This paper studies a Nystr\"om type subsampling approach to large kernel learning methods in the misspecified case, where the target function is not assumed to belong to the reproducing kernel Hilbert space generated by the underlying kernel. This case is less understood, in spite of its practical importance. To model such a case, the smoothness of target functions is described in terms of general source conditions. It is surprising that almost for the whole range of the source conditions, describing the misspecified case, the corresponding learning rate bounds can be achieved with just one value of the regularization parameter. This observation allows a formulation of mild conditions under which the plain Nystr\"om subsampling can be realized with subquadratic cost maintaining the guaranteed learning rates.

Logistic Regression is one of the most used Machine Learning algorithms for binary classification. It is a simple Algorithm that you can use as a performance baseline, it is easy to implement and it will do well enough in many tasks. Therefore every Machine Learning engineer should be familiar with its concepts. The building block concepts of Logistic Regression can also be helpful in deep learning while building neural networks. In this post, you will learn what Logistic Regression is, how it works, what are advantages and disadvantages and much more.

Supervised Machine Learning (SML) algorithms such as Gradient Boosting, Random Forest, and Neural Networks have become popular in recent years due to their increased predictive performance over traditional statistical methods. This is especially true with large data sets (millions or more observations and hundreds to thousands of predictors). However, the complexity of the SML models makes them opaque and hard to interpret without additional tools. There has been a lot of interest recently in developing global and local diagnostics for interpreting and explaining SML models. In this paper, we propose locally interpretable models and effects based on supervised partitioning (trees) referred to as LIME-SUP. This is in contrast with the KLIME approach that is based on clustering the predictor space. We describe LIME-SUP based on fitting trees to the fitted response (LIM-SUP-R) as well as the derivatives of the fitted response (LIME-SUP-D). We compare the results with KLIME and describe its advantages using simulation and real data.

Orthogonal matching pursuit (OMP) is a widely used algorithm for recovering sparse high dimensional vectors in linear regression models. The optimal performance of OMP requires \textit{a priori} knowledge of either the sparsity of regression vector or noise statistics. Both these statistics are rarely known \textit{a priori} and are very difficult to estimate. In this paper, we present a novel technique called residual ratio thresholding (RRT) to operate OMP without any \textit{a priori} knowledge of sparsity and noise statistics and establish finite sample and large sample support recovery guarantees for the same. Both analytical results and numerical simulations in real and synthetic data sets indicate that RRT has a performance comparable to OMP with \textit{a priori} knowledge of sparsity and noise statistics.

Predictive models are extremely useful for forecasting future outcomes and estimating metrics that are impractical to measure. For example, data scientists could use predictive models to forecast crop yields based on rainfall and temperature, or to determine whether patients with certain traits are more likely to react badly to a new medication. Before we talk about linear regression specifically, let's remind ourselves what a typical data science workflow might look like. A lot of the time, we'll start with a question we want to answer, and do something like the following: Linear regression is one of the simplest and most common supervised machine learning algorithms that data scientists use for predictive modeling. In this post, we'll use linear regression to build a model that predicts cherry tree volume from metrics that are much easier for folks who study trees to measure.

A lab excercise is show cased to calculate ROC and AUC for a sample data set of logistic regression model. Learn and apply the practical code to test the data. Data Scientists take an enormous mass of messy data points (unstructured and structured) and use their formidable skills in math, statistics, and programming to clean, massage and organize. But worry not we are here to the rescue and teach you how to be a data scientist, more importantly, upgrade your analytic skills to tackle any problem in the field of data science. Join us on "statinfer.com" for becoming a "scientist in data science" Our "Machine Learning" course is now available on Udemy https://www.udemy.com/machine-learnin... Part 1 – Introduction to R Programming.

In this tutorial, we will see how to predict whether a person has diabetes or not, based on information like blood pressure, body mass index (BMI), age, etc. The data was collected and made available by "National Institute of Diabetes and Digestive and Kidney Diseases" as part of the Pima Indians Diabetes Database. Several constraints were placed on the selection of these instances from a larger database. In particular, all patients here belong to the Pima Indian heritage (subgroup of Native Americans), and are females of ages 21 and above. We will be using Python as our programming language, and making use of some popular python machine learning and data science related packages.

We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are drawn from a Gaussian distribution $\mathcal{N}(0, \Sigma)$ on $\mathbb{R}^d$. We give nearly tight upper bounds and computational lower bounds for this problem. Specifically, our main contributions are as follows: For the case that the covariance matrix is known to be the identity, we give a sample near-optimal and computationally efficient algorithm that outputs a candidate hypothesis vector $\widehat{\beta}$ which approximates the unknown regression vector $\beta$ within $\ell_2$-norm $O(\epsilon \log(1/\epsilon) \sigma)$, where $\sigma$ is the standard deviation of the random observation noise. An error of $\Omega (\epsilon \sigma)$ is information-theoretically necessary, even with infinite sample size. Prior work gave an algorithm for this problem with sample complexity $\tilde{\Omega}(d^2/\epsilon^2)$ whose error guarantee scales with the $\ell_2$-norm of $\beta$. For the case of unknown covariance, we show that we can efficiently achieve the same error guarantee as in the known covariance case using an additional $\tilde{O}(d^2/\epsilon^2)$ unlabeled examples. On the other hand, an error of $O(\epsilon \sigma)$ can be information-theoretically attained with $O(d/\epsilon^2)$ samples. We prove a Statistical Query (SQ) lower bound providing evidence that this quadratic tradeoff in the sample size is inherent. More specifically, we show that any polynomial time SQ learning algorithm for robust linear regression (in Huber's contamination model) with estimation complexity $O(d^{2-c})$, where $c>0$ is an arbitrarily small constant, must incur an error of $\Omega(\sqrt{\epsilon} \sigma)$.

The demand of metals by modern technology has been shifting from common base metals to a variety of minor metals, such as cobalt or indium. The industrial importance and limited geological availability of some minor metals have led to them being considered more "critical," and there is a growing interest in such critical metals and their producing companies. In this research, we create a novel framework, Dynamic Advisor-Based Ensemble (dynABE), to predict the stock trend of major critical metal producers. Specifically, dynABE first utilizes domain knowledge to group the features into different "advisors," each advisor dealing with a particular economic sector. Then through ensembles of weak classifiers, each advisor produces a prediction result, and all the advisors are combined again in a biased online update fashion to dynamically make the final prediction. Based on a misclassification error of 32% for Jinchuan Group's stock (HKG: 2362), we further test a simple stock trading strategy, which leads to a back-tested return of 296%, or an excess return of 130% within one year. In addition, the feature set selected by dynABE also suggests potentially influential factors to metal criticality, because stock prices of major producers influence metal production. Therefore, not only does this research propose a novel framework for specialized stock trend prediction, it also provides domain insights into dynamic features that potentially influence metal criticality.

Logistic regression predicts the probability of the outcome being true. In this exercise, we will implement a logistic regression and apply it to two different data sets. To learn the basics of Logistic Regression in R read this post. In the first part of this exercise, we will build a logistic regression model to predict whether a student gets admitted into a university. Suppose that you are the administrator of a university department and you want to determine each applicant's chance of admission based on their results on two exams.