Python and Machine Learning (1) Mathematics and Basic Algorithms

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Python and Machine Learning

Overview

Python will be a general-purpose programming language with many excellent features, such as being easy to learn, easy to write readable code, and usable for a wide range of applications Python was developed by Guido van Rossum in 1991.

Because Python is a relatively new language, it can utilize a variety of effective programming techniques such as object-oriented programming, procedural programming, and functional programming. It is also widely used in web applications, desktop applications, scientific and technical computing, machine learning, artificial intelligence, and other fields because of the many libraries and frameworks available. Furthermore, Python is cross-platform and runs on many operating systems, including Windows, Mac, and Linux, etc. Because Python is an interpreted language, it does not require compilation and has a REPL-like structure, which speeds up the development cycle.

The following development environments are available for Python

• Anaconda: Anaconda is an all-in-one data science platform that includes the necessary packages and libraries for data science in Python, as well as tools such as Jupyter Notebook to easily start data analysis and machine learning projects. It will also include tools such as Jupyter Notebook to make it easy to get started with data analysis and machine learning projects.
• PyCharm: PyCharm is a Python integrated development environment (IDE) developed by JetBrains that provides many features necessary for Python development, such as debugging, auto-completion, testing, project management, and version control to improve the quality and productivity of your projects. It is designed to improve the quality and productivity of your projects.
• Visual Studio Code: Visual Studio Code is an open source code editor developed by Microsoft that also supports Python development. It has a rich set of extensions that make it easy to add the functionality needed for Python development.
• IDLE: IDLE is a simple, easy-to-use, standard development environment that comes with Python and is ideal for learning Python.

These environments will be used to implement web applications and machine learning code. frameworks for web applications will provide many of the features needed for web application development, such as functionality based on the MVC architecture, security, databases, authentication, etc. The following are some of the most common

• Django: Django is one of the most widely used web application frameworks in Python, allowing the development of fast and robust applications based on the MVC architecture.
• Flask: Flask is a lightweight and flexible web application framework with a lower learning cost than Django, and is used by both beginners and advanced programmers.
• Pyramid: Pyramid is a web application framework with a flexible architecture and rich feature set that is more highly customizable than Django or Flask, making it suitable for large-scale applications.
• Bottle: Bottle is a lightweight and simple web application framework that makes it easy to build small applications and APIs.

Finally, here are some libraries for dealing with machine learning.

• Scikit-learn: Scikit-learn is the most widely used machine learning library in Python. It offers a variety of machine learning algorithms, including classification, regression, clustering, and dimensionality reduction.
• TensorFlow: TensorFlow is an open source machine learning library developed by Google that provides many features for building, training, and inference of neural networks.
• PyTorch: PyTorch is an open source machine learning library developed by Facebook that provides many of the same features as TensorFlow, including neural network construction, training, and inference.
• Keras: Keras is a library that provides a high-level neural network API and supports TensorFlow, Theano, and Microsoft Cognitive Toolkit backends.
• Pandas: Pandas is a library for data processing and can handle tabular data. In machine learning, it is often used for data preprocessing.

Various applications can be built by successfully combining these libraries and frameworks.

Python and Machine Learning

Python is a high-level language that is programmed using abstract instructions given by the designer (synonyms include low-level, which is programmed at the machine level using instructions and data objects), a general-purpose language that can be applied to a variety of purposes (synonyms include ), general-purpose languages that can be applied to a variety of applications (synonyms include targted to an application, in which the language is optimized for a specific use), and source code, in which the instructions written by the programmer are executed directly (by the interpreter) (synonyms include ) into basic machine-level instructions first.

Python is a versatile programming language that can be used to create almost any program efficiently without the need for direct access to computer hardware, and is not suitable for programs that require a high level of reliability (due to weak checks on static semantics). Python is not suitable for programs that require high reliability (due to weak checks on static semantics), nor (for the same reason) for programs that involve a large number of people or are developed and maintained over a long period of time.

However, Python is a relatively simple language that is easy to learn, and because it is designed as an interpreted language, it provides immediate feedback, which is very useful for novice programmers. It also has a number of freely available libraries that can be used to extend the language.

Python was developed by Guido von Rossum in 1990, and for the first decade it was a little-known and rarely used language, but Python 2.0 in 2000 marked a shift in the evolutionary path with a number of important improvements to the language itself. In 2008, Python 3.0 was released. In 2008, Python 3.0 was released. This version of Python improved many inconsistencies in Python 2. In 2008, Python 3.0 was released. This version of Python improved many inconsistencies of Python 2, but it was not backward compatible (most programs written in previous versions of Python would not work).

In the last few years, most of the important public domain Python libraries have been ported to Python3 and are being used by many more people.

In this blog, we discuss the following topics related to Python.

Mathematics

What is information geometry?

What is information geometry?. Information geometry is a field that studies the geometrical structure of probability distributions and statistical models used in statistics, information theory, machine learning, etc. Its essential idea is to regard probability distributions and statistical models as geometric spaces and to analyse the properties of these models by introducing geometric structures (distance, curvature, connection etc.) are introduced to analyse the properties of these models.

Riemannian Optimisation algorithms and implementation examples

Riemannian Optimisation algorithms and implementation examples. Riemannian Optimisation (Riemannian Optimisation) is an approach where the usual optimisation methods are performed on Riemannian manifolds. A manifold here is a mathematical tool that represents ‘a space that is locally simple but overall complex’, such as a circumference that looks like a straight line but is closed overall, or a sphere that looks like a plane but has no edges and a closed structure, which locally is a simple structure but overall It will represent a complex structure. A Riemannian manifold is a space with a smooth geometric structure in which each point of this manifold has a defined inner product, which makes it possible to define measures such as distances and angles.

Overview of Cross Entropy and Related Algorithms and Implementations

Overview of Cross Entropy and Related Algorithms and Implementations. Cross Entropy is a concept commonly used in information theory and machine learning, especially in classification problems to quantify the difference between model predictions and actual data. Cross-entropy is derived from information theory, which uses the concept of “entropy” as a measure of the amount of information. Entropy is a measure of the uncertainty or difficulty of predicting information. It is greatest when the probability distribution is even and decreases as the probability concentrates on a particular value.

Overview of Singular Value Decomposition (SVD) and examples of algorithms and implementations

Overview of Singular Value Decomposition (SVD) and examples of algorithms and implementations. Singular Value Decomposition (SVD) is a method for decomposing a matrix into a product of three matrices.

Overview of non-negative-valued matrix factorisation (NMF) and examples of algorithms and implementations

Overview of non-negative-valued matrix factorisation (NMF) and examples of algorithms and implementations. Non-negative matrix factorisation (NMF) is a method for decomposing a given non-negative matrix into the product of two non-negative matrices. Specifically, the non-negative matrix \(V\) of a given\(m \times n\) is decomposed as follows.

Overview of Alternating Least Squares for Matrix Factorisation (ALS-MF) and examples of algorithms and implementations

Overview of Alternating Least Squares for Matrix Factorisation (ALS-MF) and examples of algorithms and implementations. Alternating Least Squares for Matrix Factorization (ALS-MF) is a matrix factorisation technique that extracts the latent structure of a given matrix by decomposing it into a product of several submatrices. Specifically, the given matrix \(R\) (usually a user-item valuation matrix) is decomposed as follows.

