Mathematics and Basic Algorithms for Artificial Intelligence Technology
The term “artificial intelligence” was born at the Dartmouth Conference in 1956. In the 65 years since then, a variety of technologies have been proposed. While machine learning is a technology that specializes in finding patterns (meanings) in data, artificial intelligence is a technology related to knowledge and intelligence. Specifically, it is a technology that deals with how to process data (data modeling/structuring) and how to handle it (data processing algorithms).
Knowledge is described in textbooks as sentences or diagrams (some kind of symbols), but in order to understand the content, it is necessary to understand the meaning of the symbols described in the textbooks. As described in “Handling the Meaning of Symbols with Computers,” the meaning of symbols is like invisible dark matter, and can only be handled as hidden variables behind observable real-world things (images, sounds, sensor information, text information, etc.).
To be able to handle this knowledge with a computer, the observable real-world things must be transformed into a form that can be computed in some way. The candidates are symbolic representations (graphs and trees) and distributed representations (vectors and matrices), as described in “Two approaches to the meaning of language (fusion of symbolic and distributed representations).
One aspect of knowledge handling is abstraction and inference. Abstraction, as described in “Concrete and Abstract – Semantics and Explanation in Natural Language“, is the process of grouping together common features from a large number of events and things to form a single concept, and is a common function of pattern recognition by machine learning using vectors and matrices. Inference, on the other hand, traces the relationships among events and things, and is similar to logical (set-theoretic) functions using graphs and trees. Furthermore, there are various approaches that combine abstraction and inference, such as Markov logic networks and probabilistic logic programming approaches, and it is thought that intelligence activities are realized by combining these functions.
The artificial intelligence technologies introduced in this blog include natural language processing technology, which converts information produced by humans (linguistic information) into data that can be handled by machines; semantic web technology, which automatically generates various types of data using the semantic relationships between data; chatbot technology, which lets machines talk instead of humans; and machine reasoning technology, which performs various types of inferences. These technologies can be combined with machine learning technologies.
These can be combined with machine learning technologies to become even more powerful tools. Reference information on artificial intelligence technologies is given below.
Information Theory & Computer Engineering
Shannon’s information theory was proposed by Claude Shannon in 1948 to deal quantitatively with the quantity of information and the reliability of transmission. In Shannon’s information theory, the quantity of information is defined as the “information content. The quantity of information is a measure of the uncertainty of a message output by an information source; the greater the quantity of information, the more uncertain the message. Shannon’s information theory also considers the reliability of information transmission. Because of the effects of errors and noise in information transmission, there is no guarantee that the transmitted information will be received accurately. To cope with such cases, methods to improve the reliability of information transmission have been studied.
Turing’s Theory of Computation is a theory proposed by Alan Turing that theorizes the fundamental concepts of computers. This theory provides the basis for understanding how computers work and what computation is, and consists of the following elements
Neural Turing machine refers to a model of computation that combines neural networks and Turing machines.
Using chatGPT, various algebraic problems can be solved as shown below. Since chatGPT not only gives simple answers, but also shows solutions by applying various formulas, it gives the illusion that it is a universal AI.
However, when we actually perform the calculations, we find that the answers given by chatGPT are sometimes incorrect. This is because chatGPT only estimates what character will appear next based on a vast amount of training data, and does not perform essential calculations.
- Auto-Grading (automatic grading) technology
Auto-grading refers to the process of using computer programmes and algorithms to automatically assess and score learning activities and assessment tasks. This technology is mainly used in the fields of education and assessment.
The Science of the Artificial (1969) is a book by Herbert A. Simon on the field of learning science and artificial intelligence, which has particularly influenced design theory. The book is concerned with how man-made phenomena should be categorised and discusses whether such phenomena belong in the realm of ‘science’. System Design and Decision-making Systems.
Quantum computers have been attracting renewed attention since the “demonstration of quantum transcendence” by a Google research team was reported. How could this change our world? This special issue provides an overview of the current state of quantum information science, from its history and theoretical foundations to its latest achievements, and considers the future of the quantum age from a variety of perspectives, including politics, economics, philosophy, and literature.
