12 Questions
What is the defining characteristic of a (first-order) Markov chain?
The next state only depends on the current state.
How can higher-order Markov chains be reduced to first-order?
By the cross product.
Give an example to illustrate the Markov property.
The weather tomorrow depends on the current weather, not on last year’s weather.
How can Markov chains be used for text generation?
By treating each word as a state.
What method is used to estimate transition probabilities in text generation with Markov chains?
By counting in the training data.
What is an application of Hidden Markov Models mentioned in the text?
Generating fake tweets, like in Automatic Donald Trump.
What is a typical task in natural language processing that involves Hidden Markov Models?
Part-of-speech annotation
In a Hidden Markov Model, what do the transition matrix and observation probability matrix represent?
Transition matrix: probabilities of changing to a state when in a certain state. Observation probability matrix: probabilities of producing an observation when in a certain state.
What are the three main problems to solve with Hidden Markov Models?
Evaluation Problem, Decoding Problem, Learning Problem
What does the Evaluation Problem in Hidden Markov Models involve?
Computing the probability of a specific result given the model parameters
What is the Decoding Problem in Hidden Markov Models?
Finding the hidden states that most likely led to a given observation sequence
What is the Learning Problem in the context of Hidden Markov Models?
Finding the optimal model parameters based on input-output sequences
Explore the concept of Markov chains, a popular model for discrete and memory-less processes where transitions depend only on the current state. Learn about transition probabilities and the Markov property. Delve into higher-order Markov chains and their reduction to first-order chains. Example applications include text generation.
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