Overview of the Gauss-Zeidel method and examples of algorithms and implementations

Overview of the Gauss-Zeidel method and examples of algorithms and implementations. The Gauss-Zeidel method is one of the iterative methods for finding solutions to a system of linear equations, and is particularly effective when the coefficient matrix has non-zero diagonal elements and diagonal dominance. In this method, each variable in the equation is assumed in turn, the solution is calculated with the other variables known, then the next variable is updated using the calculated solution, and so on until all variables converge.

CP (CANDECOMP/PARAFAC) Decomposition Overview, Algorithm and Implementation Example

CP (CANDECOMP/PARAFAC) Decomposition Overview, Algorithm and Implementation Example. CP decomposition (CANDECOMP/PARAFAC) is a type of tensor decomposition and is one of the decomposition methods for multidimensional data. CP decomposition approximates a tensor as the sum of multiple rank-1 tensors. It is usually applied to tensors of three or more dimensions, and we will use a three-dimensional tensor as an example here.

Overview of Non-Negative Tensor Factorization (NTF) and Examples of Algorithms and Implementations

Overview of Non-Negative Tensor Factorization (NTF) and Examples of Algorithms and Implementations. Non-Negative Tensor Factorization (NTF) is a method for obtaining a representation of multidimensional data by decomposing a tensor (multidimensional array) into non-negative elements. and signal analysis, feature extraction, and dimensionality reduction.

Tucker Decomposition Overview, Algorithm and Implementation Example

Tucker Decomposition Overview, Algorithm and Implementation Example. Tucker decomposition is a method for decomposing multidimensional data and is a type of tensor decomposition; Tucker decomposition approximates a tensor as a product of several low-rank tensors.

Mode-based Tensor Decomposition Overview, Algorithm, and Implementation Example

Mode-based Tensor Decomposition Overview, Algorithm, and Implementation Example. Mode-based tensor decomposition is a method for decomposing a multidimensional data tensor into a product of lower-rank tensors, which are specifically used to decompose the tensor and extract latent structures and patterns in the data set. Tensor decomposition can also be viewed as a multidimensional extension of matrix decomposition (e.g., SVD).

PARAFAC2 (Parallel Factor 2) Decomposition Overview, Algorithm, and Implementation Example

PARAFAC2 (Parallel Factor 2) Decomposition Overview, Algorithm, and Implementation Example. PARAFAC2 (Parallel Factor 2) decomposition is one of the tensor decomposition methods, and is a type of mode-based tensor decomposition described in “Overview, Algorithm, and Implementation Examples of Mode-based Tensor Decomposition”. The usual PARAFAC (canonical decomposition) approximates tensors of three or more dimensions as a sum of lower-ranked tensors, but PARAFAC2 can be applied to tensors of more general geometry.

Overview of Tensor Power Method and Examples of Algorithms and Implementations

Overview of Tensor Power Method and Examples of Algorithms and Implementations. The Tensor Power Method is a type of iterative method for solving tensor singular value decomposition and eigenvalue problems, and is useful for finding approximate solutions to tensor singular values and eigenvalues. The following is a basic overview of the Tensor Power Method.

Overview of Alternating Least Squares (ALS) and Related Algorithms and Examples of Implementations

Overview of Alternating Least Squares (ALS) and Related Algorithms and Examples of Implementations. Alternating Least Squares (ALS) is a method for solving optimization problems using the Least Squares method, which is often used in the context of matrix and tensor decomposition. An overview of ALS is given below.

Recommendation systems in Netflix

Recommendation systems in Netflix. The Netflix recommendation system will be based on information such as a user’s viewing history, ratings, search history, browsing time and favourites list, with the aim of suggesting the best content for that user. The system uses a combination of machine learning and algorithms. Specifically, the system can identify the user’s favourite genres, actors, directors, etc., based on their past viewing history, suggest content containing similar elements, and, by evaluating the films selected by the user, collect data to provide content tailored to the user’s preferred trends. The system is designed to

Recommendation systems using knowledge graphs

Recommendation systems using knowledge graphs. A knowledge graph is a graph that expresses relationships between entities (people, objects, concepts, etc.) and is a data format capable of representing entities with multiple relationships, making recommendation using knowledge graphs one recommendation method that can more accurately reflect user preferences and interests.

Recommendation systems for streaming data

Recommendation systems for streaming data. Matrix Factorisation, described in ‘Recommendation systems in Netflix’, is also a useful method when dealing with streaming data. Usually, Matrix Factorisation learns feature vectors by combining all evaluation data into a matrix, but in the case of streaming data, it is not possible to learn all the data together because the data flows at a constant rate. In such cases, it is possible to use online learning, as described in ‘Overview of online learning, various algorithms, application examples and concrete implementations’, where new data can be learnt immediately as it streams in. In Matrix Factorisation, online learning can also be used to learn streaming data in real-time.

Overview of Alternating Least Squares for Tensor Factorization (ALS-TF) and Examples of Algorithms and Implementations

Overview of Alternating Least Squares for Tensor Factorization (ALS-TF) and Examples of Algorithms and Implementations. Alternating Least Squares for Tensor Factorization (ALS-TF) is a method for tensor factorization. ALS-TF is especially applied to recommendation systems and tensor data analysis.

Overview of Alternating Least Squares for Non-Negative Matrix Factorization (ALS-NMF), Algorithm and Example Implementation

Overview of Alternating Least Squares for Non-Negative Matrix Factorization (ALS-NMF), Algorithm and Example Implementation. Alternating Least Squares for Non-Negative Matrix Factorization (ALS-NMF) is a type of Non-Negative Matrix Factorization (NMF). NMF is a method for decomposing a matrix \(V \) with non-negativity constraints into a product of a non-negative matrix \(W \) and \(H \), and ALS-NMF optimizes it while keeping the non-negativity constraints.

Overview of Block Term Decomposition (BTD) and Examples of Algorithms and Implementations

Overview of Block Term Decomposition (BTD) and Examples of Algorithms and Implementations. Block Term Decomposition (BTD) is one of the methods for tensor data analysis. Tensor data is a multi-dimensional data structure similar to a two-dimensional matrix, and BTD aims to decompose the tensor data into low-rank block structures.

Overview of Random Algorithms for Tensor Decomposition and Examples of Implementations

Overview of Random Algorithms for Tensor Decomposition and Examples of Implementations. The random algorithm for tensor decomposition is a method for decomposing a large tensor into a product of smaller tensors, where the tensor is a multidimensional array and the tensor decomposition will aim to decompose that tensor into a product of multiple rank 1 tensors (or tensors of smaller rank). The random algorithm begins by approximating the tensor with a random matrix, and this approximation matrix is used as an initial estimate for finding a low-rank approximation of the tensor

Overview of Higher Order Singular Value Decomposition (HOSVD) and examples of algorithms and implementations

Overview of Higher Order Singular Value Decomposition (HOSVD) and examples of algorithms and implementations. Higher Order Singular Value Decomposition (HOSVD) is a method for dimensionality reduction and data compression of tensors (multidimensional arrays of three or more dimensions). HOSVD captures the structure of the original tensor by decomposing it into many smaller tensors and compressing the information in each tensor. Specifically, HOSVD decomposes a tensor into multiple dimensions using singular value decomposition (SVD) and, in each mode (dimension), decomposes the tensor using the left and right singular matrices obtained by the singular value decomposition.

