Last year, we announced Snap ML, a python-based machine learning framework that is designed to be a high-performance machine learning software framework. Snap ML is bundled as part of the WML Community Edition or WML CE (aka PowerAI) software distribution that is available for free on Power systems. The first release of Snap ML enabled GPU-acceleration of generalized linear models (GLMs) and also enabled scaling these models to multiple GPUs and multiple servers. GLMs are popular machine learning algorithms, which include logistic regression, linear regression, ridge and lasso regression, and support vector machines (SVMs). Our previous blog showed that Logistic Regression using Snap ML is 46 times faster than other methods, which rely on CPUs alone.

The course "Machine Learning Basics: Building a Regression model in R" teaches you all the steps of creating a Linear Regression model, which is the most popular Machine Learning model, to solve business problems. Machine Learning is a field of computer science which gives the computer the ability to learn without being explicitly programmed. It is a branch of artificial intelligence based on the idea that systems can learn from data, identify patterns and make decisions with minimal human intervention. What is the Linear regression technique of Machine learning? Linear Regression is a simple machine learning model for regression problems, i.e., when the target variable is a real value.

Bayesian additive regression trees (BART) (Chipman et. al., 2010) is a powerful predictive model that often outperforms alternative models at out-of-sample prediction. BART is especially well-suited to settings with unstructured predictor variables and substantial sources of unmeasured variation as is typical in the social, behavioral and health sciences. This paper develops a modified version of BART that is amenable to fast posterior estimation. We present a stochastic hill climbing algorithm that matches the remarkable predictive accuracy of previous BART implementations, but is many times faster and less memory intensive. Simulation studies show that the new method is comparable in computation time and more accurate at function estimation than both random forests and gradient boosting.

Electronic health records are an increasingly important resource for understanding the interactions between patient health, environment, and clinical decisions. In this paper we report an empirical study of predictive modeling of several patient outcomes using three state-of-the-art machine learning methods. Our primary goal is to validate the models by interpreting the importance of predictors in the final models. Central to interpretation is the use of feature importance scores, which vary depending on the underlying methodology. In order to assess feature importance, we compared univariate statistical tests, information-theoretic measures, permutation testing, and normalized coefficients from multivariate logistic regression models. In general we found poor correlation between methods in their assessment of feature importance, even when their performance is comparable and relatively good. However, permutation tests applied to random forest and gradient boosting models showed the most agreement, and the importance scores matched the clinical interpretation most frequently.

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this paper, we present an inexact augmented Lagrangian method to solve the Lasso problem with linear equality constraints. By fully exploiting second-order sparsity of the problem, we are able to greatly reduce the computational cost and obtain highly efficient implementations. Furthermore, numerical results on both synthetic data and real data show that our algorithm is superior to existing first-order methods in terms of both running time and solution accuracy.

We present a novel approach for nonparametric regression using wavelet basis functions. Our proposal, $\texttt{waveMesh}$, can be applied to non-equispaced data with sample size not necessarily a power of 2. We develop an efficient proximal gradient descent algorithm for computing the estimator and establish adaptive minimax convergence rates. The main appeal of our approach is that it naturally extends to additive and sparse additive models for a potentially large number of covariates. We prove minimax optimal convergence rates under a weak compatibility condition for sparse additive models. The compatibility condition holds when we have a small number of covariates. Additionally, we establish convergence rates for when the condition is not met. We complement our theoretical results with empirical studies comparing $\texttt{waveMesh}$ to existing methods.

One of the perks of using Google Cloud Platform (GCP) is having BigQuery, Google's cloud hosted data warehouse solution at your disposal. BigQuery gives GCP users access to the key features of Dremel, Google's very own internal data warehouse solution. Under the hood Dremel stores data in columnar format and uses a tree architecture to parallelise queries across thousands of machines, with each query scanning the entire table. So, what is so great about that? With BigQuery you can run SQL queries on a table with billions of rows and get the results in seconds!

It is nice to have logistic regression on your resume, as many jobs request it, especially in some fields such as biostatistics. And if you learned the details during your college classes, good for you. However, for a beginner, this is not the first thing you should learn. In my career, being an isolated statistician (working with marketing guys, sales people, or engineers) in many of my roles, I had the flexibility to choose which tools and methodology to use. Many practitioners today are in a similar environment.

Interest in derivative-free optimization (DFO) and "evolutionary strategies" (ES) has recently surged in the Reinforcement Learning (RL) community, with growing evidence that they match state of the art methods for policy optimization tasks. However, blackbox DFO methods suffer from high sampling complexity since they require a substantial number of policy rollouts for reliable updates. They can also be very sensitive to noise in the rewards, actuators or the dynamics of the environment. In this paper we propose to replace the standard ES derivative-free paradigm for RL based on simple reward-weighted averaged random perturbations for policy updates, that has recently become a subject of voluminous research, by an algorithm where gradients of blackbox RL functions are estimated via regularized regression methods. In particular, we propose to use L1/L2 regularized regression-based gradient estimation to exploit sparsity and smoothness, as well as LP decoding techniques for handling adversarial stochastic and deterministic noise. Our methods can be naturally aligned with sliding trust region techniques for efficient samples reuse to further reduce sampling complexity. This is not the case for standard ES methods requiring independent sampling in each epoch. We show that our algorithms can be applied in locomotion tasks, where training is conducted in the presence of substantial noise, e.g. for learning in sim transferable stable walking behaviors for quadruped robots or training quadrupeds how to follow a path. We further demonstrate our methods on several $\mathrm{OpenAI}$ $\mathrm{Gym}$ $\mathrm{Mujoco}$ RL tasks. We manage to train effective policies even if up to $25\%$ of all measurements are arbitrarily corrupted, where standard ES methods produce sub-optimal policies or do not manage to learn at all. Our empirical results are backed by theoretical guarantees.

This blog is the first in a series about regression analysis in RAPIDS, an open GPU data science platform. There are many varieties of regression techniques, and we're working to include them all in RAPIDS. In this blog edition, I use Ordinary Least Squares (OLS) and Ridge regression to choose a model to predict Washington, D.C. bikeshare rentals¹. I want to take a moment to tell the origin story of regression analysis, which will explain why it has that name. I believe that of all the common machine learning techniques (K-means, kNN, PCA), "regression analysis" has the most opaque name.