Statistics is the process of gathering, analyzing, and interpreting information in order to help people make decisions when faced with uncertainty.

Statistics

The linear algebra necessary to further explain Machine Learning in our capacity, requires a basic understanding of 
- Linear Systems of Equations
- Linear Transformations
- Vector Spaces
- Orthogonality
- Eigenvalues


Linear Algebra

Information theory is the mathematical understanding of parameters and rules of transmitting and processing information through communication systems.

Information Theory

- Computation of transforms
- Computations in finite fields
- Computations on matrices
- Computations on polynomials
- Number-theoretic computations
- Interpolation
- Numerical differentiation
- Interval arithmetic
- Arbitrary-precision arithmetic
- Automatic differentiation
- Mesh generation
- Discretization

Numerical Analysis

- Discrete mathematics
- Probability and statistics
- Mathematical software
- Information theory
- Mathematical analysis
- Continuous mathematics

University of Michigan - Ann Arbor

- Hardware
- Computer systems organization
- Networks
- Software and its engineering
- Theory of computation
- Mathematics of computing
- Information systems
- Security and privacy
- Human-centered computing
- Computing methodologies
- Applied computing
- Social and professional topics

ACM Computing Classification

The study of quantity (number theory), space (geometry), structure (algebra) and change (mathematical analysis)

Math

In the dominant machine learning approach, rather than designing explicit step-by-step rules to map inputs to outputs, practitioners define a flexible program whose behavior is governed by a set of adjustable parameters. By presenting this program with a large dataset of examples and labels, a learning algorithm determines the optimal parameter values that maximize the model's performance on the desired task.

Machine Learning Approach

[dl.acm.org/ccs](https://dl.acm.org/ccs) 

ACM Computing Classification System

- Printed circuit boards
- Communication hardware, interfaces and storage
- Integrated circuits
- Very large scale integration design
- Power and energy
- Electronic design automation
- Hardware validation
- Hardware test
- Robustness
- Emerging technologies

Hardware in ACM Computing Classification

- Architectures
- Embedded and cyber-physical systems
- Real-time systems
- Dependable and fault-tolerant systems and networks

Computer systems organization in ACM Computing Classification

- Network architectures
- Network protocols
- Network components
- Network algorithms
- Network performance evaluation
- Network properties
- Network services
- Network types

Networks in ACM Computing Classification

- Software organization and properties
- Software notations and tools
- Software creation and management

Software and its engineering in ACM Computing Classification

- Models of computation
- Formal languages and automata theory
- Computational complexity and cryptography
- Logic
- Design and analysis of algorithms
- Randomness, geometry and discrete structures
- Theory and algorithms for application domains
- Semantics and reasoning

Theory of computation in ACM Computing Classification

Mathematics of computing in ACM Computing Classification

- Data management systems
- Information storage systems
- Information systems applications
- World Wide Web
- Information retrieval

Information systems in ACM Computing Classification

- Cryptography
- Formal methods and theory of security
- Security services
- Intrusion/anomaly detection and malware mitigation
- Security in hardware
- Systems security
- Network security
- Database and storage security
- Software and application security
- Human and societal aspects of security and privacy

Security and privacy in ACM Computing Classification

- Human computer interaction (HCI)
- Interaction design
- Collaborative and social computing
- Ubiquitous and mobile computing
- Data Visualization
- Accessibility

Human-centered computing in ACM Computing Classification

- Symbolic and algebraic manipulation
- Parallel computing methodologies
- Artificial intelligence
- Machine learning
- Modeling and simulation
- Computer graphics
- Distributed computing methodologies
- Concurrent computing methodologies

Computing methodologies in ACM Computing Classification

- Electronic commerce
- Enterprise computing
- Physical sciences and engineering
- Life and medical sciences
- Law, social and behavioral sciences
- Computer forensics
- Arts and humanities
- Computers in other domains
- Operations research
- Learning Science
- Document management and text processing

Applied computing in ACM Computing Classification

- Professional topics
- Computing / technology policy
- User characteristics

Social and professional topics in ACM Computing Classification

Pure:
- Quantity (number theory)
- Space (geometry)
- Structure (Algebra)
- Change (mathematical analysis)
- Combinatorics
- Topology

Applied:
- Probability Theory
- Computational Science
- Mathematical Physics
- Operational Research

Focuses of Math

The marriage of Statistics, Computer Science, and Domin knowledge built Data Science.

