Deduction

What is deduction?

Deduction is a term from logic and comes from the Latin word deductiowhich means "derivation" or "derivation". It denotes a logical conclusion from the general to the particular. It is also understood as theory to empiricism.

The basis is the inheritance of properties of higher-level elements to their subsets. Through a general theory, statements can thus be made about concrete individual cases. The precondition or assumption is also called premise. From one or more premises, the logical consequence follows with the help of inference rules, which is compellingly or deductively valid. The truth of the premise leads to the truth of the conclusion. No false conclusion may arise from a true premise.

Deductive inferences, like other scientific methods, are not verifiable, but only falsifiable. That is, their validity is assumed as long as there is no counter-evidence or new knowledge. In the field of artificial intelligence deduction plays an essential role in logic programming and automatic proof.

What are examples of deduction?

A classic example of deductive reasoning comes from Aristotle:

All human beings are mortal. Socrates is a human being. It follows that Socrates is mortal.

The premises "all human beings are mortal" and "Socrates is a human being" are true. The property "mortal" of the superordinate category human being is transferred to the concrete example of Socrates.

Another example of deductive reasoning is:

Pilots have a quick reaction time. He is a pilot. He has a quick reaction time.

The premise here is that the characteristic of a quick reaction time applies to pilots in general. According to the premise, a concrete representative of the category therefore possesses a fast reaction capability, otherwise he would not be a pilot. The statement is therefore true.

Also in the detective stories Sherlock Holmes the deductive method is present. In The blue carbuncle Holmes estimates the socio-economic background of the wearer of an old hat based on general phenomena. The size and quality of the found hat indicate an intellectual and wealthy person. However, since the hat is aging and full of dust, Holmes logically assumes that the owner is no longer financially well off and rarely leaves the house.

What are the differences between induction and abduction?

Deduction vs. induction

Induction (lat. inducere "bring about") is the reverse process to deduction. Here, a general conclusion is formed from a concrete observation or phenomenon. The path is therefore from empiricism to theory. Collecting data on individual elements leads to the realisation of properties that all representatives of a group or category possess.

Example:

The little sparrow lays eggs. The sparrow is a bird. All birds lay eggs.

The specific premise here is the egg-laying sparrow, which belongs to the group of birds. From the observation of the sparrow follows the abstract conclusion about the behaviour of all birds.

Induction and deduction never occur in pure form. The premises used in deductive reasoning are closely linked to empirical findings and induction to already established theory. The procedures differ essentially in the question of whether a regularity is to be verified (deduction) or a new one formed (induction).

Deduction vs. abduction

A third method of logical reasoning is the Abduction (lat. abducere "to lead away"). The term was introduced by the American philosopher Charles Sanders Peirce. It differs from induction and deduction in that it extends knowledge. An unknown cause is derived from two known conclusions.

Example:

These apples are red. All the apples from this basket are red. These apples are from this basket.

From the result, the rule "all apples from this basket are red" is used to infer the case "these apples are from this basket". Abductive reasoning is a presumption based on circumstantial evidence.

DALL-E

What is DALL-E?

DALL-E is a neural network, which is based on artificial intelligence and creates images from descriptions. It was unveiled in early 2021 by OpenAI after years of work preceding the programme. OpenAI is a company dedicated to the research and development of artificial intelligence. Investors include Elon Musk and Microsoft. The name is a combination of the term WALL-E, a science fiction film by Pixar, and the name of the surrealist artist Salvador Dalí.

Function of the algorithm

DALL-E uses a 12-billion-parameter version of the GPT-3 Transformer model. The abbreviation GPT stands for Generative Pre-Trained and the "3" for the now third generation. GPT-3 is an autoregressive language model. It uses the method of the Deep Learningto produce human-like text. The quality is now so high that it is not always easy to tell whether the text was written by a machine or a human.

DALL-E interprets input in natural language and generates images from it. It uses a database of pairs of images and texts. To do this, it works with the zero-shot learning method. It generates a pictorial output from a description without further training and works together with CLIP. CLIP was also developed by OpenAI and means "Connecting Text and Images". It is a separate neural network that understands and classifies the text output.

Text and image come from a single data stream containing up to 1280 tokens. The algorithm is trained under the maximum probability of generating all tokens in succession. The Training data enable the neural network to create images from scratch as well as revise existing images.

What are the capabilities of DALL-E?

DALL-E has a wide range of capabilities. It can display photorealistic images of both real and non-real objects, or output paintings and emojis. It can also manipulate or rearrange images.

In addition, in many cases the neural network is able to fill in gaps and display details on images that were not explicitly mentioned in the description. For example, the algorithm has already converted the following representations from text descriptions:

  • a blue rectangular circle within a green square
  • the cross-section of a cut apple
  • a painting of a cat
  • the façade of a shop with a certain lettering

Deep Generative Models

What are Deep Generative Models?

A Deep Generative Model (DGM) is a neural network in the subdomain of the Deep Learningswhich follow the generative modelling approach. The opposite of this approach is the discriminative modelling, which is designed to find the best solution on the basis of the existing Training data Identify decision boundaries and classify the input accordingly.

The generative approach, on the other hand, follows the strategy of learning the data distribution from training data and creating new data points based on the learned or approximated distribution according to the word origin. While discriminative modelling is attributed to supervised learning, generative modelling is usually based on unsupervised learning.

