A pseudocount is a count added to observed data in order to change the probability in a model of those data, which is known not to be zero, to being negligible rather than being zero. Observation is an activity of a sapient or sentient living being, which senses and assimiliates the knowledge of a phenomenon in its framework of previous knowledge and ideas. ... In general, data consist of propositions that reflect reality. ... Probability is the extent to which something is likely to happen or be the case[1]. Probability theory is used extensively in areas such as statistics, mathematics, science, philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems. ... An abstract model (or conceptual model) is a theoretical construct that represents physical, biological or social processes, with a set of variables and a set of logical and quantitative relationships between them. ... 0 (zero) is both a number and a numerical digit used to represent that number in numerals. ...

In any observed data set or sample there is the possibility, especially with low-probability events and/or small data sets, of a possible event not occurring. Its observed frequency is therefore 0, implying a probability of 0. This is an oversimplification and is often unhelpful, particularly in probability-based machine learning techniques such as artificial neural networks and hidden Markov models. Sample can refer to any of the following. ... In probability theory, an event is a set of outcomes (a subset of the sample space) to which a probability is assigned. ... As a broad subfield of artificial intelligence, Machine learning is concerned with the development of algorithms and techniques that allow computers to learn. At a general level, there are two types of learning: inductive, and deductive. ... An artificial neural network (ANN) or commonly just neural network (NN) is an interconnected group of artificial neurons that uses a mathematical model or computational model for information processing based on a connectionist approach to computation. ... State transitions in a hidden Markov model (example) x — hidden states y — observable outputs a — transition probabilities b — output probabilities A hidden Markov model (HMM) is a statistical model where the system being modeled is assumed to be a Markov process with unknown parameters, and the challenge is to determine...

The simplest approach is to add 1 to each observed number of events including the zero-count one. This is sometimes called "Laplace's rule" (more formally known as Laplace's rule of succession). A more complex approach is to estimate the probability of the events from other factors and adjust accordingly. Neither approach is completely satisfactory and both are a bit of a fudge. In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem. ... In probability and statistics, density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. ...

See also

• Principle of indifference
• prior probability
• offset
• substitution matrix
• n-gram

The principle of indifference is a rule for assigning epistemic probabilities. ... A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ... In computer science, an offset within an array or other data structure object is an integer indicating the distance (displacement) from the beginning of the object up until a given element or point, presumably within the same object. ... In bioinformatics, a substitution matrix estimates the rate at which each possible residue in a sequence changes to each other residue over time. ... An N-gram is a sub-sequence of n items from a given sequence. ...

External links

• Pseudocounts
  • Bayesian interpretation of pseudocount regularizers