We introduce a simple and fast method for comparing graphs of different sizes. Existing approaches are often either limited to comparing graphs with the same number of vertices or are computationally unscalable. We propose the Embedded Laplacian Distance (ELD) for comparing graphs of potentially vastly different sizes. Our approach first projects the graphs onto a common, low-dimensional Laplacian embedding space that respects graphical structure. This reduces the problem to that of comparing point clouds in a Euclidean space. A distance can then be computed efficiently via a natural sliced Wasserstein approach. We show that the ELD is a pseudo-metric and is invariant under graph isomorphism. We provide intuitive interpretations of the ELD using tools from spectral graph theory. We test the efficacy of the ELD approach extensively on both simulated and real data. Results obtained are excellent.

We address the following foundational question: what is the population, and sample, Frechet mean (or median) graph of an ensemble of inhomogeneous Erdos-Renyi random graphs? We prove that if we use the Hamming distance to compute distances between graphs, then the Frechet mean (or median) graph of an ensemble of inhomogeneous random graphs is obtained by thresholding the expected adjacency matrix of the ensemble. We show that the result also holds for the sample mean (or median) when the population expected adjacency matrix is replaced with the sample mean adjacency matrix. Consequently, the Frechet mean (or median) graph of inhomogeneous Erdos-Renyi random graphs exhibits a sharp threshold: it is either the empty graph, or the complete graph. This novel theoretical result has some significant practical consequences; for instance, the Frechet mean of an ensemble of sparse inhomogeneous random graphs is always the empty graph.

Newgen Software, a leading provider of a unified digital transformation platform, is pleased to announce that it is acquiring India-based Number Theory, an AI/ML (artificial intelligence and machine learning) data science platform company, subject to the completion of conditions as stated in the approved Share Purchase Agreement. Number Theory's platform, AI Studio, brings intuitive AI/ML to every enterprise, while unifying the entire lifecycle of data engineering, from data preparation to model development and monitoring. It empowers both citizen and expert data scientists to work faster and more efficiently, thereby helping in accomplishing key machine learning tasks in just hours or days, not months. This acquisition will further strengthen Newgen's low code digital transformation platform, NewgenONE, with AI/ML modeling and data analytics capabilities. "Our customers are increasingly looking to leverage data for deeper insights and accelerated growth. Number Theory will bring domain expertise, along with a powerful engine to extract actionable insights in real time. AI/ML projects often get complex, expensive, and not rewarding. What we like about Number Theory's platform is that it is for every enterprise. It lets fusion teams build, deploy, and collaborate on the entire modeling lifecycle in low code and on cloud. We look forward to welcoming the Number Theory team to the Newgen family," said Virender Jeet, CEO, Newgen.

Description Linear Algebra for Machine Learning is a training course on the application of linear algebra in data science and machine learning, published by the Informit Academy. In this training course, you will get acquainted with the theoretical and practical issues of linear algebra and you will implement it in a completely practical way in projects related to machine learning. Machine learning and data science are two of the most widely used disciplines in today's digital world, and learning them can bring you many career opportunities. What you will learn in Linear Algebra for Machine Learning: Familiarity with the application of algebra and the principles of mathematics in the field of machine learning Familiarity with the basics of linear algebra Familiarity with different approaches to developing machine learning based solutions In-depth understanding of the working process of machine learning-based algorithms Improve the skills of mathematical intuition In-depth understanding of other topics related to machine learning such as calculus, statistics, optimization algorithms and… Course specifications Publisher: InformIT Instructor: Jon Krohn Language: English Level: Medium Courses: 58 Duration: 6 hours and 32 minutes Course topics Lesson 1: Orientation to Linear Algebra Lesson 2: Data Structures for Algebra Lesson 3: Common Tensor Operations Lesson 4: Solving Linear Systems Lesson 5: Matrix Multiplication Lesson 6: Special Matrices and Matrix Operations Lesson 7: Eigenvectors and Eigenvalues Lesson 8: Matrix Determinants and Decomposition Lesson 9: Machine Learning with Linear Algebra Prerequisites for Linear Algebra for Machine LearningMathematics: Familiarity with secondary school-level mathematics will make the course easier to follow. If you are comfortable dealing with quantitative information - such as understanding charts and rearranging simple equations - then you should be well-prepared to follow along with all of the mathematics.