It was in 1948 that Claude Shannon published his monumental paper “A Mathematical Theory of Communication”. More than 60 years later, information theory is now applied not only to telecommunications, but also to a wide range of fields, including the life sciences, brain science, and social sciences. Although information theory uses advanced mathematics, its essence becomes clear when we understand the “law of large numbers. From Shannon’s ideas to the basics of information geometry, this book provides a clear explanation that even beginners can understand.
Digital processing, which is the basis of computers, is represented by two numbers “0” and “1” (binary digits). While a bit can represent only two states, “0” and “1,” a byte can represent 256 states (1 byte = 28=256).
Paul Nurse, the author of this book, saw a butterfly fluttering into his garden one early spring day and felt that, although very different from himself, the butterfly was unmistakably alive, just like himself, able to move, feel, and react, and moving toward its “purpose. What does it mean to be alive? WHAT IS LIFE” is a tribute to the physicist Erwin Schrodinger’s “What is Life?
One test for determining that a machine is intelligent is the Turing Test, described in “Conversation and AI (Thinking from the Turing Test).” The basic idea of the Turing test is based on the hypothesis that if an AI is so intelligent that it is indistinguishable from a human in a conversation with a human, then the AI can be considered as intelligent as a human. In contrast, Searle argues, “Computational systems that follow algorithms cannot be intelligent, because computation is by definition a formal process. Computation is by definition a formal symbolic operation, and there is no understanding of meaning.
ReAct (Reasoning and Acting), which refers to the ability of an AI system to use knowledge to reason and take appropriate actions based on the results, is one of the key research topics in the field of artificial intelligence (AI), and is an important step in the evolution and development of AI, and a new method for addressing more complex tasks The main goal of ReAct is to enhance the ability of AI systems to solve problems and adapt to their environment more effectively by integrating reasoning and action, thereby enabling AI to deal with more complex situations and make better decisions.
In this article, I would like to discuss the history of emotion recognition and its relevance to Buddhist philosophy and artificial intelligence technology.
As described in “Meditation, Enlightenment, and Problem Solving,” mindfulness meditation and Zen vipassana meditation are “insight meditation” that emphasize “awareness” and “attention as it is,” an approach that focuses on developing concentration and observing things as they are. A similar approach is also described in “Invitation to Cognitive Science. In cognitive science, which is also discussed in the “Reading Notes,” it is called “metacognition,” which refers to an individual’s way of thinking and perceiving knowledge, and is thought of as an understanding of what one knows and understands.
AI technology offers a feasible approach to various aspects of such metacognition.
The main approaches to using artificial intelligence techniques to extract emotions include (1) natural language processing, (2) speech recognition, (3) image recognition, and (4) biometric analysis. These methods are combined with algorithms such as machine learning and deep learning, and are basically detected using large amounts of training data. Approaches that combine different modalities (text, voice, images, biometric information, etc.) to comprehensively understand emotions are also more accurate methods.
To “awareness” means to observe or perceive something carefully, and when a person notices a situation or thing, it means that he or she is aware of some information or phenomenon and has a feeling or understanding about it. Becoming aware is an important process of gaining new information and understanding by paying attention to changes and events in the external world. In this article, I will discuss this awareness and the application of artificial intelligence technology to it.
Behavioural economics, described in “The economy is driven by ’emotions'”, is one of the current trends in modern psychology, which focuses on irrational thoughts and behaviours and tries to reveal the common laws of irrationality, in contrast to conventional economics based on rational human activities. Two systems are envisaged in our minds, one being a quick, automatic, unintentional and unconscious system, such as intuitive judgement, and the other being a deliberate and conscious system, such as logical judgement, which is time-consuming but controllable. AI technology, which is also described in this blog, aims to take the rational decision-making of System 2 to the extreme instead of humans, and IA, which is also described in “Overview of Intelligence Augmentation (IA) and its application examples”, is an approach to how to connect the useful parts of System 1 and System 2. The IA described in “Overview of IA (Intelligence Augmentation) and its application examples” can be said to be an approach to how to connect the useful parts of System 1 with System 2.
Priming is also an interesting concept in the field of AI, and there is active research into using the concept of priming to improve human-AI interactions. For example, in AI-based experience (UX) design, when a user performs a specific task, an AI assistant can more accurately understand the user’s intentions and present relevant information and context in advance, so that subsequent operations can proceed smoothly, such as Priming can be considered.
