independent variables and dependent variables, thus makes prediction accordingly. The simplest form is y b0 b1x. When there is only one input feature, linear regression model fits the line in a 2 dimensional space, in order to minimize the residuals between predicted values and actual values. The common cost function to measure the magnitude of residuals is residual sum of squared (RSS). As more features are introduced, simple linear regression evolves into multiple linear regression y b0 b1x1 b2x2 … bnxn. Feel free to check out my article if you want the specific guide to simple linear regression model.

A common approach in forecasting problems is to estimate a least-squares regression (or other statistical learning models) from past data, which is then applied to predict future outcomes. An underlying assumption is that the same correlations that were observed in the past still hold for the future. We propose a model for situations when this assumption is not met: adopting methods from the state space literature, we model how regression coefficients change over time. Our approach can shed light on the large uncertainties associated with forecasting the future, and how much of this is due to changing dynamics of the past. Our simulation study shows that accurate estimates are obtained when the outcome is continuous, but the procedure fails for binary outcomes.