Overview of Tensor Train Decomposition and examples of algorithms and implementations

Overview of Tensor Train Decomposition and examples of algorithms and implementations. Tensor Train Decomposition (TT decomposition) is one of the methods for dimensionality reduction and data compression of multidimensional tensors and is an approach that provides an efficient data representation by approximating a tensor as a product of multiple low-rank tensors. vector and reconstructing the column vectors into specific products (tensor columns), allowing each element of the tensor to be represented as an inner product of the tensor columns.

Overview of HOOI (High-Order Orthogonal Iteration) and examples of algorithms and implementations

Overview of HOOI (High-Order Orthogonal Iteration) and examples of algorithms and implementations. High-Order Orthogonal Iteration (HOOI) is one of the methods based on the high-dimensional singular value decomposition (SVD) of a tensor; HOOI iteratively applies the singular value decomposition in each mode of the tensor to obtain a low-rank approximation of the tensor.

Overview of the TTM (Tensor-Train Matrix) and examples of algorithms and implementations

Overview of the TTM (Tensor-Train Matrix) and examples of algorithms and implementations. Tensor-Train Matrix (TTM) is a unique representation form of tensor, an approach that allows the representation of a matrix in tensor form through the tensorisation of the matrix TTM uses the technique of matrixisation of tensors to approximate a high-dimensional matrix as a product of low-rank tensors. TTM is the application of the Tensor Train (TT) decomposition to matrices, where the TT decomposition is a technique for approximating a tensor as the product of several low-rank tensors.

Optimization Algorithm

• Overview of Iterative Optimization Algorithms and Examples of Implementations

Iterative optimization algorithms are an approach that iteratively improves an approximate solution in order to find the optimal solution to a given problem. These algorithms are particularly useful in optimization problems and are used in a variety of fields. The following is an overview of iterative optimization algorithms.

• Overview of mini-batch learning and examples of algorithms and implementations

Mini-batch learning is one of the most widely used and efficient learning methods in machine learning, which is computationally more efficient and applicable to large data sets compared to the usual Gradient Descent method. This section provides an overview of mini-batch learning. Mini-batch learning is a learning method in which multiple samples (called mini-batches) are processed in batches, rather than the entire dataset at once, and the gradient of the loss function is calculated for each mini-batch and the parameters are updated using the gradient.

• Overview of interpolation methods and examples of algorithms and implementations

Interpolation is a method of estimating or complementing values between known data points, connecting points in a data set to generate a smooth curve or surface, which can then be used to estimate values at unknown points. Several major interpolation methods are discussed below.

• Various feature engineering methods and their implementation in python

Feature engineering refers to the extraction of useful information from a dataset and the creation of input features that machine learning models can use to make predictions and classification, and is an important process in the context of machine learning and data analysis. This section describes various methods and implementations of feature engineering.

• Negative Log-Likelihood overview, algorithm and implementation examples

Negative Log-Likelihood (NLL) is a loss function for optimising the parameters of models in statistics and machine learning, especially those often used in models based on probability distributions (such as classification models). It is a measure of a model’s performance based on the probability that the observed data were predicted by the model, and its purpose is to optimise the parameters of the model so that the model can explain the observed data with a high probability.

• Contrastive Divergence (CD) overview, algorithm and implementation examples

Contrastive Divergence (CD) is a learning algorithm mainly used for training Restricted Boltzmann Machines (RBM), a generative model for modelling the probability distribution of data, and CD is a method for efficiently learning its parameters.

• Noise Contrastive Estimation (NCE) overview, algorithm and implementation examples

Noise Contrastive Estimation (NCE) is a method for estimating the parameters of a probabilistic model, and is a particularly effective approach for processing large data sets and high-dimensional data. Use.

• Overview of negative sampling, algorithms and implementation examples

Negative sampling is a learning algorithm in natural language processing and machine learning, especially used in word embedding models such as Word2Vec as described in ‘Word2Vec’. It is a method for selective sampling of infrequent data (negative examples) for efficient learning of large datasets.

• Model Quantization and Distillation

Model quantization (Quantization) and distillation (Knowledge Distillation) are methods for improving the efficiency of machine learning models and reducing resources during deployment.

• Overview of Model Distillation with Soft Target and Examples of Algorithms and Implementations

Model distillation by soft target (Soft Target) is a technique for transferring the knowledge of a large and computationally expensive teacher model to a small and efficient student model. Typically, soft target distillation focuses on teaching the probability distribution of the teacher model to the student model in a class classification task. Below we provide an overview of model distillation by soft targets.

• Model Lightening through Pruning and Quantization

Model lightening is an important technique for converting deep learning models to smaller, faster, and more energy efficient models. There are various approaches to model lightening, including pruning and quantization The following is a list of some of the most common approaches to model lightening.

• Measures for Dealing with Unknown Models in Machine Learning

Measures for machine learning models to deal with unknown data have two aspects: ways to improve the generalization performance of the model and ways to design how the model should deal with unknown data.

How to Deal with Overlearning in Machine Learning

How to Deal with Overlearning in Machine Learning. Overfitting is a phenomenon in which a machine learning model overfits the training data, resulting in poor generalization performance for new data.

• Overview of Hard Negative Mining and Examples of Algorithms and Implementations

Hard Negative Mining is a method of focusing on difficult negative samples (negative examples) in the field of machine learning, especially in tasks such as anomaly detection and object detection. This allows the model to deal with more difficult cases and is expected to improve performance.

Counting Problem Overview, Algorithm and Implementation Examples

Counting Problem Overview, Algorithm and Implementation Examples. Counting problems (counting problems) are one of the most frequently tackled problems in mathematics, such as combinatorics and probability theory, which are tasks often associated with finding the number of combinations or permutations as a problem of counting the total number of objects satisfying certain conditions. These problems are solved using mathematical principles and formulas, and concepts such as permutations, combinations, and binomial coefficients are often used, and depending on the problem, the respective formula must be chosen according to the nature of the problem.

Overview of Optimization by Integer Linear Programming (ILP) and Examples of Algorithms and Implementations

Overview of Optimization by Integer Linear Programming (ILP) and Examples of Algorithms and Implementations. Integer Linear Programming (ILP) is a method for solving mathematical optimization problems, especially for finding integer solutions under constraints. ILP is a type of Linear Programming (LP) with the additional conditions that the objective function and constraints are linear and the variables take integer values.

Overview of the Sequential Quadratic Programming (SQP) method, algorithm and implementation examples

Overview of the Sequential Quadratic Programming (SQP) method, algorithm and implementation examples. Sequential Quadratic Programming (SQP) is a numerical algorithm for solving non-linear constrained optimisation problems, where the objective function is optimised while satisfying constraints. SQP is characterised by its ‘efficiency’ in obtaining solutions to constrained problems with higher-order accuracy, often converging faster than other methods (e.g. gradient descent or interior point methods), and its ‘generality’ in being applicable to a variety of problems involving non-linear objective functions and constraints, Convergence: in general, it has quadratic convergence to a local optimum solution (when the problem satisfies the appropriate conditions).

Overview, algorithms and implementation examples of linear quadratic programming (LQ problem)

Overview, algorithms and implementation examples of linear quadratic programming (LQ problem). Linear quadratic programming (LQ problem, Linear Quadratic Problem) is a widely used method in control theory and optimisation problems, and is particularly important in the field of optimal control.

