We all know that in Linear Regression we aim to minimise the Sum of Squares Error (SSE) as our objective. However, why is it the SSE and where does this expression even come from? In this article I hope to answer this question using something called the Maximum Likelihood Estimator. Spending enough time in the Data Science community I am confident you would have come across the term Maximum Likelihood Estimator (MLE). I am not going to give a super in detail analysis of MLE, primarily because it has been done so many times in different ways that are probably better than I could ever explain it.

Data Scientists have the role to extract information from raw data. They aren't engineers, nor they are software developers. They dig inside data and extract the gold from the mine. Knowing what a model does and how it works is part of this job. Black-boxes models, although sometimes work better than other models, aren't a good idea if we need to learn something from our data.

Recently, the use of machine learning in meteorology has increased greatly. While many machine learning methods are not new, university classes on machine learning are largely unavailable to meteorology students and are not required to become a meteorologist. The lack of formal instruction has contributed to perception that machine learning methods are 'black boxes' and thus end-users are hesitant to apply the machine learning methods in their every day workflow. To reduce the opaqueness of machine learning methods and lower hesitancy towards machine learning in meteorology, this paper provides a survey of some of the most common machine learning methods. A familiar meteorological example is used to contextualize the machine learning methods while also discussing machine learning topics using plain language. The following machine learning methods are demonstrated: linear regression; logistic regression; decision trees; random forest; gradient boosted decision trees; naive Bayes; and support vector machines. Beyond discussing the different methods, the paper also contains discussions on the general machine learning process as well as best practices to enable readers to apply machine learning to their own datasets. Furthermore, all code (in the form of Jupyter notebooks and Google Colaboratory notebooks) used to make the examples in the paper is provided in an effort to catalyse the use of machine learning in meteorology.

Measuring the stability of conclusions derived from Ordinary Least Squares linear regression is critically important, but most metrics either only measure local stability (i.e. against infinitesimal changes in the data), or are only interpretable under statistical assumptions. Recent work proposes a simple, global, finite-sample stability metric: the minimum number of samples that need to be removed so that rerunning the analysis overturns the conclusion, specifically meaning that the sign of a particular coefficient of the estimated regressor changes. However, besides the trivial exponential-time algorithm, the only approach for computing this metric is a greedy heuristic that lacks provable guarantees under reasonable, verifiable assumptions; the heuristic provides a loose upper bound on the stability and also cannot certify lower bounds on it. We show that in the low-dimensional regime where the number of covariates is a constant but the number of samples is large, there are efficient algorithms for provably estimating (a fractional version of) this metric. Applying our algorithms to the Boston Housing dataset, we exhibit regression analyses where we can estimate the stability up to a factor of $3$ better than the greedy heuristic, and analyses where we can certify stability to dropping even a majority of the samples.

We propose MetaNOR, a meta-learnt approach for transfer-learning operators based on the nonlocal operator regression. The overall goal is to efficiently provide surrogate models for new and unknown material-learning tasks with different microstructures. The algorithm consists of two phases: (1) learning a common nonlocal kernel representation from existing tasks; (2) transferring the learned knowledge and rapidly learning surrogate operators for unseen tasks with a different material, where only a few test samples are required. We apply MetaNOR to model the wave propagation within 1D metamaterials, showing substantial improvements on the sampling efficiency for new materials.

Databricks is a business software startup that provides Data Engineering tools for processing and transforming massive amounts of data to develop machine learning models. Traditional Big Data procedures are not only slow to complete jobs but also take more time to build up Hadoop clusters. However, Databricks is built on top of distributed Cloud computing infrastructures like Azure, AWS, or Google Cloud, which allow programmes to execute on CPUs or GPUs according to analytical needs. In this article, we will be learning about building a machine learning model in Databricks. Following are the topics to be covered. In this article, we will be building a multivariate linear regression model for predicting the charges on insurance offered by the company based on different features.

Atmospheric Extreme Events (EEs) cause severe damages to human societies and ecosystems. The frequency and intensity of EEs and other associated events are increasing in the current climate change and global warming risk. The accurate prediction, characterization, and attribution of atmospheric EEs is therefore a key research field, in which many groups are currently working by applying different methodologies and computational tools. Machine Learning (ML) methods have arisen in the last years as powerful techniques to tackle many of the problems related to atmospheric EEs. This paper reviews the ML algorithms applied to the analysis, characterization, prediction, and attribution of the most important atmospheric EEs. A summary of the most used ML techniques in this area, and a comprehensive critical review of literature related to ML in EEs, are provided. A number of examples is discussed and perspectives and outlooks on the field are drawn.

With graduation season just around the corner, I've had a few family members ask how often they would use the information they learned over the years. One cousin, in particular, was not a huge fan of math. However, he built his gaming PC and otherwise enjoys learning about computer hardware. At one point it was mentioned that computers will do all the necessary math, so why memorize formulas? While I saw his perspective to a degree, math is a building block to learning more about computers especially, and being able to verify results never hurt as a programmer. That train thought brought me back to Algebra 1, where I remember learning about graphs and modeling methods such as Linear Regression.

In this paper, we study the problem of sparse mixed linear regression on an unlabeled dataset that is generated from linear measurements from two different regression parameter vectors. Since the data is unlabeled, our task is not only to figure out a good approximation of the regression parameter vectors but also to label the dataset correctly. In its original form, this problem is NP-hard. The most popular algorithms to solve this problem (such as Expectation-Maximization) have a tendency to stuck at local minima. We provide a novel invex relaxation for this intractable problem which leads to a solution with provable theoretical guarantees. This relaxation enables exact recovery of data labels. Furthermore, we recover a close approximation of the regression parameter vectors which match the true parameter vectors in support and sign. Our formulation uses a carefully constructed primal dual witnesses framework for the invex problem. Furthermore, we show that the sample complexity of our method is only logarithmic in terms of the dimension of the regression parameter vectors.

Further probability values estimated using a machine learning algorithm with 30 chemical descriptors as inputs yielded an area under the ROC curve of …