The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site. This textbook considers statistical learning applications when interest centers on the conditional distribution of a response variable, given a set of predictors, and in the absence of a credible model that can be specified before the data analysis begins. Consistent with modern data analytics, it emphasizes that a proper statistical learning data analysis depends in an integrated fashion on sound data collection, intelligent data management, appropriate statistical procedures, and an
This chapter explores sequence analysis (SA), which conceives the social world as happening in processes, in series of events experienced by social entities. SA refers to a set of tools used to summarize, represent, and compare sequences — i.e. ordered lists of items. Job careers (succession of job positions) are typical examples of sequences. Various other topics have been studied through SA, such as steps in traditional English dances, country-level adoption of welfare policies over one century, or individual and family time-diaries. Andrew Abbott played a pioneering role in the diffusion of SA. With colleagues, Abbott introduced optimal matching analysis (OMA) in the social sciences, a tool to compare sequences borrowed from computer science and previously adapted to DNA sequences. Abbott’s work on SA was part of a wider methodological thinking on social processes. The chapter then looks at the most common type of sequences in social science: categorical time series — i.e. successions of states with a duration defined on a more or less refined chronological scale.
The innovative preprint repository, arXiv, was created in the early 1990s to improve access to scientific research. arXiv contains millions of Open Access articles in physics, mathematics, computer science, quantitative biology, quantitative finance, statistics, electrical engineering and systems science, and economics. All articles are available for free download on the open web. Often research findings are available on arXiv before they are published in a peer-reviewed journal. arXiv relies on a collaborative support business model where institutions that most heavily utilize arXiv contribute financially. Support also comes from Cornell University and the Simons Foundation.
TensorFlow is an interface for expressing machine learning algorithms, and an implementation for executing such algorithms. A computation expressed using TensorFlow can be executed with little or no change on a wide variety of heterogeneous systems, ranging from mobile devices such as phones and tablets up to large-scale distributed systems of hundreds of machines and thousands of computational devices such as GPU cards. The system is flexible and can be used to express a wide variety of algorithms, including training and inference algorithms for deep neural network models, and it has been used for conducting research and for deploying machine learning systems into production across more than a dozen areas of computer science and other fields, including speech recognition, computer vision, robotics, information retrieval, natural language processing, geographic information extraction, and computational drug discovery. This paper describes the TensorFlow interface and an implementation of that interface that we have built at Google. The TensorFlow API and a reference implementation were released as an open-source package under the Apache 2.0 license in November, 2015 and are available at www.tensorflow.org.
Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast and questions notions generally held to be “laws of nature" by practitioners of numerical computing: \beginlist \item High-level dynamic programs have to be slow. \item One must prototype in one language and then rewrite in another language for speed or deployment. \item There are parts of a system appropriate for the programmer, and other parts that are best left untouched as they have been built by the experts. \endlist We introduce the Julia programming language and its design---a dance between specialization and abstraction. Specialization allows for custom treatment. Multiple dispatch, a technique from computer science, picks the right algorithm for the right circumstance. Abstraction, which is what good computation is really about, recognizes what remains the same after dif...
Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. As the theory of quantum physics is fundamentally stochastic, randomness and uncertainty are deeply rooted in quantum computation, quantum simulation and quantum information. Consequently quantum algorithms are random in nature, and quantum simulation utilizes Monte Carlo techniques extensively. Thus statistics can play an important role in quantum computation and quantum simulation, which in turn offer great potential to revolutionize computational statistics. While only pseudo-random numbers can be generated by classical computers, quantum computers are able to produce genuine random numbers; quantum computers can exponentially or quadratically speed up median evaluation, Monte Carlo integration and Markov chain simulation. This paper gives a brief review on quantum computation, quantum simulation and quantum information. We introduce the basic concepts of quantum computation and quantum simulation and present quantum algorithms that are known to be much faster than the available classic algorithms. We provide a statistical framework for the analysis of quantum algorithms and quantum simulation.
In recent years generative artificial intelligence has been used to create data to support scientific analysis. For example, generative adversarial networks (GANs) have been trained using Monte Carlo simulated input and then used to generate data for the same problem. This has the advantage that a GAN creates data in a significantly reduced computing time. $N$ training events for a GAN can result in $NG$ generated events with the gain factor $G$ being greater than one. This appears to violate the principle that one cannot get information for free. This is not the only way to amplify data so this process will be referred to as data amplification which is studied using information theoretic concepts. It is shown that a gain greater than one is possible whilst keeping the information content of the data unchanged. This leads to a mathematical bound, $2\log (\text{Generated}\ \text{Events}) \unicode{x2A7E} {\text{3log(Training Events)}}$ , which only depends on the number of generated and training events. This study determined the conditions for both the underlying and reconstructed probability distributions to ensure this bound. In particular, the resolution of variables in amplified data is not improved by the process but the increase in sample size can still improve statistical significance. The bound was confirmed using computer simulation and analysis of GAN generated data from the literature.
Joanna Siwek, Konrad Pierzyński, Przemysław Siwek
et al.
This paper introduces a novel artificial intelligence model that integrates artificial empathy into the decision-making processes of collaborative agent systems. The existing models of collaborative behaviors, especially in swarm applications, lack the aspect of empathy, known to improve cooperation in human teams. Emphasizing both cognitive and emotional aspects of empathy, the introduced model navigates communication uncertainties and ambiguities, transforming these challenges into opportunities for learning and adaptation in dynamic environments. A significant feature of this model is its handling of imprecision through fuzzy logic, using fuzzy similarity measures in the decision process. The main objective of the presented research is to introduce a new model for improving cooperativeness in multi-agent systems with the use of cognitive empathy. Future research focus on implementing the model on physical platform and optimize the artificial empathy algorithms in the decision-making module.