In THE UNIVERSE IN A BOX, the ‘Simulation Hypothesis’ describes the possibility that everything, including our own bodies and minds, is inside a computer. There are several approaches to thinking about whether where we are now is real or simulated. One is the classical logic approach and the other is the non-classical logic approach.
- Frame problem in agent systems
The frame problem in agent systems refers to the difficulty for agents to properly understand the state and changes in the environment and to make decisions when acquiring new information. This is specifically the case in the following cases.
- The Universal Computer: From Leibniz to Turing Reading Notes
- Neumann, Gödel, Turing Reading notes
- A Box of Spirits: The Adventure of the Turing Machine
Mathematics for Artificial Intelligence Technology
Mathematics is at the root of computer science. For example, machine learning used in deep learning, natural language processing, etc., starts with functions and uses optimization calculations based on differentiation/integration, while symbolic approaches used in artificial intelligence use set theory as a basis for evaluating expressions. It is important to organize the knowledge of each basic element before considering their digital transformation applications and IT system applications.
- Structures, Algorithms, and Functions Relationships between elements from a mathematical point of view
Structure, according to wiki, is “a way of combining the parts that make up a single thing [1]. It is a general term for relationships such as conflict, contradiction, and dependence among the elements that make up a whole [2]. It is also used to refer to “the arrangement and relationship of the parts and elements of a complex thing. In the world of mathematics, the basic approach is to abstract the “parts that make up a thing” as much as possible and seek the relationship between them.
For example, geometry is the study of space and shapes, not necessarily the study of numbers. Toyama takes this to mean that the origin of mathematics is mankind’s ability to recognize patterns in things. According to this book, this ability to recognize and weave patterns has enabled us to cut the complex world into an understandable form, sublimate it as a discipline, and make it into mathematics. For example, the simple number concept of 1, 2, 3, … is not simply a number, but an abstract concept of 2, which is derived from the abstraction of common forms or patterns between different things, such as two apples, two oranges, two people, two dogs, etc. The following is an example of this concept.
- Formal Languages and Mathematical Logics Language as a combination of strings
The programming languages mentioned above are a type of language called a formal language. A formal language is a set of strings (words) that can be generated from a set of symbols (alphabet, etc.) and rules of generation (grammar).
Mathematical logic is the foundation of mathematics, and is the study of defining and proving everything in mathematics using set theory, proof theory, and so on. One of the most famous examples is the proof of classical mathematical systems using the ZFC axiomatic system. Roughly speaking, what is done here is to define the basic parts and combine them to construct a large world.
The theme of the book is programming, but unlike most programming books, in addition to algorithms and code, it includes mathematical proofs and historical background on mathematical discoveries from ancient times to the present.
To be more specific, the theme is generic programming. Generic programming is a programming technique that emerged in the 1980s, with the development of the Standard Template Library (TL) in C++ in the 1990s. Here, generic programming is a programming method that focuses on designing algorithms and data structures to make them work in the most common environment without reducing efficiency.
What role does it play in modern mathematics?
Modern mathematics cannot develop without sets. The question of what is a set is the deepest question in modern mathematics, involving the search for new set axioms. This is a reissue of the famous book that explains the profound mysteries of the set concept and the romantic spirit of creativity hidden in set theory to people who are not trained in mathematics, with the addition of Cantor’s biography.
Basic Algorithms for Artificial Intelligence Technology
Algorithmic Thinking (Algorithmic Thinking) refers to the ability or process of thinking about logical procedures and approaches in problem solving and task execution. Having algorithmic thinking is an important skill that can help when dealing with a variety of complex challenges. ‘Problem partitioning’ in algorithmic thinking is the process of dividing a large problem into a number of smaller sub-problems, an approach that allows complex problems to be broken down into manageable units, making large tasks more understandable and allowing each sub-problem to be solved individually and efficiently. Problem Partitioning can be seen as the first step in the general problem-solving process.
- Search engine matching algorithms Matching strings in search engines
The 9 Most Powerful Algorithms in the World” by John McCormick is a medium beginner’s read that explains in simple terms the concepts on which current computer technology is based. The “algorithms” discussed here are not in the general sense of sorting or data structures, but rather are based on computer science theory to explain the principles of search engines, machine learning, and how software works. I would like to introduce some of them.