Linear Quadratic Control (LQC) overview, algorithms and implementation examples

Linear Quadratic Control (LQC) overview, algorithms and implementation examples. Linear Quadratic Control (LQR) is a control theory and one of the optimal control methods for systems with linear dynamics.LQR is a method for obtaining feedback control laws to optimally control the state of a system, in particular to minimise the quadratic cost function, which is performance is used in designing control strategies that minimise the cost function based on the state and control inputs in order to optimise the performance of the system.

Hesse Matrices and Regularity

Hesse Matrices and Regularity. A Hesse matrix is a matrix representation of the second-order partial derivatives of a multivariate function, in which the second-order partial derivatives for each variable of the multivariate function are stored in the Hesse matrix, just as the second-order derivatives of a single variable function are considered as second-order derivatives. Hesse matrices play an important role in many mathematical and scientific applications, such as nonlinear optimization and numerical analysis.

Cross-Entropy Loss

Cross-Entropy Loss. Cross-Entropy Loss is one of the common loss functions used in machine learning and deep learning to evaluate and optimize the performance of models in classification tasks, especially in binary classification (selecting one of two classes) and multi-class classification (selecting one of three or more It is a widely used method for binary classification (selecting one of two classes) and multiclass classification (selecting one of three or more classes) problems, among others.

Overview of the Gelman-Rubin Statistic and Related Algorithms and Examples of Implementations

Overview of the Gelman-Rubin Statistic and Related Algorithms and Examples of Implementations. The Gelman-Rubin statistic (or Gelman-Rubin diagnostic, Gelman-Rubin statistical test) is a statistical method for diagnosing convergence of Markov chain Monte Carlo (MCMC) sampling methods, particularly when MCMC sampling is done with multiple chains, where each chain will be used to evaluate whether they are sampled from the same distribution. This technique is often used in the context of Bayesian statistics. Specifically, the Gelman-Rubin statistic evaluates the ratio between the variability of the sample from multiple MCMC chains and the variability within each chain, and this ratio will be close to 1 if statistical convergence is achieved.

Overview of Kronecker-factored Approximate Curvature (K-FAC) matrix and related algorithms and implementation examples

Overview of Kronecker-factored Approximate Curvature (K-FAC) matrix and related algorithms and implementation examples. Kronecker-factored Approximate Curvature (K-FAC) is a method for efficiently approximating the inverse of the Hessian matrix in machine learning optimization problems, as described in “Hesse Matrix and Regularity”. This method has attracted attention as an efficient and scalable optimization method, especially in the training of neural networks. K-FAC was developed to efficiently approximate the Fisher information matrix or the inverse of the Hesse matrix in neural network optimization problems, as described in “Overview of the Fisher Information Matrix and Related Algorithms and Examples of Implementations. This makes it possible to train neural networks with high efficiency even at large scales.

Overview of the Fisher Information Matrix and Related Algorithms and Examples of Implementations

Overview of the Fisher Information Matrix and Related Algorithms and Examples of Implementations. The Fisher information matrix is a concept used in statistics and information theory to provide information about probability distributions. This matrix is used to provide information about the parameters of a statistical model and to evaluate its accuracy. Specifically, it contains information about the expected value of the derivative of the probability density function (or probability mass function) with respect to its parameters.

Overview of Classification Problems Using Fisher’s Computational Method and Examples of Algorithms and Implementations

Overview of Classification Problems Using Fisher’s Computational Method and Examples of Algorithms and Implementations. Fisher’s Linear Discriminant is a method for constructing a linear discriminant model to distinguish between two classes, which aims to find a projection that maximizes the variance between classes and minimizes the variance within classes. Specifically, the following steps are used to construct the model.

Block K-FAC Overview, Algorithm, and Implementation Examples

Block K-FAC Overview, Algorithm, and Implementation Examples. Block K-FAC (Block Kronecker-factored Approximate Curvature) is a kind of curve chart (curvature information) approximation method used in deep learning model optimization.

Derivation of the Cramér-Rao Lower Bound (CRLB)

Derivation of the Cramér-Rao Lower Bound (CRLB). The Cramér-Rao lower bound provides a lower bound in statistics to measure how much uncertainty an estimator has. Information Matrix” described in “Overview of the Fisher Information Matrix and Related Algorithms and Examples of Implementations. The procedure for deriving the CRLB is described below.

Overview of Monte Carlo Dropout and Examples of Algorithms and Implementations

Overview of Monte Carlo Dropout and Examples of Algorithms and Implementations. Monte Carlo Dropout is a method for estimating uncertainty in neural network inference using dropout. Usually, dropout is a method to promote network generalization by randomly disabling nodes during training, but Monte Carlo Dropout uses this method during inference.

Overview of Procrustes Analysis and Related Algorithms and Examples of Implementations

Overview of Procrustes Analysis and Related Algorithms and Examples of Implementations. Procrustes analysis is a method for finding the optimal rotation, scaling, and translation between corresponding point clouds of two datasets. This method is mainly used when two datasets represent the same object or shape, but need to be aligned by rotation, scaling, or translation.

About Sequential Quadratic Programming

About Sequential Quadratic Programming. Sequential Quadratic Programming (SQP) is an iterative optimization algorithm for solving nonlinear optimization problems with nonlinear constraints. The SQP method is widely used as a numerical solution method for constrained optimization problems, especially in engineering, economics, transportation planning, machine learning, control system design, and many other areas of application.

Overview of Newton’s method and its algorithm and implementation

Overview of Newton’s method and its algorithm and implementation. Newton’s method (Newton’s method) is one of the iterative optimization algorithms for finding numerical solutions to nonlinear equations and functions, and is mainly used to find roots of equations, making it a suitable method for finding minima and maxima of continuous functions as well. Newton’s method is used in many machine learning algorithms because of its fast convergence.

Modified Newton Method

Modified Newton Method. The Modified Newton Method is an algorithm developed to improve the regular Newton-Raphson method to address several issues, and the main objective of the Modified Newton Method will be to improve convergence and numerical stability.

Quasi-Newton Method

Quasi-Newton Method. The Quasi-Newton Method (QNM) is an iterative method for solving nonlinear optimization problems. This algorithm is a generalization of the Newton method, which searches for the minimum of the objective function without computing higher derivatives (Hesse matrix). The quasi-Newton method is relatively easy to implement because it uses an approximation of the Hesse matrix and does not require an exact calculation of the Hesse matrix.

Newton-Raphson Method

Newton-Raphson Method. The Newton-Raphson Method (Newton-Raphson Method) is an iterative method for numerical solution of nonlinear equations and for finding the roots of a function, and the algorithm is used to approximate the zero point of a continuous function, starting from an initial estimated solution. The Newton-Raphson method converges quickly when the function is sufficiently smooth and is particularly effective when first derivatives (gradients) and second derivatives (Hesse matrices) can be computed.

Newton method rescaling

Newton method rescaling. Rescaling of Newton’s method is one of the methods used in numerical optimisation to improve convergence speed and to avoid problems related to singularities and locally optimal solutions. to improve convergence and stability of the calculation.

How to deal with singularities in Newton’s method

How to deal with singularities in Newton’s method. The Newton method, described in ‘Overview of the Newton method and its algorithm and implementation’, is a powerful method for finding solutions to non-linear equations, but problems can arise at singularities (e.g. points where the Jacobi matrix is singular or approximately singular). There are several methods for dealing with singularities, and the appropriate method should be chosen according to the type of problem and the characteristics of the solution.

