Philosophical perspectives on probability
The concept of probability has different perspectives. The different perspectives on probability are discussed below.
1. frequentist (frequency approach): as discussed in ‘Probability and the relationship between uncertainty and randomness’, frequentists interpret probability as a long-term relative frequency. In other words, the probability of an event occurring is understood as the ratio of the number of times the event appears in an experiment repeated an infinite number of times. In this position, probability is objective and observable, and it is possible to assign probabilities to individual events.
2. Bayesianism (Bayesian approach): also discussed in ‘Overview and various implementations of Bayesian estimation’, Bayesians interpret probability as a degree of belief or knowledge. Probabilities represent the strength of belief that a hypothesis is true and are updated based on observations. In the Bayesian approach, the probability of an event is based on an individual’s subjective beliefs, which depend on the updating of ‘prior probabilities’ and ‘posterior probabilities’.
3. randomness and causality: probability is also questioned, from a philosophical perspective, how it relates to causality, which is discussed in ‘Considerations towards causal inference and strong AI’. Randomness means that future outcomes are not uniquely determined from past events, which raises the debate as to whether this means that causality does not exist, or whether there are just hidden variables.
4. interpretation of probability and free will: the interpretation of probability theory is also related to philosophical issues concerning free will and human decision-making, which are also discussed in ‘Free will, AI technology and Zhuangzi’s freedom’. There is also the question of how human behaviour should be positioned in a probabilistic future and how probability should be understood in terms of free will.
5. determinism and probability: In determinism, all events are determined according to the law of cause and effect, but the probabilistic nature of quantum mechanical observations, which is also discussed in ‘Quantum mechanics, artificial intelligence and natural language processing’, causes a philosophical conflict between determinism and probability. The uncertainty principle in quantum theory (e.g. the indeterminacy of the simultaneous measurement of position and momentum) is seen as supporting the idea of a probabilistic element as the basis of reality.
6. probability and information: probability is also closely related to information theory. When probability is used to measure uncertainty in the amount of information, probability is a measure of how much information is missing or how many options exist.’ Shannon Information Theory, which is also discussed in ‘Shannon’s Information Theory Overview and Reference Books’, uses probability as a measure of information content.
As also noted in ‘Nine probability and statistics stories that changed humans and society Reading notes’, the history of probability began with frequentism, a gambling prediction, and has developed through Bayesian perspectives and mathematical theory building, as also noted in ‘Introduction to probability theory Reading notes’, in a variety of applications.
Uncertainty and AI technology
Given that real-world problems are solved from probabilities, the perspectives of prediction and uncertainty are of paramount importance. This uncertainty and AI technology are closely related, and how AI handles decision-making in uncertain environments is an important topic in AI design and application. Uncertainty means that future outcomes are not entirely predictable, and how AI handles that uncertainty influences different technological approaches.
Uncertainty in AI technologies can be categorised into two main types
- Epistemic uncertainty (knowledge uncertainty): uncertainty that arises when the system does not have sufficient information about the problem or the information is incomplete. For example, the training data may be biased or only part of the environment is observable. For more information, see Epistemic Uncertainty and AI Complementation.
- Aleatoric uncertainty: Uncertainty due to environmental variability and unpredictable factors. This uncertainty appears when randomness or stochastic elements are involved, e.g. in situations that obey physical laws but whose details cannot be predicted (e.g. quantum mechanical phenomena). For more information, see ‘Aleatory Uncertainty and the AI Solution’.
How AI technologies handle these uncertainties depends on a number of different approaches. They are mainly the following approaches.
- Bayesian inference: described in ‘Bayesian inference and machine learning with graphical models’, is a powerful tool for dealing with epistemic uncertainty and is a probabilistic estimation technique. It calculates posterior probabilities by updating the parameters and predictions in an AI model based on historical data and newly obtained information. Using this method, AI can update the probabilities each time new information is obtained, reducing uncertainty.
- Reinforcement Learning (RL): ‘Why do we need reinforcement learning? Reinforcement learning is a method whereby an agent learns optimal behaviour by interacting with its environment, and it is important to handle uncertainty in this process, Since the agent initially has little information about the environment and is uncertain about the outcome of its actions, it learns the optimal policy through trial and error, reducing uncertainty in the learning process by striking a balance between exploration and exploitation.
- Probabilistic programming: also described in ‘Probabilistic Programming with Clojure’ Probabilistic programming is a framework for incorporating uncertainty into models, explicitly including probabilistic elements in the code, and probabilistic reasoning The system will be designed to do the following. This allows AI systems to make more robust predictions and decisions based on uncertainty.
- Uncertainty quantification and risk assessment: AI also has techniques for quantifying uncertainty in forecasting and decision-making, as described e.g. in ‘Overview of causal inference using Meta-Learners, algorithms and implementation examples’. For example, by calculating confidence intervals and probability distributions for the output of a prediction model, it is possible to indicate how reliable the prediction is, which enables risk to be assessed and decisions to be made based on uncertainty.
- Deep learning and uncertainty: Deep learning, discussed in ‘About deep learning’, also has ways of dealing with uncertainty. For example, the Dropout technique reflects the uncertainty in predictions by randomly disabling neurons when training a model. In this way, it is possible to indicate how confident the model is in its predictions.
In addition, AI predictions and decisions are probabilistic and cannot be made with complete certainty. Therefore, AI is often required to make final decisions, using AI as a complement to human expertise and judgement.’ Dealing with uncertainty as part of IA technology, as described in ‘Intelligence Augmentation (IA) overview and examples of its application’, is also important as human judgement and intuition also play an important role.