We have outlined search technology before. In this article, we will discuss Page Rank technology, the innovative search algorithm that has propelled Google to its current position. This is the latter of the two elements of search engines described in the previous article, and is the technology used to rank search results.
Hyperlink technology is used as a prerequisite for this page rank technology. This is a function that allows users to jump to another web page by clicking on it, which is the part of this blog with the underline. The idea of pagerank was also mentioned in “As We May Think,” written by American engineer Vanevar Bushji in 1945, as “a mechanism for storing documents and automatically indexing them” and “associative indexing, i.e., any item can be indexed immediately and automatically by selecting other items at will. It is already described as a machine called memex with “a mechanism for saving documents and automatically indexing them” and “associative indexing, i.e., any item can immediately and automatically select any other item at will”.
- Database Algorithms (1) Database Consistency
The wiki definition of a database is “a collection of information organized for easy retrieval and storage. Usually, a database is a computerized database. In this book, the concept of “storing” is used to refer to a database.
In this document, the concept of “storing” is explored a little more deeply, and the biggest difference between databases and other information storage methods is that the information in a database has a predefined structure. Another characteristic of databases is consistency.
- Database algorithms (2) Relational databases
In this article, we will discuss the last remaining important algorithm, the “relational database”. A database is data with a structure, and the simplest one will have a table structure. It is sometimes more efficient to divide a table structure into several parts instead of one.
- Data compression algorithm (1) Lossless compression
There are two main types of compression technology: “lossy compression” and “lossy compression. Lossy compression can reproduce the original data perfectly even when it is compressed, so it is normally sufficient to have only one compression technique, but it has the problem that the compression ratio cannot be that good, so lossy compression is used.
The basic principle of “lossless compression” is to find the repetitive parts of the data and omit them.
- Data compression algorithm (2) Lossy compression
An introduction to data compression algorithms used in image information (JPEG) and other applications.
- Proof of Indeterminacy About problems that cannot be calculated
This article is about what computers (algorithms) cannot do. The algorithms here are not about hard problems like driving a car perfectly or evaluating a student’s performance, but essentially about problems that cannot be computed.
The subject of the explanation is about a checking tool that detects bugs and crashes in software. The conclusion is that it can be proven that it is impossible for any program tool to find all possible crash locations.
It defines the three jobs that a computer does. The first is to perform calculations, the second is to store data, and the third is to transmit data. From a software point of view, the function of storing data is represented by database technology, and the function of transmitting data is represented by the Internet and other web technologies.
When considering the transmission and storage of data, the most important thing is to store or transmit the data “completely and accurately. On the other hand, hardware such as memory and communication is always subject to noise and malfunctions, and 100% operation cannot be guaranteed. Therefore, it is necessary to ensure “complete accuracy” by using software, and one of the technologies to achieve this is “error correction technology”.
The method of storing and transmitting data with “perfect accuracy” is to increase the redundancy of the data. For example, if the number “5123” is transmitted in the form of “five one two three,” in the former case, even if a single character error occurs, the original data will be completely lost, but in the latter case, for example, even if one of the characters in “five” is replaced by “fave,” there is a high possibility that it can be corrected to “five” using the information before and after. In the latter case, for example, even if one of the letters in “five” is replaced by “fave,” it is likely to be corrected to “five” with the information before and after.
The “signature” of a digital signature is defined as something that can be read but cannot be copied by anyone. This is the complete opposite of the concept of “digital” which can be copied by anyone. Digital signatures provide a solution to this paradox.
The purpose of a digital signature is not to sign something that you send to someone else, like a regular letter, but to check a computer when someone sends you something that is signed by someone else.
There are two requirements for a signature: (1) the place where the original signature is kept must be a trustworthy place, and (2) the signature cannot be easily forged by a third party.
The simplest cryptographic technique starts with “having a secret to share”. When you send some data to a specific person, you have a secret number that you share only with that person. (e.g. 322) Then, when you send 8 as data, you send the added number to the other person (322+8=400), and the other person can subtract the shared number from the sent number.
To make this even more practical, you can send a longer number, for example, one that is not easily recognized as a shared number. (For example, there are 999 ways to use a 3-digit number as a secret number, but a computer can easily try all combinations at this level. This is a larger number than a trillion times a trillion. It would take a billion years to calculate this on a current computer, so we can conclude that it is a secure method.