How to improve linear convergence in Newton’s method

How to improve linear convergence in Newton’s method. The Newton method, described in ‘Overview of the Newton method and its algorithm and implementation’, is a very powerful method, especially for solving convex optimisation problems and non-linear equations, but the convergence speed is sometimes only linear. The following methods have been proposed to improve this.

Overview of penalty function methods, algorithms and implementation examples

Overview of penalty function methods, algorithms and implementation examples. The Penalty Function Method is a method for converting a constrained optimisation problem into an unconstrained optimisation problem, which allows existing unconstrained optimisation algorithms (e.g. the gradient method and the Newton method described in ‘Overview, algorithm and implementation of the Newton method’) to be used to solve the constrained problem. This makes it possible to solve constrained problems using existing unconstrained optimisation algorithms (e.g. the gradient method and the Newton method described in ‘Overview, algorithms and implementation of the Newton method’).

Overview, algorithms and implementation examples of Trust-Region Methods

Overview, algorithms and implementation examples of Trust-Region Methods. Trust-Region Methods are one of the algorithms for solving non-linear optimisation problems, designed to overcome the problems of the Newton method as described in ‘Overview, Algorithms and Implementations of Gradient Descent Methods and Newton Methods’. In this method, the approach is to approximate the optimisation problem within a small domain (the confidence region) and iteratively find the optimal solution within that domain.

Alternative Methods of Numerical Differentiation in Calculating Derivatives of Newton’s Method

Alternative Methods of Numerical Differentiation in Calculating Derivatives of Newton’s Method. In Newton’s method, the derivative \(f'(x)\) is used to find the roots of the function\(f(x)\), but when it is difficult to find the derivative analytically or the function is only given numerically, it is necessary to consider alternative methods of numerical differentiation. A standard method is to approximate derivatives using finite differences, and the following methods are commonly used.

Overview of the Leapfrog Method and Examples of Algorithms and Implementations

Overview of the Leapfrog Method and Examples of Algorithms and Implementations. The Leapfrog Method is a type of time integration method for numerically solving time-evolving equations of motion (especially Hamiltonian dynamical systems), and is often used to solve Newton’s equation of motion (F=ma). It is often used in molecular dynamics simulations and celestial mechanics.

The vanishing gradient problem and its countermeasures

The vanishing gradient problem and its countermeasures. The vanishing gradient problem is one of the problems that occur mainly in deep neural networks and often occurs when the network is very deep or when a specific architecture is used.

Overview of the Hilbert Wand Transform and Examples of Algorithms and Implementations

Overview of the Hilbert Wand Transform and Examples of Algorithms and Implementations. The Hilbert transform (Hilbert transform) is an operation widely used in signal processing and mathematics, and it can be a technique used to introduce an analyticity (analytic property) of a signal. The Hilbert transform converts a real-valued signal into a complex-valued signal, and the complex-valued signal obtained by the Hilbert transform can be used to extract phase and amplitude information from the original real-valued signal.

About Residual Coupling

About Residual Coupling. Residual Connection is a method for directly transferring information across layers in deep learning networks, which was introduced to address the problem of gradient loss and gradient explosion, especially when training deep networks. Residual coupling was proposed by Kaiming He et al. at Microsoft Research in 2015 and has since been very successful.

Overview of the Davidon-Fletcher-Powell (DFP) method, its algorithm, and examples of its implementation

Overview of the Davidon-Fletcher-Powell (DFP) method, its algorithm, and examples of its implementation. The DFP method (Davidon-Fletcher-Powell method) is one of the numerical optimization methods and is particularly suitable for nonlinear optimization problems. This method is characterized by using a quadratic approximation approach to find the optimal search direction, and the DFP method belongs to the category of quasi-Newton methods, which seek the optimal solution while updating the approximation of the inverse of the Hesse matrix.

Overview of the Frank-Wolfe method and examples of applications and implementations

Overview of the Frank-Wolfe method and examples of applications and implementations. The Frank-Wolfe method is a numerical algorithm for solving non-linear optimisation problems, proposed by Marguerite Frank and Philippe Wolfe in 1956. The Frank-Wolfe method is also related to linear programming problems and can be applied to continuous optimisation problems. However, its convergence speed may be slower than that of general optimisation algorithms, and therefore other efficient algorithms may be preferred for high-dimensional problems. The Frank-Wolff method is useful in large-scale and constrained optimisation problems and is widely used in machine learning, signal processing and image processing. The Frank-Wolff method is also often used in combination with other optimisation methods.

Overview of Exponential Smoothing and Examples of Algorithms and Implementations

Overview of Exponential Smoothing and Examples of Algorithms and Implementations. Exponential Smoothing is a statistical method used for forecasting and smoothing time series data, especially for forecasting future values based on past observations. Exponential smoothing is a simple but effective method that allows for weighting against time and adjusting for the effect of past data.

Overview of linear programming and examples of algorithms and implementations

Overview of linear programming and examples of algorithms and implementations. Linear Programming (LP) is a mathematical method for solving the problem of optimising (maximising or minimising) a linear function, which is applied to many optimisation problems and is widely used, especially in resource allocation, scheduling and transport planning.

Overview of the Gradient Method and Examples of Algorithms and Implementations

Overview of the Gradient Method and Examples of Algorithms and Implementations. The gradient method is one of the widely used methods in machine learning and optimization algorithms, whose main goal is to iteratively update parameters in order to find the minimum (or maximum) value of a function. In machine learning, the goal is usually to minimize the cost function (also called loss function). For example, in regression and classification problems, a cost function is defined to represent the error between predicted and actual values, and it helps to find the parameter values that minimize this cost function.

This section describes various algorithms for this gradient method and examples of implementations in various languages.

Stochastic Gradient Descent (SGD) Overview, Algorithm and Implementation Examples

Stochastic Gradient Descent (SGD) Overview, Algorithm and Implementation Examples. Stochastic Gradient Descent (SGD) is an optimization algorithm widely used in machine learning and deep learning. parameters are updated. The basic concepts and features of SGD are described below.

Overview of Natural Gradient Descent and Examples of Algorithms and Implementations

Overview of Natural Gradient Descent and Examples of Algorithms and Implementations. Natural Gradient Descent is a type of Stochastic Gradient Descent (SGD) described in “Overview of Stochastic Gradient Descent (SGD), Algorithms, and Implementation Examples. It is a type of Stochastic Gradient Descent (SGD), which is an optimization method for efficiently updating model parameters, and is an approach that takes into account the geometric structure of the model parameter space and appropriately scales the gradient information.

Gaussian-Hermite Integration Overview, Algorithm and Implementation

Gaussian-Hermite Integration Overview, Algorithm and Implementation. Gaussian-Hermite Integration is a method of numerical integration often used for stochastic problems, especially those in which the probability density function has a Gaussian distribution (normal distribution), and for integrals such as the wave function in quantum mechanics. The Gauss-Hermite polynomial is used to approximate the integral. This section provides an overview, algorithm, and implementation of the Gauss-Hermite integral.

Overview of the Ornstein-Uhlenbeck process and examples of algorithms and implementations

Overview of the Ornstein-Uhlenbeck process and examples of algorithms and implementations. The Ornstein-Uhlenbeck process is a type of stochastic process, especially one used to model the motion of a random variable in continuous time. The process has been widely applied in various fields, including physics, finance, statistics, and machine learning. The Ornstein-Uhlenbeck process is obtained by introducing resilience into Brownian motion (or Wiener process). Normally, Brownian motion represents random fluctuations, but in the Ornstein-Uhlenbeck process, a recovery force is added to that random fluctuation to move it back toward some average.