Data science is interdisciplinary

The list of helpful broad references about ML is categorized as follows:
1- ML books
2- ML online courses
3- ML research papers

Machine Learning references

There are several categories for ML algorithms, including:
 - Supervised Learning
 - Semi-supervised Learning
 - Unsupervised Learning
 - Reinforcement Learning
 - Feature Learning (Representation Learning)

The types of machine learning algorithms differ in their approach, the type of data they input and output, and the type of task or problem that they are intended to solve.


Machine Learning Categories

Python is widely used for machine learning various reasons.
- It is relatively easy to learn.
- The data handling capacity is better than most other languages.
- The community is large, as well as support for other platforms.
- Its’s Open Source.
- It supports developers with frameworks and libraries such as TensorFlow


Machine Learning with Python


here is a cycle for doing machine learning evaluation and selection. The first is representation. You extract and select object features. The second is train. You train the model by fitting the estimator to the data. Afterwards, you evaluate the model to look at its accuracy, recall and all the relevant metrics. Finally you refine the model and feature and go back to step one.

Represent/Train/Evaluate/Refine Cycle

1.Identify diseases and diagnosis
2.Drug discovery and manufacturing
3.Medical imaging diagnosis
4.Personalized medicine
5.Machine learning-based behavioral modification
6.Smart health records
7.Clinical trial and research
8.Crowdsourced data collection
9.Better Radiotherapy
10.Outbreak prediction

Machine learning and applications in healthcare

Almost all deep learning algorithms can be described as specific instances of a simple recipe: combine a data set specification, a cost function, an optimization process, and a model.


Building a Machine Learning Algorithm

A good machine learning practitioner needs to know how to choose an algorithm for a particular application and how to monitor and respond to feed back obtained from experiments in order to improve a machine learning system. We recommend the following practical design process:
- Determine your goals—what error metric to use, and your target value forthis error metric. These goals and error metrics should be driven by the problem that the application is intended to solve.
- Establish a working end-to-end pipeline as soon as possible, including the estimation of the appropriate performance metrics.
- Instrument the system well to determine bottlenecks in performance. Diagnose which components are performing worse than expected and whether poor performance is due to overﬁtting, underﬁtting, or a defect in the data or software.
- Repeatedly make incremental changes such as gathering new data, adjusting hyperparameters, or changing algorithms, based on speciﬁc ﬁndings from your instrumentation.

Practical Methodology

For example, the linear regression algorithm combines a dataset consisting of X and y, the cost function


The cost function typically includes at least one term that causes the learningprocess to perform statistical estimation. The most common cost function is the negative log-likelihood, so that minimizing the cost function causes maximum likelihood estimation. 

In simple terms, the cost function is used to evaluate whether the parameter value W is reasonable.

Cost Function

Graph Representation Learning is the application of machine learning techniques on graph-structured data. A few examples of growing topics in Graph Representation Learning include techniques for deep graph embeddings, Graph Neural Networks (GNNs), and applications to knowledge graphs.

Graph Representation Learning

Hamilton, W.L. Graph Representation Learning. *Synthesis Lectures on Artificial Intelligence and Machine Learning*. 2020, 14(3), 1–159. https://doi.org/10.2200/S01045ED1V01Y202009AIM046

Graph Representation Learning by William Hamilton

Active learning (AL) attempts to maximize a model’s performance gain while annotating the fewest samples possible.

Active Learning

In machine learning, parameters can be intuitively understood as adjustable 'knobs' that dictate the behavior of a flexible program. By manipulating these parameters, practitioners can change how the program maps inputs to outputs. Once these parameter values are determined and fixed, the resulting program is referred to as a model.

Machine Learning Model Parameter

A learning algorithm is a 'meta-program' that utilizes a dataset to determine the optimal parameter values for a machine learning model. Instead of explicitly coding the model's behavior, the learning algorithm automatically discovers the best configuration of parameters to improve the model's performance on a specific task.

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