Linear models have a wide appeal. Even with a basic understanding of Excel, it is possible to create a model that explains patterns in data. After attaching weights (coefficients) to explanatory variables (features), it is easy to assess the importance of individual variables when explaining the data. It is not surprising that linear models have been around for many decades, and are widely used throughout many domains, ranging from psychology to business administration and from machine learning to statistics. Despite the superficial simplicity of linear models, many things can go wrong with them.

Not too long ago, data deficiency was a major impediment towards making informed decisions, understanding customer behavior, predictions and forecasting. In the modern digital age, where data continuously streams in all shapes, sizes and from all directions, enterprises are constantly challenged with sifting through petabytes of data to infer key indicators. Making sense of "the right data at the right time" yields a huge competitive edge. Blending real-time streams, batch processing, external data sources and machine learning -- Google BigQuery transcends traditional data warehouse solutions with the ability to offer business insights into data across 3 dimensions -- historical, real-time and predictive. BigQuery democratizes machine learning by letting users develop and operationalize ML models with just SQL skills.

In two previous articles I covered two of the most basic models used in machine learning -- linear regression and logistic regression. In both cases, we were interested in searching for the set of model parameters m that result in the best model predictions d' of the observed targets d, and in both cases this was done by minimizing some loss function L(m), which measures the error between d' and d. A good proportion of machine learning -- from simple linear regression to deep learning models, essentially involves the minimization of some sort of loss function -- and yet, many data science or machine learning books/tutorials/materials tend to place more emphasis on the model itself than on the loss function! In this article, we will continue on where we left off from the previous two articles and focus on loss functions before exploring more advanced models in future articles! Now, just as "best" is a very subjective word, so are loss functions!

Linear regression is a supervised method that has been widely used in classification tasks. In order to apply linear regression to classification tasks, a technique for relaxing regression targets was proposed. However, methods based on this technique ignore the pressure on a single transformation matrix due to the complex information contained in the data. A single transformation matrix in this case is too strict to provide a flexible projection, thus it is necessary to adopt relaxation on transformation matrix. This paper proposes a double transformation matrices learning method based on latent low-rank feature extraction. The core idea is to use double transformation matrices for relaxation, and jointly projecting the learned principal and salient features from two directions into the label space, which can share the pressure of a single transformation matrix. Firstly, the low-rank features are learned by the latent low rank representation (LatLRR) method which processes the original data from two directions. In this process, sparse noise is also separated, which alleviates its interference on projection learning to some extent. Then, two transformation matrices are introduced to process the two features separately, and the information useful for the classification is extracted. Finally, the two transformation matrices can be easily obtained by alternate optimization methods. Through such processing, even when a large amount of redundant information is contained in samples, our method can also obtain projection results that are easy to classify. Experiments on multiple data sets demonstrate the effectiveness of our approach for classification, especially for complex scenarios.

In traditional logistic regression models, the link function is often assumed to be linear and continuous in predictors. Here, we consider a threshold model that all continuous features are discretized into ordinal levels, which further determine the binary responses. Both the threshold points and regression coefficients are unknown and to be estimated. For high dimensional data, we propose a fusion penalized logistic threshold regression (FILTER) model, where a fused lasso penalty is employed to control the total variation and shrink the coefficients to zero as a method of variable selection. Under mild conditions on the estimate of unknown threshold points, we establish the non-asymptotic error bound for coefficient estimation and the model selection consistency. With a careful characterization of the error propagation, we have also shown that the tree-based method, such as CART, fulfill the threshold estimation conditions. We find the FILTER model is well suited in the problem of early detection and prediction for chronic disease like diabetes, using physical examination data. The finite sample behavior of our proposed method are also explored and compared with extensive Monte Carlo studies, which supports our theoretical discoveries.

This article implements Passing-Bablok regression in SAS. Passing-Bablok regression is a one-variable regression technique that is used to compare measurements from different instruments or medical devices. The measurements of the two variables (X and Y) are both measured with errors. Consequently, you cannot use ordinary linear regression, which assumes that one variable (X) is measured without error. Passing-Bablok regression is a robust nonparametric regression method that does not make assumptions about the distribution of the expected values or the error terms in the model.

Non-negative and bounded-variable linear regression problems arise in a variety of applications in machine learning and signal processing. In this paper, we propose a technique to accelerate existing solvers for these problems by identifying saturated coordinates in the course of iterations. This is akin to safe screening techniques previously proposed for sparsity-regularized regression problems. The proposed strategy is provably safe as it provides theoretical guarantees that the identified coordinates are indeed saturated in the optimal solution. Experimental results on synthetic and real data show compelling accelerations for both non-negative and bounded-variable problems.

Machine learning algorithms, models, strategies, and other influential features are assisting us in unlocking a wide range of applications. These computer systems are capable of self-learning and making business decisions, as well as assisting research and improving technology. As machine learning finds new applications across various sectors, the demand for professionals in the field is growing. According to the US Bureau of Labor Statistics, the job outlook will rise 22 percent until 2030 for computer and information research scientists. Whichever area of machine learning interests you more, you must first familiarize yourself with machine learning terminology.

One of the most common questions that data science aspirants have is "how much math do I need to know for machine learning?" Students looking to break into machine learning often see math as a huge barrier to entry. Gatekeepers in the industry don't help with this concern, labelling students as unqualified unless they have a Master's degree of PhD in the subject. So how much math do you need to know in order to work in the data science industry? The answer: Not as much as you think.

This article was published as a part of the Data Science Blogathon. Will tomorrow be a sunny day? What are the chances that a student will get into that dream university? These and many more real-world "decision" scenarios need a standard mechanism. Step in Logistic Regression may be stated very simply as an estimation of the probability of an event occurring. In the next few minutes, we shall understand Logistic Regression from A-to-Z.