Broyden-Fletcher-Goldfarb-Shanno (BFGS) Method

Broyden-Fletcher-Goldfarb-Shanno (BFGS) Method. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is a type of numerical optimization algorithm for solving nonlinear optimization problems. The BFGS method is known as the quasi-Newton method and provides effective solutions to many real-world optimization problems.

Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) Method

Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) Method. The Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method is an algorithm that uses the “Broyden-Fletcher -The L-BFGS method, like the BFGS method, is a form of the quasi-Newton method that uses an inverse approximation of the Hesse matrix The L-BFGS method, like the BFGS method, is a form of quasi-Newtonian method that minimizes the objective function using an inverse approximation of the Hesse matrix. However, the L-BFGS method is designed to reduce memory consumption and is particularly suited to high-dimensional problems.

Conjugate Gradient Method

Conjugate Gradient Method. The conjugate gradient method is a numerical algorithm used for solving linear systems of linear equations and nonlinear optimization problems. It can also be applied as a quasi-Newtonian method for nonlinear optimization problems.

Trust Region Method

Trust Region Method. The Trust Region Method is an optimization algorithm for solving nonlinear optimization problems, which is used to find a solution under constraints in minimizing (or maximizing) an objective function. The Trust Region Method is suitable for constrained optimization problems and nonlinear least squares problems, and is particularly useful for finding globally optimal solutions.

Overview of Maximum Likelihood Estimation and its Algorithm and Implementation

Overview of Maximum Likelihood Estimation and its Algorithm and Implementation. Maximum Likelihood Estimation (MLE) is an estimation method used in statistics. This method is used to estimate the parameters of a model based on given data or observations. Maximum likelihood estimation attempts to maximize the probability that data will be observed when the values of the parameters are changed. This section provides an overview of this maximum likelihood estimation method, its algorithm, and an example implementation in python.

EM Algorithm and Examples of Various Application Implementations

EM Algorithm and Examples of Various Application Implementations. The EM algorithm (Expectation-Maximization Algorithm) is an iterative optimization algorithm widely used in statistical estimation and machine learning. In particular, it is often used for parameter estimation of stochastic models with latent variables.

Here, we provide an overview of the EM algorithm, the flow of applying the EM algorithm to mixed models, HMMs, missing value estimation, and rating prediction, respectively, and an example implementation in python.

Solving Constraint Satisfaction Problems Using the EM Algorithm

Solving Constraint Satisfaction Problems Using the EM Algorithm. 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.

Stochastic Gradient Langevin Dynamics (SGLD) Overview, Algorithm and Implementation Examples

Stochastic Gradient Langevin Dynamics (SGLD) Overview, Algorithm and Implementation Examples. Stochastic Gradient Langevin Dynamics (SGLD) is a stochastic optimization algorithm that combines stochastic gradient and Monte Carlo methods. SGLD is widely used in Bayesian machine learning and Bayesian statistical modeling to estimate the posterior distribution.

Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) Overview, Algorithm, and Implementation Examples

Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) Overview, Algorithm, and Implementation Examples. Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) is a type of Hamiltonian Monte Carlo (HMC), which is a stochastic sampling method combined with a stochastic gradient method and is used to estimate the posterior distribution of large data sets and high-dimensional parameter spaces. data sets and high-dimensional parameter space, making it suitable for Bayesian statistical inference.

Search and Ranking Algorithm

Overview of Search Algorithms and Various Algorithms and Implementations

Overview of Search Algorithms and Various Algorithms and Implementations. Search Algorithm (Search Algorithm) refers to a family of computational methods used to find a target within a problem space. These algorithms have a wide range of applications in a variety of domains, including information retrieval, combinatorial optimization, game play, route planning, and more. This section describes various algorithms, their applications, and specific implementations with respect to these search algorithms.

Overview of Maximum Marginal Relevance (MMR) and Examples of Algorithms and Implementations

Overview of Maximum Marginal Relevance (MMR) and Examples of Algorithms and Implementations. Maximum Marginal Relevance (MMR) is a ranking method for information retrieval and information filtering that aims to optimize the ranking of documents provided to users by information retrieval systems. MMR was developed as a method for selecting documents that are relevant to the user’s interests from among multiple documents. The method will rank documents based on both the relevance and diversity of each document, specifically emphasizing the selection of documents that are highly relevant but have low similarity to other options.

Overview, algorithm and implementation examples of Diversity-Enhanced Ranking

Overview, algorithm and implementation examples of Diversity-Enhanced Ranking. Diversity-Enhanced Ranking is a ranking method that aims to display a variety of items higher in search results and recommendation systems, rather than just on the basis of relevance and popularity. This gives users access to a variety of options, increasing satisfaction and increasing opportunities for new discoveries. Traditional ranking algorithms typically determine the top results based on relevance, click-through rate and popularity for a user’s query, but this method can lead to a concentration of items of the same type or genre at the top, limiting the options available to users. For this reason, diversity-promoting ranking has the following objectives

Overview of location bias-corrected ranking, algorithm and implementation examples

Overview of location bias-corrected ranking, algorithm and implementation examples. Position bias-corrected ranking is a method of creating rankings that more accurately reflect actual quality and popularity by correcting for click and selection bias (bias) due to an item’s display position in search results and product lists. This bias correction can correct the tendency for higher click rates to be displayed at the top and lower click rates to be displayed at the bottom. Items in search results and listings are more likely to be clicked on if they appear higher up, and less likely to be clicked on if they appear lower down. This ‘position bias’ may not accurately reflect the actual quality or popularity of the item, and the purpose of position bias correction is to correct this bias and provide a ranking that reflects the true value of the item.

Heuristic Search (Hill Climbing, Greedy Search, etc.) Based Structural Learning

Heuristic Search (Hill Climbing, Greedy Search, etc.) Based Structural Learning. Structural learning based on heuristic search is a method that combines heuristic methods for searching the architecture and hyperparameters of machine learning models to find the optimal model or structure, and heuristics are intuitive and simple rules or approach. Below we describe some common methods related to heuristic search-based structure learning.

Overview of Self-Adaptive Search Algorithms and Examples of Applications and Implementations

Overview of Self-Adaptive Search Algorithms and Examples of Applications and Implementations. Self-Adaptive Search Algorithms, or Self-Adaptive Search Algorithms, are a family of algorithms used in the context of evolutionary computation and optimization, where the parameters and strategies within the algorithm are characterized by adaptive adjustment to the problem. These algorithms are designed to adapt to changes in the nature of the problem and the environment in order to efficiently find the optimal solution. This section describes various algorithms and examples of implementations with respect to this self-adaptive search algorithm.

Overview of Multi-Objective Search Algorithm and Examples of Application and Implementation

Overview of Multi-Objective Search Algorithm and Examples of Application and Implementation. Multi-Objective Search Algorithm (Multi-Objective Optimization Algorithm) is an algorithm for optimizing multiple objective functions simultaneously. Multi-objective optimization aims to find a balanced solution (Pareto optimal solution set) among multiple optimal solutions rather than a single optimal solution, and such problems have been applied to many complex systems and decision-making problems in the real world. This section provides an overview of this multi-objective search algorithm and examples of algorithms and implementations.