In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. In latent space random graphs, nodes are associated to unknown latent variables. One may then seek to compute distances directly in the latent space, using only the graph structure. In this paper, we show that it is possible to consistently estimate entropic-regularized Optimal Transport (OT) distances between groups of nodes in the latent space. We provide a general stability result for entropic OT with respect to perturbations of the cost matrix. We then apply it to several examples of random graphs, such as graphons or $\epsilon$-graphs on manifolds. Along the way, we prove new concentration results for the so-called Universal Singular Value Thresholding estimator, and for the estimation of geodesic distances on a manifold.

The article describes the approaches for forming different predictive features of tweet data sets and using them in the predictive analysis for decision-making support. The graph theory as well as frequent itemsets and association rules theory is used for forming and retrieving different features from these datasests. The use of these approaches makes it possible to reveal a semantic structure in tweets related to a specified entity. It is shown that quantitative characteristics of semantic frequent itemsets can be used in predictive regression models with specified target variables.

We demonstrate that a neural network pre-trained on text and fine-tuned on code solves Mathematics problems by program synthesis. We turn questions into programming tasks, automatically generate programs, and then execute them, perfectly solving university-level problems from MIT's large Mathematics courses (Single Variable Calculus 18.01, Multivariable Calculus 18.02, Differential Equations 18.03, Introduction to Probability and Statistics 18.05, Linear Algebra 18.06, and Mathematics for Computer Science 6.042), Columbia University's COMS3251 Computational Linear Algebra course, as well as questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems specifically designed to assess mathematical reasoning. We explore prompt generation methods that enable Transformers to generate question solving programs for these subjects, including solutions with plots. We generate correct answers for a random sample of questions in each topic. We quantify the gap between the original and transformed questions and perform a survey to evaluate the quality and difficulty of generated questions. This is the first work to automatically solve, grade, and generate university-level Mathematics course questions at scale. This represents a milestone for higher education.

The most common approaches for solving multistage stochastic programming problems in the research literature have been to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the impact of a decision now on the future. By contrast, common industry practice is to use a deterministic approximation of the future which is easier to understand and solve, but which is criticized for ignoring uncertainty. We show that a parameterized version of a deterministic optimization model can be an effective way of handling uncertainty without the complexity of either stochastic programming or dynamic programming. We present the idea of a parameterized deterministic optimization model, and in particular a deterministic lookahead model, as a powerful strategy for many complex stochastic decision problems. This approach can handle complex, high-dimensional state variables, and avoids the usual approximations associated with scenario trees or value function approximations. Instead, it introduces the offline challenge of designing and tuning the parameterization. We illustrate the idea by using a series of application settings, and demonstrate its use in a nonstationary energy storage problem with rolling forecasts.

This thesis reviews numerical optimization methods with machine learning problems in mind. Since machine learning models are highly parametrized, we focus on methods suited for high dimensional optimization. We build intuition on quadratic models to figure out which methods are suited for non-convex optimization, and develop convergence proofs on convex functions for this selection of methods. With this theoretical foundation for stochastic gradient descent and momentum methods, we try to explain why the methods used commonly in the machine learning field are so successful. Besides explaining successful heuristics, the last chapter also provides a less extensive review of more theoretical methods, which are not quite as popular in practice. So in some sense this work attempts to answer the question: Why are the default Tensorflow optimizers included in the defaults?

This course will allow you to become a professional who understands the math on which algorithms are built, rather than someone who applies them blindly without knowing what happens behind the scenes. But let's answer a pressing question you probably have at this point: "What can I expect from this course and how it will help my professional development?" In brief, we will provide you with the theoretical and practical foundations for two fundamental parts of data science and statistical analysis – linear algebra and dimensionality reduction. Linear algebra is often overlooked in data science courses, despite being of paramount importance. Most instructors tend to focus on the practical application of specific frameworks rather than starting with the fundamentals, which leaves you with knowledge gaps and a lack of full understanding.