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Certain Investigations on Different Mathematical Models in Machine Learning and Artificial Intelligence

Ms. Akshatha Y* and Dr. S Pravinth Raja┼

Dept. of CSE, Presidency University, Bengaluru, Karnataka, India

Abstract

Artificial Intelligence (AI) is as wide as the other branches of computer science, including computational methods, language analysis, programming systems, and hardware systems. Machine learning algorithm has brought greater change in the field of artificial intelligence which has supported the power of human perception in a splendid way. The algorithm has different sections, of which the most common segment is classification. Decision tree, logistic regression, naïve bays algorithm, support vector machine algorithm, boosted tree, random forest and k nearest neighbor algorithm come under the classification of algorithms. The classification process requires some pre-defined method leading the process of choosing train data from the user's sample data. A host of AI Advanced AI programming languages and methodologies can provide high-level frameworks for implementing numerical models and approaches, resulting in simpler computational mechanics codes, easier to write, and more adaptable. A range of heuristic search, planning, and geometric reasoning algorithms can provide efficient and comprehensive mechanisms for resolving problems such as shape description and transformation, and model representation based on constraints. So behind every algorithm there lies a strong mathematical model, based on conditional probability. This article is the analysis of those mathematical models and logic behind different classification algorithms that allow users to make the training dataset based on which computer can predict the correct performance.

Keywords: Artificial intelligence, classification, computation, machine learning

1.1 Introduction

The increasing popularity of large computing power in recent years, due to the availability of big data and the relevant developments in algorithms, has contributed to an exponential growth in Machine Learning (ML) applications for predictive tasks related to complex systems. In general, by utilizing an appropriate broad dataset of input features coupled to the corresponding predicted outputs, ML automatically constructs a model of the scheme under analysis. Although automatically learning data models is an extremely powerful approach, the generalization capability of ML models can easily be reduced in the case of complex systems dynamics, i.e., the predictions can be incorrect if the model is extended beyond the limits of ML models [1]. A collection of AI ideas and techniques has the potential to influence mathematical modelling study. In particular, information-based systems and environments may include representations and associated problem-solving techniques that can be used in model generation and result analysis to encode domain knowledge and domain-specific strategies for a variety of ill-structured problems. Advanced AI programming languages and methodologies may include high-level frameworks to implement numerical models and solutions, resulting in codes for computational mechanics that are cleaner, easier to write and more adaptable. A variety of heuristic search, scheduling, and geometric reasoning algorithms may provide efficient and comprehensive mechanisms for addressing issues such as shape definition and transformation, and model representation based on constraints. We study knowledge-based expert systems and problem-solving methods briefly before exploring the applications of AI in mathematical modelling.

1.1.1 Knowledge-Based Expert Systems

Knowledge-based systems are about a decade old as a distinctly separate AI research field. Many changes in the emphasis put on different elements of methodology have been seen in this decade of study. Methodological transition is the most characteristic; the emphasis has changed from application areas and implementation instruments to architectures and unifying concepts underlying a range of tasks for problem-solving. The presentation and analysis were at two levels in the early days of knowledge-based systems: 1) the primitive mechanisms of representation (rules, frames, etc.) and their related primitive mechanisms of inference (forward and backward chaining, inheritance, demon firing, etc.), and 2) the definition of the problem.

A level of definition is needed that describes adequately what heuristic programmers do and know, a computational characterization of their competence that is independent of the implementation of both the task domain and the programming language. Recently in the study, many characterizations of generic tasks that exist in a multitude of domains have been described. The kind of information they rely on and their control of problem solving are represented by generic tasks. For expert systems architecture, generic tasks constitute higher-level building blocks. Their characteristics form the basis for the study of the content of the knowledge base (completeness, accuracy, etc.) in order to explain system operations and limitations and to establish advanced tools for acquiring knowledge.

1.1.2 Problem-Solving Techniques

Several problem-solving tasks can be formulated as a state-space search. A state space is made up of all the domain states and a set of operators that transform one state into another. In a connected graph, the states can best be thought of as nodes and the operators as edges. Some nodes are designated as target nodes, and when a path from an initial state to a goal state has been identified, a problem is said to be solved. State spaces can get very big, and different search methods are necessary to monitor the effectiveness of the search [7].

A) Problem Reduction: To make searching simpler, this strategy requires transforming the problem space. Examples of problem reduction include: (a) organizing in an abstract space with macro operators before getting to the real operator details; (b) mean-end analysis, which tries to reason backwards from a known objective; and (c) sub-goaling.

B) Search Reduction: This approach includes demonstrating that the solution to the problem cannot rely on searching for a certain node. There are several explanations why this may be true: (a) There can be no solution in this node's subtree. This approach has been referred to as "constraint satisfaction" and includes noting that the circumstances that can be accomplished in the subtree below a node are inadequate to create any minimum solution requirement. (b) In the subtree below this node, the solution in another direction is superior to any possible solution. (c) In the quest, the node has already been investigated elsewhere.

C) Use information of domains: The addition of additional information to non-goal nodes is one way to monitor the quest. This knowledge could take the form of a distance from a hypothetical target, operators that can be applied to it usefully, possible positions of backtracking, similarities to other nodes that could be used to prune the search, or some general formation goodness.

D) Adaptive searching techniques: In order to extend the "next best" node, these strategies use assessment functions. The node most likely to contain the optimal solution will be extended by certain algorithms (A *). The node that is most likely to add the most information to the solution process will be expanded by others (B *).

1.2 Mathematical Models of Classification Algorithm of Machine Learning

In the artificial learning area, the machine learning algorithm has brought about a growing change, knowledge that spoke of human discerning power in a splendid manner. There are various types of algorithms, the most common feature of which is grouping. Computer algorithm, logistic regression, naive bay algorithm, decision tree, enhanced tree, all under classification algorithms, random forest and k nearest neighbour algorithm support vector support. The classification process involves some predefined method that leads to the train data method of selection from the sample data provided by the user. Decision-making is the centre of all users, and the algorithm of classification as supervised learning stands out from the decision of the user.

Machine learning (ML) and deep learning (DL) are common right now, as there is a lot of fascinating work going on there, and for good reason. The hype makes it easy to forget about more tried and tested methods of mathematical modelling, but that doesn't make it easier to forget about those methods.

We can look at the landscape in terms of the Gartner Hype Cycle:

Figure 1.1 is curve that first ramps up to a peak, then falls down into a low and gets back up into a plateau. We think that ML, and DL in particular, is (or at least is very close to) the Height of Unrealistic Expectations. Meanwhile, the Shortage of Productivity has several other methods. People understand them and use them all the time, but nobody speaks about them. They're workhorses. They're still important, though, and we at Manifold understand that. You also have to deploy the full spectrum of available resources, well beyond ML, to build effective data items. What does that mean in practice?

Figure 1.1 Gartner hyper cycle.

1.2.1 Tried and True Tools

Let's look at a couple of these advanced tools that continue to be helpful: the theory of control, signal processing, and optimization of mathematics.

Control...