Deep generative models thus ask the question of how data are generated in a probability model, while discriminative models aim to make classifications based on the existing training data. The generative models try to understand the probability distribution of the training data and generate new or similar data on the basis of this. For this reason, one area of application of deep generative models is image generation based on sample images, such as in the neural network DALL-E.

What are Flow-based Deep Generative Models?

A flow-based deep generative model is a generative model that is able to interpret and model a probability distribution of data. This can be illustrated with the help of the so-called "normalising flow".

The normalising flow describes a statistical method with which density functions of probability distributions can be estimated. In contrast to other types of generative models, such as the Generative Adversarial Networks (GAN) or Variational Autoencoder (VAE), flow-based deep generative models generate the "flow" through a sequence of invertible transformations. This allows the likelihood function to be represented and thus the true probability distribution to be learned.

In Generative Adversarial Networks, on the other hand, the methodology consists of a generator and a discriminator, which are to be seen as opponents. The generator produces data which the discriminator tries to identify as falsification (i.e. as not being part of the given, real distribution). The goal of the generator, on the other hand, is to ensure that the generated data is not identified as a forgery and that the generated distribution of the generator thus approximates the real distribution through training. In the Variational Autoencoder, the distribution is optimised by maximising ELBO (Evidence Lower Bound).

Where are these models applied?

Deep Generative Models have extensive applications in the field of Deep Learning.

For example, they are used in the Image generation used. For this purpose, new, artificial faces with human facial features are created from human faces in the training data. This method can also be used in the film and computer games sector. A special form of application of generative models is the so-called deepfakes. In this case, media content is artificially created, but gives the appearance of being real.

Also the Creation of genuine-looking handwriting can be implemented by means of generative models. For example, one can also be generated on the basis of a textual description of a photo.

The achievements of deep generative models can also be used in medicine. For example, in the essay "Disease variant prediction with deep generative models of evolutionary data" referred to the fact that Predicting previously unknown disease variants with the help of generative models. can. Specifically, the article refers to the detection of protein variants in disease-related genes that have the ability to cause disease. The disadvantage of previous methods (primarily using supervised learning) was that the models were based on known disease labels and no new ones could be predicted. This is to be improved with Deep Generative Models.

Decision Tree Learning

What is Decision Tree Learning?

Decision Tree Learning is a technique used in machine learning. Decision trees are a widely used way of regression or classification over a large, diverse data set. Areas of application are the classification of the creditworthiness of bank customers or a function for the prediction of purchasing power.

Decision trees are a popular tool in computer science and mechanical engineering for design structures. In data science, algorithms are used that Automatically generate tree structures from a set of known data and an automatic Classification or regression can make. Decision trees are used in supervised machine learning to form hierarchical structures with as few decision paths as possible.

Elements of a decision tree

A decision tree consists of nodes, edges and leaves. The nodes are used to test for a value of a certain attribute. The edges correspond to a final result of a test and they connect to the next node or leaf. The leaves are end nodes that predict the result. A classification then goes as follows.

  1. Start at the root node
  2. Perform the test
  3. Sequence of the corresponding edge to the result
  4. As long as it is not a leaf, go back to 2. and repeat the process
  5. Make a prediction for the outcome associated with the leaf

In decision tree learning, a new example is classified and sent through a series of tests to obtain a class label for the example. These tests are organised in a hierarchical structure called a decision tree. The training examples are used to select appropriate tests in the decision tree. The tree is built from top to bottom, with tests that maximise the information gain about the classification being selected first.

What is Decision Tree Learning used for?

A decision tree is used as a predictive model to reach conclusions about the corresponding target value of an element represented in the branches by making observations about the element represented in the leaves. Decision Tree Learning is one of the predictive modelling approaches for statistics, machine learning and Data mining. The tree models where the target variable assumes a certain discrete range of values are called classification trees. The leaves of the tree structures represent class labels and the branches represent connections of the features and these lead to class labels. If target variables lead to continuous values (real numbers), these decision trees are called regression trees

What are Random Forests?

Random forests are decision forests that consist of a large number of decision trees. A decision tree is a tree-like and directed diagram for decision-making. A decision tree is a mathematical model and diagram for determining decisions.

Data warehouse architecture

A data warehouse is a central data storage system designed to encompass all data across the enterprise. It is a topic-oriented, integrated, time-dependent and non-volatile collection of data. It supports the decision-making process of management levels by providing a coherent view of all enterprise-wide data.

It is an architectural blueprint, more precisely a logical (intangible) concept. The DWH architecture is usually integrated and realised via several, dependent database systems. The goal of DWH is to bundle all of an organisation's data into one system. However, it is not uncommon for companies to maintain multiple DWHs, depending on their size. The characteristics of a DWH are: 

  • Integrated: A data warehouse architecture integrates data from multiple data sources that are otherwise distributed across (or beyond) an organisation. 
  • Topic-oriented: The aim is to provide its users with a view of specific subject areas, e.g. "sales", and to analyse them. 
  • Time-dependent: DWHs store accumulating data permanently. This contrasts with transactional systems, which only store the most recent records. 
  • Non-volatile: The goal of a DWH is to store data continuously to provide a picture of what has happened, not to change that picture. Therefore, once data is stored in the DWH, it typically does not change. 

For decades, data warehouse architectures were the architectural solution of choice for how data should be moved and stored in an organisation.

The goal of a DWH is to organise the movement of data in a company, from its collection to its use; to ensure this, it is a unified, centralised solution that stores all the data present in a company.