Furthermore, an important aspect of AI’s handling of uncertainty is the issue of ethical considerations and bias: AI makes decisions in response to an uncertain environment, but inappropriate biases can enter into the process, for example, by using biased data sets, which can lead to AI treating uncertainty incorrectly and thus making unfair Fairness and ethical considerations need to be considered in the design of AI systems, as decisions may be made.
Dealing with uncertainty is a key challenge in the development of AI AI is a powerful tool for managing uncertainty and optimising decision-making, but choosing the right methods for its implementation is important, and ethical and social considerations are also essential AI can be used to reduce uncertainty helpful, but it is necessary to understand that the process should always be accompanied by human judgement and oversight.
Specific application examples
Specific applications of these are described below.
1. eliminating uncertainty in medical diagnosis
- Applications: an AI uses probabilistic models to assist in the diagnosis of diseases and the selection of treatments. In particular, the use of Bayesian networks enables diagnosis that takes into account the uncertainty of a patient’s symptoms and test results.
- Examples: Bayesian statistics, which calculates the probability of the appearance of certain symptoms in the early detection of cancer and suggests the next tests and treatments to be performed by the doctor; deep learning, which analyses medical images and improves the accuracy of diagnosis by presenting the probability of the presence of cancer cells.
- Related technologies: bayesian networks, Markov chain Monte Carlo (MCMC)
2. risk avoidance in automated driving
- Applications: automated vehicles make probabilistic estimates of their surroundings based on data acquired from sensors to determine their next course of action. Uncertainty can be taken into account to enable obstacle avoidance and safe route selection.
- Examples: particle filters that probabilistically predict the movements of surrounding vehicles and pedestrians to generate safe routes, probabilistic decision-making that optimises the choice of stopping or proceeding in real-time in response to changes in the environment, etc.
- Related technologies: probabilistic logic, reinforcement learning
3. weather forecasting
- Applications: AI uses probabilistic methods to make short- and long-term weather forecasts to clarify uncertainties and improve efficiency in agriculture and disaster management.
- Examples: e.g. Monte Carlo simulations for probabilistic modelling of future forecasts of temperature and precipitation, and ensemble models that integrate different weather models and provide confidence intervals for forecasts.
- Related technologies: Monte Carlo methods, Bayesian estimation.
4. risk management in the financial sector
- Applications: as forecasts of stock prices and exchange rates are highly uncertain, stochastic methods are used to quantify risk and enable the design of optimal investment and hedging strategies.
- Examples: value at risk (VaR) models for probabilistically assessing the risk of loss in asset portfolios, stochastic model predictive control (MPC) for real-time portfolio optimisation that takes uncertainty into account, etc.
- Related technologies: Gaussian processes, Markov decision processes.
5. disaster prediction and risk mitigation
- Applications: for natural disasters such as earthquakes and floods, AI uses probabilistic models to assess risks and provide early warning systems.
- Examples: real-time Bayesian estimation to calculate the probability of earthquakes and identify high-risk areas, AI simulations to predict the probability of floods and assist residents in evacuation planning, etc.
- Related technologies: time series analysis, dynamic Bayesian networks.
6. supply chain optimisation
- Applications: probabilistic assessment of uncertainty in demand forecasting and logistics planning to minimise over- and under-supply.
- Examples: Bayesian demand forecasting for stochastic estimation of demand for goods, taking into account seasons and trends; dynamic inventory management for real-time stock replenishment strategies that take uncertainty into account.
- Related techniques: stochastic optimisation, reinforcement learning.
7. market design and auctions
- Applications: stochastic modelling of uncertainty and optimal matching in auction platforms and market design.
- Examples: e.g. Bayesian auction theory, which probabilistically models bidders’ strategies to support fair and efficient auction design, and probabilistic matching algorithms to calculate optimal matching in labour and marriage markets.
- Related techniques: bayesian games, stable matching theory.
reference book
Reference books are discussed below.
Probability and philosophical perspectives
1. ‘Philosophy of Probability’
3. ‘The Emergence of Probability: A Philosophical Study of Early Ideas about Probability, Induction, and Statistical Inference’
Ian Hacking
– 4. a detailed analysis of how the concept of probability developed and how it influenced philosophical issues.
AI solutions to uncertainty.
4. ‘Artificial Intelligence: A Guide to Intelligent Systems’
Michael Negnevitsky
– Comprehensive explanation of how AI models and solves uncertainty, including fuzzy logic and Bayesian networks.
5. ‘Probabilistic Robotics’.
Sebastian Thrun, Wolfram Burgard, Dieter Fox
– Explains the use of probabilistic methods in robotics and provides a foundation for AI algorithms dealing with uncertainty.
6. ‘Probabilistic Machine Learning: An Introduction’
Kevin P. Murphy
– Provides a comprehensive overview of AI methods for dealing with uncertainty, focusing on Bayesian statistics and probabilistic inference.
The Philosophy of Artificial Intelligence
7. ‘The Philosophy of Artificial Intelligence’
8. ‘Artificial intelligence and uncertainty’
Use of Bayesian statistics.
9. ‘Bayesian Reasoning and Machine Learning’ by
By David Barber
– A comprehensive introduction to modelling uncertainty and using AI based on Bayesian theory.
10.‘An Introduction to Bayesian Networks’
Finn V. Jensen.
– An introduction to uncertainty resolution through Bayesian networks.
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