Data sorting (reordering) is the basis of algorithms. The following sorting algorithms are used.
Bubble sort,” in which adjacent values are repeatedly compared and replaced; “quick sort,” in which elements are replaced by repeatedly sorting a group of data into two groups, one above and one below a specified standard value called a pipot; and “merge sort,” in which data is broken down to the smallest unit (a single element) and sorting and merging (merging) are repeated to sort elements from the smallest unit. Merge Sort, which sorts elements by repeatedly sorting and merging (merging) from the smallest unit (single element).
AlphaGo, a computer Go program developed by Google DeepMind, became the first computer Go program to defeat a human professional Go player in an even-handed (no handicap) game in October 2015. The victory of an artificial intelligence in Go, a field that had been considered the most difficult for computers to beat humans, was a shock to the world, and the appearance of AlphaGo went beyond a simple victory or defeat in a single game to widely publicize the usefulness of artificial intelligence, triggering a global AI boom. It also triggered a global AI boom. In this issue, I will discuss the relationship between AI and board games, including Go, and will also include notes from my reading of the book “Why AlphaGo Beat Humans” and “The Strongest Go AI: AlphaGo Demystified: Its Mechanism from the Perspective of Deep Learning, Monte Carlo Trees, and Reinforcement Learning”.
- Othello game solution algorithms and GNNs
The game of Othello (Othello) is a board game played between two players using black and white discs, with the basic rule of competition being that players place a disc of their own colour and change it to their own colour by flipping it between their opponent’s discs.
Logic
- Making Logic – Part 1 Starting Logic Reading Memo
Logic was never this interesting! This is a masterpiece text that does not explain ready-made logic in a descent style, but clarifies the purpose of logic and shares the process of creating it with readers so that they can understand the “why” of the ideas. You can master elementary logic by yourself. What is logic – Creating an artificial language of logic – Giving meaning to an artificial language (semantics of propositional logic) – Logic that even machines can understand (semantic tableaux)
- Making Logic – Part 2 Expanding Logic Reading Memo
Extending the target language of logic (predicate logic) – oh, the semantics of predicate logic was not yet available – further extending the logic language (PPL) – further extending the logic language even further (IPL)
Let’s use Natural Deduction (Natural Deduction with Identity Symbols) – Approaching the Goal of Logic from the Viewpoint of Syntax (The Idea of Axiomatic Systems)
Welcome to the dazzling world of non-classical logic (classical logic is the logic of God, the dubiousness of the binary principle and the law of exhaustion, multi-valued logic, intuitionistic logic, modal logic as an extension of classical logic) – There is still much to learn in classical logic (the completeness of the languages FOL and AFOL, the language of fully armed predicate logic and some results some results obtained, first-order theory, isomorphisms between models, second-order logic)
The Satisfiability of Propositional Logic (SAT: Boolean Satisfiability) is the problem of determining whether or not there exists a variable assignment for which a given propositional logic expression is true. For example, if there is a problem “whether there exists an assignment of A, B, C, D, E, or F such that A and (B or C) and (D or E or F) are true,” this problem is converted into a propositional logic formula and whether the formula is satisfiable is determined.
Such problem setting plays an important role in many application fields, for example, circuit design, program analysis, problems in the field of artificial intelligence, and cryptography theory. From a theoretical aspect, it is known that the algorithm that can solve the SAT problem is an “NP-complete problem,” and current computers have not found an efficient solution for large-scale problems. Therefore, this is a field of technology where research is still being conducted to improve algorithm efficiency, such as increasing speed and developing heuristic search algorithms.
The EM (Expectation Maximization) algorithm can also be used as a method for solving the Constraint Satisfaction Problem. This approach is particularly useful when there is incomplete information, such as missing or incomplete data. This paper describes various applications of the constraint satisfaction problem using the EM algorithm and its implementation in python.
Labeling of image information can be achieved by various machine learning approaches, as described below. This time, we would like to consider the fusion of these machine learning approaches and the constraint satisfaction approach, which is a rule-based approach. These approaches can be extended to labeling text data using natural language processing, etc.
- Mathematics with Logic
- Foundations of Logic
- Can you prove that theory?
- Answer Set Programming : A Brief History of Logic Programming and ASP
From “Solution Set Programming” from the Journal of the Japanese Society for Artificial Intelligence (2010.5) Trends in Logic-based Reasoning Research, a reference paper on logic programming for constructing complex knowledge information in artificial intelligence technology.