Alpha-beta pruning: overview, algorithm, and implementation examples

Alpha-beta pruning: overview, algorithm, and implementation examples. Alpha-beta pruning is a type of search algorithm used in the fields of artificial intelligence and computer games. This is a common approach used in combination with tree search algorithms such as the minimax method described in “Overview of the Minimax Method, Algorithms and Examples of Implementation. This algorithm is used to efficiently find a solution by reducing unnecessary search when searching the tree structure of a game. Specifically, the possible combinations of moves in a game are represented by a tree structure, and unnecessary moves are removed during the search, thereby reducing computation time.

Overview of Monte Carlo Tree Search and Examples of Algorithms and Implementations

Overview of Monte Carlo Tree Search and Examples of Algorithms and Implementations. Monte Carlo Tree Search (MCTS), a type of decision tree search, is a probabilistic method for exploring the state space of a game to find the optimal action, and is a particularly effective approach in games and decision-making problems.

Overview of UCT (Upper Confidence Bounds for Trees), Algorithm and Example Implementation

Overview of UCT (Upper Confidence Bounds for Trees), Algorithm and Example Implementation. UCT (Upper Confidence Bounds for Trees) is an algorithm used in the selection phase of Monte Carlo Tree Search (MCTS), which aims to balance the search value of each node in the search. It is important to strike a balance between exploration and utilization. That is, the more nodes being explored are visited, the higher the value of the node will be estimated, but at the same time, the unexplored nodes will be given an appropriate opportunity to be explored.

Overview of Information Set Monte Carlo Tree Search (ISMCTS) and Examples of Algorithms and Implementations

Overview of Information Set Monte Carlo Tree Search (ISMCTS) and Examples of Algorithms and Implementations. Information Set Monte Carlo Tree Search (ISMCTS) is a variant of Monte Carlo Tree Search (MCTS) used in games such as incomplete information games (e.g. poker) and information hiding games (e.g. Go, Shogi). The characteristic feature of this method is that it handles groups of game states, called information sets, when searching the game tree by applying MCTS.

Overview of Nested Monte Carlo Search (NMC) and Examples of Algorithms and Implementations

Overview of Nested Monte Carlo Search (NMC) and Examples of Algorithms and Implementations. Nested Monte Carlo Search (NMC) is a type of Monte Carlo Tree Search (MCTS), which is a method for efficiently exploring a search space.

Rapid Action Value Estimation (RAVE) Overview, Algorithm, and Example Implementation

Rapid Action Value Estimation (RAVE) Overview, Algorithm, and Example Implementation. Rapid Action Value Estimation (RAVE) is a game tree search method developed as an extension of Monte Carlo Tree Search (MCTS) described in “Overview of Monte Carlo Tree Search, Algorithms and Examples”. RAVE is used to estimate the value of moves selected during game tree search. While the usual MCTS uses statistics of the moves explored to estimate the value of moves when the model is incomplete or as the search progresses, RAVE improves on this and aims to find suitable moves more quickly.

Overview of Ranking Algorithms and Examples of Implementations

Overview of Ranking Algorithms and Examples of Implementations. A ranking algorithm is a method for sorting a given set of items in order of most relevance to the user, and is widely used in various fields such as search engines, online shopping, and recommendation systems. This section provides an overview of common ranking algorithms.

Random Forest Ranking Overview, Algorithm and Implementation Examples

Random Forest Ranking Overview, Algorithm and Implementation Examples. Random Forest is a very popular ensemble learning method in the field of machine learning (a method that combines multiple machine learning models to obtain better performance than individual models). This approach combines multiple Decision Trees to build a more powerful model. There are many variations in ranking features using random forests.

Diversity-Promoting Ranking Overview, Algorithm, and Implementation Example

Diversity-Promoting Ranking Overview, Algorithm, and Implementation Example. Diversity-Promoting Ranking is one of the methods that play an important role in information retrieval and recommendation systems, which aim to make users’ information retrieval results and the list of recommended items more diverse and balanced. This will be the case. Usually, the purpose of ranking is to display items that match the user’s interests at the top, but at this time, multiple items with similar content and characteristics may appear at the top. For example, in a product recommendation system, similar items or items in the same category often appear at the top of the list. However, because these items are similar, they may not adequately cover the user’s interests, leading to information bias and limiting choices, and diversity promotion ranking is used to address these issues.

Exploratory Ranking Overview, Algorithm and Example Implementation

Exploratory Ranking Overview, Algorithm and Example Implementation. Exploratory Ranking is a technique for identifying items that are likely to be of interest to users in ranking tasks such as information retrieval and recommendation systems. This technique aims to find the items of most interest to the user among ranked items based on the feedback given by the user.

Overview of Rank SVM, Algorithm and Implementation Example

Overview of Rank SVM, Algorithm and Implementation Example. Rank SVM (Ranking Support Vector Machine) is a type of machine learning algorithm applied to ranking tasks, especially for ranking problems in information retrieval and recommendation systems. Related papers include “Optimizing Search Engines using Clickthrough Data” and “Ranking Support Vector Machine with Kernel Approximation”.

Diversified Top-k Retrieval (DTkR) Overview, Algorithm and Example Implementation

Diversified Top-k Retrieval (DTkR) Overview, Algorithm and Example Implementation. Diversified Top-k Retrieval (DTkR) is a method for obtaining diversified top-k search results in information retrieval and ranking tasks, aiming to obtain search results with different perspectives and diversity rather than simple Top-k results. In general Top-k search, the objective is simply to obtain the top k results with the highest scores, but similar results tend to rank high and lack diversity. On the other hand, DTkR aims to make the search results more diverse and different, and can perform information retrieval with diversity that cannot be obtained with simple Top-k search results.

Overview of Submodular Diversification and examples of algorithms and implementations

Overview of Submodular Diversification and examples of algorithms and implementations. Submodular Diversification is a method for selecting the top k items with diversity in information retrieval and ranking tasks. The basis of Submodular Diversification is the Submodular function, also described in “Submodular Optimisation and Machine Learning”, which is a set function \( f: 2^V \rightarrow \mathbb{R} \), with the following properties.

Overview, algorithms and implementation examples of neural ranking models

Overview, algorithms and implementation examples of neural ranking models. A neural ranking model is a type of machine learning model used in search engines and recommendation systems, where the main objective is to sort items (e.g. web pages, products, etc.) in the best ranking based on given queries and user information. For a typical search engine, it is important to display first the web pages that are most relevant to the user’s query, and to achieve this, the search engine considers a number of factors to determine the ranking of web pages. These include keyword match, page credibility and the user’s previous click history.

Overview, algorithms and implementation examples of personalised ranking

Overview, algorithms and implementation examples of personalised ranking. Personalised ranking is a ranking method that provides items in the most suitable rank for each user. While general ranking systems present items in the same rank for all users, personalised ranking takes into account the individual preferences and behaviour of the user and Personalised ranking takes into account the user’s individual preferences and behaviour and ranks items in the most appropriate order for that user. The purpose of personalised ranking is to increase user engagement by showing items that are likely to be of interest to the user at a higher rank, increase user engagement, increase user purchases, clicks and other actions, and increase conversion rates Increased conversion rates, users find the information and products they are looking for more quickly, which increases user satisfaction, which increases user satisfaction, and so on.

