Two subsets are said to be linearly separable if there exists a hyperplane that separates the elements of each set in a way that all elements of one set resides on the opposite side of the hyperplane from the other set. In 2D plotting, we can depict this through a separation line, and in 3D plotting through a hyperplane. In simple words, the expression above states that H and M are linearly separable if there exists a hyperplane that completely separates the elements of and elements of . In the figure above, (A) shows a linear classification problem and (B) shows a non-linear classification problem. In (A) our decision boundary is a linear one that completely separates the blue dots from the green dots. In this scenario several linear classifiers can be implemented.

This post is part three of a series of posts introducing the Redis-ML module. The first article in the series can be found here. The sample code for this post requires several Python libraries and a Redis instance running Redis-ML. Detailed setup instructions to run the code can be found in either part one or part two of the series. Logistic regression is another linear model for building predictive models from observed data.

Nowadays, machine learning is a breakthrough in the technology world. Although machine learning started from advanced research in cybernetics and robotics, now it is frequently focused on the mathematical algorithms and software applied to accomplishing certain types of tasks. Machine learning is not a particular method or technology but is preferably a sphere of computational science that combines various technologies to create systems that can learn from the data in their environment and then make predictions and take actions when faced with a new situation. Since we are also going to use machine learning in Vinnd, let us tell you what algorithms and technologies ML uses. Machine learning algorithms can't be fully preprogrammed and fixed previously because application meanings can differ hugely.

Machine learning (ML) has received a lot of attention recently, and not without good reason. It has already revolutionized fields from image recognition to healthcare to transportation.

We live in a start of revolutionized era due to development of data analytics, large computing power, and cloud computing. Machine learning will definitely have a huge role there and the brains behind Machine Learning is based on algorithms. This article covers 10 most popular Machine Learning Algorithms which uses currently. These algorithms can be categorized into 3 main categories. Following algorithms are going to be covered in this article.

The analysis of large datasets is often complicated by the presence of missing entries, mainly because most of the current machine learning algorithms are designed to work with full data. The main focus of this work is to introduce a clustering algorithm, that will provide good clustering even in the presence of missing data. The proposed technique solves an $\ell_0$ fusion penalty based optimization problem to recover the clusters. We theoretically analyze the conditions needed for the successful recovery of the clusters. We also propose an algorithm to solve a relaxation of this problem using saturating non-convex fusion penalties. The method is demonstrated on simulated and real datasets, and is observed to perform well in the presence of large fractions of missing entries.

Summary: Motivation: Second generation sequencing technologies are being increasingly used for genetic association studies, where the main research interest is to identify sets of genetic variants that contribute to various phenotype. The phenotype can be univariate disease status, multivariate responses and even high-dimensional outcomes. Considering the genotype and phenotype as two complex objects, this also poses a general statistical problem of testing association between complex objects. Results: We here proposed a similarity-based test, generalized similarity U (GSU), that can test the association between complex objects. We first studied the theoretical properties of the test in a general setting and then focused on the application of the test to sequencing association studies. Based on theoretical analysis, we proposed to use Laplacian kernel based similarity for GSU to boost power and enhance robustness. Through simulation, we found that GSU did have advantages over existing methods in terms of power and robustness. We further performed a whole genome sequencing (WGS) scan for Alzherimer's Disease Neuroimaging Initiative (ADNI) data, identifying three genes, APOE, APOC1 and TOMM40, associated with imaging phenotype. Availability: We developed a C package for analysis of whole genome sequencing data using GSU. Contact: weichangshuai@gmail.com Key words: Weighted U Statistic; Sequencing Study; Nonparametric Statistics. 1. Introduction The ongoing sequencing studies allowed researchers to comprehensively investigate the role of a deep catalog of human genome variations in complex diseases(Cirulli and Goldstein, 2010). Although these studies hold great promise for uncovering novel disease-associated variants, the massive sequencing data bring tremendous computational and statistical challenges to data analysis. Sequencing data is characterized with high-dimensionality and sparsity, where a large portion of genetic variants are rare variants with minor allele frequency (MAF) smaller than 5%. Even with a large effect size, a rare variant is hard to detect because of its low MAF.

We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregular shaped spaces arising as subsets or submanifolds of R, R2, R3 and beyond. For example, in-GPs can accommodate spatial domains arising as complex subsets of Euclidean space. in-GPs respect the potentially complex boundary or interior conditions as well as the intrinsic geometry of the spaces. The key novelty of the proposed approach is to utilise the relationship between heat kernels and the transition density of Brownian motion on manifolds for constructing and approximating valid and computationally feasible covariance kernels. This enables in-GPs to be practically applied in great generality, while existing approaches for smoothing on constrained domains are limited to simple special cases. The broad utilities of the in-GP approach is illustrated through simulation studies and data examples.

We introduce an efficient algorithmic framework for model selection in online learning, also known as parameter-free online learning. Departing from previous work, which has focused on highly structured function classes such as nested balls in Hilbert space, we propose a generic meta-algorithm framework that achieves online model selection oracle inequalities under minimal structural assumptions. We give the first computationally efficient parameter-free algorithms that work in arbitrary Banach spaces under mild smoothness assumptions; previous results applied only to Hilbert spaces. We further derive new oracle inequalities for matrix classes, non-nested convex sets, and $\mathbb{R}^{d}$ with generic regularizers. Finally, we generalize these results by providing oracle inequalities for arbitrary non-linear classes in the online supervised learning model. These results are all derived through a unified meta-algorithm scheme using a novel "multi-scale" algorithm for prediction with expert advice based on random playout, which may be of independent interest.

We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new nonconvex algorithm for robust phase retrieval, namely Robust Wirtinger Flow to jointly estimate the unknown signal and the sparse corruption. We show that our proposed algorithm is guaranteed to converge linearly to the unknown true signal up to a minimax optimal statistical precision in such a challenging setting. Compared with existing robust phase retrieval methods, we achieve an optimal sample complexity of $O(n)$ in both noisy and noise-free settings. Thorough experiments on both synthetic and real datasets corroborate our theory.