Transition matrix
A transition matrix is a matrix whose entries represent the probabilities of moving between states in a stochastic process.
Statistics Every Programmer Needs
A transition matrix is a matrix whose entries specify the probabilities of moving between states in a stochastic process.
- How it is used
- Forecasts future state distributions for decisions about market shares, engine condition, and delinquent accounts.
- How deep it goes
- Defines conditional matrix entries, works through vector multiplication and iteration, then partitions a matrix to calculate absorption probabilities.
- Examples
- Uses four-provider market shares, a running-or-not-running engine, and delinquency states with NumPy arrays and printed forecasts.
- What you can do after
- Apply it via NumPy to forecast successive state distributions, inspect stabilization, and calculate eventual absorbing-state probabilities.
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Machine Learning Algorithms in Depth
A transition matrix is a matrix whose entries specify the probabilities of moving between states of a stochastic process.
- How it is used
- Represents one-step state changes in Markov chains and turns web links into probabilities for page ranking.
- How deep it goes
- Derives distribution updates and stationary behavior, then gives a page-ranking construction and power-iteration listing.
- Examples
- Uses a two-state Markov model and a directed web-page graph with link-following and random jumps.
- What you can do after
- Build it from scratch for a page graph, then compute its stationary distribution by repeated matrix multiplication.
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Related concepts
- Markov chainused by · A Markov chain is a stochastic process of states whose transition probabilities depend on the current state rather than the full preceding history.
- PageRankused by · PageRank is a link-analysis algorithm that estimates the relative importance of nodes in a directed graph from the structure and importance of incoming links.
- arraykind of · An array is an indexed, ordered collection of elements arranged in one or more dimensions, with elements accessed by position.
- transition probabilityhas part · A transition probability is the conditional probability that a stochastic process moves to a specified next state, possibly given its current state and an action.
- embeddinguses · A numerical vector representation of an item or input that encodes features or relationships useful for computational tasks.
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