Prolog, a logic programming language developed in the early 1970s, has attracted attention as a new artificial intelligence language that combines declarative statements based on predicate logic and computational procedures based on theorem proving, and has been widely used in expert systems, natural language processing, and computational databases in the 1980s Prolog is a Turing-complete language.
While Prolog is Turing-complete and has high computational power, it has also become clear that its base Horn clause logic program has limited applicability to real-world knowledge representation and problem solving due to its syntactic limitations and lack of reasoning capability.
An application of Bayesian estimation previously mentioned is Bayesian nets. Bayesian nets are a modeling method that expresses causal relationships (strictly speaking, probabilistic dependencies) among various events in a graph structure, and are used and studied in various fields such as failure diagnosis, weather prediction, medical decision support, marketing, and recommendation systems.
To express this mathematically, a finite number of random variables X1,. XN as nodes and a conditional probability table (CPT) associated with each node. XN, and the simultaneous distribution P(X1=x1,. XN=xn) is represented by the following graph structure.
In the previous article, we discussed SRL (statistical relational learning), which was developed in North America. This time, we will discuss its European counterpart, probabilistic logic learning (PLL).
SRLs such as PRM (probabilistic relational model) and MLN (Markov logic network) are based on the idea of enriching probabilistic models by using relational and logic formulas. However, enriching post-operative logic with probability is not the direct goal of SRL. On the other hand, knowledge representation by post-operative logic has long been studied in the field of artificial intelligence, and attempts to incorporate probability into it to represent not only logical knowledge, which is always valid, but also probabilistic knowledge have been attempted since before the statistical machine learning boom.
The idea of possible worlds (Possible Worlds) is a concept used primarily in the fields of philosophy and logic, and refers to a possible world that is different from the real world. This is to say that it is a world in which different elements and events may unfold in different ways, unconstrained by physical constraints or laws.
Probability Theory (Probability Theory), on the other hand, is a field of mathematics that deals with uncertainty and randomness and provides a framework for predicting the probability of events occurring and their outcomes. From this perspective, probability theory not only evaluates the probability of events in the real world, but also considers the probability of events in the possible world.
Artificial Intelligence (AI) technology is a generic term for technologies that enable computer systems to perform intelligent tasks, which can be divided into subfields such as machine learning, deep learning, natural language processing, and computer vision. AI is the use of probability theory and statistical methods The main purpose of AI is to analyze real-world events and data, and to make predictions and decisions by utilizing probability theory and statistical methods.
In recent years, there has been a development of techniques to rank and recommend relevant entities through keyword searches. Another trend in the field of information retrieval (IR) is to evaluate the relevance of documents by considering the temporal characteristics of queries. However, while this has become an established feature in document search engines, the importance of time has not yet been recognized in entity recommendation. This paper addresses this gap by introducing a time-aware entity recommendation task. Utilizing heterogeneous knowledge of entities extracted from various data sources available on the Web, this paper proposes the first probabilistic model that considers time in entity recommendation. Extensive evaluation of the proposed method shows significant improvements over the time-insensitive recommendation method.
Category Theory
- Gendai Shiso July 2020 Special Feature: The World of Category Theory — The Forefront of Modern Mathematics Reading Memo
Arrows” draw you to the forefront of modern mathematics with abundance. Sphere theory is one of the most important fields in modern mathematics. Its high level of abstraction and generality are now being used to great effect in a wide range of fields, including physics, computer science, biology, linguistics, and aesthetics. This special issue introduces and discusses the basics of sphere theory, its various practical applications, and even its philosophical ramifications, in order to get to the heart of this mathematical way of thinking, which is now attracting a great deal of attention.
- Abstractness in Mathematics
- Monads
- Type inference
Combinatorial optimization problems and discrete mathematics
Combinatorial optimization theory has been applied to many real-world problems such as transportation planning, scheduling, placement, combinatorial problems, and optimization problems. The problem is to find a subset of a set consisting of a certain number of elements that satisfies a set of constraints and to find the best solution among them. It is one of the mathematical methods to deal with discrete optimization problems to find the optimal solution under certain constraints.
