Tools to crack your data science Interviews
Viterbi algorithm is a dynamic programming approach to find the most probable sequence of hidden states given the observed data, as modeled by a HMM. Without dynamic programming, it becomes an exponential problem as there are exponential number of possible sequences for a given observation(How – explained in answer below). Let the transition probabilities(state transition)…
This problem can be solved with a HMM. Using a HMM involves finding the transition probabilities (what is the probability of going from one POS tag to another and emission/output probabilities (what is the probability of observing a word given a POS tag) as explained in the question How do you train an hMM. Once…
The joint probability distribution for the HMM model is given by the following equation where are the observed data points and the corresponding latent states: Before proceeding to answer the question on training a HMM, it makes sense to ask following questions What is the problem in hand for which we are training…
Both the hMM and Naive Bayes have conditional independence assumption. hMM can be expressed by the equation below : Second equation implies a conditional independence assumption: Given the state observed variable is conditionally independent of previous observed variables, i.e. and Naive Bayes Model is expressed as: is the feature…
The HMM is a latent variable model where the observed sequence of variables are assumed to be generated from a set of temporally connected latent variables . The joint distribution of the observed variables or data and the latent variables can be written as : One possible interpretation of the latent variables in…
An n-grams model makes order n-1 Markov assumption. This assumption implies: given the previous n-1 words, probability of word is independent of words prior to words. Suppose we have k words in a sentence, their joint probability can be expressed as follows using chain rule: Now, the Markov assumption can be used to make…
Language models can be built using the following popular methods – Using n-gram language model n-gram language models make assumption for the value of n. Larger the value of n, longer the dependency. One can refer to what is the significance of n-grams in a language model for further reading. Using hidden Markov Model(HMM) HMM maintains long…