Machine learning uses the gradient method to find the optimization. I will explain it using an example. There are 30 cranes or turtles in total. The total number of their legs is 100, and a crane has 2 legs, and a turtle has 4 legs, respectively. How many turtles are there in this case?

There are three ways to find the number of cranes and turtles: simultaneous equations, matrices, and gradient methods. The matrix method uses the inverse matrix to find the answer, which is the most advanced method. However, machine learning uses the gradient method, in which an error is calculated with an input number and the error will be minimized by changing the number little by little. The minimum value of the error can be calculated by being squared more easily.

Artificial intelligence (AI) calculates the difference between the actual value and the predicted value which is calculated by input values and parameters. Then, AI finds the parameters to produce the minimum error by changing parameters little by little. Input values, parameters, output values, and observed values can be effectively expressed by being packed in the form of vector or matrix, which is a set of vectors.

The theory of computation is simple, but computer can perform a huge amount of calculation at high speed. As a result, it can carry out much more sophisticated calculation than human beings.

Machine learning utilizes multivariable differentiation (partial differentiation) because calculation for the minimum error requires finding the place in which the slope of the function amounts to zero. Moreover, the sequence plays a great role for the use of the gradient method. The sequence is expressed by a recurrence formula or a general form. Machine learning generally includes multiple variables and multiple sequences are related with each other, thus utilizes simultaneous recurrence formulas. Partial differentiation of this simultaneous recurrence formulas can finally lead to estimation of the minimum error. The structure of each layer of artificial intelligence can be expressed by forming simultaneous recurrence formulas into a matrix.

In differentiation, a method of approximate formula is employed to obtain the slope at and the change from a certain point. Artificial intelligence has multiple layers and the relationship between input and output variables will be made up of composite function accordingly. Therefore, multiple variables will be used, and differentiation will be conducted after division into multiple differential formulas according to the chain rule.

In artificial intelligence, it is essential to apply the sequence for the gradient method, partial differentiation for multiple variables, and the chain rule for multiple intermediate layers.

In this lecture, we learned how to create a machine learning model by using training data as well as to evaluate the model with the test data.

Here, the data of independent and target variables were split into training and test data, respectively so that they account for 80% and 20 %, respectively. Next, these independent variables were converted with polynomial features with 10^th degree, then a linear regression model was created with the training data. After this process, target values were predicted by using the model and the independent variable of the test data.

The figure shows the relationship between the actual values in the test data in blue plots as well as the relationship between the independent variable in the test data and the predicted values in a red line.

Finally, the mean squared error was calculated as to the model with the test data to estimate the accuracy of the model. As a result, the mean squared error was around 82%.

Generative Adversarial Networks (GANs) is an artificial intelligence (AI) model that consists of a generative model (generator) and a discriminative model (discriminator) to generate synthetic data, such as synthetic images. The generative model creates data that are similar to the actual data x from the actual data x by using the input random numbers z. The discriminative model distinguishes between the actual data x and the synthetic data G (z). Both models continue this process and enhance each other’s capability to generate natural synthetic data that are difficult to distinguish from the actual data.

This GANs is also beginning to be used for medical imaging. For instance, pigmented spots, such as spots are caused by exposure to ultraviolet rays and aging and cause actinic keratosis and squamous cell cancer. It is possible to quantitatively measure pigmented spots using ultraviolet photography by utilizing the property of melanocytes to absorb ultraviolet rays, which is however difficult to carry out regularly in daily life. Therefore, a GANs model can be used to detect pigment spots from ordinary color photographs after learning synthesis of ultraviolet photographs from ordinary color photographs.

At present, natural language processing (NLP) by artificial intelligence (AI) is used in various fields, including medical and health fields. Rapid improvement is also observed in the accuracy of machine translation and sentence comprehension, which are typical examples of NLP. At the moment, the meaning of a word is analyzed by a mathematical model after the characteristics of the word is converted into a vector. Different AI models have also been developed. The combination of pre-train and fine-tuning has been established as a training method of AI model. There are also some reports that AI’s capabilities for NLP have exceeded those of humans.

However, AI is still weak at understanding languages deeply or combining knowledge and reasoning. It is proposed to combine conventional symbol inference and the latest technology of deep learning for the purpose of further development of NLP. The aim is to be able to use NLP for flexible reasoning of knowledge written in language. It is expected in the future that AI will also be able to correct writing, evaluate written answers, and carry out interactive guidance on essays.

At present, artificial intelligence (AI) is undergoing rapid progress in its development and is being introduced into various daily lives as well as industries. It is expected that the intellectual ability of AI may exceed that of human beings in the near future. General people are also recognizing the existence of AI and have more expectation and anxiety for AI than before. AI is particularly expected to play an active role in the future in healthcare, autonomous driving, communication, office work, general housework, energy development, and set forth.

On the other hand, many general people are concerned about the dangers of accidents and social turmoil caused by AI system errors, uncontrollability due to its intelligence beyond humans, attacks on human beings by AI, unemployment of human beings, and human rights violations, and so on. It is not guaranteed that correctness of science can always be accepted in the society. This is also true with AI. No matter how great AI is developed, it is indispensable to introduce it so that this AI will be accepted by the general public. For this purpose, it is important to understand the culture of each region.