Marginal distributionIn probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. This contrasts with a conditional distribution, which gives the probabilities contingent upon the values of the other variables. Marginal variables are those variables in the subset of variables being retained.
Algorithmic probabilityIn algorithmic information theory, algorithmic probability, also known as Solomonoff probability, is a mathematical method of assigning a prior probability to a given observation. It was invented by Ray Solomonoff in the 1960s. It is used in inductive inference theory and analyses of algorithms. In his general theory of inductive inference, Solomonoff uses the method together with Bayes' rule to obtain probabilities of prediction for an algorithm's future outputs.
Stable distributionIn probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, (see panel).
Physical neural networkA physical neural network is a type of artificial neural network in which an electrically adjustable material is used to emulate the function of a neural synapse or a higher-order (dendritic) neuron model. "Physical" neural network is used to emphasize the reliance on physical hardware used to emulate neurons as opposed to software-based approaches. More generally the term is applicable to other artificial neural networks in which a memristor or other electrically adjustable resistance material is used to emulate a neural synapse.
Bayesian networkA Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). It is one of several forms of causal notation. Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms.
Artificial intelligenceArtificial intelligence (AI) is the intelligence of machines or software, as opposed to the intelligence of human beings or animals. AI applications include advanced web search engines (e.g., Google Search), recommendation systems (used by YouTube, Amazon, and Netflix), understanding human speech (such as Siri and Alexa), self-driving cars (e.g., Waymo), generative or creative tools (ChatGPT and AI art), and competing at the highest level in strategic games (such as chess and Go).
Student's t-distributionIn probability and statistics, Student's t-distribution (or simply the t-distribution) is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However, has heavier tails and the amount of probability mass in the tails is controlled by the parameter . For the Student's t distribution becomes the standard Cauchy distribution, whereas for it becomes the standard normal distribution .
Frequency domainIn mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies. A frequency-domain representation consists of both the magnitude and the phase of a set of sinusoids (or other basis waveforms) at the frequency components of the signal.
Inductive probabilityInductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns. It is a source of knowledge about the world. There are three sources of knowledge: inference, communication, and deduction. Communication relays information found using other methods. Deduction establishes new facts based on existing facts. Inference establishes new facts from data. Its basis is Bayes' theorem.
Bayesian probabilityBayesian probability (ˈbeɪziən or ˈbeɪʒən ) is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown.
InferenceInferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BCE). Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion.
BroadbandIn telecommunications, broadband is the wide-bandwidth data transmission that transports multiple signals at a wide range of frequencies and Internet traffic types, which enables messages to be sent simultaneously and is used in fast internet connections. The medium can be coaxial cable, optical fiber, wireless Internet (radio), twisted pair, or satellite. In the context of Internet access, broadband is used to mean any high-speed Internet access that is always on and faster than dial-up access over traditional analog or ISDN PSTN services.