Overview of Beam Search and Examples of Algorithms and Implementations

Overview of Beam Search and Examples of Algorithms and Implementations. Beam Search is a search algorithm mainly applied to combinatorial optimization and finding meaningful solutions. It is mainly used in areas such as machine translation, speech recognition, and natural language processing.

evolutionary algorithm

Overview of evolutionary algorithms and examples of algorithms and implementations

Overview of evolutionary algorithms and examples of algorithms and implementations. Evolutionary algorithms are optimisation techniques designed based on the principles of natural selection and genetic information transfer in evolutionary biology. In evolutionary algorithms, candidate solutions are represented as individuals, and individuals are evolved through genetic manipulation (crossover, mutation, etc.) to search for the optimal solution.

SADE(Self-Adaptive Differential Evolution) Overview, Algorithms and Implementation Examples

SADE(Self-Adaptive Differential Evolution) Overview, Algorithms and Implementation Examples. Self-Adaptive Differential Evolution (SADE) is a method based on Differential Evolution (DE), a type of evolutionary algorithm, in which parameter adjustment is automated and the adaptability of the algorithm is enhanced. In normal Differential Evolution (DE), multiple parameters (e.g. mutation rate \(F\) and crossover rate \(CR\)) need to be set in advance during the search, but these settings are problem-dependent and therefore difficult to adjust, SADE adjusts these parameters in a self-adaptive manner in the evolutionary process, thereby improving search efficiency and The method improves the quality of the solution.

Overview of Evolutionary Annealing-Search (EAS), algorithms and implementation examples

Overview of Evolutionary Annealing-Search (EAS), algorithms and implementation examples. EAS (Evolutionary Annealing-Search) is a meta-heuristic optimisation algorithm that integrates the Evolutionary Algorithm (EA) and the Simulated Annealing (SA) method. It aims to provide efficient solutions to complex optimisation problems by combining an evolutionary search mechanism with the temperature parameter adjustment mechanism of the annealing method.

ABC (Artificial Bee Colony Algorithm) overview, algorithm and implementation examples

ABC (Artificial Bee Colony Algorithm) overview, algorithm and implementation examples. ABC (Artificial Bee Colony Algorithm) is an optimisation algorithm based on swarm intelligence, which mimics the foraging behaviour of bees in nature. It is widely used as a simple but effective method, with particularly good performance in continuous optimisation problems.

Overview of Adaptive PSO (Self-Adaptive Particle Swarm Optimisation), algorithm and implementation examples

Overview of Adaptive PSO (Self-Adaptive Particle Swarm Optimisation), algorithm and implementation examples. Adaptive PSO (self-adaptive particle swarm optimisation) is a type of particle swarm optimisation algorithm described in ‘Overview and implementation of particle swarm optimisation’, which aims to improve search performance by dynamically adjusting the algorithm parameters.

Overview of the Calton Method (Cultural Algorithm) and Examples of Application and Implementation

Overview of the Calton Method (Cultural Algorithm) and Examples of Application and Implementation. Cultural Algorithm is a type of evolutionary algorithm that extends evolutionary algorithms by introducing cultural elements. programming are representative examples. The Calton method introduces a cultural component to these evolutionary algorithms, and becomes one that takes into account not only the evolution of individuals, but also the transfer of knowledge and information between individuals.

NSGA-II (Non-dominated Sorting Genetic Algorithm II) Overview, Algorithm and Implementation Examples

NSGA-II (Non-dominated Sorting Genetic Algorithm II) Overview, Algorithm and Implementation Examples. NSGA-II (Non-dominated Sorting Genetic Algorithm II) is a type of Evolutionary Algorithm (EA) for solving multi-objective optimization problems. It is designed to optimize multiple objective functions simultaneously based on the Genetic Algorithm (GA) described in “Overview of Genetic Algorithm and Examples of Application and Implementation”.

MOEA/D (Multi-Objective Evolutionary Algorithm based on Decomposition) Overview, Algorithm, and Implementation Examples

MOEA/D (Multi-Objective Evolutionary Algorithm based on Decomposition) Overview, Algorithm, and Implementation Examples. MOEA/D (Multi-Objective Evolutionary Algorithm Based on Decomposition) is a type of evolutionary algorithm (EA) for solving multi-objective optimization problems (MOP) and was proposed by Zhang and Li in 2007.

SPEA2 (Strength Pareto Evolutionary Algorithm 2) Overview, Algorithm, and Implementation Examples

SPEA2 (Strength Pareto Evolutionary Algorithm 2) Overview, Algorithm, and Implementation Examples. SPEA2 (Strength Pareto Evolutionary Algorithm 2) is an evolutionary algorithm for solving multi-objective optimization problems and will be an improved method for finding Pareto optimal solutions. It is an improved version of the original SPEA (Strength Pareto Evolutionary Algorithm), specifically using strength and density-based selection pressure to find superior solutions more efficiently. and has become a very popular multiobjective evolutionary algorithm as NAGA-II described in “Overview of NSGA-II (Non-dominated Sorting Genetic Algorithm II), algorithm and implementation examples“.

Overview, Algorithm and Implementation of NSGA-III

Overview, Algorithm and Implementation of NSGA-III. NSGA-III is an Evolutionary Algorithm (EA) for Multi-Objective Optimization (MOO), specifically designed to solve problems with more than three objective functions (Many-Objective Optimization). The algorithm is designed to solve problems with more than three objective functions (Many-Objective Optimization).It is an extended version of NSGA-II (Non-dominated Sorting Genetic Algorithm II) described in “Overview of NSGA-II (Non-dominated Sorting Genetic Algorithm II), algorithm and implementation examples” and is especially designed for solving problems with higher dimensional It aims to control the distribution of solutions appropriately, especially in high-dimensional objective spaces (four or more objectives).

MOPSO (Multi-Objective Particle Swarm Optimization) Overview, Algorithm, and Implementation Example

MOPSO (Multi-Objective Particle Swarm Optimization) Overview, Algorithm, and Implementation Example. Multi-Objective Particle Swarm Optimization (MOPSO) is an evolutionary algorithm for simultaneously optimizing multiple objectives and is a multi-objective version of Particle Swarm Optimization (PSO) described in “Overview and Implementation of Particle Swarm Optimization. PSO is an algorithm inspired by the migration of a flock of birds or a school of fish, in which individual “particles” explore the solution space and cooperate to find the optimal solution; MOPSO extends this basic idea and is adapted to solve problems with multiple objectives.

Overview of genetic algorithms, application examples, and implementation examples

Overview of genetic algorithms, application examples, and implementation examples. Genetic algorithm (GA) is a type of evolutionary computation, and is an optimization algorithm for optimizing problems by imitating the evolutionary process in nature, and is used for optimization, exploration, machine learning, and machine design. This is a method that has been applied to a variety of problems. The basic elements and mechanism of the genetic algorithm are described below.

Overview of Genetic Programming (GP) and its algorithms and implementations

Overview of Genetic Programming (GP) and its algorithms and implementations. Genetic Programming (GP) is a type of evolutionary algorithm that is widely used in machine learning and optimization. An overview of GP is given below.

Overview of Gene Expression Programming (GEP) and Examples of Algorithms and Implementations

Overview of Gene Expression Programming (GEP) and Examples of Algorithms and Implementations. Gene Expression Programming (GEP) is a type of evolutionary algorithm, a method that is particularly suited for the evolutionary generation of mathematical expressions and programs. This technique is used to evolve the form of a mathematical expression or program to help find the best solution for a particular task or problem. The main features and overview of GEP are described below.