There are four criteria for decision making that are also used in reinforcement learning algorithms: the Maxmin criterion, the Maxmax criterion, the expected value criterion, and multiple prior (multiple belief).
Game theory is a theory for determining the optimal strategy when there are multiple decision makers (players) who influence each other, such as in competition or cooperation, by mathematically modeling their strategies and their outcomes. It is used primarily in economics, social sciences, and political science.
Various methods are used as algorithms for game theory, including minimax methods, Monte Carlo tree search described in “Overview of Monte Carlo Tree Search and Examples of Algorithms and Implementations“, deep learning, and reinforcement learning. Here we describe examples of implementations in R, Python, and Clojure.
Submodular optimization is a type of combinatorial optimization that solves the problem of maximizing or minimizing a submodular function, a function with specific properties. This section describes various algorithms, their applications, and their implementations for submodular optimization.
Mixed integer optimization is a type of mathematical optimization and refers to problems that simultaneously deal with continuous and integer variables. The goal of mixed integer optimization is to find optimal values of variables under constraints when maximizing or minimizing an objective function. This section describes various algorithms and implementations for this mixed integer optimization.
Graph Data Algorithm and Artificial Intelligence
Graphs are a way of expressing connections between objects such as objects and states. Since many problems can be attributed to graphs, many algorithms have been proposed for graphs.
In the following pages of this blog, we discuss the basic algorithms for graph data, such as the search algorithm, shortest path algorithm, minimum global tree algorithm, data flow algorithm, DAG based on strongly connected component decomposition, SAT, LCA, decision tree, etc., and applications such as knowledge data processing and Bayesian processing based on graph structures.
Dynamic Programming
Dynamic Programming is a mathematical method for solving optimization problems, especially those with overlapping subproblems. Dynamic programming provides an efficient solution method because it dramatically reduces the amount of exponential computation by saving and reusing the results once computed. This section describes various algorithms and specific implementations in python for this dynamic programming.
There are several types of speech recognition depending on the application, and the methods differ accordingly. First, there are the following classifications based on differences in what can be generated. In addition, from the user’s point of view, there are specific speaker recognition and unspecified speaker recognition. First, discrete word recognition. The recognition method that recognizes “words” generated by the user is called isolated word recognition. The vocabulary is predefined, and the user must know in advance what vocabulary words can be generated. The algorithm is simplified because there is no need to consider the relationship between words.
It is an effective approach to improve efficiency in programming and algorithm design by recording the results of a calculation in a memo and reusing it, while avoiding the waste of repeating the same calculation. One such approach is dynamic programming. Here, we consider the problem of selecting some numbers from a sequence and finding out whether m can be constructed by summing them in a total search. This problem can be solved by recursion and divide-and-conquer methods, but they are not efficient. However, it can be speeded up by applying dynamic programming. The algorithm is as follows.
- Planning Problem (1) – Approach using Dynamic Programming and theoretical support
From the Machine Learning Professional Series “Reinforcement Learning,” a reference book on reinforcement learning, which is machine learning that deals with the problem of an agent in a certain environment observing its current state and deciding what action to take. In this article, we discuss the planning problem, which is a sequential decision-making problem when the environment is known.
- Planning Problem (2)-Implementation of Dynamic Programming (Value Iterative Method and Measure Iterative Method)
From the Machine Learning Professional Series “Reinforcement Learning,” a reference book on reinforcement learning, which is machine learning that deals with the problem of an agent in a certain environment observing its current state and deciding what action to take. In the previous article, I described a theoretical overview of the planning problem, which is a sequential decision-making problem when the environment is known. In this article, I will describe the actual algorithm for the planning problem.
meta-heuristic algorithm
In the previous article, we described an iterative similarity computation approach using a set of similarity equations. In this article, we will discuss optimization approaches that further extend these approaches. In this article, we first discuss two of these approaches: expectation maximization and particle swarm optimization.
Particle Swarm Optimization (PSO) is a type of evolutionary computation algorithm inspired by swarming behavior in nature, modeling the behavior of flocks of birds and fish. PSO is characterized by its ability to search a wider search space than genetic algorithms, which tend to fall into local solutions. PSO is widely used to solve machine learning and optimization problems, and numerous studies and practical examples have been reported.
In the previous article, we discussed machine learning for sorting alignments. In this article, we will discuss tuning approaches for matching.
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