Mathematical Problems in Data Science : Theoretical and Practical Methods [Hardcover]
We try to find best fit lines using regression or split the data into clusters using PCA, k-means clustering, or SVMs, but what if that is not enough? In my research, I use topological methods to find higher dimensional structure in big data sets, and then use this structure to better understand the world around me. On the one had, we use tools such as graph theory, algebraic topology and category theory, largely developed in the purest of the pure mathematical contexts over the last century.
On the other hand, these tools have been used to understand structure in data arising from a myriad of sources, including medicine, biology, psychology, image analysis, sensor networks, and many others. This interplay between the pure and applied gives rise to a wealth of interesting questions and directions of study and has an extremely active research community.
Charles Micchelli The ideas and techniques developed by Professor Micchelli and others have been used and developed to understand the performance of learning algorithms. For instance, learning theory aims to establish mathematical and statistical foundations for learning algorithms This often involves investigating mathematical problems concerning approximation, representation, and estimation of functions.
To resolve such mathematical problems arising from data science, the field of learning theory has drawn ideas and tools from approximation theory, computational mathematics and numerical optimization, and has proven itself extremely useful in not only providing theoretical understanding of learning algorithms but also designing new practical algorithms.
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I am enthusiastic about machine learning applications to real data problems in computer vision and biomedical research. The goal of my research is to address the computational and statistical challenges arising in modern data analysis, helping the discovery of hidden information from increasingly big and complex data.
The Role of Theory in Data Analysis
Classic academic conduits aren't providing Data Scientists -- this talent gap will be closed differently. Academic credentials are important but not necessary for high-quality data science. The core aptitudes — curiosity, intellectual agility, statistical fluency, research stamina, scientific rigor, skeptical nature — that distinguish the best data scientists are widely distributed throughout the population.
This is an introduction geared toward those with at least a minimum understanding of programming , and perhaps obviously an interest in the components of Data Science like statistics and distributed computing. Out of personal preference and need for focus, I geared the original curriculum toward Python tools and resources.
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R resources can be found here.